**NAME**

aux_lin - auxFunctionssubroutinealadhd(IOUNIT, PATH)ALADHDsubroutinealaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M,N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)ALAERHsubroutinealaesm(PATH, OK, NOUT)ALAESMsubroutinealahd(IOUNIT, PATH)ALAHDsubroutinealareq(PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT)ALAREQsubroutinealasum(TYPE, NOUT, NFAIL, NRUN, NERRS)ALASUMsubroutinealasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)ALASVMsubroutineicopy(N, SX, INCX, SY, INCY)ICOPYinteger functionilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)ILAENVsubroutinexlaenv(ISPEC, NVALUE)XLAENV

**Detailed** **Description**

This is the group of auxiliary LAPACK TESTING LIN routines.

**Function** **Documentation**

subroutinealadhd(integerIOUNIT,character*3PATH)ALADHDPurpose:ALADHD prints header information for the driver routines test paths.Parameters:IOUNITIOUNIT is INTEGER The unit number to which the header information should be printed.PATHPATH is CHARACTER*3 The name of the path for which the header information is to be printed. Current paths are _GE: General matrices _GB: General band _GT: General Tridiagonal _PO: Symmetric or Hermitian positive definite _PS: Symmetric or Hermitian positive semi-definite _PP: Symmetric or Hermitian positive definite packed _PB: Symmetric or Hermitian positive definite band _PT: Symmetric or Hermitian positive definite tridiagonal _SY: Symmetric indefinite, with partial (Bunch-Kaufman) pivoting _SR: Symmetric indefinite, with "rook" (bounded Bunch-Kaufman) pivoting _SP: Symmetric indefinite packed, with partial (Bunch-Kaufman) pivoting _HE: (complex) Hermitian indefinite, with partial (Bunch-Kaufman) pivoting _HR: (complex) Hermitian indefinite, with "rook" (bounded Bunch-Kaufman) pivoting _HP: (complex) Hermitian indefinite packed, with partial (Bunch-Kaufman) pivoting The first character must be one of S, D, C, or Z (C or Z only if complex).Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2013subroutinealaerh(character*3PATH,character*(*)SUBNAM,integerINFO,integerINFOE,character*(*)OPTS,integerM,integerN,integerKL,integerKU,integerN5,integerIMAT,integerNFAIL,integerNERRS,integerNOUT)ALAERHPurpose:ALAERH is an error handler for the LAPACK routines. It prints the header if this is the first error message and prints the error code and form of recovery, if any. The character evaluations in this routine may make it slow, but it should not be called once the LAPACK routines are fully debugged.Parameters:PATHPATH is CHARACTER*3 The LAPACK path name of subroutine SUBNAM.SUBNAMSUBNAM is CHARACTER*(*) The name of the subroutine that returned an error code.INFOINFO is INTEGER The error code returned from routine SUBNAM.INFOEINFOE is INTEGER The expected error code from routine SUBNAM, if SUBNAM were error-free. If INFOE = 0, an error message is printed, but if INFOE.NE.0, we assume only the return code INFO is wrong.OPTSOPTS is CHARACTER*(*) The character options to the subroutine SUBNAM, concatenated into a single character string. For example, UPLO = 'U', TRANS = 'T', and DIAG = 'N' for a triangular routine would be specified as OPTS = 'UTN'.MM is INTEGER The matrix row dimension.NN is INTEGER The matrix column dimension. Accessed only if PATH = xGE or xGB.KLKL is INTEGER The number of sub-diagonals of the matrix. Accessed only if PATH = xGB, xPB, or xTB. Also used for NRHS for PATH = xLS.KUKU is INTEGER The number of super-diagonals of the matrix. Accessed only if PATH = xGB.N5N5 is INTEGER A fifth integer parameter, may be the blocksize NB or the number of right hand sides NRHS.IMATIMAT is INTEGER The matrix type.NFAILNFAIL is INTEGER The number of prior tests that did not pass the threshold; used to determine if the header should be printed.NERRSNERRS is INTEGER On entry, the number of errors already detected; used to determine if the header should be printed. On exit, NERRS is increased by 1.NOUTNOUT is INTEGER The unit number on which results are to be printed.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2013subroutinealaesm(character*3PATH,logicalOK,integerNOUT)ALAESMPurpose:ALAESM prints a summary of results from one of the -ERR- routines.Parameters:PATHPATH is CHARACTER*3 The LAPACK path name.OKOK is LOGICAL The flag from CHKXER that indicates whether or not the tests of error exits passed.NOUTNOUT is INTEGER The unit number on which results are to be printed. NOUT >= 0.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011subroutinealahd(integerIOUNIT,character*3PATH)ALAHDPurpose:ALAHD prints header information for the different test paths.Parameters:IOUNITIOUNIT is INTEGER The unit number to which the header information should be printed.PATHPATH is CHARACTER*3 The name of the path for which the header information is to be printed. Current paths are _GE: General matrices _GB: General band _GT: General Tridiagonal _PO: Symmetric or Hermitian positive definite _PS: Symmetric or Hermitian positive semi-definite _PP: Symmetric or Hermitian positive definite packed _PB: Symmetric or Hermitian positive definite band _PT: Symmetric or Hermitian positive definite tridiagonal _SY: Symmetric indefinite, with partial (Bunch-Kaufman) pivoting _SR: Symmetric indefinite, with "rook" (bounded Bunch-Kaufman) pivoting _SP: Symmetric indefinite packed, with partial (Bunch-Kaufman) pivoting _HE: (complex) Hermitian indefinite, with partial (Bunch-Kaufman) pivoting _HR: Symmetric indefinite, with "rook" (bounded Bunch-Kaufman) pivoting _HP: (complex) Hermitian indefinite packed, with partial (Bunch-Kaufman) pivoting _TR: Triangular _TP: Triangular packed _TB: Triangular band _QR: QR (general matrices) _LQ: LQ (general matrices) _QL: QL (general matrices) _RQ: RQ (general matrices) _QP: QR with column pivoting _TZ: Trapezoidal _LS: Least Squares driver routines _LU: LU variants _CH: Cholesky variants _QS: QR variants _QT: QRT (general matrices) _QX: QRT (triangular-pentagonal matrices) The first character must be one of S, D, C, or Z (C or Z only if complex).Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2015subroutinealareq(character*3PATH,integerNMATS,logical,dimension(*)DOTYPE,integerNTYPES,integerNIN,integerNOUT)ALAREQPurpose:ALAREQ handles input for the LAPACK test program. It is called to evaluate the input line which requested NMATS matrix types for PATH. The flow of control is as follows: If NMATS = NTYPES then DOTYPE(1:NTYPES) = .TRUE. else Read the next input line for NMATS matrix types Set DOTYPE(I) = .TRUE. for each valid type I endifParameters:PATHPATH is CHARACTER*3 An LAPACK path name for testing.NMATSNMATS is INTEGER The number of matrix types to be used in testing this path.DOTYPEDOTYPE is LOGICAL array, dimension (NTYPES) The vector of flags indicating if each type will be tested.NTYPESNTYPES is INTEGER The maximum number of matrix types for this path.NINNIN is INTEGER The unit number for input. NIN >= 1.NOUTNOUT is INTEGER The unit number for output. NOUT >= 1.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011subroutinealasum(character*3TYPE,integerNOUT,integerNFAIL,integerNRUN,integerNERRS)ALASUMPurpose:ALASUM prints a summary of results from one of the -CHK- routines.Parameters:TYPETYPE is CHARACTER*3 The LAPACK path name.NOUTNOUT is INTEGER The unit number on which results are to be printed. NOUT >= 0.NFAILNFAIL is INTEGER The number of tests which did not pass the threshold ratio.NRUNNRUN is INTEGER The total number of tests.NERRSNERRS is INTEGER The number of error messages recorded.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011subroutinealasvm(character*3TYPE,integerNOUT,integerNFAIL,integerNRUN,integerNERRS)ALASVMPurpose:ALASVM prints a summary of results from one of the -DRV- routines.Parameters:TYPETYPE is CHARACTER*3 The LAPACK path name.NOUTNOUT is INTEGER The unit number on which results are to be printed. NOUT >= 0.NFAILNFAIL is INTEGER The number of tests which did not pass the threshold ratio.NRUNNRUN is INTEGER The total number of tests.NERRSNERRS is INTEGER The number of error messages recorded.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011subroutineicopy(integerN,integer,dimension(*)SX,integerINCX,integer,dimension(*)SY,integerINCY)ICOPYPurpose:ICOPY copies an integer vector x to an integer vector y. Uses unrolled loops for increments equal to 1.Parameters:NN is INTEGER The length of the vectors SX and SY.SXSX is INTEGER array, dimension (1+(N-1)*abs(INCX)) The vector X.INCXINCX is INTEGER The spacing between consecutive elements of SX.SYSY is INTEGER array, dimension (1+(N-1)*abs(INCY)) The vector Y.INCYINCY is INTEGER The spacing between consecutive elements of SY.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011integerfunctionilaenv(integerISPEC,character*(*)NAME,character*(*)OPTS,integerN1,integerN2,integerN3,integerN4)ILAENVPurpose:ILAENV returns problem-dependent parameters for the local environment. See ISPEC for a description of the parameters. In this version, the problem-dependent parameters are contained in the integer array IPARMS in the common block CLAENV and the value with index ISPEC is copied to ILAENV. This version of ILAENV is to be used in conjunction with XLAENV in TESTING and TIMING.Parameters:ISPECISPEC is INTEGER Specifies the parameter to be returned as the value of ILAENV. = 1: the optimal blocksize; if this value is 1, an unblocked algorithm will give the best performance. = 2: the minimum block size for which the block routine should be used; if the usable block size is less than this value, an unblocked routine should be used. = 3: the crossover point (in a block routine, for N less than this value, an unblocked routine should be used) = 4: the number of shifts, used in the nonsymmetric eigenvalue routines = 5: the minimum column dimension for blocking to be used; rectangular blocks must have dimension at least k by m, where k is given by ILAENV(2,...) and m by ILAENV(5,...) = 6: the crossover point for the SVD (when reducing an m by n matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds this value, a QR factorization is used first to reduce the matrix to a triangular form.) = 7: the number of processors = 8: the crossover point for the multishift QR and QZ methods for nonsymmetric eigenvalue problems. = 9: maximum size of the subproblems at the bottom of the computation tree in the divide-and-conquer algorithm =10: ieee NaN arithmetic can be trusted not to trap =11: infinity arithmetic can be trusted not to trap Other specifications (up to 100) can be added later.NAMENAME is CHARACTER*(*) The name of the calling subroutine.OPTSOPTS is CHARACTER*(*) The character options to the subroutine NAME, concatenated into a single character string. For example, UPLO = 'U', TRANS = 'T', and DIAG = 'N' for a triangular routine would be specified as OPTS = 'UTN'.N1N1 is INTEGERN2N2 is INTEGERN3N3 is INTEGERN4N4 is INTEGER Problem dimensions for the subroutine NAME; these may not all be required.Returns:ILAENV ILAENV is INTEGER >= 0: the value of the parameter specified by ISPEC < 0: if ILAENV = -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 2011FurtherDetails:The following conventions have been used when calling ILAENV from the LAPACK routines: 1) OPTS is a concatenation of all of the character options to subroutine NAME, in the same order that they appear in the argument list for NAME, even if they are not used in determining the value of the parameter specified by ISPEC. 2) The problem dimensions N1, N2, N3, N4 are specified in the order that they appear in the argument list for NAME. N1 is used first, N2 second, and so on, and unused problem dimensions are passed a value of -1. 3) The parameter value returned by ILAENV is checked for validity in the calling subroutine. For example, ILAENV is used to retrieve the optimal blocksize for STRTRI as follows: NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) IF( NB.LE.1 ) NB = MAX( 1, N )subroutinexlaenv(integerISPEC,integerNVALUE)XLAENVPurpose:XLAENV sets certain machine- and problem-dependent quantities which will later be retrieved by ILAENV.Parameters:ISPECISPEC is INTEGER Specifies the parameter to be set in the COMMON array IPARMS. = 1: the optimal blocksize; if this value is 1, an unblocked algorithm will give the best performance. = 2: the minimum block size for which the block routine should be used; if the usable block size is less than this value, an unblocked routine should be used. = 3: the crossover point (in a block routine, for N less than this value, an unblocked routine should be used) = 4: the number of shifts, used in the nonsymmetric eigenvalue routines = 5: the minimum column dimension for blocking to be used; rectangular blocks must have dimension at least k by m, where k is given by ILAENV(2,...) and m by ILAENV(5,...) = 6: the crossover point for the SVD (when reducing an m by n matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds this value, a QR factorization is used first to reduce the matrix to a triangular form) = 7: the number of processors = 8: another crossover point, for the multishift QR and QZ methods for nonsymmetric eigenvalue problems. = 9: maximum size of the subproblems at the bottom of the computation tree in the divide-and-conquer algorithm (used by xGELSD and xGESDD) =10: ieee NaN arithmetic can be trusted not to trap =11: infinity arithmetic can be trusted not to trapNVALUENVALUE is INTEGER The value of the parameter specified by ISPEC.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011

**Author**

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