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
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