**NAME**

aux_eig - auxFunctionssubroutinealahdg(IOUNIT, PATH)ALAHDGsubroutinealareq(PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT)ALAREQsubroutinealarqg(PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT)ALARQGsubroutinealasmg(TYPE, NOUT, NFAIL, NRUN, NERRS)ALASMGsubroutinealasum(TYPE, NOUT, NFAIL, NRUN, NERRS)ALASUMsubroutinealasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)ALASVMinteger functionilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)ILAENVsubroutinexerbla(SRNAME, INFO)XERBLAsubroutinexlaenv(ISPEC, NVALUE)XLAENV

**Detailed** **Description**

This is the group of auxiliary LAPACK TESTING EIG routines.

**Function** **Documentation**

subroutinealahdg(integerIOUNIT,character*3PATH)ALAHDGPurpose:ALAHDG 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 GQR: GQR (general matrices) GRQ: GRQ (general matrices) LSE: LSE Problem GLM: GLM Problem GSV: Generalized Singular Value Decomposition CSD: CS DecompositionAuthor:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011subroutinealareq(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 2011subroutinealarqg(character*3PATH,integerNMATS,logical,dimension(*)DOTYPE,integerNTYPES,integerNIN,integerNOUT)ALARQGPurpose:ALARQG 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 2011subroutinealasmg(character*3TYPE,integerNOUT,integerNFAIL,integerNRUN,integerNERRS)ALASMGPurpose:ALASMG 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 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 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 12 <= ISPEC <= 16: xHSEQR or one of its subroutines, see IPARMQ for detailed explanation 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 )subroutinexerbla(character*(*)SRNAME,integerINFO)XERBLAPurpose:This is a special version of XERBLA to be used only as part of the test program for testing error exits from the LAPACK routines. Error messages are printed if INFO.NE.INFOT or if SRNAME.NE.SRNAMT, where INFOT and SRNAMT are values stored in COMMON.Parameters:SRNAMESRNAME is CHARACTER*(*) The name of the subroutine calling XERBLA. This name should match the COMMON variable SRNAMT.INFOINFO is INTEGER The error return code from the calling subroutine. INFO should equal the COMMON variable INFOT.Author:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:November 2011FurtherDetails:The following variables are passed via the common blocks INFOC and SRNAMC: INFOT INTEGER Expected integer return code NOUT INTEGER Unit number for printing error messages OK LOGICAL Set to .TRUE. if INFO = INFOT and SRNAME = SRNAMT, otherwise set to .FALSE. LERR LOGICAL Set to .TRUE., indicating that XERBLA was called SRNAMT CHARACTER*(*) Expected name of calling subroutinesubroutinexlaenv(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 trap 12 <= ISPEC <= 16: xHSEQR or one of its subroutines, see IPARMQ for detailed explanationNVALUENVALUE 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**

Generated automatically by Doxygen for LAPACK from the source code.