complex16_eig

NAME

complex16_eig - complex16

SYNOPSIS

Functions

program zchkee
ZCHKEE

Detailed Description

This is the group of complex16 LAPACK TESTING EIG routines.

Function Documentation

program zchkee

ZCHKEE

Purpose:

ZCHKEE tests the COMPLEX*16 LAPACK subroutines for the matrix
eigenvalue problem. The test paths in this version are

NEP (Nonsymmetric Eigenvalue Problem):
Test ZGEHRD, ZUNGHR, ZHSEQR, ZTREVC, ZHSEIN, and ZUNMHR

SEP (Hermitian Eigenvalue Problem):
Test ZHETRD, ZUNGTR, ZSTEQR, ZSTERF, ZSTEIN, ZSTEDC,
and drivers ZHEEV(X), ZHBEV(X), ZHPEV(X),
ZHEEVD, ZHBEVD, ZHPEVD

SVD (Singular Value Decomposition):
Test ZGEBRD, ZUNGBR, and ZBDSQR
and the drivers ZGESVD, ZGESDD

ZEV (Nonsymmetric Eigenvalue/eigenvector Driver):
Test ZGEEV

ZES (Nonsymmetric Schur form Driver):
Test ZGEES

ZVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver):
Test ZGEEVX

ZSX (Nonsymmetric Schur form Expert Driver):
Test ZGEESX

ZGG (Generalized Nonsymmetric Eigenvalue Problem):
Test ZGGHD3, ZGGBAL, ZGGBAK, ZHGEQZ, and ZTGEVC

ZGS (Generalized Nonsymmetric Schur form Driver):
Test ZGGES

ZGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver):
Test ZGGEV

ZGX (Generalized Nonsymmetric Schur form Expert Driver):
Test ZGGESX

ZXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver):
Test ZGGEVX

ZSG (Hermitian Generalized Eigenvalue Problem):
Test ZHEGST, ZHEGV, ZHEGVD, ZHEGVX, ZHPGST, ZHPGV, ZHPGVD,
ZHPGVX, ZHBGST, ZHBGV, ZHBGVD, and ZHBGVX

ZHB (Hermitian Band Eigenvalue Problem):
Test ZHBTRD

ZBB (Band Singular Value Decomposition):
Test ZGBBRD

ZEC (Eigencondition estimation):
Test ZTRSYL, ZTREXC, ZTRSNA, and ZTRSEN

ZBL (Balancing a general matrix)
Test ZGEBAL

ZBK (Back transformation on a balanced matrix)
Test ZGEBAK

ZGL (Balancing a matrix pair)
Test ZGGBAL

ZGK (Back transformation on a matrix pair)
Test ZGGBAK

GLM (Generalized Linear Regression Model):
Tests ZGGGLM

GQR (Generalized QR and RQ factorizations):
Tests ZGGQRF and ZGGRQF

GSV (Generalized Singular Value Decomposition):
Tests ZGGSVD, ZGGSVP, ZTGSJA, ZLAGS2, ZLAPLL, and ZLAPMT

CSD (CS decomposition):
Tests ZUNCSD

LSE (Constrained Linear Least Squares):
Tests ZGGLSE

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

ZHS or NEP 21 ZCHKHS
ZST or SEP 21 ZCHKST (routines)
18 ZDRVST (drivers)
ZBD or SVD 16 ZCHKBD (routines)
5 ZDRVBD (drivers)
ZEV 21 ZDRVEV
ZES 21 ZDRVES
ZVX 21 ZDRVVX
ZSX 21 ZDRVSX
ZGG 26 ZCHKGG (routines)
ZGS 26 ZDRGES
ZGX 5 ZDRGSX
ZGV 26 ZDRGEV
ZXV 2 ZDRGVX
ZSG 21 ZDRVSG
ZHB 15 ZCHKHB
ZBB 15 ZCHKBB
ZEC - ZCHKEC
ZBL - ZCHKBL
ZBK - ZCHKBK
ZGL - ZCHKGL
ZGK - ZCHKGK
GLM 8 ZCKGLM
GQR 8 ZCKGQR
GSV 8 ZCKGSV
CSD 3 ZCKCSD
LSE 8 ZCKLSE

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

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 ’ZHS’ for the
nonsymmetric eigenvalue routines.

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

SEP or ZSG 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 ’ZST’ for the
Hermitian eigenvalue routines and driver routines, and
’ZSG’ 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 ’ZBD’ for both the
SVD routines and the SVD driver routines.

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

ZEV and ZES data files:

line 1: ’ZEV’ or ’ZES’ 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 ’ZEV’ to test CGEEV, or
’ZES’ to test CGEES.

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

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

line 1: ’ZVX’ 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 ’ZVX’ 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 ZSX data is like ZVX. The first part is identical to ZEV, and the
second part consists of test matrices with precomputed solutions.

line 1: ’ZSX’ 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 ’ZSX’ 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.

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

ZGG 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 ’ZGG’ for the generalized
eigenvalue problem routines and driver routines.

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

ZGS and ZGV input files:

line 1: ’ZGS’ or ’ZGV’ 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 ’ZGS’ for the generalized
eigenvalue problem routines and driver routines.

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

ZGX input file:
line 1: ’ZGX’ 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.

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

ZXV input files:
line 1: ’ZXV’ 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.

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

ZHB 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 ’ZHB’.

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

ZBB 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 ’ZBB’.

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

ZEC 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.

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

ZBL and ZBK input files:

line 1: ’ZBL’ in columns 1-3 to test CGEBAL, or ’ZBK’ in
columns 1-3 to test CGEBAK.

The remaining lines consist of specially constructed test cases.

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

ZGL and ZGK input files:

line 1: ’ZGL’ in columns 1-3 to test ZGGBAL, or ’ZGK’ in
columns 1-3 to test ZGGBAK.

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 ZGG.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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