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

NAME

       complex_eig - complex

SYNOPSIS

   Functions
       program cchkee
           CCHKEE

Detailed Description

       This is the group of complex LAPACK TESTING EIG routines.

Function Documentation

   program cchkee
       CCHKEE

       Purpose:

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

            NEP (Nonsymmetric Eigenvalue Problem):
                Test CGEHRD, CUNGHR, CHSEQR, CTREVC, CHSEIN, and CUNMHR

            SEP (Hermitian Eigenvalue Problem):
                Test CHETRD, CUNGTR, CSTEQR, CSTERF, CSTEIN, CSTEDC,
                and drivers CHEEV(X), CHBEV(X), CHPEV(X),
                            CHEEVD,   CHBEVD,   CHPEVD

            SVD (Singular Value Decomposition):
                Test CGEBRD, CUNGBR, and CBDSQR
                and the drivers CGESVD, CGESDD

            CEV (Nonsymmetric Eigenvalue/eigenvector Driver):
                Test CGEEV

            CES (Nonsymmetric Schur form Driver):
                Test CGEES

            CVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver):
                Test CGEEVX

            CSX (Nonsymmetric Schur form Expert Driver):
                Test CGEESX

            CGG (Generalized Nonsymmetric Eigenvalue Problem):
                Test CGGHD3, CGGBAL, CGGBAK, CHGEQZ, and CTGEVC

            CGS (Generalized Nonsymmetric Schur form Driver):
                Test CGGES

            CGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver):
                Test CGGEV

            CGX (Generalized Nonsymmetric Schur form Expert Driver):
                Test CGGESX

            CXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver):
                Test CGGEVX

            CSG (Hermitian Generalized Eigenvalue Problem):
                Test CHEGST, CHEGV, CHEGVD, CHEGVX, CHPGST, CHPGV, CHPGVD,
                CHPGVX, CHBGST, CHBGV, CHBGVD, and CHBGVX

            CHB (Hermitian Band Eigenvalue Problem):
                Test CHBTRD

            CBB (Band Singular Value Decomposition):
                Test CGBBRD

            CEC (Eigencondition estimation):
                Test CTRSYL, CTREXC, CTRSNA, and CTRSEN

            CBL (Balancing a general matrix)
                Test CGEBAL

            CBK (Back transformation on a balanced matrix)
                Test CGEBAK

            CGL (Balancing a matrix pair)
                Test CGGBAL

            CGK (Back transformation on a matrix pair)
                Test CGGBAK

            GLM (Generalized Linear Regression Model):
                Tests CGGGLM

            GQR (Generalized QR and RQ factorizations):
                Tests CGGQRF and CGGRQF

            GSV (Generalized Singular Value Decomposition):
                Tests CGGSVD, CGGSVP, CTGSJA, CLAGS2, CLAPLL, and CLAPMT

            CSD (CS decomposition):
                Tests CUNCSD

            LSE (Constrained Linear Least Squares):
                Tests CGGLSE

            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

            CHS or NEP      21     CCHKHS
            CST or SEP      21     CCHKST (routines)
                            18     CDRVST (drivers)
            CBD or SVD      16     CCHKBD (routines)
                             5     CDRVBD (drivers)
            CEV             21     CDRVEV
            CES             21     CDRVES
            CVX             21     CDRVVX
            CSX             21     CDRVSX
            CGG             26     CCHKGG (routines)
            CGS             26     CDRGES
            CGX              5     CDRGSX
            CGV             26     CDRGEV
            CXV              2     CDRGVX
            CSG             21     CDRVSG
            CHB             15     CCHKHB
            CBB             15     CCHKBB
            CEC              -     CCHKEC
            CBL              -     CCHKBL
            CBK              -     CCHKBK
            CGL              -     CCHKGL
            CGK              -     CCHKGK
            GLM              8     CCKGLM
            GQR              8     CCKGQR
            GSV              8     CCKGSV
            CSD              3     CCKCSD
            LSE              8     CCKLSE

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

            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 'CHS' for the
                     nonsymmetric eigenvalue routines.

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

            SEP or CSG 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 valid 3-character path names are 'SEP' or 'CST' for the
                     Hermitian eigenvalue routines and driver routines, and
                     'CSG' for the routines for the Hermitian 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 'CBD' for both the
                     SVD routines and the SVD driver routines.

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

            CEV and CES data files:

            line 1:  'CEV' or 'CES' 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:  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.

            lines 8 and following:  Lines specifying matrix types, as for NEP.
                     The 3-character path name is 'CEV' to test CGEEV, or
                     'CES' to test CGEES.

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

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

            line 1:  'CVX' 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:  NEWSD, INTEGER

            If line 6 was 2:

            line 7:  INTEGER array, dimension (4)

            lines 8 and following: The first line contains 'CVX' 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+N+N**2 lines, where N is
                     its dimension. The first line contains the dimension N and
                     ISRT (two integers). ISRT indicates whether the last N lines
                     are sorted by increasing real part of the eigenvalue
                     (ISRT=0) or by increasing imaginary part (ISRT=1). The next
                     N**2 lines contain the matrix rowwise, one entry 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 eigenvalues, the imaginary part of the eigenvalue, the
                     reciprocal condition number of the eigenvalues, and the
                     reciprocal condition number of the vector 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 CSX data is like CVX. The first part is identical to CEV, and the
            second part consists of test matrices with precomputed solutions.

            line 1:  'CSX' 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:  NEWSD, INTEGER

            If line 6 was 2:

            line 7:  INTEGER array, dimension (4)

            lines 8 and following: The first line contains 'CSX' 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**2 lines, where N is
                     its dimension. The first line contains the dimension N, the
                     dimension M of an invariant subspace, and ISRT. 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 (if ISRT=0) or
                     by increasing imaginary part (if ISRT=1)). The next N**2
                     lines contain the matrix rowwise. 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 in
                     indicated by a line containing N=0, M=0, and ISRT = 0.  Even
                     if no data is to be tested, there must be at least one line
                     containing N=0, M=0 and ISRT=0.

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

            CGG 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, NBCOL, 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 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 'CGG' for the generalized
                     eigenvalue problem routines and driver routines.

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

            CGS and CGV input files:

            line 1:  'CGS' or 'CGV' 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 'CGS' for the generalized
                     eigenvalue problem routines and driver routines.

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

            CGX input file:
            line 1:  'CGX' 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*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*N
                     lines contain the matrix A, one element per line. The next N*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.

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

            CXV input files:
            line 1:  'CXV' 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*N lines, where N is
                     its dimension. The first line contains the dimension (a
                     single integer). The next N*N lines contain the matrix A, one
                     element per line. The next N*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.

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

            CHB 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 'CHB'.

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

            CBB 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 'CBB'.

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

            CEC 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.

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

            CBL and CBK input files:

            line 1:  'CBL' in columns 1-3 to test CGEBAL, or 'CBK' in
                     columns 1-3 to test CGEBAK.

            The remaining lines consist of specially constructed test cases.

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

            CGL and CGK input files:

            line 1:  'CGL' in columns 1-3 to test CGGBAL, or 'CGK' in
                     columns 1-3 to test CGGBAK.

            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+20) 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 CGG.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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