Provided by: liblapack-doc_3.11.0-2build1_all bug

NAME

       single_eig - real

SYNOPSIS

   Functions
       program schkee
           SCHKEE

Detailed Description

       This is the group of real LAPACK TESTING EIG routines.

Function Documentation

   program schkee
       SCHKEE

       Purpose:

            SCHKEE tests the REAL LAPACK subroutines for the matrix
            eigenvalue problem.  The test paths in this version are

            NEP (Nonsymmetric Eigenvalue Problem):
                Test SGEHRD, SORGHR, SHSEQR, STREVC, SHSEIN, and SORMHR

            SEP (Symmetric Eigenvalue Problem):
                Test SSYTRD, SORGTR, SSTEQR, SSTERF, SSTEIN, SSTEDC,
                and drivers SSYEV(X), SSBEV(X), SSPEV(X), SSTEV(X),
                            SSYEVD,   SSBEVD,   SSPEVD,   SSTEVD

            SVD (Singular Value Decomposition):
                Test SGEBRD, SORGBR, SBDSQR, SBDSDC
                and the drivers SGESVD, SGESDD

            SEV (Nonsymmetric Eigenvalue/eigenvector Driver):
                Test SGEEV

            SES (Nonsymmetric Schur form Driver):
                Test SGEES

            SVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver):
                Test SGEEVX

            SSX (Nonsymmetric Schur form Expert Driver):
                Test SGEESX

            SGG (Generalized Nonsymmetric Eigenvalue Problem):
                Test SGGHD3, SGGBAL, SGGBAK, SHGEQZ, and STGEVC

            SGS (Generalized Nonsymmetric Schur form Driver):
                Test SGGES

            SGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver):
                Test SGGEV

            SGX (Generalized Nonsymmetric Schur form Expert Driver):
                Test SGGESX

            SXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver):
                Test SGGEVX

            SSG (Symmetric Generalized Eigenvalue Problem):
                Test SSYGST, SSYGV, SSYGVD, SSYGVX, SSPGST, SSPGV, SSPGVD,
                SSPGVX, SSBGST, SSBGV, SSBGVD, and SSBGVX

            SSB (Symmetric Band Eigenvalue Problem):
                Test SSBTRD

            SBB (Band Singular Value Decomposition):
                Test SGBBRD

            SEC (Eigencondition estimation):
                Test SLALN2, SLASY2, SLAEQU, SLAEXC, STRSYL, STREXC, STRSNA,
                STRSEN, and SLAQTR

            SBL (Balancing a general matrix)
                Test SGEBAL

            SBK (Back transformation on a balanced matrix)
                Test SGEBAK

            SGL (Balancing a matrix pair)
                Test SGGBAL

            SGK (Back transformation on a matrix pair)
                Test SGGBAK

            GLM (Generalized Linear Regression Model):
                Tests SGGGLM

            GQR (Generalized QR and RQ factorizations):
                Tests SGGQRF and SGGRQF

            GSV (Generalized Singular Value Decomposition):
                Tests SGGSVD, SGGSVP, STGSJA, SLAGS2, SLAPLL, and SLAPMT

            CSD (CS decomposition):
                Tests SORCSD

            LSE (Constrained Linear Least Squares):
                Tests SGGLSE

            Each test path has a different set of inputs, but the data sets for
            the driver routines xEV, xES, xVX, and xSX can be concatenated in a
            single input file.  The first line of input should contain one of the
            3-character path names in columns 1-3.  The number of remaining lines
            depends on what is found on the first line.

            The number of matrix types used in testing is often controllable from
            the input file.  The number of matrix types for each path, and the
            test routine that describes them, is as follows:

            Path name(s)  Types    Test routine

            SHS or NEP      21     SCHKHS
            SST or SEP      21     SCHKST (routines)
                            18     SDRVST (drivers)
            SBD or SVD      16     SCHKBD (routines)
                             5     SDRVBD (drivers)
            SEV             21     SDRVEV
            SES             21     SDRVES
            SVX             21     SDRVVX
            SSX             21     SDRVSX
            SGG             26     SCHKGG (routines)
            SGS             26     SDRGES
            SGX              5     SDRGSX
            SGV             26     SDRGEV
            SXV              2     SDRGVX
            SSG             21     SDRVSG
            SSB             15     SCHKSB
            SBB             15     SCHKBB
            SEC              -     SCHKEC
            SBL              -     SCHKBL
            SBK              -     SCHKBK
            SGL              -     SCHKGL
            SGK              -     SCHKGK
            GLM              8     SCKGLM
            GQR              8     SCKGQR
            GSV              8     SCKGSV
            CSD              3     SCKCSD
            LSE              8     SCKLSE

           -----------------------------------------------------------------------

            NEP input file:

            line 2:  NN, INTEGER
                     Number of values of N.

            line 3:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix dimension N.

            line 4:  NPARMS, INTEGER
                     Number of values of the parameters NB, NBMIN, NX, NS, and
                     MAXB.

            line 5:  NBVAL, INTEGER array, dimension (NPARMS)
                     The values for the blocksize NB.

            line 6:  NBMIN, INTEGER array, dimension (NPARMS)
                     The values for the minimum blocksize NBMIN.

            line 7:  NXVAL, INTEGER array, dimension (NPARMS)
                     The values for the crossover point NX.

            line 8:  INMIN, INTEGER array, dimension (NPARMS)
                     LAHQR vs TTQRE crossover point, >= 11

            line 9:  INWIN, INTEGER array, dimension (NPARMS)
                     recommended deflation window size

            line 10: INIBL, INTEGER array, dimension (NPARMS)
                     nibble crossover point

            line 11:  ISHFTS, INTEGER array, dimension (NPARMS)
                     number of simultaneous shifts)

            line 12:  IACC22, INTEGER array, dimension (NPARMS)
                     select structured matrix multiply: 0, 1 or 2)

            line 13: THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.  To have all of the test
                     ratios printed, use THRESH = 0.0 .

            line 14: NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 14 was 2:

            line 15: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 15-EOF:  The remaining lines occur in sets of 1 or 2 and allow
                     the user to specify the matrix types.  Each line contains
                     a 3-character path name in columns 1-3, and the number
                     of matrix types must be the first nonblank item in columns
                     4-80.  If the number of matrix types is at least 1 but is
                     less than the maximum number of possible types, a second
                     line will be read to get the numbers of the matrix types to
                     be used.  For example,
            NEP 21
                     requests all of the matrix types for the nonsymmetric
                     eigenvalue problem, while
            NEP  4
            9 10 11 12
                     requests only matrices of type 9, 10, 11, and 12.

                     The valid 3-character path names are 'NEP' or 'SHS' for the
                     nonsymmetric eigenvalue routines.

           -----------------------------------------------------------------------

            SEP or SSG input file:

            line 2:  NN, INTEGER
                     Number of values of N.

            line 3:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix dimension N.

            line 4:  NPARMS, INTEGER
                     Number of values of the parameters NB, NBMIN, and NX.

            line 5:  NBVAL, INTEGER array, dimension (NPARMS)
                     The values for the blocksize NB.

            line 6:  NBMIN, INTEGER array, dimension (NPARMS)
                     The values for the minimum blocksize NBMIN.

            line 7:  NXVAL, INTEGER array, dimension (NPARMS)
                     The values for the crossover point NX.

            line 8:  THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 9:  TSTCHK, LOGICAL
                     Flag indicating whether or not to test the LAPACK routines.

            line 10: TSTDRV, LOGICAL
                     Flag indicating whether or not to test the driver routines.

            line 11: TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 12: NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 12 was 2:

            line 13: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 13-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path names are 'SEP' or 'SST' for the
                     symmetric eigenvalue routines and driver routines, and
                     'SSG' for the routines for the symmetric generalized
                     eigenvalue problem.

           -----------------------------------------------------------------------

            SVD input file:

            line 2:  NN, INTEGER
                     Number of values of M and N.

            line 3:  MVAL, INTEGER array, dimension (NN)
                     The values for the matrix row dimension M.

            line 4:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix column dimension N.

            line 5:  NPARMS, INTEGER
                     Number of values of the parameter NB, NBMIN, NX, and NRHS.

            line 6:  NBVAL, INTEGER array, dimension (NPARMS)
                     The values for the blocksize NB.

            line 7:  NBMIN, INTEGER array, dimension (NPARMS)
                     The values for the minimum blocksize NBMIN.

            line 8:  NXVAL, INTEGER array, dimension (NPARMS)
                     The values for the crossover point NX.

            line 9:  NSVAL, INTEGER array, dimension (NPARMS)
                     The values for the number of right hand sides NRHS.

            line 10: THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 11: TSTCHK, LOGICAL
                     Flag indicating whether or not to test the LAPACK routines.

            line 12: TSTDRV, LOGICAL
                     Flag indicating whether or not to test the driver routines.

            line 13: TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 14: NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 14 was 2:

            line 15: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 15-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path names are 'SVD' or 'SBD' for both the
                     SVD routines and the SVD driver routines.

           -----------------------------------------------------------------------

            SEV and SES data files:

            line 1:  'SEV' or 'SES' in columns 1 to 3.

            line 2:  NSIZES, INTEGER
                     Number of sizes of matrices to use. Should be at least 0
                     and at most 20. If NSIZES = 0, no testing is done
                     (although the remaining  3 lines are still read).

            line 3:  NN, INTEGER array, dimension(NSIZES)
                     Dimensions of matrices to be tested.

            line 4:  NB, NBMIN, NX, NS, NBCOL, INTEGERs
                     These integer parameters determine how blocking is done
                     (see ILAENV for details)
                     NB     : block size
                     NBMIN  : minimum block size
                     NX     : minimum dimension for blocking
                     NS     : number of shifts in xHSEQR
                     NBCOL  : minimum column dimension for blocking

            line 5:  THRESH, REAL
                     The test threshold against which computed residuals are
                     compared. Should generally be in the range from 10. to 20.
                     If it is 0., all test case data will be printed.

            line 6:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits.

            line 7:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 7 was 2:

            line 8:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9 and following:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'SEV' to test SGEEV, or
                     'SES' to test SGEES.

           -----------------------------------------------------------------------

            The SVX data has two parts. The first part is identical to SEV,
            and the second part consists of test matrices with precomputed
            solutions.

            line 1:  'SVX' in columns 1-3.

            line 2:  NSIZES, INTEGER
                     If NSIZES = 0, no testing of randomly generated examples
                     is done, but any precomputed examples are tested.

            line 3:  NN, INTEGER array, dimension(NSIZES)

            line 4:  NB, NBMIN, NX, NS, NBCOL, INTEGERs

            line 5:  THRESH, REAL

            line 6:  TSTERR, LOGICAL

            line 7:  NEWSD, INTEGER

            If line 7 was 2:

            line 8:  INTEGER array, dimension (4)

            lines 9 and following: The first line contains 'SVX' in columns 1-3
                     followed by the number of matrix types, possibly with
                     a second line to specify certain matrix types.
                     If the number of matrix types = 0, no testing of randomly
                     generated examples is done, but any precomputed examples
                     are tested.

            remaining lines : Each matrix is stored on 1+2*N lines, where N is
                     its dimension. The first line contains the dimension (a
                     single integer). The next N lines contain the matrix, one
                     row per line. The last N lines correspond to each
                     eigenvalue. Each of these last N lines contains 4 real
                     values: the real part of the eigenvalue, the imaginary
                     part of the eigenvalue, the reciprocal condition number of
                     the eigenvalues, and the reciprocal condition number of the
                     eigenvector.  The end of data is indicated by dimension N=0.
                     Even if no data is to be tested, there must be at least one
                     line containing N=0.

           -----------------------------------------------------------------------

            The SSX data is like SVX. The first part is identical to SEV, and the
            second part consists of test matrices with precomputed solutions.

            line 1:  'SSX' in columns 1-3.

            line 2:  NSIZES, INTEGER
                     If NSIZES = 0, no testing of randomly generated examples
                     is done, but any precomputed examples are tested.

            line 3:  NN, INTEGER array, dimension(NSIZES)

            line 4:  NB, NBMIN, NX, NS, NBCOL, INTEGERs

            line 5:  THRESH, REAL

            line 6:  TSTERR, LOGICAL

            line 7:  NEWSD, INTEGER

            If line 7 was 2:

            line 8:  INTEGER array, dimension (4)

            lines 9 and following: The first line contains 'SSX' in columns 1-3
                     followed by the number of matrix types, possibly with
                     a second line to specify certain matrix types.
                     If the number of matrix types = 0, no testing of randomly
                     generated examples is done, but any precomputed examples
                     are tested.

            remaining lines : Each matrix is stored on 3+N lines, where N is its
                     dimension. The first line contains the dimension N and the
                     dimension M of an invariant subspace. The second line
                     contains M integers, identifying the eigenvalues in the
                     invariant subspace (by their position in a list of
                     eigenvalues ordered by increasing real part). The next N
                     lines contain the matrix. The last line contains the
                     reciprocal condition number for the average of the selected
                     eigenvalues, and the reciprocal condition number for the
                     corresponding right invariant subspace. The end of data is
                     indicated by a line containing N=0 and M=0. Even if no data
                     is to be tested, there must be at least one line containing
                     N=0 and M=0.

           -----------------------------------------------------------------------

            SGG input file:

            line 2:  NN, INTEGER
                     Number of values of N.

            line 3:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix dimension N.

            line 4:  NPARMS, INTEGER
                     Number of values of the parameters NB, NBMIN, NS, MAXB, and
                     NBCOL.

            line 5:  NBVAL, INTEGER array, dimension (NPARMS)
                     The values for the blocksize NB.

            line 6:  NBMIN, INTEGER array, dimension (NPARMS)
                     The values for NBMIN, the minimum row dimension for blocks.

            line 7:  NSVAL, INTEGER array, dimension (NPARMS)
                     The values for the number of shifts.

            line 8:  MXBVAL, INTEGER array, dimension (NPARMS)
                     The values for MAXB, used in determining minimum blocksize.

            line 9:  IACC22, INTEGER array, dimension (NPARMS)
                     select structured matrix multiply: 1 or 2)

            line 10: NBCOL, INTEGER array, dimension (NPARMS)
                     The values for NBCOL, the minimum column dimension for
                     blocks.

            line 11: THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 12: TSTCHK, LOGICAL
                     Flag indicating whether or not to test the LAPACK routines.

            line 13: TSTDRV, LOGICAL
                     Flag indicating whether or not to test the driver routines.

            line 14: TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 15: NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 15 was 2:

            line 16: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 17-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'SGG' for the generalized
                     eigenvalue problem routines and driver routines.

           -----------------------------------------------------------------------

            SGS and SGV input files:

            line 1:  'SGS' or 'SGV' in columns 1 to 3.

            line 2:  NN, INTEGER
                     Number of values of N.

            line 3:  NVAL, INTEGER array, dimension(NN)
                     Dimensions of matrices to be tested.

            line 4:  NB, NBMIN, NX, NS, NBCOL, INTEGERs
                     These integer parameters determine how blocking is done
                     (see ILAENV for details)
                     NB     : block size
                     NBMIN  : minimum block size
                     NX     : minimum dimension for blocking
                     NS     : number of shifts in xHGEQR
                     NBCOL  : minimum column dimension for blocking

            line 5:  THRESH, REAL
                     The test threshold against which computed residuals are
                     compared. Should generally be in the range from 10. to 20.
                     If it is 0., all test case data will be printed.

            line 6:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits.

            line 7:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 17 was 2:

            line 7:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 7-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'SGS' for the generalized
                     eigenvalue problem routines and driver routines.

           -----------------------------------------------------------------------

            SXV input files:

            line 1:  'SXV' in columns 1 to 3.

            line 2:  N, INTEGER
                     Value of N.

            line 3:  NB, NBMIN, NX, NS, NBCOL, INTEGERs
                     These integer parameters determine how blocking is done
                     (see ILAENV for details)
                     NB     : block size
                     NBMIN  : minimum block size
                     NX     : minimum dimension for blocking
                     NS     : number of shifts in xHGEQR
                     NBCOL  : minimum column dimension for blocking

            line 4:  THRESH, REAL
                     The test threshold against which computed residuals are
                     compared. Should generally be in the range from 10. to 20.
                     Information will be printed about each test for which the
                     test ratio is greater than or equal to the threshold.

            line 5:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 6:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 6 was 2:

            line 7: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            If line 2 was 0:

            line 7-EOF: Precomputed examples are tested.

            remaining lines : Each example is stored on 3+2*N lines, where N is
                     its dimension. The first line contains the dimension (a
                     single integer). The next N lines contain the matrix A, one
                     row per line. The next N lines contain the matrix B.  The
                     next line contains the reciprocals of the eigenvalue
                     condition numbers.  The last line contains the reciprocals of
                     the eigenvector condition numbers.  The end of data is
                     indicated by dimension N=0.  Even if no data is to be tested,
                     there must be at least one line containing N=0.

           -----------------------------------------------------------------------

            SGX input files:

            line 1:  'SGX' in columns 1 to 3.

            line 2:  N, INTEGER
                     Value of N.

            line 3:  NB, NBMIN, NX, NS, NBCOL, INTEGERs
                     These integer parameters determine how blocking is done
                     (see ILAENV for details)
                     NB     : block size
                     NBMIN  : minimum block size
                     NX     : minimum dimension for blocking
                     NS     : number of shifts in xHGEQR
                     NBCOL  : minimum column dimension for blocking

            line 4:  THRESH, REAL
                     The test threshold against which computed residuals are
                     compared. Should generally be in the range from 10. to 20.
                     Information will be printed about each test for which the
                     test ratio is greater than or equal to the threshold.

            line 5:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 6:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 6 was 2:

            line 7: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            If line 2 was 0:

            line 7-EOF: Precomputed examples are tested.

            remaining lines : Each example is stored on 3+2*N lines, where N is
                     its dimension. The first line contains the dimension (a
                     single integer).  The next line contains an integer k such
                     that only the last k eigenvalues will be selected and appear
                     in the leading diagonal blocks of $A$ and $B$. The next N
                     lines contain the matrix A, one row per line.  The next N
                     lines contain the matrix B.  The last line contains the
                     reciprocal of the eigenvalue cluster condition number and the
                     reciprocal of the deflating subspace (associated with the
                     selected eigencluster) condition number.  The end of data is
                     indicated by dimension N=0.  Even if no data is to be tested,
                     there must be at least one line containing N=0.

           -----------------------------------------------------------------------

            SSB input file:

            line 2:  NN, INTEGER
                     Number of values of N.

            line 3:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix dimension N.

            line 4:  NK, INTEGER
                     Number of values of K.

            line 5:  KVAL, INTEGER array, dimension (NK)
                     The values for the matrix dimension K.

            line 6:  THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 7 was 2:

            line 8:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 8-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'SSB'.

           -----------------------------------------------------------------------

            SBB input file:

            line 2:  NN, INTEGER
                     Number of values of M and N.

            line 3:  MVAL, INTEGER array, dimension (NN)
                     The values for the matrix row dimension M.

            line 4:  NVAL, INTEGER array, dimension (NN)
                     The values for the matrix column dimension N.

            line 4:  NK, INTEGER
                     Number of values of K.

            line 5:  KVAL, INTEGER array, dimension (NK)
                     The values for the matrix bandwidth K.

            line 6:  NPARMS, INTEGER
                     Number of values of the parameter NRHS

            line 7:  NSVAL, INTEGER array, dimension (NPARMS)
                     The values for the number of right hand sides NRHS.

            line 8:  THRESH
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 9:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 9 was 2:

            line 10: INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 10-EOF:  Lines specifying matrix types, as for SVD.
                     The 3-character path name is 'SBB'.

           -----------------------------------------------------------------------

            SEC input file:

            line  2: THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            lines  3-EOF:

            Input for testing the eigencondition routines consists of a set of
            specially constructed test cases and their solutions.  The data
            format is not intended to be modified by the user.

           -----------------------------------------------------------------------

            SBL and SBK input files:

            line 1:  'SBL' in columns 1-3 to test SGEBAL, or 'SBK' in
                     columns 1-3 to test SGEBAK.

            The remaining lines consist of specially constructed test cases.

           -----------------------------------------------------------------------

            SGL and SGK input files:

            line 1:  'SGL' in columns 1-3 to test SGGBAL, or 'SGK' in
                     columns 1-3 to test SGGBAK.

            The remaining lines consist of specially constructed test cases.

           -----------------------------------------------------------------------

            GLM data file:

            line 1:  'GLM' in columns 1 to 3.

            line 2:  NN, INTEGER
                     Number of values of M, P, and N.

            line 3:  MVAL, INTEGER array, dimension(NN)
                     Values of M (row dimension).

            line 4:  PVAL, INTEGER array, dimension(NN)
                     Values of P (row dimension).

            line 5:  NVAL, INTEGER array, dimension(NN)
                     Values of N (column dimension), note M <= N <= M+P.

            line 6:  THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 8:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 8 was 2:

            line 9:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'GLM' for the generalized
                     linear regression model routines.

           -----------------------------------------------------------------------

            GQR data file:

            line 1:  'GQR' in columns 1 to 3.

            line 2:  NN, INTEGER
                     Number of values of M, P, and N.

            line 3:  MVAL, INTEGER array, dimension(NN)
                     Values of M.

            line 4:  PVAL, INTEGER array, dimension(NN)
                     Values of P.

            line 5:  NVAL, INTEGER array, dimension(NN)
                     Values of N.

            line 6:  THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 8:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 8 was 2:

            line 9:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'GQR' for the generalized
                     QR and RQ routines.

           -----------------------------------------------------------------------

            GSV data file:

            line 1:  'GSV' in columns 1 to 3.

            line 2:  NN, INTEGER
                     Number of values of M, P, and N.

            line 3:  MVAL, INTEGER array, dimension(NN)
                     Values of M (row dimension).

            line 4:  PVAL, INTEGER array, dimension(NN)
                     Values of P (row dimension).

            line 5:  NVAL, INTEGER array, dimension(NN)
                     Values of N (column dimension).

            line 6:  THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 8:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 8 was 2:

            line 9:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'GSV' for the generalized
                     SVD routines.

           -----------------------------------------------------------------------

            CSD data file:

            line 1:  'CSD' in columns 1 to 3.

            line 2:  NM, INTEGER
                     Number of values of M, P, and N.

            line 3:  MVAL, INTEGER array, dimension(NM)
                     Values of M (row and column dimension of orthogonal matrix).

            line 4:  PVAL, INTEGER array, dimension(NM)
                     Values of P (row dimension of top-left block).

            line 5:  NVAL, INTEGER array, dimension(NM)
                     Values of N (column dimension of top-left block).

            line 6:  THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 8:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 8 was 2:

            line 9:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'CSD' for the CSD routine.

           -----------------------------------------------------------------------

            LSE data file:

            line 1:  'LSE' in columns 1 to 3.

            line 2:  NN, INTEGER
                     Number of values of M, P, and N.

            line 3:  MVAL, INTEGER array, dimension(NN)
                     Values of M.

            line 4:  PVAL, INTEGER array, dimension(NN)
                     Values of P.

            line 5:  NVAL, INTEGER array, dimension(NN)
                     Values of N, note P <= N <= P+M.

            line 6:  THRESH, REAL
                     Threshold value for the test ratios.  Information will be
                     printed about each test for which the test ratio is greater
                     than or equal to the threshold.

            line 7:  TSTERR, LOGICAL
                     Flag indicating whether or not to test the error exits for
                     the LAPACK routines and driver routines.

            line 8:  NEWSD, INTEGER
                     A code indicating how to set the random number seed.
                     = 0:  Set the seed to a default value before each run
                     = 1:  Initialize the seed to a default value only before the
                           first run
                     = 2:  Like 1, but use the seed values on the next line

            If line 8 was 2:

            line 9:  INTEGER array, dimension (4)
                     Four integer values for the random number seed.

            lines 9-EOF:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'GSV' for the generalized
                     SVD routines.

           -----------------------------------------------------------------------

            NMAX is currently set to 132 and must be at least 12 for some of the
            precomputed examples, and LWORK = NMAX*(5*NMAX+5)+1 in the parameter
            statements below.  For SVD, we assume NRHS may be as big as N.  The
            parameter NEED is set to 14 to allow for 14 N-by-N matrices for SGG.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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