Provided by: liblapack-doc-man_3.6.0-2ubuntu2_all 
NAME
double_lin - double
Functions
program dchkaa
DCHKAA
program dchkab
DCHKAB
subroutine dchkeq (THRESH, NOUT)
DCHKEQ
subroutine dchkgb (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, A,
LA, AFAC, LAFAC, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKGB
subroutine dchkge (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR,
NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKGE
subroutine dchkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK,
RWORK, IWORK, NOUT)
DCHKGT
subroutine dchklq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR,
NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
DCHKLQ
subroutine dchkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A,
AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKPB
subroutine dchkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A,
AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKPO
subroutine dchkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKPP
subroutine dchkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A,
AFAC, PERM, PIV, WORK, RWORK, NOUT)
DCHKPS
subroutine dchkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT,
WORK, RWORK, NOUT)
DCHKPT
subroutine dchkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S,
TAU, WORK, IWORK, NOUT)
DCHKQ3
subroutine dchkql (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR,
NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
DCHKQL
subroutine dchkqr (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR,
NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
DCHKQR
subroutine dchkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
DCHKQRT
subroutine dchkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
DCHKQRTP
program dchkrfp
DCHKRFP
subroutine dchkrq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR,
NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
DCHKRQ
subroutine dchksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKSP
subroutine dchksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A,
AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKSY
subroutine dchksy_rook (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A,
AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKSY_ROOK
subroutine dchktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
DCHKTB
subroutine dchktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
DCHKTP
subroutine dchktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A,
AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKTR
subroutine dchktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK,
NOUT)
DCHKTZ
subroutine ddrvab (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK,
SWORK, IWORK, NOUT)
DDRVAB
subroutine ddrvac (DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK,
SWORK, NOUT)
DDRVAC
subroutine ddrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B,
BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
DDRVGB
subroutine ddrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV,
X, XACT, S, WORK, RWORK, IWORK, NOUT)
DDRVGE
subroutine ddrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK,
IWORK, NOUT)
DDRVGT
subroutine ddrvls (DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH,
TSTERR, A, COPYA, B, COPYB, C, S, COPYS, WORK, IWORK, NOUT)
DDRVLS
subroutine ddrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV,
X, XACT, S, WORK, RWORK, IWORK, NOUT)
DDRVPB
subroutine ddrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV,
X, XACT, S, WORK, RWORK, IWORK, NOUT)
DDRVPO
subroutine ddrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV,
X, XACT, S, WORK, RWORK, IWORK, NOUT)
DDRVPP
subroutine ddrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK,
RWORK, NOUT)
DDRVPT
subroutine ddrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK)
DDRVRF1
subroutine ddrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV)
DDRVRF2
subroutine ddrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, D_WORK_DLANGE,
D_WORK_DGEQRF, TAU)
DDRVRF3
subroutine ddrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, D_WORK_DLANGE)
DDRVRF4
subroutine ddrvrfp (NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, THRESH, A, ASAV, AFAC, AINV,
B, BSAV, XACT, X, ARF, ARFINV, D_WORK_DLATMS, D_WORK_DPOT01, D_TEMP_DPOT02,
D_TEMP_DPOT03, D_WORK_DLANSY, D_WORK_DPOT02, D_WORK_DPOT03)
DDRVRFP
subroutine ddrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
DDRVSP
subroutine ddrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
DDRVSY
subroutine ddrvsy_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
DDRVSY_ROOK
subroutine debchvxx (THRESH, PATH)
DEBCHVXX
subroutine derrab (NUNIT)
DERRAB
subroutine derrac (NUNIT)
DERRAC
subroutine derrge (PATH, NUNIT)
DERRGE
subroutine derrgt (PATH, NUNIT)
DERRGT
subroutine derrlq (PATH, NUNIT)
DERRLQ
subroutine derrls (PATH, NUNIT)
DERRLS
subroutine derrpo (PATH, NUNIT)
DERRPO
subroutine derrps (PATH, NUNIT)
DERRPS
subroutine derrql (PATH, NUNIT)
DERRQL
subroutine derrqp (PATH, NUNIT)
DERRQP
subroutine derrqr (PATH, NUNIT)
DERRQR
subroutine derrqrt (PATH, NUNIT)
DERRQRT
subroutine derrqrtp (PATH, NUNIT)
DERRQRTP
subroutine derrrfp (NUNIT)
DERRRFP
subroutine derrrq (PATH, NUNIT)
DERRRQ
subroutine derrsy (PATH, NUNIT)
DERRSY
subroutine derrtr (PATH, NUNIT)
DERRTR
subroutine derrtz (PATH, NUNIT)
DERRTZ
subroutine derrvx (PATH, NUNIT)
DERRVX
subroutine dgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
DGBT01
subroutine dgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
DGBT02
subroutine dgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR,
BERR, RESLTS)
DGBT05
subroutine dgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
DGELQS
logical function dgennd (M, N, A, LDA)
DGENND
subroutine dgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
DGEQLS
subroutine dgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
DGEQRS
subroutine dgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
DGERQS
subroutine dget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
DGET01
subroutine dget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DGET02
subroutine dget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DGET03
subroutine dget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
double precision function dget06 (RCOND, RCONDC)
DGET06
subroutine dget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR,
BERR, RESLTS)
DGET07
subroutine dget08 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DGET08
subroutine dgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
DGTT01
subroutine dgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
DGTT02
subroutine dgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR,
RESLTS)
DGTT05
subroutine dlahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO)
DLAHILB
subroutine dlaord (JOB, N, X, INCX)
DLAORD
subroutine dlaptm (N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
DLAPTM
subroutine dlarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB,
ISEED, INFO)
DLARHS
subroutine dlatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
subroutine dlatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB5
subroutine dlattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, INFO)
DLATTB
subroutine dlattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, B, WORK, INFO)
DLATTP
subroutine dlattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, INFO)
DLATTR
subroutine dlavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
DLAVSP
subroutine dlavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
subroutine dlavsy_rook (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY_ROOK
subroutine dlqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DLQT01
subroutine dlqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DLQT02
subroutine dlqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DLQT03
subroutine dpbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
DPBT01
subroutine dpbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPBT02
subroutine dpbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR,
RESLTS)
DPBT05
subroutine dpot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
DPOT01
subroutine dpot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
subroutine dpot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DPOT03
subroutine dpot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR,
RESLTS)
DPOT05
subroutine dpot06 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT06
subroutine dppt01 (UPLO, N, A, AFAC, RWORK, RESID)
DPPT01
subroutine dppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
DPPT02
subroutine dppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
DPPT03
subroutine dppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPPT05
subroutine dpst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
DPST01
subroutine dptt01 (N, D, E, DF, EF, WORK, RESID)
DPTT01
subroutine dptt02 (N, NRHS, D, E, X, LDX, B, LDB, RESID)
DPTT02
subroutine dptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPTT05
subroutine dqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQLT01
subroutine dqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQLT02
subroutine dqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQLT03
double precision function dqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
DQPT01
subroutine dqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQRT01
subroutine dqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQRT01P
subroutine dqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQRT02
subroutine dqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DQRT03
subroutine dqrt04 (M, N, NB, RESULT)
DQRT04
subroutine dqrt05 (M, N, L, NB, RESULT)
DQRT05
double precision function dqrt11 (M, K, A, LDA, TAU, WORK, LWORK)
DQRT11
double precision function dqrt12 (M, N, A, LDA, S, WORK, LWORK)
DQRT12
subroutine dqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED)
DQRT13
double precision function dqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK)
DQRT14
subroutine dqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED,
WORK, LWORK)
DQRT15
subroutine dqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DQRT16
double precision function dqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C,
WORK, LWORK)
DQRT17
subroutine drqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DRQT01
subroutine drqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DRQT02
subroutine drqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
DRQT03
double precision function drzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
DRZT01
double precision function drzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
DRZT02
subroutine dspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
DSPT01
subroutine dsyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01
subroutine dsyt01_rook (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01_ROOK
subroutine dtbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RESID)
DTBT02
subroutine dtbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX,
B, LDB, WORK, RESID)
DTBT03
subroutine dtbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT,
FERR, BERR, RESLTS)
DTBT05
subroutine dtbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, WORK, RAT)
DTBT06
subroutine dtpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID)
DTPT01
subroutine dtpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RESID)
DTPT02
subroutine dtpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB,
WORK, RESID)
DTPT03
subroutine dtpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR,
BERR, RESLTS)
DTPT05
subroutine dtpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT)
DTPT06
subroutine dtrt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, WORK, RESID)
DTRT01
subroutine dtrt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
DTRT02
subroutine dtrt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B,
LDB, WORK, RESID)
DTRT03
subroutine dtrt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR,
BERR, RESLTS)
DTRT05
subroutine dtrt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK, RAT)
DTRT06
subroutine sdrvsy_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
XACT, WORK, RWORK, IWORK, NOUT)
SDRVSY_ROOK
Detailed Description
This is the group of double LAPACK TESTING LIN routines.
Function Documentation
program dchkaa ()
DCHKAA
Purpose:
DCHKAA is the main test program for the DOUBLE PRECISION LAPACK
linear equation routines
The program must be driven by a short data file. The first 15 records
(not including the first comment line) specify problem dimensions
and program options using list-directed input. The remaining lines
specify the LAPACK test paths and the number of matrix types to use
in testing. An annotated example of a data file can be obtained by
deleting the first 3 characters from the following 40 lines:
Data file for testing DOUBLE PRECISION LAPACK linear eqn. routines
7 Number of values of M
0 1 2 3 5 10 16 Values of M (row dimension)
7 Number of values of N
0 1 2 3 5 10 16 Values of N (column dimension)
1 Number of values of NRHS
2 Values of NRHS (number of right hand sides)
5 Number of values of NB
1 3 3 3 20 Values of NB (the blocksize)
1 0 5 9 1 Values of NX (crossover point)
3 Number of values of RANK
30 50 90 Values of rank (as a % of N)
20.0 Threshold value of test ratio
T Put T to test the LAPACK routines
T Put T to test the driver routines
T Put T to test the error exits
DGE 11 List types on next line if 0 < NTYPES < 11
DGB 8 List types on next line if 0 < NTYPES < 8
DGT 12 List types on next line if 0 < NTYPES < 12
DPO 9 List types on next line if 0 < NTYPES < 9
DPS 9 List types on next line if 0 < NTYPES < 9
DPP 9 List types on next line if 0 < NTYPES < 9
DPB 8 List types on next line if 0 < NTYPES < 8
DPT 12 List types on next line if 0 < NTYPES < 12
DSY 10 List types on next line if 0 < NTYPES < 10
DSR 10 List types on next line if 0 < NTYPES < 10
DSP 10 List types on next line if 0 < NTYPES < 10
DTR 18 List types on next line if 0 < NTYPES < 18
DTP 18 List types on next line if 0 < NTYPES < 18
DTB 17 List types on next line if 0 < NTYPES < 17
DQR 8 List types on next line if 0 < NTYPES < 8
DRQ 8 List types on next line if 0 < NTYPES < 8
DLQ 8 List types on next line if 0 < NTYPES < 8
DQL 8 List types on next line if 0 < NTYPES < 8
DQP 6 List types on next line if 0 < NTYPES < 6
DTZ 3 List types on next line if 0 < NTYPES < 3
DLS 6 List types on next line if 0 < NTYPES < 6
DEQ
DQT
DQX
NMAX INTEGER
The maximum allowable value for M and N.
MAXIN INTEGER
The number of different values that can be used for each of
M, N, NRHS, NB, NX and RANK
MAXRHS INTEGER
The maximum number of right hand sides
MATMAX INTEGER
The maximum number of matrix types to use for testing
NIN INTEGER
The unit number for input
NOUT INTEGER
The unit number for output
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
program dchkab ()
DCHKAB
Purpose:
DCHKAB is the test program for the DOUBLE PRECISION LAPACK
DSGESV/DSPOSV routine
The program must be driven by a short data file. The first 5 records
specify problem dimensions and program options using list-directed
input. The remaining lines specify the LAPACK test paths and the
number of matrix types to use in testing. An annotated example of a
data file can be obtained by deleting the first 3 characters from the
following 10 lines:
Data file for testing DOUBLE PRECISION LAPACK DSGESV
7 Number of values of M
0 1 2 3 5 10 16 Values of M (row dimension)
1 Number of values of NRHS
2 Values of NRHS (number of right hand sides)
20.0 Threshold value of test ratio
T Put T to test the LAPACK routines
T Put T to test the error exits
DGE 11 List types on next line if 0 < NTYPES < 11
DPO 9 List types on next line if 0 < NTYPES < 9
NMAX INTEGER
The maximum allowable value for N
MAXIN INTEGER
The number of different values that can be used for each of
M, N, NRHS, NB, and NX
MAXRHS INTEGER
The maximum number of right hand sides
NIN INTEGER
The unit number for input
NOUT INTEGER
The unit number for output
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
subroutine dchkeq (double precision THRESH, integer NOUT)
DCHKEQ
Purpose:
DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
Parameters:
THRESH
THRESH is DOUBLE PRECISION
Threshold for testing routines. Should be between 2 and 10.
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkgb (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
double precision, dimension( * ) A, integer LA, double precision, dimension( * ) AFAC,
integer LAFAC, double precision, dimension( * ) B, double precision, dimension( * ) X,
double precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double
precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKGB
Purpose:
DCHKGB tests DGBTRF, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (LA)
LA
LA is INTEGER
The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX
where KLMAX is the largest entry in the local array KLVAL,
KUMAX is the largest entry in the local array KUVAL and
NMAX is the largest entry in the input array NVAL.
AFAC
AFAC is DOUBLE PRECISION array, dimension (LAFAC)
LAFAC
LAFAC is INTEGER
The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX
where KLMAX is the largest entry in the local array KLVAL,
KUMAX is the largest entry in the local array KUVAL and
NMAX is the largest entry in the input array NVAL.
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX,NMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkge (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AFAC,
double precision, dimension( * ) AINV, double precision, dimension( * ) B, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * )
IWORK, integer NOUT)
DCHKGE
Purpose:
DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(2*NMAX,2*NSMAX+NWORK))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkgt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
double precision, dimension( * ) A, double precision, dimension( * ) AF, double precision,
dimension( * ) B, double precision, dimension( * ) X, double precision, dimension( * )
XACT, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer, dimension( * ) IWORK, integer NOUT)
DCHKGT
Purpose:
DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (NMAX*4)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*4)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchklq (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer, dimension( * ) NXVAL, integer NRHS, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AF,
double precision, dimension( * ) AQ, double precision, dimension( * ) AL, double
precision, dimension( * ) AC, double precision, dimension( * ) B, double precision,
dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * )
TAU, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer NOUT)
DCHKLQ
Purpose:
DCHKLQ tests DGELQF, DORGLQ and DORMLQ.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AQ
AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AL
AL is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AC
AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
TAU
TAU is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkpb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL,
double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension( * ) A,
double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV, double
precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKPB
Purpose:
DCHKPB tests DPBTRF, -TRS, -RFS, and -CON.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkpo (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL,
double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension( * ) A,
double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV, double
precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKPO
Purpose:
DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkpp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AFAC,
double precision, dimension( * ) AINV, double precision, dimension( * ) B, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * )
IWORK, integer NOUT)
DCHKPP
Purpose:
DCHKPP tests DPPTRF, -TRI, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AFAC
AFAC is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AINV
AINV is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkps (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNB, integer, dimension( * ) NBVAL, integer NRANK, integer, dimension( * )
RANKVAL, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
PERM, integer, dimension( * ) PIV, double precision, dimension( * ) WORK, double
precision, dimension( * ) RWORK, integer NOUT)
DCHKPS
Purpose:
DCHKPS tests DPSTRF.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the block size NB.
NRANK
NRANK is INTEGER
The number of values of RANK contained in the vector RANKVAL.
RANKVAL
RANKVAL is INTEGER array, dimension (NBVAL)
The values of the block size NB.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
PERM
PERM is DOUBLE PRECISION array, dimension (NMAX*NMAX)
PIV
PIV is INTEGER array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*3)
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkpt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
double precision, dimension( * ) A, double precision, dimension( * ) D, double precision,
dimension( * ) E, double precision, dimension( * ) B, double precision, dimension( * ) X,
double precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double
precision, dimension( * ) RWORK, integer NOUT)
DCHKPT
Purpose:
DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (NMAX*2)
D
D is DOUBLE PRECISION array, dimension (NMAX*2)
E
E is DOUBLE PRECISION array, dimension (NMAX*2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkq3 (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer, dimension( * ) NXVAL, double precision THRESH, double precision, dimension( * )
A, double precision, dimension( * ) COPYA, double precision, dimension( * ) S, double
precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer, dimension(
* ) IWORK, integer NOUT)
DCHKQ3
Purpose:
DCHKQ3 tests DGEQP3.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
A
A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
where MMAX is the maximum value of M in MVAL and NMAX is the
maximum value of N in NVAL.
COPYA
COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
S
S is DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
TAU
TAU is DOUBLE PRECISION array, dimension (MMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(MMAX*NMAX + 4*NMAX + MMAX)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkql (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer, dimension( * ) NXVAL, integer NRHS, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AF,
double precision, dimension( * ) AQ, double precision, dimension( * ) AL, double
precision, dimension( * ) AC, double precision, dimension( * ) B, double precision,
dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * )
TAU, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer NOUT)
DCHKQL
Purpose:
DCHKQL tests DGEQLF, DORGQL and DORMQL.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AQ
AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AL
AL is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AC
AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
TAU
TAU is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dchkqr (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer, dimension( * ) NXVAL, integer NRHS, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AF,
double precision, dimension( * ) AQ, double precision, dimension( * ) AR, double
precision, dimension( * ) AC, double precision, dimension( * ) B, double precision,
dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * )
TAU, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer, dimension( * ) IWORK, integer NOUT)
DCHKQR
Purpose:
DCHKQR tests DGEQRF, DORGQR and DORMQR.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AQ
AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AR
AR is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AC
AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
TAU
TAU is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dchkqrt (double precision THRESH, logical TSTERR, integer NM, integer, dimension( *
) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * )
NBVAL, integer NOUT)
DCHKQRT
Purpose:
DCHKQRT tests DGEQRT and DGEMQRT.
Parameters:
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchkqrtp (double precision THRESH, logical TSTERR, integer NM, integer, dimension(
* ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * )
NBVAL, integer NOUT)
DCHKQRTP
Purpose:
DCHKQRTP tests DTPQRT and DTPMQRT.
Parameters:
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
program dchkrfp ()
DCHKRFP
Purpose:
DCHKRFP is the main test program for the DOUBLE PRECISION linear
equation routines with RFP storage format
MAXIN INTEGER
The number of different values that can be used for each of
M, N, or NB
MAXRHS INTEGER
The maximum number of right hand sides
NTYPES INTEGER
NMAX INTEGER
The maximum allowable value for N.
NIN INTEGER
The unit number for input
NOUT INTEGER
The unit number for output
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
subroutine dchkrq (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL,
integer, dimension( * ) NXVAL, integer NRHS, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AF,
double precision, dimension( * ) AQ, double precision, dimension( * ) AR, double
precision, dimension( * ) AC, double precision, dimension( * ) B, double precision,
dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * )
TAU, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer, dimension( * ) IWORK, integer NOUT)
DCHKRQ
Purpose:
DCHKRQ tests DGERQF, DORGRQ and DORMRQ.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AQ
AQ is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AR
AR is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AC
AC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
TAU
TAU is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*NMAX)
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchksp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AFAC,
double precision, dimension( * ) AINV, double precision, dimension( * ) B, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * )
IWORK, integer NOUT)
DCHKSP
Purpose:
DCHKSP tests DSPTRF, -TRI, -TRS, -RFS, and -CON
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AFAC
AFAC is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AINV
AINV is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(2,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array,
dimension (NMAX+2*NSMAX)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchksy (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL,
double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension( * ) A,
double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV, double
precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKSY
Purpose:
DCHKSY tests DSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine dchksy_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * )
NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * )
NSVAL, double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension(
* ) A, double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV,
double precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKSY_ROOK
Purpose:
DCHKSY_ROOK tests DSYTRF_ROOK, -TRI_ROOK, -TRS_ROOK,
and -CON_ROOK.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NBVAL)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dchktb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) AB, double precision, dimension( * ) AINV,
double precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKTB
Purpose:
DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The leading dimension of the work arrays.
NMAX >= the maximum value of N in NVAL.
AB
AB is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchktp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR,
integer NMAX, double precision, dimension( * ) AP, double precision, dimension( * ) AINVP,
double precision, dimension( * ) B, double precision, dimension( * ) X, double precision,
dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DCHKTP
Purpose:
DCHKTP tests DTPTRI, -TRS, -RFS, and -CON, and DLATPS
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The leading dimension of the work arrays. NMAX >= the
maximumm value of N in NVAL.
AP
AP is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AINVP
AINVP is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchktr (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL,
double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension( * ) A,
double precision, dimension( * ) AINV, double precision, dimension( * ) B, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * )
IWORK, integer NOUT)
DCHKTR
Purpose:
DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB
NNB is INTEGER
The number of values of NB contained in the vector NBVAL.
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The leading dimension of the work arrays.
NMAX >= the maximum value of N in NVAL.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dchktz (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, double precision THRESH, logical TSTERR, double
precision, dimension( * ) A, double precision, dimension( * ) COPYA, double precision,
dimension( * ) S, double precision, dimension( * ) TAU, double precision, dimension( * )
WORK, integer NOUT)
DCHKTZ
Purpose:
DCHKTZ tests DTZRZF.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
where MMAX is the maximum value of M in MVAL and NMAX is the
maximum value of N in NVAL.
COPYA
COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
S
S is DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
TAU
TAU is DOUBLE PRECISION array, dimension (MMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(MMAX*NMAX + 4*NMAX + MMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine ddrvab (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, integer NMAX, double
precision, dimension( * ) A, double precision, dimension( * ) AFAC, double precision,
dimension( * ) B, double precision, dimension( * ) X, double precision, dimension( * )
WORK, double precision, dimension( * ) RWORK, real, dimension(*) SWORK, integer,
dimension( * ) IWORK, integer NOUT)
DDRVAB
Purpose:
DDRVAB tests DSGESV
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
NMAX
NMAX is INTEGER
The maximum value permitted for M or N, used in dimensioning
the work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(2*NMAX,2*NSMAX+NWORK))
SWORK
SWORK is REAL array, dimension
(NMAX*(NSMAX+NMAX))
IWORK
IWORK is INTEGER array, dimension
NMAX
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvac (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, integer NMAX, double
precision, dimension( * ) A, double precision, dimension( * ) AFAC, double precision,
dimension( * ) B, double precision, dimension( * ) X, double precision, dimension( * )
WORK, double precision, dimension( * ) RWORK, real, dimension(*) SWORK, integer NOUT)
DDRVAC
Purpose:
DDRVAC tests DSPOSV.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NM
NM is INTEGER
The number of values of N contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
X
X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(2*NMAX,2*NSMAX+NWORK))
SWORK
SWORK is REAL array, dimension
(NMAX*(NSMAX+NMAX))
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvgb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, double precision, dimension( * ) A,
integer LA, double precision, dimension( * ) AFB, integer LAFB, double precision,
dimension( * ) ASAV, double precision, dimension( * ) B, double precision, dimension( * )
BSAV, double precision, dimension( * ) X, double precision, dimension( * ) XACT, double
precision, dimension( * ) S, double precision, dimension( * ) WORK, double precision,
dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVGB DDRVGBX
Purpose:
DDRVGB tests the driver routines DGBSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (LA)
LA
LA is INTEGER
The length of the array A. LA >= (2*NMAX-1)*NMAX
where NMAX is the largest entry in NVAL.
AFB
AFB is DOUBLE PRECISION array, dimension (LAFB)
LAFB
LAFB is INTEGER
The length of the array AFB. LAFB >= (3*NMAX-2)*NMAX
where NMAX is the largest entry in NVAL.
ASAV
ASAV is DOUBLE PRECISION array, dimension (LA)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (2*NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS,NMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NRHS))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
Purpose:
DDRVGB tests the driver routines DGBSV, -SVX, and -SVXX.
Note that this file is used only when the XBLAS are available,
otherwise ddrvgb.f defines this subroutine.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (LA)
LA
LA is INTEGER
The length of the array A. LA >= (2*NMAX-1)*NMAX
where NMAX is the largest entry in NVAL.
AFB
AFB is DOUBLE PRECISION array, dimension (LAFB)
LAFB
LAFB is INTEGER
The length of the array AFB. LAFB >= (3*NMAX-2)*NMAX
where NMAX is the largest entry in NVAL.
ASAV
ASAV is DOUBLE PRECISION array, dimension (LA)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (2*NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS,NMAX))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NRHS))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvge (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
ASAV, double precision, dimension( * ) B, double precision, dimension( * ) BSAV, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) S, double precision, dimension( * ) WORK, double precision, dimension( * )
RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVGE DDRVGEX
Purpose:
DDRVGE tests the driver routines DGESV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (2*NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (2*NRHS+NMAX)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
Purpose:
DDRVGE tests the driver routines DGESV, -SVX, and -SVXX.
Note that this file is used only when the XBLAS are available,
otherwise ddrvge.f defines this subroutine.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (2*NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (2*NRHS+NMAX)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
subroutine ddrvgt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, double precision, dimension( * ) A,
double precision, dimension( * ) AF, double precision, dimension( * ) B, double precision,
dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * )
WORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVGT
Purpose:
DDRVGT tests DGTSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand sides, NRHS >= 0.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (NMAX*4)
AF
AF is DOUBLE PRECISION array, dimension (NMAX*4)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NRHS))
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvls (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL,
integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL,
integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, double
precision THRESH, logical TSTERR, double precision, dimension( * ) A, double precision,
dimension( * ) COPYA, double precision, dimension( * ) B, double precision, dimension( * )
COPYB, double precision, dimension( * ) C, double precision, dimension( * ) S, double
precision, dimension( * ) COPYS, double precision, dimension( * ) WORK, integer,
dimension( * ) IWORK, integer NOUT)
DDRVLS
Purpose:
DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSY,
and DGELSD.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
The matrix of type j is generated as follows:
j=1: A = U*D*V where U and V are random orthogonal matrices
and D has random entries (> 0.1) taken from a uniform
distribution (0,1). A is full rank.
j=2: The same of 1, but A is scaled up.
j=3: The same of 1, but A is scaled down.
j=4: A = U*D*V where U and V are random orthogonal matrices
and D has 3*min(M,N)/4 random entries (> 0.1) taken
from a uniform distribution (0,1) and the remaining
entries set to 0. A is rank-deficient.
j=5: The same of 4, but A is scaled up.
j=6: The same of 5, but A is scaled down.
NM
NM is INTEGER
The number of values of M contained in the vector MVAL.
MVAL
MVAL is INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
NNB
NNB is INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL
NBVAL is INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL
NXVAL is INTEGER array, dimension (NNB)
The values of the crossover point NX.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
where MMAX is the maximum value of M in MVAL and NMAX is the
maximum value of N in NVAL.
COPYA
COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
where MMAX is the maximum value of M in MVAL and NSMAX is the
maximum value of NRHS in NSVAL.
COPYB
COPYB is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
C
C is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
S
S is DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
COPYS
COPYS is DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
WORK
WORK is DOUBLE PRECISION array,
dimension (MMAX*NMAX + 4*NMAX + MMAX).
IWORK
IWORK is INTEGER array, dimension (15*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine ddrvpb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
ASAV, double precision, dimension( * ) B, double precision, dimension( * ) BSAV, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) S, double precision, dimension( * ) WORK, double precision, dimension( * )
RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVPB
Purpose:
DDRVPB tests the driver routines DPBSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvpo (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
ASAV, double precision, dimension( * ) B, double precision, dimension( * ) BSAV, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) S, double precision, dimension( * ) WORK, double precision, dimension( * )
RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVPO DDRVPOX
Purpose:
DDRVPO tests the driver routines DPOSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Purpose:
DDRVPO tests the driver routines DPOSV, -SVX, and -SVXX.
Note that this file is used only when the XBLAS are available,
otherwise ddrvpo.f defines this subroutine.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine ddrvpp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
ASAV, double precision, dimension( * ) B, double precision, dimension( * ) BSAV, double
precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision,
dimension( * ) S, double precision, dimension( * ) WORK, double precision, dimension( * )
RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVPP
Purpose:
DDRVPP tests the driver routines DPPSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AFAC
AFAC is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
ASAV
ASAV is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
S
S is DOUBLE PRECISION array, dimension (NMAX)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvpt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, double precision, dimension( * ) A,
double precision, dimension( * ) D, double precision, dimension( * ) E, double precision,
dimension( * ) B, double precision, dimension( * ) X, double precision, dimension( * )
XACT, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK,
integer NOUT)
DDRVPT
Purpose:
DDRVPT tests DPTSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
A
A is DOUBLE PRECISION array, dimension (NMAX*2)
D
D is DOUBLE PRECISION array, dimension (NMAX*2)
E
E is DOUBLE PRECISION array, dimension (NMAX*2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(3,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension
(max(NMAX,2*NRHS))
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvrf1 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, double precision
THRESH, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension(
* ) ARF, double precision, dimension( * ) WORK)
DDRVRF1
Purpose:
DDRVRF1 tests the LAPACK RFP routines:
DLANSF
Parameters:
NOUT
NOUT is INTEGER
The unit number for output.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
A
A is DOUBLE PRECISION array, dimension (LDA,NMAX)
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,NMAX).
ARF
ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
WORK
WORK is DOUBLE PRECISION array, dimension ( NMAX )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvrf2 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, double precision,
dimension( lda, * ) A, integer LDA, double precision, dimension( * ) ARF, double
precision, dimension(*) AP, double precision, dimension( lda, * ) ASAV)
DDRVRF2
Purpose:
DDRVRF2 tests the LAPACK RFP convertion routines.
Parameters:
NOUT
NOUT is INTEGER
The unit number for output.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
A
A is DOUBLE PRECISION array, dimension (LDA,NMAX)
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,NMAX).
ARF
ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
AP
AP is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
ASAV
ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvrf3 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, double precision
THRESH, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension(
* ) ARF, double precision, dimension( lda, * ) B1, double precision, dimension( lda, * )
B2, double precision, dimension( * ) D_WORK_DLANGE, double precision, dimension( * )
D_WORK_DGEQRF, double precision, dimension( * ) TAU)
DDRVRF3
Purpose:
DDRVRF3 tests the LAPACK RFP routines:
DTFSM
Parameters:
NOUT
NOUT is INTEGER
The unit number for output.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
A
A is DOUBLE PRECISION array, dimension (LDA,NMAX)
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,NMAX).
ARF
ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2).
B1
B1 is DOUBLE PRECISION array, dimension (LDA,NMAX)
B2
B2 is DOUBLE PRECISION array, dimension (LDA,NMAX)
D_WORK_DLANGE
D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
D_WORK_DGEQRF
D_WORK_DGEQRF is DOUBLE PRECISION array, dimension (NMAX)
TAU
TAU is DOUBLE PRECISION array, dimension (NMAX)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvrf4 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, double precision
THRESH, double precision, dimension( ldc, * ) C1, double precision, dimension( ldc, *) C2,
integer LDC, double precision, dimension( * ) CRF, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) D_WORK_DLANGE)
DDRVRF4
Purpose:
DDRVRF4 tests the LAPACK RFP routines:
DSFRK
Parameters:
NOUT
NOUT is INTEGER
The unit number for output.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To
have every test ratio printed, use THRESH = 0.
C1
C1 is DOUBLE PRECISION array,
dimension (LDC,NMAX)
C2
C2 is DOUBLE PRECISION array,
dimension (LDC,NMAX)
LDC
LDC is INTEGER
The leading dimension of the array A.
LDA >= max(1,NMAX).
CRF
CRF is DOUBLE PRECISION array,
dimension ((NMAX*(NMAX+1))/2).
A
A is DOUBLE PRECISION array,
dimension (LDA,NMAX)
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,NMAX).
D_WORK_DLANGE
D_WORK_DLANGE is DOUBLE PRECISION array, dimension (NMAX)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvrfp (integer NOUT, integer NN, integer, dimension( nn ) NVAL, integer NNS,
integer, dimension( nns ) NSVAL, integer NNT, integer, dimension( nnt ) NTVAL, double
precision THRESH, double precision, dimension( * ) A, double precision, dimension( * )
ASAV, double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV, double
precision, dimension( * ) B, double precision, dimension( * ) BSAV, double precision,
dimension( * ) XACT, double precision, dimension( * ) X, double precision, dimension( * )
ARF, double precision, dimension( * ) ARFINV, double precision, dimension( * )
D_WORK_DLATMS, double precision, dimension( * ) D_WORK_DPOT01, double precision,
dimension( * ) D_TEMP_DPOT02, double precision, dimension( * ) D_TEMP_DPOT03, double
precision, dimension( * ) D_WORK_DLANSY, double precision, dimension( * ) D_WORK_DPOT02,
double precision, dimension( * ) D_WORK_DPOT03)
DDRVRFP
Purpose:
DDRVRFP tests the LAPACK RFP routines:
DPFTRF, DPFTRS, and DPFTRI.
This testing routine follow the same tests as DDRVPO (test for the full
format Symmetric Positive Definite solver).
The tests are performed in Full Format, convertion back and forth from
full format to RFP format are performed using the routines DTRTTF and
DTFTTR.
First, a specific matrix A of size N is created. There is nine types of
different matrixes possible.
1. Diagonal 6. Random, CNDNUM = sqrt(0.1/EPS)
2. Random, CNDNUM = 2 7. Random, CNDNUM = 0.1/EPS
*3. First row and column zero 8. Scaled near underflow
*4. Last row and column zero 9. Scaled near overflow
*5. Middle row and column zero
(* - tests error exits from DPFTRF, no test ratios are computed)
A solution XACT of size N-by-NRHS is created and the associated right
hand side B as well. Then DPFTRF is called to compute L (or U), the
Cholesky factor of A. Then L (or U) is used to solve the linear system
of equations AX = B. This gives X. Then L (or U) is used to compute the
inverse of A, AINV. The following four tests are then performed:
(1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
(2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
(3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
(4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
where EPS is the machine precision, RCOND the condition number of A, and
norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
Errors occur when INFO parameter is not as expected. Failures occur when
a test ratios is greater than THRES.
Parameters:
NOUT
NOUT is INTEGER
The unit number for output.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NNS
NNS is INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL
NSVAL is INTEGER array, dimension (NNS)
The values of the number of right-hand sides NRHS.
NNT
NNT is INTEGER
The number of values of MATRIX TYPE contained in the vector NTVAL.
NTVAL
NTVAL is INTEGER array, dimension (NNT)
The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
ASAV
ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
BSAV
BSAV is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
ARF
ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
ARFINV
ARFINV is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
D_WORK_DLATMS
D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( 3*NMAX )
D_WORK_DPOT01
D_WORK_DPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
D_TEMP_DPOT02
D_TEMP_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX*MAXRHS )
D_TEMP_DPOT03
D_TEMP_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX*NMAX )
D_WORK_DLATMS
D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( NMAX )
D_WORK_DLANSY
D_WORK_DLANSY is DOUBLE PRECISION array, dimension ( NMAX )
D_WORK_DPOT02
D_WORK_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
D_WORK_DPOT03
D_WORK_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine ddrvsp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
AINV, double precision, dimension( * ) B, double precision, dimension( * ) X, double
precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double precision,
dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVSP
Purpose:
DDRVSP tests the driver routines DSPSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AFAC
AFAC is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
AINV
AINV is DOUBLE PRECISION array, dimension
(NMAX*(NMAX+1)/2)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(2,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvsy (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL,
integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision,
dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * )
AINV, double precision, dimension( * ) B, double precision, dimension( * ) X, double
precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double precision,
dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVSY DDRVSYX
Purpose:
DDRVSY tests the driver routines DSYSV and -SVX.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
Purpose:
DDRVSY tests the driver routines DSYSV, -SVX, and -SVXX.
Note that this file is used only when the XBLAS are available,
otherwise ddrvsy.f defines this subroutine.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension
(NMAX*max(2,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine ddrvsy_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * )
NVAL, integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double
precision, dimension( * ) A, double precision, dimension( * ) AFAC, double precision,
dimension( * ) AINV, double precision, dimension( * ) B, double precision, dimension( * )
X, double precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double
precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)
DDRVSY_ROOK
Purpose:
DDRVSY_ROOK tests the driver routines DSYSV_ROOK.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AFAC
AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
AINV
AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
B
B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
X
X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
XACT
XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
RWORK
RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine debchvxx (double precision THRESH, character*3 PATH)
DEBCHVXX
Purpose:
DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then
compare the error bounds returned by D**SVXX to see if the returned
answer indeed falls within those bounds.
Eight test ratios will be computed. The tests will pass if they are .LT.
THRESH. There are two cases that are determined by 1 / (SQRT( N ) * EPS).
If that value is .LE. to the component wise reciprocal condition number,
it uses the guaranteed case, other wise it uses the unguaranteed case.
Test ratios:
Let Xc be X_computed and Xt be X_truth.
The norm used is the infinity norm.
Let A be the guaranteed case and B be the unguaranteed case.
1. Normwise guaranteed forward error bound.
A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and
ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS.
If these conditions are met, the test ratio is set to be
ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
B: For this case, CGESVXX should just return 1. If it is less than
one, treat it the same as in 1A. Otherwise it fails. (Set test
ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)
2. Componentwise guaranteed forward error bound.
A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i )
for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS.
If these conditions are met, the test ratio is set to be
ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
B: Same as normwise test ratio.
3. Backwards error.
A: The test ratio is set to BERR/EPS.
B: Same test ratio.
4. Reciprocal condition number.
A: A condition number is computed with Xt and compared with the one
returned from CGESVXX. Let RCONDc be the RCOND returned by D**SVXX
and RCONDt be the RCOND from the truth value. Test ratio is set to
MAX(RCONDc/RCONDt, RCONDt/RCONDc).
B: Test ratio is set to 1 / (EPS * RCONDc).
5. Reciprocal normwise condition number.
A: The test ratio is set to
MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).
6. Reciprocal componentwise condition number.
A: Test ratio is set to
MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).
.. Parameters ..
NMAX is determined by the largest number in the inverse of the hilbert
matrix. Precision is exhausted when the largest entry in it is greater
than 2 to the power of the number of bits in the fraction of the data
type used plus one, which is 24 for single precision.
NMAX should be 6 for single and 11 for double.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrab (integer NUNIT)
DERRAB
Purpose:
DERRAB tests the error exits for DSGESV.
Parameters:
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrac (integer NUNIT)
DERRAC
Purpose:
DERRAC tests the error exits for DSPOSV.
Parameters:
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrge (character*3 PATH, integer NUNIT)
DERRGE DERRGEX
Purpose:
DERRGE tests the error exits for the DOUBLE PRECISION routines
for general matrices.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Purpose:
DERRGE tests the error exits for the DOUBLE PRECISION routines
for general matrices.
Note that this file is used only when the XBLAS are available,
otherwise derrge.f defines this subroutine.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrgt (character*3 PATH, integer NUNIT)
DERRGT
Purpose:
DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal
routines.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrlq (character*3 PATH, integer NUNIT)
DERRLQ
Purpose:
DERRLQ tests the error exits for the DOUBLE PRECISION routines
that use the LQ decomposition of a general matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrls (character*3 PATH, integer NUNIT)
DERRLS
Purpose:
DERRLS tests the error exits for the DOUBLE PRECISION least squares
driver routines (DGELS, SGELSS, SGELSY, SGELSD).
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine derrpo (character*3 PATH, integer NUNIT)
DERRPO DERRPOX
Purpose:
DERRPO tests the error exits for the DOUBLE PRECISION routines
for symmetric positive definite matrices.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Purpose:
DERRPO tests the error exits for the DOUBLE PRECISION routines
for symmetric positive definite matrices.
Note that this file is used only when the XBLAS are available,
otherwise derrpo.f defines this subroutine.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine derrps (character*3 PATH, integer NUNIT)
DERRPS
Purpose:
DERRPS tests the error exits for the DOUBLE PRECISION routines
for DPSTRF.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrql (character*3 PATH, integer NUNIT)
DERRQL
Purpose:
DERRQL tests the error exits for the DOUBLE PRECISION routines
that use the QL decomposition of a general matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrqp (character*3 PATH, integer NUNIT)
DERRQP
Purpose:
DERRQP tests the error exits for DGEQP3.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine derrqr (character*3 PATH, integer NUNIT)
DERRQR
Purpose:
DERRQR tests the error exits for the DOUBLE PRECISION routines
that use the QR decomposition of a general matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrqrt (character*3 PATH, integer NUNIT)
DERRQRT
Purpose:
DERRQRT tests the error exits for the DOUBLE PRECISION routines
that use the QRT decomposition of a general matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrqrtp (character*3 PATH, integer NUNIT)
DERRQRTP
Purpose:
DERRQRTP tests the error exits for the REAL routines
that use the QRT decomposition of a triangular-pentagonal matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrrfp (integer NUNIT)
DERRRFP
Purpose:
DERRRFP tests the error exits for the DOUBLE PRECISION driver routines
for solving linear systems of equations.
DDRVRFP tests the DOUBLE PRECISION LAPACK RFP routines:
DTFSM, DTFTRI, DSFRK, DTFTTP, DTFTTR, DPFTRF, DPFTRS, DTPTTF,
DTPTTR, DTRTTF, and DTRTTP
Parameters:
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrrq (character*3 PATH, integer NUNIT)
DERRRQ
Purpose:
DERRRQ tests the error exits for the DOUBLE PRECISION routines
that use the RQ decomposition of a general matrix.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrsy (character*3 PATH, integer NUNIT)
DERRSY DERRSYX
Purpose:
DERRSY tests the error exits for the DOUBLE PRECISION routines
for symmetric indefinite matrices.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
Purpose:
DERRSY tests the error exits for the DOUBLE PRECISION routines
for symmetric indefinite matrices.
Note that this file is used only when the XBLAS are available,
otherwise derrsy.f defines this subroutine.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine derrtr (character*3 PATH, integer NUNIT)
DERRTR
Purpose:
DERRTR tests the error exits for the DOUBLE PRECISION triangular
routines.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine derrtz (character*3 PATH, integer NUNIT)
DERRTZ
Purpose:
DERRTZ tests the error exits for STZRZF.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine derrvx (character*3 PATH, integer NUNIT)
DERRVX DERRVXX
Purpose:
DERRVX tests the error exits for the DOUBLE PRECISION driver routines
for solving linear systems of equations.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
Purpose:
DERRVX tests the error exits for the DOUBLE PRECISION driver routines
for solving linear systems of equations.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT
NUNIT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dgbt01 (integer M, integer N, integer KL, integer KU, double precision, dimension(
lda, * ) A, integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC,
integer, dimension( * ) IPIV, double precision, dimension( * ) WORK, double precision
RESID)
DGBT01
Purpose:
DGBT01 reconstructs a band matrix A from its L*U factorization and
computes the residual:
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
The expression L*U - A is computed one column at a time, so A and
AFAC are not modified.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original matrix A in band storage, stored in rows 1 to
KL+KU+1.
LDA
LDA is INTEGER.
The leading dimension of the array A. LDA >= max(1,KL+KU+1).
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the banded
factors L and U from the L*U factorization, as computed by
DGBTRF. U is stored as an upper triangular band matrix with
KL+KU superdiagonals in rows 1 to KL+KU+1, and the
multipliers used during the factorization are stored in rows
KL+KU+2 to 2*KL+KU+1. See DGBTRF for further details.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC.
LDAFAC >= max(1,2*KL*KU+1).
IPIV
IPIV is INTEGER array, dimension (min(M,N))
The pivot indices from DGBTRF.
WORK
WORK is DOUBLE PRECISION array, dimension (2*KL+KU+1)
RESID
RESID is DOUBLE PRECISION
norm(L*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgbt02 (character TRANS, integer M, integer N, integer KL, integer KU, integer
NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension(
ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double
precision RESID)
DGBT02
Purpose:
DGBT02 computes the residual for a solution of a banded system of
equations A*x = b or A'*x = b:
RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
where EPS is the machine precision.
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A *x = b
= 'T': A'*x = b, where A' is the transpose of A
= 'C': A'*x = b, where A' is the transpose of A
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original matrix A in band storage, stored in rows 1 to
KL+KU+1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,KL+KU+1).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgbt05 (character TRANS, integer N, integer KL, integer KU, integer NRHS, double
precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldb, * ) B,
integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision,
dimension( ldxact, * ) XACT, integer LDXACT, double precision, dimension( * ) FERR, double
precision, dimension( * ) BERR, double precision, dimension( * ) RESLTS)
DGBT05
Purpose:
DGBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations op(A)*X = B, where A is a
general band matrix of order n with kl subdiagonals and ku
superdiagonals and op(A) = A or A**T, depending on TRANS.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgelqs (integer M, integer N, integer NRHS, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldb, *
) B, integer LDB, double precision, dimension( lwork ) WORK, integer LWORK, integer INFO)
DGELQS
Purpose:
Compute a minimum-norm solution
min || A*X - B ||
using the LQ factorization
A = L*Q
computed by DGELQF.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= M >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
Details of the LQ factorization of the original matrix A as
returned by DGELQF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
Details of the orthogonal matrix Q.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the m-by-nrhs right hand side matrix B.
On exit, the n-by-nrhs solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= N.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK must be at least NRHS,
and should be at least NRHS*NB, where NB is the block size
for this environment.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
logical function dgennd (integer M, integer N, double precision, dimension( lda, * ) A,
integer LDA)
DGENND
Purpose:
DGENND tests that its argument has a non-negative diagonal.
Parameters:
M
M is INTEGER
The number of rows in A.
N
N is INTEGER
The number of columns in A.
A
A is DOUBLE PRECISION array, dimension (LDA, N)
The matrix.
LDA
LDA is INTEGER
Leading dimension of A.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgeqls (integer M, integer N, integer NRHS, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldb, *
) B, integer LDB, double precision, dimension( lwork ) WORK, integer LWORK, integer INFO)
DGEQLS
Purpose:
Solve the least squares problem
min || A*X - B ||
using the QL factorization
A = Q*L
computed by DGEQLF.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. M >= N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QL factorization of the original matrix A as
returned by DGEQLF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (N)
Details of the orthogonal matrix Q.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the m-by-nrhs right hand side matrix B.
On exit, the n-by-nrhs solution matrix X, stored in rows
m-n+1:m.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= M.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK must be at least NRHS,
and should be at least NRHS*NB, where NB is the block size
for this environment.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgeqrs (integer M, integer N, integer NRHS, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldb, *
) B, integer LDB, double precision, dimension( lwork ) WORK, integer LWORK, integer INFO)
DGEQRS
Purpose:
Solve the least squares problem
min || A*X - B ||
using the QR factorization
A = Q*R
computed by DGEQRF.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. M >= N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of the original matrix A as
returned by DGEQRF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (N)
Details of the orthogonal matrix Q.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the m-by-nrhs right hand side matrix B.
On exit, the n-by-nrhs solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= M.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK must be at least NRHS,
and should be at least NRHS*NB, where NB is the block size
for this environment.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgerqs (integer M, integer N, integer NRHS, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldb, *
) B, integer LDB, double precision, dimension( lwork ) WORK, integer LWORK, integer INFO)
DGERQS
Purpose:
Compute a minimum-norm solution
min || A*X - B ||
using the RQ factorization
A = R*Q
computed by DGERQF.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= M >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
Details of the RQ factorization of the original matrix A as
returned by DGERQF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
Details of the orthogonal matrix Q.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the linear system.
On exit, the solution vectors X. Each solution vector
is contained in rows 1:N of a column of B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK must be at least NRHS,
and should be at least NRHS*NB, where NB is the block size
for this environment.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dget01 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA,
double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * )
IPIV, double precision, dimension( * ) RWORK, double precision RESID)
DGET01
Purpose:
DGET01 reconstructs a matrix A from its L*U factorization and
computes the residual
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original M x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the factors
L and U from the L*U factorization as computed by DGETRF.
Overwritten with the reconstructed matrix, and then with the
difference L*U - A.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,M).
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices from DGETRF.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESID
RESID is DOUBLE PRECISION
norm(L*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dget02 (character TRANS, integer M, integer N, integer NRHS, double precision,
dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
RWORK, double precision RESID)
DGET02
Purpose:
DGET02 computes the residual for a solution of a system of linear
equations A*x = b or A'*x = b:
RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
where EPS is the machine epsilon.
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A *x = b
= 'T': A'*x = b, where A' is the transpose of A
= 'C': A'*x = b, where A' is the transpose of A
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original M x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dget03 (integer N, double precision, dimension( lda, * ) A, integer LDA, double
precision, dimension( ldainv, * ) AINV, integer LDAINV, double precision, dimension(
ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision
RCOND, double precision RESID)
DGET03
Purpose:
DGET03 computes the residual for a general matrix times its inverse:
norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.
Parameters:
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original N x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AINV
AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
The inverse of the matrix A.
LDAINV
LDAINV is INTEGER
The leading dimension of the array AINV. LDAINV >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK. LDWORK >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of A, computed as
( 1/norm(A) ) / norm(AINV).
RESID
RESID is DOUBLE PRECISION
norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dget04 (integer N, integer NRHS, double precision, dimension( ldx, * ) X, integer
LDX, double precision, dimension( ldxact, * ) XACT, integer LDXACT, double precision
RCOND, double precision RESID)
DGET04
Purpose:
DGET04 computes the difference between a computed solution and the
true solution to a system of linear equations.
RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
where RCOND is the reciprocal of the condition number and EPS is the
machine epsilon.
Parameters:
N
N is INTEGER
The number of rows of the matrices X and XACT. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X and XACT. NRHS >= 0.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension( LDX, NRHS )
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the coefficient
matrix in the system of equations.
RESID
RESID is DOUBLE PRECISION
The maximum over the NRHS solution vectors of
( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function dget06 (double precision RCOND, double precision RCONDC)
DGET06
Purpose:
DGET06 computes a test ratio to compare two values for RCOND.
Parameters:
RCOND
RCOND is DOUBLE PRECISION
The estimate of the reciprocal of the condition number of A,
as computed by DGECON.
RCONDC
RCONDC is DOUBLE PRECISION
The reciprocal of the condition number of A, computed as
( 1/norm(A) ) / norm(inv(A)).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dget07 (character TRANS, integer N, integer NRHS, double precision, dimension( lda,
* ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double
precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact, * )
XACT, integer LDXACT, double precision, dimension( * ) FERR, logical CHKFERR, double
precision, dimension( * ) BERR, double precision, dimension( * ) RESLTS)
DGET07
Purpose:
DGET07 tests the error bounds from iterative refinement for the
computed solution to a system of equations op(A)*X = B, where A is a
general n by n matrix and op(A) = A or A**T, depending on TRANS.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N
N is INTEGER
The number of rows of the matrices X and XACT. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X and XACT. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original n by n matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
CHKFERR
CHKFERR is LOGICAL
Set to .TRUE. to check FERR, .FALSE. not to check FERR.
When the test system is ill-conditioned, the "true"
solution in XACT may be incorrect.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dget08 (character TRANS, integer M, integer N, integer NRHS, double precision,
dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
RWORK, double precision RESID)
DGET08
Purpose:
DGET08 computes the residual for a solution of a system of linear
equations A*x = b or A'*x = b:
RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
where EPS is the machine epsilon.
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A *x = b
= 'T': A'*x = b, where A' is the transpose of A
= 'C': A'*x = b, where A' is the transpose of A
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original M x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgtt01 (integer N, double precision, dimension( * ) DL, double precision,
dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * )
DLF, double precision, dimension( * ) DF, double precision, dimension( * ) DUF, double
precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension(
ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision
RESID)
DGTT01
Purpose:
DGTT01 reconstructs a tridiagonal matrix A from its LU factorization
and computes the residual
norm(L*U - A) / ( norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
N
N is INTEGTER
The order of the matrix A. N >= 0.
DL
DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal elements of A.
D
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.
DU
DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) super-diagonal elements of A.
DLF
DLF is DOUBLE PRECISION array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.
DF
DF is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DUF
DUF is DOUBLE PRECISION array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.
DU2
DU2 is DOUBLE PRECISION array, dimension (N-2)
The (n-2) elements of the second super-diagonal of U.
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.
WORK
WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK. LDWORK >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The scaled residual: norm(L*U - A) / (norm(A) * EPS)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgtt02 (character TRANS, integer N, integer NRHS, double precision, dimension( * )
DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double
precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B,
integer LDB, double precision RESID)
DGTT02
Purpose:
DGTT02 computes the residual for the solution to a tridiagonal
system of equations:
RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
where EPS is the machine epsilon.
Parameters:
TRANS
TRANS is CHARACTER
Specifies the form of the residual.
= 'N': B - A * X (No transpose)
= 'T': B - A'* X (Transpose)
= 'C': B - A'* X (Conjugate transpose = Transpose)
N
N is INTEGTER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
DL
DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal elements of A.
D
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.
DU
DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) super-diagonal elements of A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - op(A)*X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RESID
RESID is DOUBLE PRECISION
norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dgtt05 (character TRANS, integer N, integer NRHS, double precision, dimension( * )
DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double
precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X,
integer LDX, double precision, dimension( ldxact, * ) XACT, integer LDXACT, double
precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision,
dimension( * ) RESLTS)
DGTT05
Purpose:
DGTT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
general tridiagonal matrix of order n and op(A) = A or A**T,
depending on TRANS.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
N
N is INTEGER
The number of rows of the matrices X and XACT. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X and XACT. NRHS >= 0.
DL
DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal elements of A.
D
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.
DU
DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) super-diagonal elements of A.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlahilb (integer N, integer NRHS, double precision, dimension(lda, n) A, integer
LDA, double precision, dimension(ldx, nrhs) X, integer LDX, double precision,
dimension(ldb, nrhs) B, integer LDB, double precision, dimension(n) WORK, integer INFO)
DLAHILB
Purpose:
DLAHILB generates an N by N scaled Hilbert matrix in A along with
NRHS right-hand sides in B and solutions in X such that A*X=B.
The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all
entries are integers. The right-hand sides are the first NRHS
columns of M * the identity matrix, and the solutions are the
first NRHS columns of the inverse Hilbert matrix.
The condition number of the Hilbert matrix grows exponentially with
its size, roughly as O(e ** (3.5*N)). Additionally, the inverse
Hilbert matrices beyond a relatively small dimension cannot be
generated exactly without extra precision. Precision is exhausted
when the largest entry in the inverse Hilbert matrix is greater than
2 to the power of the number of bits in the fraction of the data type
used plus one, which is 24 for single precision.
In single, the generated solution is exact for N <= 6 and has
small componentwise error for 7 <= N <= 11.
Parameters:
N
N is INTEGER
The dimension of the matrix A.
NRHS
NRHS is NRHS
The requested number of right-hand sides.
A
A is DOUBLE PRECISION array, dimension (LDA, N)
The generated scaled Hilbert matrix.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= N.
X
X is DOUBLE PRECISION array, dimension (LDX, NRHS)
The generated exact solutions. Currently, the first NRHS
columns of the inverse Hilbert matrix.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= N.
B
B is DOUBLE PRECISION array, dimension (LDB, NRHS)
The generated right-hand sides. Currently, the first NRHS
columns of LCM(1, 2, ..., 2*N-1) * the identity matrix.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= N.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
= 1: N is too large; the data is still generated but may not
be not exact.
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlaord (character JOB, integer N, double precision, dimension( * ) X, integer INCX)
DLAORD
Purpose:
DLAORD sorts the elements of a vector x in increasing or decreasing
order.
Parameters:
JOB
JOB is CHARACTER
= 'I': Sort in increasing order
= 'D': Sort in decreasing order
N
N is INTEGER
The length of the vector X.
X
X is DOUBLE PRECISION array, dimension
(1+(N-1)*INCX)
On entry, the vector of length n to be sorted.
On exit, the vector x is sorted in the prescribed order.
INCX
INCX is INTEGER
The spacing between successive elements of X. INCX >= 0.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlaptm (integer N, integer NRHS, double precision ALPHA, double precision,
dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( ldx, *
) X, integer LDX, double precision BETA, double precision, dimension( ldb, * ) B, integer
LDB)
DLAPTM
Purpose:
DLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
matrix A and stores the result in a matrix B. The operation has the
form
B := alpha * A * X + beta * B
where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
Parameters:
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B.
ALPHA
ALPHA is DOUBLE PRECISION
The scalar alpha. ALPHA must be 1. or -1.; otherwise,
it is assumed to be 0.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E
E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal or superdiagonal elements of A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The N by NRHS matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(N,1).
BETA
BETA is DOUBLE PRECISION
The scalar beta. BETA must be 0., 1., or -1.; otherwise,
it is assumed to be 1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N by NRHS matrix B.
On exit, B is overwritten by the matrix expression
B := alpha * A * X + beta * B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(N,1).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlarhs (character*3 PATH, character XTYPE, character UPLO, character TRANS, integer
M, integer N, integer KL, integer KU, integer NRHS, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double precision,
dimension( ldb, * ) B, integer LDB, integer, dimension( 4 ) ISEED, integer INFO)
DLARHS
Purpose:
DLARHS chooses a set of NRHS random solution vectors and sets
up the right hand sides for the linear system
op( A ) * X = B,
where op( A ) may be A or A' (transpose of A).
Parameters:
PATH
PATH is CHARACTER*3
The type of the real matrix A. PATH may be given in any
combination of upper and lower case. Valid types include
xGE: General m x n matrix
xGB: General banded matrix
xPO: Symmetric positive definite, 2-D storage
xPP: Symmetric positive definite packed
xPB: Symmetric positive definite banded
xSY: Symmetric indefinite, 2-D storage
xSP: Symmetric indefinite packed
xSB: Symmetric indefinite banded
xTR: Triangular
xTP: Triangular packed
xTB: Triangular banded
xQR: General m x n matrix
xLQ: General m x n matrix
xQL: General m x n matrix
xRQ: General m x n matrix
where the leading character indicates the precision.
XTYPE
XTYPE is CHARACTER*1
Specifies how the exact solution X will be determined:
= 'N': New solution; generate a random X.
= 'C': Computed; use value of X on entry.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
matrix A is stored, if A is symmetric.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to the matrix A.
= 'N': System is A * x = b
= 'T': System is A'* x = b
= 'C': System is A'* x = b
M
M is INTEGER
The number or rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
Used only if A is a band matrix; specifies the number of
subdiagonals of A if A is a general band matrix or if A is
symmetric or triangular and UPLO = 'L'; specifies the number
of superdiagonals of A if A is symmetric or triangular and
UPLO = 'U'. 0 <= KL <= M-1.
KU
KU is INTEGER
Used only if A is a general band matrix or if A is
triangular.
If PATH = xGB, specifies the number of superdiagonals of A,
and 0 <= KU <= N-1.
If PATH = xTR, xTP, or xTB, specifies whether or not the
matrix has unit diagonal:
= 1: matrix has non-unit diagonal (default)
= 2: matrix has unit diagonal
NRHS
NRHS is INTEGER
The number of right hand side vectors in the system A*X = B.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The test matrix whose type is given by PATH.
LDA
LDA is INTEGER
The leading dimension of the array A.
If PATH = xGB, LDA >= KL+KU+1.
If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
Otherwise, LDA >= max(1,M).
X
X is or output) DOUBLE PRECISION array, dimension(LDX,NRHS)
On entry, if XTYPE = 'C' (for 'Computed'), then X contains
the exact solution to the system of linear equations.
On exit, if XTYPE = 'N' (for 'New'), then X is initialized
with random values.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vector(s) for the system of equations,
computed from B = op(A) * X, where op(A) is determined by
TRANS.
LDB
LDB is INTEGER
The leading dimension of the array B. If TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
ISEED
ISEED is INTEGER array, dimension (4)
The seed vector for the random number generator (used in
DLATMS). Modified on exit.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlatb4 (character*3 PATH, integer IMAT, integer M, integer N, character TYPE,
integer KL, integer KU, double precision ANORM, integer MODE, double precision CNDNUM,
character DIST)
DLATB4
Purpose:
DLATB4 sets parameters for the matrix generator based on the type of
matrix to be generated.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name.
IMAT
IMAT is INTEGER
An integer key describing which matrix to generate for this
path.
M
M is INTEGER
The number of rows in the matrix to be generated.
N
N is INTEGER
The number of columns in the matrix to be generated.
TYPE
TYPE is CHARACTER*1
The type of the matrix to be generated:
= 'S': symmetric matrix
= 'P': symmetric positive (semi)definite matrix
= 'N': nonsymmetric matrix
KL
KL is INTEGER
The lower band width of the matrix to be generated.
KU
KU is INTEGER
The upper band width of the matrix to be generated.
ANORM
ANORM is DOUBLE PRECISION
The desired norm of the matrix to be generated. The diagonal
matrix of singular values or eigenvalues is scaled by this
value.
MODE
MODE is INTEGER
A key indicating how to choose the vector of eigenvalues.
CNDNUM
CNDNUM is DOUBLE PRECISION
The desired condition number.
DIST
DIST is CHARACTER*1
The type of distribution to be used by the random number
generator.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlatb5 (character*3 PATH, integer IMAT, integer N, character TYPE, integer KL,
integer KU, double precision ANORM, integer MODE, double precision CNDNUM, character DIST)
DLATB5
Purpose:
DLATB5 sets parameters for the matrix generator based on the type
of matrix to be generated.
Parameters:
PATH
PATH is CHARACTER*3
The LAPACK path name.
IMAT
IMAT is INTEGER
An integer key describing which matrix to generate for this
path.
N
N is INTEGER
The number of rows and columns in the matrix to be generated.
TYPE
TYPE is CHARACTER*1
The type of the matrix to be generated:
= 'S': symmetric matrix
= 'P': symmetric positive (semi)definite matrix
= 'N': nonsymmetric matrix
KL
KL is INTEGER
The lower band width of the matrix to be generated.
KU
KU is INTEGER
The upper band width of the matrix to be generated.
ANORM
ANORM is DOUBLE PRECISION
The desired norm of the matrix to be generated. The diagonal
matrix of singular values or eigenvalues is scaled by this
value.
MODE
MODE is INTEGER
A key indicating how to choose the vector of eigenvalues.
CNDNUM
CNDNUM is DOUBLE PRECISION
The desired condition number.
DIST
DIST is CHARACTER*1
The type of distribution to be used by the random number
generator.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlattb (integer IMAT, character UPLO, character TRANS, character DIAG, integer,
dimension( 4 ) ISEED, integer N, integer KD, double precision, dimension( ldab, * ) AB,
integer LDAB, double precision, dimension( * ) B, double precision, dimension( * ) WORK,
integer INFO)
DLATTB
Purpose:
DLATTB generates a triangular test matrix in 2-dimensional storage.
IMAT and UPLO uniquely specify the properties of the test matrix,
which is returned in the array A.
Parameters:
IMAT
IMAT is INTEGER
An integer key describing which matrix to generate for this
path.
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A will be upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies whether the matrix or its transpose will be used.
= 'N': No transpose
= 'T': Transpose
= 'C': Conjugate transpose (= transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
ISEED
ISEED is INTEGER array, dimension (4)
The seed vector for the random number generator (used in
DLATMS). Modified on exit.
N
N is INTEGER
The order of the matrix to be generated.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the banded
triangular matrix A. KD >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular banded matrix A, stored in the
first KD+1 rows of AB. Let j be a column of A, 1<=j<=n.
If UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j.
If UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is DOUBLE PRECISION array, dimension (N)
WORK
WORK is DOUBLE PRECISION array, dimension (2*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlattp (integer IMAT, character UPLO, character TRANS, character DIAG, integer,
dimension( 4 ) ISEED, integer N, double precision, dimension( * ) A, double precision,
dimension( * ) B, double precision, dimension( * ) WORK, integer INFO)
DLATTP
Purpose:
DLATTP generates a triangular test matrix in packed storage.
IMAT and UPLO uniquely specify the properties of the test
matrix, which is returned in the array AP.
Parameters:
IMAT
IMAT is INTEGER
An integer key describing which matrix to generate for this
path.
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A will be upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies whether the matrix or its transpose will be used.
= 'N': No transpose
= 'T': Transpose
= 'C': Conjugate transpose (= Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
ISEED
ISEED is INTEGER array, dimension (4)
The seed vector for the random number generator (used in
DLATMS). Modified on exit.
N
N is INTEGER
The order of the matrix to be generated.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
B
B is DOUBLE PRECISION array, dimension (N)
The right hand side vector, if IMAT > 10.
WORK
WORK is DOUBLE PRECISION array, dimension (3*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlattr (integer IMAT, character UPLO, character TRANS, character DIAG, integer,
dimension( 4 ) ISEED, integer N, double precision, dimension( lda, * ) A, integer LDA,
double precision, dimension( * ) B, double precision, dimension( * ) WORK, integer INFO)
DLATTR
Purpose:
DLATTR generates a triangular test matrix.
IMAT and UPLO uniquely specify the properties of the test
matrix, which is returned in the array A.
Parameters:
IMAT
IMAT is INTEGER
An integer key describing which matrix to generate for this
path.
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A will be upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies whether the matrix or its transpose will be used.
= 'N': No transpose
= 'T': Transpose
= 'C': Conjugate transpose (= Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
ISEED
ISEED is INTEGER array, dimension (4)
The seed vector for the random number generator (used in
DLATMS). Modified on exit.
N
N is INTEGER
The order of the matrix to be generated.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
set so that A(k,k) = k for 1 <= k <= n.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (N)
The right hand side vector, if IMAT > 10.
WORK
WORK is DOUBLE PRECISION array, dimension (3*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlavsp (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( * ) A, integer, dimension( * ) IPIV, double precision,
dimension( ldb, * ) B, integer LDB, integer INFO)
DLAVSP
Purpose:
DLAVSP performs one of the matrix-vector operations
x := A*x or x := A'*x,
where x is an N element vector and A is one of the factors
from the block U*D*U' or L*D*L' factorization computed by DSPTRF.
If TRANS = 'N', multiplies by U or U * D (or L or L * D)
If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L' )
If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L' )
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the factor stored in A is upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation to be performed:
= 'N': x := A*x
= 'T': x := A'*x
= 'C': x := A'*x
DIAG
DIAG is CHARACTER*1
Specifies whether or not the diagonal blocks are unit
matrices. If the diagonal blocks are assumed to be unit,
then A = U or A = L, otherwise A = U*D or A = L*D.
= 'U': Diagonal blocks are assumed to be unit matrices.
= 'N': Diagonal blocks are assumed to be non-unit matrices.
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of vectors
x to be multiplied by A. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L, stored as a packed triangular
matrix as computed by DSPTRF.
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices from DSPTRF.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, B contains NRHS vectors of length N.
On exit, B is overwritten with the product A * B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlavsy (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double
precision, dimension( ldb, * ) B, integer LDB, integer INFO)
DLAVSY
Purpose:
DLAVSY performs one of the matrix-vector operations
x := A*x or x := A'*x,
where x is an N element vector and A is one of the factors
from the block U*D*U' or L*D*L' factorization computed by DSYTRF.
If TRANS = 'N', multiplies by U or U * D (or L or L * D)
If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the factor stored in A is upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation to be performed:
= 'N': x := A*x
= 'T': x := A'*x
= 'C': x := A'*x
DIAG
DIAG is CHARACTER*1
Specifies whether or not the diagonal blocks are unit
matrices. If the diagonal blocks are assumed to be unit,
then A = U or A = L, otherwise A = U*D or A = L*D.
= 'U': Diagonal blocks are assumed to be unit matrices.
= 'N': Diagonal blocks are assumed to be non-unit matrices.
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of vectors
x to be multiplied by A. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF.
Stored as a 2-D triangular matrix.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D,
as determined by DSYTRF.
If UPLO = 'U':
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
(If IPIV( k ) = k, no interchange was done).
If IPIV(k) = IPIV(k-1) < 0, then rows and
columns k-1 and -IPIV(k) were interchanged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If UPLO = 'L':
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
(If IPIV( k ) = k, no interchange was done).
If IPIV(k) = IPIV(k+1) < 0, then rows and
columns k+1 and -IPIV(k) were interchanged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, B contains NRHS vectors of length N.
On exit, B is overwritten with the product A * B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine dlavsy_rook (character UPLO, character TRANS, character DIAG, integer N, integer
NRHS, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV,
double precision, dimension( ldb, * ) B, integer LDB, integer INFO)
DLAVSY_ROOK
Purpose:
DLAVSY_ROOK performs one of the matrix-vector operations
x := A*x or x := A'*x,
where x is an N element vector and A is one of the factors
from the block U*D*U' or L*D*L' factorization computed by DSYTRF_ROOK.
If TRANS = 'N', multiplies by U or U * D (or L or L * D)
If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the factor stored in A is upper or lower
triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation to be performed:
= 'N': x := A*x
= 'T': x := A'*x
= 'C': x := A'*x
DIAG
DIAG is CHARACTER*1
Specifies whether or not the diagonal blocks are unit
matrices. If the diagonal blocks are assumed to be unit,
then A = U or A = L, otherwise A = U*D or A = L*D.
= 'U': Diagonal blocks are assumed to be unit matrices.
= 'N': Diagonal blocks are assumed to be non-unit matrices.
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of vectors
x to be multiplied by A. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF_ROOK.
Stored as a 2-D triangular matrix.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D,
as determined by DSYTRF_ROOK.
If UPLO = 'U':
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
(If IPIV( k ) = k, no interchange was done).
If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If UPLO = 'L':
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
(If IPIV( k ) = k, no interchange was done).
If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, B contains NRHS vectors of length N.
On exit, B is overwritten with the product A * B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine dlqt01 (integer M, integer N, double precision, dimension( lda, * ) A, double
precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) L, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DLQT01
Purpose:
DLQT01 tests DGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests DORGLQ which forms the n-by-n
orthogonal matrix Q.
DLQT01 compares L with A*Q', and checks that Q is orthogonal.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the LQ factorization of A, as returned by DGELQF.
See DGELQF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
The n-by-n orthogonal matrix Q.
L
L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L.
LDA >= max(M,N).
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGELQF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (max(M,N))
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlqt02 (integer M, integer N, integer K, double precision, dimension( lda, * ) A,
double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) L, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DLQT02
Purpose:
DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
orthonornmal rows that is defined as the product of k elementary
reflectors.
Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
the orthogonal matrix Q defined by the factorization of the first k
rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
checks that the rows of Q are orthonormal.
Parameters:
M
M is INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q to be generated.
N >= M >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DLQT01.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the LQ factorization of A, as returned by DGELQF.
See DGELQF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
L
L is DOUBLE PRECISION array, dimension (LDA,M)
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= N.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the LQ factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dlqt03 (integer M, integer N, integer K, double precision, dimension( lda, * ) AF,
double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double
precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DLQT03
Purpose:
DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
DLQT03 compares the results of a call to DORMLQ with the results of
forming Q explicitly by a call to DORGLQ and then performing matrix
multiplication by a call to DGEMM.
Parameters:
M
M is INTEGER
The number of rows or columns of the matrix C; C is n-by-m if
Q is applied from the left, or m-by-n if Q is applied from
the right. M >= 0.
N
N is INTEGER
The order of the orthogonal matrix Q. N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q. N >= K >= 0.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the LQ factorization of an m-by-n matrix, as
returned by DGELQF. See SGELQF for further details.
C
C is DOUBLE PRECISION array, dimension (LDA,N)
CC
CC is DOUBLE PRECISION array, dimension (LDA,N)
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
LDA
LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the LQ factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of WORK. LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an n-by-n orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpbt01 (character UPLO, integer N, integer KD, double precision, dimension( lda, *
) A, integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, double
precision, dimension( * ) RWORK, double precision RESID)
DPBT01
Purpose:
DPBT01 reconstructs a symmetric positive definite band matrix A from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of
L, and U' is the conjugate transpose of U.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
KD
KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric band matrix A. If UPLO = 'U', the
upper triangular part of A is stored as a band matrix; if
UPLO = 'L', the lower triangular part of A is stored. The
columns of the appropriate triangle are stored in the columns
of A and the diagonals of the triangle are stored in the rows
of A. See DPBTRF for further details.
LDA
LDA is INTEGER.
The leading dimension of the array A. LDA >= max(1,KD+1).
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the factor
L or U from the L*L' or U'*U factorization in band storage
format, as computed by DPBTRF.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC.
LDAFAC >= max(1,KD+1).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpbt02 (character UPLO, integer N, integer KD, integer NRHS, double precision,
dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
RWORK, double precision RESID)
DPBT02
Purpose:
DPBT02 computes the residual for a solution of a symmetric banded
system of equations A*x = b:
RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
where EPS is the machine precision.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
KD
KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric band matrix A. If UPLO = 'U', the
upper triangular part of A is stored as a band matrix; if
UPLO = 'L', the lower triangular part of A is stored. The
columns of the appropriate triangle are stored in the columns
of A and the diagonals of the triangle are stored in the rows
of A. See DPBTRF for further details.
LDA
LDA is INTEGER.
The leading dimension of the array A. LDA >= max(1,KD+1).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpbt05 (character UPLO, integer N, integer KD, integer NRHS, double precision,
dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldb, * ) B, integer
LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension(
ldxact, * ) XACT, integer LDXACT, double precision, dimension( * ) FERR, double precision,
dimension( * ) BERR, double precision, dimension( * ) RESLTS)
DPBT05
Purpose:
DPBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric band matrix.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpot01 (character UPLO, integer N, double precision, dimension( lda, * ) A, integer
LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, double precision,
dimension( * ) RWORK, double precision RESID)
DPOT01
Purpose:
DPOT01 reconstructs a symmetric positive definite matrix A from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
On entry, the factor L or U from the L*L' or U'*U
factorization of A.
Overwritten with the reconstructed matrix, and then with the
difference L*L' - A (or U'*U - A).
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpot02 (character UPLO, integer N, integer NRHS, double precision, dimension( lda,
* ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double
precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK,
double precision RESID)
DPOT02
Purpose:
DPOT02 computes the residual for the solution of a symmetric system
of linear equations A*x = b:
RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpot03 (character UPLO, integer N, double precision, dimension( lda, * ) A, integer
LDA, double precision, dimension( ldainv, * ) AINV, integer LDAINV, double precision,
dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK,
double precision RCOND, double precision RESID)
DPOT03
Purpose:
DPOT03 computes the residual for a symmetric matrix times its
inverse:
norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
AINV
AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
On entry, the inverse of the matrix A, stored as a symmetric
matrix in the same format as A.
In this version, AINV is expanded into a full matrix and
multiplied by A, so the opposing triangle of AINV will be
changed; i.e., if the upper triangular part of AINV is
stored, the lower triangular part will be used as work space.
LDAINV
LDAINV is INTEGER
The leading dimension of the array AINV. LDAINV >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK. LDWORK >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of A, computed as
( 1/norm(A) ) / norm(AINV).
RESID
RESID is DOUBLE PRECISION
norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpot05 (character UPLO, integer N, integer NRHS, double precision, dimension( lda,
* ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double
precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact, * )
XACT, integer LDXACT, double precision, dimension( * ) FERR, double precision, dimension(
* ) BERR, double precision, dimension( * ) RESLTS)
DPOT05
Purpose:
DPOT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric n by n matrix.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the leading n by n
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpot06 (character UPLO, integer N, integer NRHS, double precision, dimension( lda,
* ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double
precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK,
double precision RESID)
DPOT06
Purpose:
DPOT06 computes the residual for a solution of a system of linear
equations A*x = b :
RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original M x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dppt01 (character UPLO, integer N, double precision, dimension( * ) A, double
precision, dimension( * ) AFAC, double precision, dimension( * ) RWORK, double precision
RESID)
DPPT01
Purpose:
DPPT01 reconstructs a symmetric positive definite packed matrix A
from its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The original symmetric matrix A, stored as a packed
triangular matrix.
AFAC
AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the factor L or U from the L*L' or U'*U
factorization of A, stored as a packed triangular matrix.
Overwritten with the reconstructed matrix, and then with the
difference L*L' - A (or U'*U - A).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dppt02 (character UPLO, integer N, integer NRHS, double precision, dimension( * )
A, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb,
* ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID)
DPPT02
Purpose:
DPPT02 computes the residual in the solution of a symmetric system
of linear equations A*x = b when packed storage is used for the
coefficient matrix. The ratio computed is
RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
where EPS is the machine precision.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The original symmetric matrix A, stored as a packed
triangular matrix.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dppt03 (character UPLO, integer N, double precision, dimension( * ) A, double
precision, dimension( * ) AINV, double precision, dimension( ldwork, * ) WORK, integer
LDWORK, double precision, dimension( * ) RWORK, double precision RCOND, double precision
RESID)
DPPT03
Purpose:
DPPT03 computes the residual for a symmetric packed matrix times its
inverse:
norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The original symmetric matrix A, stored as a packed
triangular matrix.
AINV
AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The (symmetric) inverse of the matrix A, stored as a packed
triangular matrix.
WORK
WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK. LDWORK >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of A, computed as
( 1/norm(A) ) / norm(AINV).
RESID
RESID is DOUBLE PRECISION
norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dppt05 (character UPLO, integer N, integer NRHS, double precision, dimension( * )
AP, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension(
ldx, * ) X, integer LDX, double precision, dimension( ldxact, * ) XACT, integer LDXACT,
double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double
precision, dimension( * ) RESLTS)
DPPT05
Purpose:
DPPT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric matrix in packed storage format.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dpst01 (character UPLO, integer N, double precision, dimension( lda, * ) A, integer
LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, double precision,
dimension( ldperm, * ) PERM, integer LDPERM, integer, dimension( * ) PIV, double
precision, dimension( * ) RWORK, double precision RESID, integer RANK)
DPST01
Purpose:
DPST01 reconstructs a symmetric positive semidefinite matrix A
from its L or U factors and the permutation matrix P and computes
the residual
norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factor L or U from the L*L' or U'*U
factorization of A.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,N).
PERM
PERM is DOUBLE PRECISION array, dimension (LDPERM,N)
Overwritten with the reconstructed matrix, and then with the
difference P*L*L'*P' - A (or P*U'*U*P' - A)
LDPERM
LDPERM is INTEGER
The leading dimension of the array PERM.
LDAPERM >= max(1,N).
PIV
PIV is INTEGER array, dimension (N)
PIV is such that the nonzero entries are
P( PIV( K ), K ) = 1.
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
RANK
RANK is INTEGER
number of nonzero singular values of A.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dptt01 (integer N, double precision, dimension( * ) D, double precision, dimension(
* ) E, double precision, dimension( * ) DF, double precision, dimension( * ) EF, double
precision, dimension( * ) WORK, double precision RESID)
DPTT01
Purpose:
DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
factorization and computes the residual
norm(L*D*L' - A) / ( n * norm(A) * EPS ),
where EPS is the machine epsilon.
Parameters:
N
N is INTEGTER
The order of the matrix A.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E
E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
DF
DF is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the factor L from the L*D*L'
factorization of A.
EF
EF is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the factor L from the
L*D*L' factorization of A.
WORK
WORK is DOUBLE PRECISION array, dimension (2*N)
RESID
RESID is DOUBLE PRECISION
norm(L*D*L' - A) / (n * norm(A) * EPS)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dptt02 (integer N, integer NRHS, double precision, dimension( * ) D, double
precision, dimension( * ) E, double precision, dimension( ldx, * ) X, integer LDX, double
precision, dimension( ldb, * ) B, integer LDB, double precision RESID)
DPTT02
Purpose:
DPTT02 computes the residual for the solution to a symmetric
tridiagonal system of equations:
RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
where EPS is the machine epsilon.
Parameters:
N
N is INTEGTER
The order of the matrix A.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E
E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The n by nrhs matrix of solution vectors X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the n by nrhs matrix of right hand side vectors B.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RESID
RESID is DOUBLE PRECISION
norm(B - A*X) / (norm(A) * norm(X) * EPS)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dptt05 (integer N, integer NRHS, double precision, dimension( * ) D, double
precision, dimension( * ) E, double precision, dimension( ldb, * ) B, integer LDB, double
precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact, * )
XACT, integer LDXACT, double precision, dimension( * ) FERR, double precision, dimension(
* ) BERR, double precision, dimension( * ) RESLTS)
DPTT05
Purpose:
DPTT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric tridiagonal matrix of order n.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Parameters:
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E
E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqlt01 (integer M, integer N, double precision, dimension( lda, * ) A, double
precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) L, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQLT01
Purpose:
DQLT01 tests DGEQLF, which computes the QL factorization of an m-by-n
matrix A, and partially tests DORGQL which forms the m-by-m
orthogonal matrix Q.
DQLT01 compares L with Q'*A, and checks that Q is orthogonal.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QL factorization of A, as returned by DGEQLF.
See DGEQLF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,M)
The m-by-m orthogonal matrix Q.
L
L is DOUBLE PRECISION array, dimension (LDA,max(M,N))
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and R.
LDA >= max(M,N).
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGEQLF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqlt02 (integer M, integer N, integer K, double precision, dimension( lda, * ) A,
double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) L, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQLT02
Purpose:
DQLT02 tests DORGQL, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.
Given the QL factorization of an m-by-n matrix A, DQLT02 generates
the orthogonal matrix Q defined by the factorization of the last k
columns of A; it compares L(m-n+1:m,n-k+1:n) with
Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
orthonormal.
Parameters:
M
M is INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q to be generated.
M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DQLT01.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QL factorization of A, as returned by DGEQLF.
See DGEQLF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
L
L is DOUBLE PRECISION array, dimension (LDA,N)
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QL factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqlt03 (integer M, integer N, integer K, double precision, dimension( lda, * ) AF,
double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double
precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQLT03
Purpose:
DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
DQLT03 compares the results of a call to DORMQL with the results of
forming Q explicitly by a call to DORGQL and then performing matrix
multiplication by a call to DGEMM.
Parameters:
M
M is INTEGER
The order of the orthogonal matrix Q. M >= 0.
N
N is INTEGER
The number of rows or columns of the matrix C; C is m-by-n if
Q is applied from the left, or n-by-m if Q is applied from
the right. N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q. M >= K >= 0.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QL factorization of an m-by-n matrix, as
returned by DGEQLF. See SGEQLF for further details.
C
C is DOUBLE PRECISION array, dimension (LDA,N)
CC
CC is DOUBLE PRECISION array, dimension (LDA,N)
Q
Q is DOUBLE PRECISION array, dimension (LDA,M)
LDA
LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the QL factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of WORK. LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an m-by-m orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function dqpt01 (integer M, integer N, integer K, double precision,
dimension( lda, * ) A, double precision, dimension( lda, * ) AF, integer LDA, double
precision, dimension( * ) TAU, integer, dimension( * ) JPVT, double precision, dimension(
lwork ) WORK, integer LWORK)
DQPT01
Purpose:
DQPT01 tests the QR-factorization with pivoting of a matrix A. The
array AF contains the (possibly partial) QR-factorization of A, where
the upper triangle of AF(1:k,1:k) is a partial triangular factor,
the entries below the diagonal in the first k columns are the
Householder vectors, and the rest of AF contains a partially updated
matrix.
This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
Parameters:
M
M is INTEGER
The number of rows of the matrices A and AF.
N
N is INTEGER
The number of columns of the matrices A and AF.
K
K is INTEGER
The number of columns of AF that have been reduced
to upper triangular form.
A
A is DOUBLE PRECISION array, dimension (LDA, N)
The original matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
The (possibly partial) output of DGEQPF. The upper triangle
of AF(1:k,1:k) is a partial triangular factor, the entries
below the diagonal in the first k columns are the Householder
vectors, and the rest of AF contains a partially updated
matrix.
LDA
LDA is INTEGER
The leading dimension of the arrays A and AF.
TAU
TAU is DOUBLE PRECISION array, dimension (K)
Details of the Householder transformations as returned by
DGEQPF.
JPVT
JPVT is INTEGER array, dimension (N)
Pivot information as returned by DGEQPF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK >= M*N+N.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt01 (integer M, integer N, double precision, dimension( lda, * ) A, double
precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQRT01
Purpose:
DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n
matrix A, and partially tests DORGQR which forms the m-by-m
orthogonal matrix Q.
DQRT01 compares R with Q'*A, and checks that Q is orthogonal.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of A, as returned by DGEQRF.
See DGEQRF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,M)
The m-by-m orthogonal matrix Q.
R
R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and R.
LDA >= max(M,N).
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGEQRF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt01p (integer M, integer N, double precision, dimension( lda, * ) A, double
precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQRT01P
Purpose:
DQRT01P tests DGEQRFP, which computes the QR factorization of an m-by-n
matrix A, and partially tests DORGQR which forms the m-by-m
orthogonal matrix Q.
DQRT01P compares R with Q'*A, and checks that Q is orthogonal.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of A, as returned by DGEQRFP.
See DGEQRFP for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,M)
The m-by-m orthogonal matrix Q.
R
R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and R.
LDA >= max(M,N).
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGEQRFP.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt02 (integer M, integer N, integer K, double precision, dimension( lda, * ) A,
double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQRT02
Purpose:
DQRT02 tests DORGQR, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.
Given the QR factorization of an m-by-n matrix A, DQRT02 generates
the orthogonal matrix Q defined by the factorization of the first k
columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
and checks that the columns of Q are orthonormal.
Parameters:
M
M is INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q to be generated.
M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DQRT01.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of A, as returned by DGEQRF.
See DGEQRF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
R
R is DOUBLE PRECISION array, dimension (LDA,N)
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and R. LDA >= M.
TAU
TAU is DOUBLE PRECISION array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QR factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt03 (integer M, integer N, integer K, double precision, dimension( lda, * ) AF,
double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double
precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DQRT03
Purpose:
DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
DQRT03 compares the results of a call to DORMQR with the results of
forming Q explicitly by a call to DORGQR and then performing matrix
multiplication by a call to DGEMM.
Parameters:
M
M is INTEGER
The order of the orthogonal matrix Q. M >= 0.
N
N is INTEGER
The number of rows or columns of the matrix C; C is m-by-n if
Q is applied from the left, or n-by-m if Q is applied from
the right. N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q. M >= K >= 0.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of an m-by-n matrix, as
returned by DGEQRF. See DGEQRF for further details.
C
C is DOUBLE PRECISION array, dimension (LDA,N)
CC
CC is DOUBLE PRECISION array, dimension (LDA,N)
Q
Q is DOUBLE PRECISION array, dimension (LDA,M)
LDA
LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the QR factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of WORK. LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an m-by-m orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine dqrt04 (integer M, integer N, integer NB, double precision, dimension(6) RESULT)
DQRT04
Purpose:
DQRT04 tests DGEQRT and DGEMQRT.
Parameters:
M
M is INTEGER
Number of rows in test matrix.
N
N is INTEGER
Number of columns in test matrix.
NB
NB is INTEGER
Block size of test matrix. NB <= Min(M,N).
RESULT
RESULT is DOUBLE PRECISION array, dimension (6)
Results of each of the six tests below.
RESULT(1) = | A - Q R |
RESULT(2) = | I - Q^H Q |
RESULT(3) = | Q C - Q C |
RESULT(4) = | Q^H C - Q^H C |
RESULT(5) = | C Q - C Q |
RESULT(6) = | C Q^H - C Q^H |
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
subroutine dqrt05 (integer M, integer N, integer L, integer NB, double precision, dimension(6)
RESULT)
DQRT05
Purpose:
DQRT05 tests DTPQRT and DTPMQRT.
Parameters:
M
M is INTEGER
Number of rows in lower part of the test matrix.
N
N is INTEGER
Number of columns in test matrix.
L
L is INTEGER
The number of rows of the upper trapezoidal part the
lower test matrix. 0 <= L <= M.
NB
NB is INTEGER
Block size of test matrix. NB <= N.
RESULT
RESULT is DOUBLE PRECISION array, dimension (6)
Results of each of the six tests below.
RESULT(1) = | A - Q R |
RESULT(2) = | I - Q^H Q |
RESULT(3) = | Q C - Q C |
RESULT(4) = | Q^H C - Q^H C |
RESULT(5) = | C Q - C Q |
RESULT(6) = | C Q^H - C Q^H |
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
double precision function dqrt11 (integer M, integer K, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork )
WORK, integer LWORK)
DQRT11
Purpose:
DQRT11 computes the test ratio
|| Q'*Q - I || / (eps * m)
where the orthogonal matrix Q is represented as a product of
elementary transformations. Each transformation has the form
H(k) = I - tau(k) v(k) v(k)'
where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
[ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
in A(k+1:m,k).
Parameters:
M
M is INTEGER
The number of rows of the matrix A.
K
K is INTEGER
The number of columns of A whose subdiagonal entries
contain information about orthogonal transformations.
A
A is DOUBLE PRECISION array, dimension (LDA,K)
The (possibly partial) output of a QR reduction routine.
LDA
LDA is INTEGER
The leading dimension of the array A.
TAU
TAU is DOUBLE PRECISION array, dimension (K)
The scaling factors tau for the elementary transformations as
computed by the QR factorization routine.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK >= M*M + M.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function dqrt12 (integer M, integer N, double precision, dimension( lda, * )
A, integer LDA, double precision, dimension( * ) S, double precision, dimension( lwork )
WORK, integer LWORK)
DQRT12
Purpose:
DQRT12 computes the singular values `svlues' of the upper trapezoid
of A(1:M,1:N) and returns the ratio
|| s - svlues||/(||svlues||*eps*max(M,N))
Parameters:
M
M is INTEGER
The number of rows of the matrix A.
N
N is INTEGER
The number of columns of the matrix A.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix A. Only the upper trapezoid is referenced.
LDA
LDA is INTEGER
The leading dimension of the array A.
S
S is DOUBLE PRECISION array, dimension (min(M,N))
The singular values of the matrix A.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
max(M,N), M*N+2*MIN( M, N )+4*N).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt13 (integer SCALE, integer M, integer N, double precision, dimension( lda, * )
A, integer LDA, double precision NORMA, integer, dimension( 4 ) ISEED)
DQRT13
Purpose:
DQRT13 generates a full-rank matrix that may be scaled to have large
or small norm.
Parameters:
SCALE
SCALE is INTEGER
SCALE = 1: normally scaled matrix
SCALE = 2: matrix scaled up
SCALE = 3: matrix scaled down
M
M is INTEGER
The number of rows of the matrix A.
N
N is INTEGER
The number of columns of A.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A.
NORMA
NORMA is DOUBLE PRECISION
The one-norm of A.
ISEED
ISEED is integer array, dimension (4)
Seed for random number generator
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function dqrt14 (character TRANS, integer M, integer N, integer NRHS, double
precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X,
integer LDX, double precision, dimension( lwork ) WORK, integer LWORK)
DQRT14
Purpose:
DQRT14 checks whether X is in the row space of A or A'. It does so
by scaling both X and A such that their norms are in the range
[sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
(if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
and returning the norm of the trailing triangle, scaled by
MAX(M,N,NRHS)*eps.
Parameters:
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, check for X in the row space of A
= 'T': Transpose, check for X in the row space of A'.
M
M is INTEGER
The number of rows of the matrix A.
N
N is INTEGER
The number of columns of the matrix A.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of X.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
If TRANS = 'N', the N-by-NRHS matrix X.
IF TRANS = 'T', the M-by-NRHS matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X.
WORK
WORK is DOUBLE PRECISION array dimension (LWORK)
LWORK
LWORK is INTEGER
length of workspace array required
If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
if TRANS = 'T', LWORK >= (N+NRHS)*(M+2).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt15 (integer SCALE, integer RKSEL, integer M, integer N, integer NRHS, double
precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B,
integer LDB, double precision, dimension( * ) S, integer RANK, double precision NORMA,
double precision NORMB, integer, dimension( 4 ) ISEED, double precision, dimension( lwork
) WORK, integer LWORK)
DQRT15
Purpose:
DQRT15 generates a matrix with full or deficient rank and of various
norms.
Parameters:
SCALE
SCALE is INTEGER
SCALE = 1: normally scaled matrix
SCALE = 2: matrix scaled up
SCALE = 3: matrix scaled down
RKSEL
RKSEL is INTEGER
RKSEL = 1: full rank matrix
RKSEL = 2: rank-deficient matrix
M
M is INTEGER
The number of rows of the matrix A.
N
N is INTEGER
The number of columns of A.
NRHS
NRHS is INTEGER
The number of columns of B.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A.
B
B is DOUBLE PRECISION array, dimension (LDB, NRHS)
A matrix that is in the range space of matrix A.
LDB
LDB is INTEGER
The leading dimension of the array B.
S
S is DOUBLE PRECISION array, dimension MIN(M,N)
Singular values of A.
RANK
RANK is INTEGER
number of nonzero singular values of A.
NORMA
NORMA is DOUBLE PRECISION
one-norm of A.
NORMB
NORMB is DOUBLE PRECISION
one-norm of B.
ISEED
ISEED is integer array, dimension (4)
seed for random number generator.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
length of work space required.
LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dqrt16 (character TRANS, integer M, integer N, integer NRHS, double precision,
dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
RWORK, double precision RESID)
DQRT16
Purpose:
DQRT16 computes the residual for a solution of a system of linear
equations A*x = b or A'*x = b:
RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
where EPS is the machine epsilon.
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A *x = b
= 'T': A'*x = b, where A' is the transpose of A
= 'C': A'*x = b, where A' is the transpose of A
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original M x N matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB
LDB is INTEGER
The leading dimension of the array B. IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function dqrt17 (character TRANS, integer IRESID, integer M, integer N,
integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision,
dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB,
double precision, dimension( ldb, * ) C, double precision, dimension( lwork ) WORK,
integer LWORK)
DQRT17
Purpose:
DQRT17 computes the ratio
|| R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
where R = op(A)*X - B, op(A) is A or A', and
alpha = ||B|| if IRESID = 1 (zero-residual problem)
alpha = ||R|| if IRESID = 2 (otherwise).
Parameters:
TRANS
TRANS is CHARACTER*1
Specifies whether or not the transpose of A is used.
= 'N': No transpose, op(A) = A.
= 'T': Transpose, op(A) = A'.
IRESID
IRESID is INTEGER
IRESID = 1 indicates zero-residual problem.
IRESID = 2 indicates non-zero residual.
M
M is INTEGER
The number of rows of the matrix A.
If TRANS = 'N', the number of rows of the matrix B.
If TRANS = 'T', the number of rows of the matrix X.
N
N is INTEGER
The number of columns of the matrix A.
If TRANS = 'N', the number of rows of the matrix X.
If TRANS = 'T', the number of rows of the matrix B.
NRHS
NRHS is INTEGER
The number of columns of the matrices X and B.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= M.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
If TRANS = 'N', the n-by-nrhs matrix X.
If TRANS = 'T', the m-by-nrhs matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X.
If TRANS = 'N', LDX >= N.
If TRANS = 'T', LDX >= M.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
If TRANS = 'N', the m-by-nrhs matrix B.
If TRANS = 'T', the n-by-nrhs matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B.
If TRANS = 'N', LDB >= M.
If TRANS = 'T', LDB >= N.
C
C is DOUBLE PRECISION array, dimension (LDB,NRHS)
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK >= NRHS*(M+N).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2015
subroutine drqt01 (integer M, integer N, double precision, dimension( lda, * ) A, double
precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DRQT01
Purpose:
DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests DORGRQ which forms the n-by-n
orthogonal matrix Q.
DRQT01 compares R with A*Q', and checks that Q is orthogonal.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the RQ factorization of A, as returned by DGERQF.
See DGERQF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
The n-by-n orthogonal matrix Q.
R
R is DOUBLE PRECISION array, dimension (LDA,max(M,N))
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L.
LDA >= max(M,N).
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by DGERQF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (max(M,N))
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine drqt02 (integer M, integer N, integer K, double precision, dimension( lda, * ) A,
double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double
precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DRQT02
Purpose:
DRQT02 tests DORGRQ, which generates an m-by-n matrix Q with
orthonornmal rows that is defined as the product of k elementary
reflectors.
Given the RQ factorization of an m-by-n matrix A, DRQT02 generates
the orthogonal matrix Q defined by the factorization of the last k
rows of A; it compares R(m-k+1:m,n-m+1:n) with
A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
orthonormal.
Parameters:
M
M is INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q to be generated.
N >= M >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DRQT01.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the RQ factorization of A, as returned by DGERQF.
See DGERQF for further details.
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
R
R is DOUBLE PRECISION array, dimension (LDA,M)
LDA
LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= N.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the RQ factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (2)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine drqt03 (integer M, integer N, integer K, double precision, dimension( lda, * ) AF,
double precision, dimension( lda, * ) C, double precision, dimension( lda, * ) CC, double
precision, dimension( lda, * ) Q, integer LDA, double precision, dimension( * ) TAU,
double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * )
RWORK, double precision, dimension( * ) RESULT)
DRQT03
Purpose:
DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
DRQT03 compares the results of a call to DORMRQ with the results of
forming Q explicitly by a call to DORGRQ and then performing matrix
multiplication by a call to DGEMM.
Parameters:
M
M is INTEGER
The number of rows or columns of the matrix C; C is n-by-m if
Q is applied from the left, or m-by-n if Q is applied from
the right. M >= 0.
N
N is INTEGER
The order of the orthogonal matrix Q. N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q. N >= K >= 0.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the RQ factorization of an m-by-n matrix, as
returned by DGERQF. See SGERQF for further details.
C
C is DOUBLE PRECISION array, dimension (LDA,N)
CC
CC is DOUBLE PRECISION array, dimension (LDA,N)
Q
Q is DOUBLE PRECISION array, dimension (LDA,N)
LDA
LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.
TAU
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the RQ factorization in AF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of WORK. LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.
RWORK
RWORK is DOUBLE PRECISION array, dimension (M)
RESULT
RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an n-by-n orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function drzt01 (integer M, integer N, double precision, dimension( lda, * )
A, double precision, dimension( lda, * ) AF, integer LDA, double precision, dimension( * )
TAU, double precision, dimension( lwork ) WORK, integer LWORK)
DRZT01
Purpose:
DRZT01 returns
|| A - R*Q || / ( M * eps * ||A|| )
for an upper trapezoidal A that was factored with DTZRZF.
Parameters:
M
M is INTEGER
The number of rows of the matrices A and AF.
N
N is INTEGER
The number of columns of the matrices A and AF.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original upper trapezoidal M by N matrix A.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
The output of DTZRZF for input matrix A.
The lower triangle is not referenced.
LDA
LDA is INTEGER
The leading dimension of the arrays A and AF.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
Details of the Householder transformations as returned by
DTZRZF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The length of the array WORK. LWORK >= m*n + m*nb.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
double precision function drzt02 (integer M, integer N, double precision, dimension( lda, * )
AF, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork
) WORK, integer LWORK)
DRZT02
Purpose:
DRZT02 returns
|| I - Q'*Q || / ( M * eps)
where the matrix Q is defined by the Householder transformations
generated by DTZRZF.
Parameters:
M
M is INTEGER
The number of rows of the matrix AF.
N
N is INTEGER
The number of columns of the matrix AF.
AF
AF is DOUBLE PRECISION array, dimension (LDA,N)
The output of DTZRZF.
LDA
LDA is INTEGER
The leading dimension of the array AF.
TAU
TAU is DOUBLE PRECISION array, dimension (M)
Details of the Householder transformations as returned by
DTZRZF.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
length of WORK array. LWORK >= N*N+N*NB.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dspt01 (character UPLO, integer N, double precision, dimension( * ) A, double
precision, dimension( * ) AFAC, integer, dimension( * ) IPIV, double precision, dimension(
ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID)
DSPT01
Purpose:
DSPT01 reconstructs a symmetric indefinite packed matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The original symmetric matrix A, stored as a packed
triangular matrix.
AFAC
AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The factored form of the matrix A, stored as a packed
triangular matrix. AFAC contains the block diagonal matrix D
and the multipliers used to obtain the factor L or U from the
block L*D*L' or U*D*U' factorization as computed by DSPTRF.
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices from DSPTRF.
C
C is DOUBLE PRECISION array, dimension (LDC,N)
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dsyt01 (character UPLO, integer N, double precision, dimension( lda, * ) A, integer
LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( *
) IPIV, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension(
* ) RWORK, double precision RESID)
DSYT01
Purpose:
DSYT01 reconstructs a symmetric indefinite matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the block
diagonal matrix D and the multipliers used to obtain the
factor L or U from the block L*D*L' or U*D*U' factorization
as computed by DSYTRF.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices from DSYTRF.
C
C is DOUBLE PRECISION array, dimension (LDC,N)
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine dsyt01_rook (character UPLO, integer N, double precision, dimension( lda, * ) A,
integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, integer,
dimension( * ) IPIV, double precision, dimension( ldc, * ) C, integer LDC, double
precision, dimension( * ) RWORK, double precision RESID)
DSYT01_ROOK
Purpose:
DSYT01_ROOK reconstructs a symmetric indefinite matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The number of rows and columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The original symmetric matrix A.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N)
AFAC
AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the block
diagonal matrix D and the multipliers used to obtain the
factor L or U from the block L*D*L' or U*D*U' factorization
as computed by DSYTRF_ROOK.
LDAFAC
LDAFAC is INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices from DSYTRF_ROOK.
C
C is DOUBLE PRECISION array, dimension (LDC,N)
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,N).
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
subroutine dtbt02 (character UPLO, character TRANS, character DIAG, integer N, integer KD,
integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision,
dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB,
double precision, dimension( * ) WORK, double precision RESID)
DTBT02
Purpose:
DTBT02 computes the residual for the computed solution to a
triangular system of linear equations A*x = b or A' *x = b when
A is a triangular band matrix. Here A' is the transpose of A and
x and b are N by NRHS matrices. The test ratio is the maximum over
the number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A'*x = b (Transpose)
= 'C': A'*x = b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtbt03 (character UPLO, character TRANS, character DIAG, integer N, integer KD,
integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision
SCALE, double precision, dimension( * ) CNORM, double precision TSCAL, double precision,
dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB,
double precision, dimension( * ) WORK, double precision RESID)
DTBT03
Purpose:
DTBT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b or A'*x = s*b when A is a
triangular band matrix. Here A' is the transpose of A, s is a scalar,
and x and b are N by NRHS matrices. The test ratio is the maximum
over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A'*x = b (Transpose)
= 'C': A'*x = b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
SCALE
SCALE is DOUBLE PRECISION
The scaling factor s used in solving the triangular system.
CNORM
CNORM is DOUBLE PRECISION array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal.
TSCAL
TSCAL is DOUBLE PRECISION
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtbt05 (character UPLO, character TRANS, character DIAG, integer N, integer KD,
integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision,
dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldxact, * ) XACT, integer LDXACT, double precision,
dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( *
) RESLTS)
DTBT05
Purpose:
DTBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular band matrix.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtbt06 (double precision RCOND, double precision RCONDC, character UPLO, character
DIAG, integer N, integer KD, double precision, dimension( ldab, * ) AB, integer LDAB,
double precision, dimension( * ) WORK, double precision RAT)
DTBT06
Purpose:
DTBT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTBCON. Information about the triangular matrix A is
used if one estimate is zero and the other is non-zero to decide if
underflow in the estimate is justified.
Parameters:
RCOND
RCOND is DOUBLE PRECISION
The estimate of the reciprocal condition number obtained by
forming the explicit inverse of the matrix A and computing
RCOND = 1/( norm(A) * norm(inv(A)) ).
RCONDC
RCONDC is DOUBLE PRECISION
The estimate of the reciprocal condition number computed by
DTBCON.
UPLO
UPLO is CHARACTER
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG
DIAG is CHARACTER
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
KD
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
AB
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RAT
RAT is DOUBLE PRECISION
The test ratio. If both RCOND and RCONDC are nonzero,
RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
If RAT = 0, the two estimates are exactly the same.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtpt01 (character UPLO, character DIAG, integer N, double precision, dimension( * )
AP, double precision, dimension( * ) AINVP, double precision RCOND, double precision,
dimension( * ) WORK, double precision RESID)
DTPT01
Purpose:
DTPT01 computes the residual for a triangular matrix A times its
inverse when A is stored in packed format:
RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The original upper or lower triangular matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
AINVP
AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the (triangular) inverse of the matrix A, packed
columnwise in a linear array as in AP.
On exit, the contents of AINVP are destroyed.
RCOND
RCOND is DOUBLE PRECISION
The reciprocal condition number of A, computed as
1/(norm(A) * norm(AINV)).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtpt02 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( * ) AP, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
WORK, double precision RESID)
DTPT02
Purpose:
DTPT02 computes the residual for the computed solution to a
triangular system of linear equations A*x = b or A'*x = b when
the triangular matrix A is stored in packed format. Here A' is the
transpose of A and x and b are N by NRHS matrices. The test ratio is
the maximum over the number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A'*x = b (Transpose)
= 'C': A'*x = b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtpt03 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( * ) AP, double precision SCALE, double precision, dimension(
* ) CNORM, double precision TSCAL, double precision, dimension( ldx, * ) X, integer LDX,
double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
WORK, double precision RESID)
DTPT03
Purpose:
DTPT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b or A'*x = s*b when the triangular
matrix A is stored in packed format. Here A' is the transpose of A,
s is a scalar, and x and b are N by NRHS matrices. The test ratio is
the maximum over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = s*b (No transpose)
= 'T': A'*x = s*b (Transpose)
= 'C': A'*x = s*b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
SCALE
SCALE is DOUBLE PRECISION
The scaling factor s used in solving the triangular system.
CNORM
CNORM is DOUBLE PRECISION array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal.
TSCAL
TSCAL is DOUBLE PRECISION
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtpt05 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( * ) AP, double precision, dimension( ldb, * ) B, integer LDB,
double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact,
* ) XACT, integer LDXACT, double precision, dimension( * ) FERR, double precision,
dimension( * ) BERR, double precision, dimension( * ) RESLTS)
DTPT05
Purpose:
DTPT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular matrix in packed storage format.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtpt06 (double precision RCOND, double precision RCONDC, character UPLO, character
DIAG, integer N, double precision, dimension( * ) AP, double precision, dimension( * )
WORK, double precision RAT)
DTPT06
Purpose:
DTPT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTPCON. Information about the triangular matrix A is
used if one estimate is zero and the other is non-zero to decide if
underflow in the estimate is justified.
Parameters:
RCOND
RCOND is DOUBLE PRECISION
The estimate of the reciprocal condition number obtained by
forming the explicit inverse of the matrix A and computing
RCOND = 1/( norm(A) * norm(inv(A)) ).
RCONDC
RCONDC is DOUBLE PRECISION
The estimate of the reciprocal condition number computed by
DTPCON.
UPLO
UPLO is CHARACTER
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG
DIAG is CHARACTER
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RAT
RAT is DOUBLE PRECISION
The test ratio. If both RCOND and RCONDC are nonzero,
RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
If RAT = 0, the two estimates are exactly the same.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtrt01 (character UPLO, character DIAG, integer N, double precision, dimension(
lda, * ) A, integer LDA, double precision, dimension( ldainv, * ) AINV, integer LDAINV,
double precision RCOND, double precision, dimension( * ) WORK, double precision RESID)
DTRT01
Purpose:
DTRT01 computes the residual for a triangular matrix A times its
inverse:
RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AINV
AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
On entry, the (triangular) inverse of the matrix A, in the
same storage format as A.
On exit, the contents of AINV are destroyed.
LDAINV
LDAINV is INTEGER
The leading dimension of the array AINV. LDAINV >= max(1,N).
RCOND
RCOND is DOUBLE PRECISION
The reciprocal condition number of A, computed as
1/(norm(A) * norm(AINV)).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtrt02 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, *
) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision,
dimension( * ) WORK, double precision RESID)
DTRT02
Purpose:
DTRT02 computes the residual for the computed solution to a
triangular system of linear equations A*x = b or A'*x = b.
Here A is a triangular matrix, A' is the transpose of A, and x and b
are N by NRHS matrices. The test ratio is the maximum over the
number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A'*x = b (Transpose)
= 'C': A'*x = b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtrt03 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( lda, * ) A, integer LDA, double precision SCALE, double
precision, dimension( * ) CNORM, double precision TSCAL, double precision, dimension( ldx,
* ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double
precision, dimension( * ) WORK, double precision RESID)
DTRT03
Purpose:
DTRT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b or A'*x = s*b.
Here A is a triangular matrix, A' is the transpose of A, s is a
scalar, and x and b are N by NRHS matrices. The test ratio is the
maximum over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = s*b (No transpose)
= 'T': A'*x = s*b (Transpose)
= 'C': A'*x = s*b (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SCALE
SCALE is DOUBLE PRECISION
The scaling factor s used in solving the triangular system.
CNORM
CNORM is DOUBLE PRECISION array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal.
TSCAL
TSCAL is DOUBLE PRECISION
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A.
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RESID
RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtrt05 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS,
double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, *
) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision,
dimension( ldxact, * ) XACT, integer LDXACT, double precision, dimension( * ) FERR, double
precision, dimension( * ) BERR, double precision, dimension( * ) RESLTS)
DTRT05
Purpose:
DTRT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular n by n matrix.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS
TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
DIAG
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT
LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X.
BERR
BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution).
RESLTS
RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine dtrt06 (double precision RCOND, double precision RCONDC, character UPLO, character
DIAG, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision,
dimension( * ) WORK, double precision RAT)
DTRT06
Purpose:
DTRT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by DTRCON. Information about the triangular matrix A is
used if one estimate is zero and the other is non-zero to decide if
underflow in the estimate is justified.
Parameters:
RCOND
RCOND is DOUBLE PRECISION
The estimate of the reciprocal condition number obtained by
forming the explicit inverse of the matrix A and computing
RCOND = 1/( norm(A) * norm(inv(A)) ).
RCONDC
RCONDC is DOUBLE PRECISION
The estimate of the reciprocal condition number computed by
DTRCON.
UPLO
UPLO is CHARACTER
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG
DIAG is CHARACTER
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading n by n lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N)
RAT
RAT is DOUBLE PRECISION
The test ratio. If both RCOND and RCONDC are nonzero,
RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
If RAT = 0, the two estimates are exactly the same.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
subroutine sdrvsy_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * )
NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, real, dimension( * ) A,
real, dimension( * ) AFAC, real, dimension( * ) AINV, real, dimension( * ) B, real,
dimension( * ) X, real, dimension( * ) XACT, real, dimension( * ) WORK, real, dimension( *
) RWORK, integer, dimension( * ) IWORK, integer NOUT)
SDRVSY_ROOK
Purpose:
SDRVSY_ROOK tests the driver routines SSYSV_ROOK.
Parameters:
DOTYPE
DOTYPE is LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN
NN is INTEGER
The number of values of N contained in the vector NVAL.
NVAL
NVAL is INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS
NRHS is INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH
THRESH is DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR
TSTERR is LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX
NMAX is INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A
A is REAL array, dimension (NMAX*NMAX)
AFAC
AFAC is REAL array, dimension (NMAX*NMAX)
AINV
AINV is REAL array, dimension (NMAX*NMAX)
B
B is REAL array, dimension (NMAX*NRHS)
X
X is REAL array, dimension (NMAX*NRHS)
XACT
XACT is REAL array, dimension (NMAX*NRHS)
WORK
WORK is REAL array, dimension
(NMAX*max(2,NRHS))
RWORK
RWORK is REAL array, dimension (NMAX+2*NRHS)
IWORK
IWORK is INTEGER array, dimension (2*NMAX)
NOUT
NOUT is INTEGER
The unit number for output.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
Author
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