floraachy
/
OpenBLAS
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Implement truncated QR with pivoting (Reference-LAPACK PR 891)

This commit is contained in:
Martin Kroeker 2023-11-15 09:53:06 +01:00 committed by GitHub
parent 40109c0392
commit 387830b9d5
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
30 changed files with 4132 additions and 238 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

11
lapack-netlib/TESTING/LIN/CMakeLists.txt
View File

@ -9,7 +9,7 @@ set(DZLNTST dlaord.f)
set(SLINTST schkaa.F
schkeq.f schkgb.f schkge.f schkgt.f
schklq.f schkpb.f schkpo.f schkps.f schkpp.f
schkpt.f schkq3.f schkql.f schkqr.f schkrq.f
schkpt.f schkq3.f schkqp3rk.f schkql.f schkqr.f schkrq.f
schksp.f schksy.f schksy_rook.f schksy_rk.f
schksy_aa.f schksy_aa_2stage.f
schktb.f schktp.f schktr.f
@ -56,7 +56,7 @@ set(CLINTST cchkaa.F
cchkhe.f cchkhe_rook.f cchkhe_rk.f
cchkhe_aa.f cchkhe_aa_2stage.f
cchkhp.f cchklq.f cchkpb.f
cchkpo.f cchkps.f cchkpp.f cchkpt.f cchkq3.f cchkql.f
cchkpo.f cchkps.f cchkpp.f cchkpt.f cchkq3.f cchkqp3rk.f cchkql.f
cchkqr.f cchkrq.f cchksp.f cchksy.f cchksy_rook.f cchksy_rk.f
cchksy_aa.f cchksy_aa_2stage.f
cchktb.f
@ -110,7 +110,7 @@ endif()
set(DLINTST dchkaa.F
dchkeq.f dchkgb.f dchkge.f dchkgt.f
dchklq.f dchkpb.f dchkpo.f dchkps.f dchkpp.f
dchkpt.f dchkq3.f dchkql.f dchkqr.f dchkrq.f
dchkpt.f dchkq3.f dchkqp3rk.f dchkql.f dchkqr.f dchkrq.f
dchksp.f dchksy.f dchksy_rook.f dchksy_rk.f
dchksy_aa.f dchksy_aa_2stage.f
dchktb.f dchktp.f dchktr.f
@ -158,7 +158,7 @@ set(ZLINTST zchkaa.F
zchkhe.f zchkhe_rook.f zchkhe_rk.f
zchkhe_aa.f zchkhe_aa_2stage.f
zchkhp.f zchklq.f zchkpb.f
zchkpo.f zchkps.f zchkpp.f zchkpt.f zchkq3.f zchkql.f
zchkpo.f zchkps.f zchkpp.f zchkpt.f zchkq3.f zchkqp3rk.f zchkql.f
zchkqr.f zchkrq.f zchksp.f zchksy.f zchksy_rook.f zchksy_rk.f
zchksy_aa.f zchksy_aa_2stage.f
zchktb.f
@ -239,8 +239,7 @@ set(ZLINTSTRFP zchkrfp.f zdrvrfp.f zdrvrf1.f zdrvrf2.f zdrvrf3.f zdrvrf4.f zerrr
macro(add_lin_executable name)
add_executable(${name} ${ARGN})
target_link_libraries(${name} openblas${SUFFIX64_UNDERSCORE})
#${TMGLIB} ${LAPACK_LIBRARIES} ${BLAS_LIBRARIES})
target_link_libraries(${name} ${TMGLIB} ${LAPACK_LIBRARIES} ${BLAS_LIBRARIES})
endmacro()
if(BUILD_SINGLE)

48
lapack-netlib/TESTING/LIN/Makefile
View File

@ -45,7 +45,7 @@ DZLNTST = dlaord.o
SLINTST = schkaa.o \
schkeq.o schkgb.o schkge.o schkgt.o \
schklq.o schkpb.o schkpo.o schkps.o schkpp.o \
schkpt.o schkq3.o schkql.o schkqr.o schkrq.o \
schkpt.o schkq3.o schkqp3rk.o schkql.o schkqr.o schkrq.o \
schksp.o schksy.o schksy_rook.o schksy_rk.o \
schksy_aa.o schksy_aa_2stage.o schktb.o schktp.o schktr.o \
schktz.o \
@ -89,7 +89,7 @@ CLINTST = cchkaa.o \
cchkeq.o cchkgb.o cchkge.o cchkgt.o \
cchkhe.o cchkhe_rook.o cchkhe_rk.o \
cchkhe_aa.o cchkhe_aa_2stage.o cchkhp.o cchklq.o cchkpb.o \
cchkpo.o cchkps.o cchkpp.o cchkpt.o cchkq3.o cchkql.o \
cchkpo.o cchkps.o cchkpp.o cchkpt.o cchkq3.o cchkqp3rk.o cchkql.o \
cchkqr.o cchkrq.o cchksp.o cchksy.o cchksy_rook.o cchksy_rk.o \
cchksy_aa.o cchksy_aa_2stage.o cchktb.o \
cchktp.o cchktr.o cchktz.o \
@ -137,7 +137,7 @@ endif
DLINTST = dchkaa.o \
dchkeq.o dchkgb.o dchkge.o dchkgt.o \
dchklq.o dchkpb.o dchkpo.o dchkps.o dchkpp.o \
dchkpt.o dchkq3.o dchkql.o dchkqr.o dchkrq.o \
dchkpt.o dchkq3.o dchkqp3rk.o dchkql.o dchkqr.o dchkrq.o \
dchksp.o dchksy.o dchksy_rook.o dchksy_rk.o \
dchksy_aa.o dchksy_aa_2stage.o dchktb.o dchktp.o dchktr.o \
dchktz.o \
@ -182,7 +182,7 @@ ZLINTST = zchkaa.o \
zchkeq.o zchkgb.o zchkge.o zchkgt.o \
zchkhe.o zchkhe_rook.o zchkhe_rk.o zchkhe_aa.o zchkhe_aa_2stage.o \
zchkhp.o zchklq.o zchkpb.o \
zchkpo.o zchkps.o zchkpp.o zchkpt.o zchkq3.o zchkql.o \
zchkpo.o zchkps.o zchkpp.o zchkpt.o zchkq3.o zchkqp3rk.o zchkql.o \
zchkqr.o zchkrq.o zchksp.o zchksy.o zchksy_rook.o zchksy_rk.o \
zchksy_aa.o zchksy_aa_2stage.o zchktb.o \
zchktp.o zchktr.o zchktz.o \
@ -269,35 +269,35 @@ proto-double: xlintstds xlintstrfd
proto-complex: xlintstrfc
proto-complex16: xlintstzc xlintstrfz
xlintsts: $(ALINTST) $(SLINTST) $(SCLNTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintsts: $(ALINTST) $(SLINTST) $(SCLNTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstc: $(ALINTST) $(CLINTST) $(SCLNTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstc: $(ALINTST) $(CLINTST) $(SCLNTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstd: $(ALINTST) $(DLINTST) $(DZLNTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstd: $(ALINTST) $(DLINTST) $(DZLNTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstz: $(ALINTST) $(ZLINTST) $(DZLNTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstz: $(ALINTST) $(ZLINTST) $(DZLNTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(XBLASLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstds: $(DSLINTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstds: $(DSLINTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstzc: $(ZCLINTST) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstzc: $(ZCLINTST) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfs: $(SLINTSTRFP) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfs: $(SLINTSTRFP) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfd: $(DLINTSTRFP) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfd: $(DLINTSTRFP) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfc: $(CLINTSTRFP) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfc: $(CLINTSTRFP) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfz: $(ZLINTSTRFP) $(TMGLIB) $(VARLIB) ../$(LAPACKLIB) $(BLASLIB)
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
xlintstrfz: $(ZLINTSTRFP) $(TMGLIB) $(VARLIB) $(LAPACKLIB) $(BLASLIB)
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
$(ALINTST): $(FRC)
$(SCLNTST): $(FRC)

17
lapack-netlib/TESTING/LIN/alaerh.f
View File

@ -797,6 +797,18 @@
WRITE( NOUT, FMT = 9978 )
$ SUBNAM(1:LEN_TRIM( SUBNAM )), INFO, M, N, IMAT
END IF
*
ELSE IF( LSAMEN( 2, P2, 'QK' ) ) THEN
*
* xQK: truncated QR factorization with pivoting
*
IF( LSAMEN( 7, SUBNAM( 2: 8 ), 'GEQP3RK' ) ) THEN
WRITE( NOUT, FMT = 9930 )
$ SUBNAM(1:LEN_TRIM( SUBNAM )), INFO, M, N, KL, N5, IMAT
ELSE IF( LSAMEN( 5, SUBNAM( 2: 6 ), 'LATMS' ) ) THEN
WRITE( NOUT, FMT = 9978 )
$ SUBNAM(1:LEN_TRIM( SUBNAM )), INFO, M, N, IMAT
END IF
*
ELSE IF( LSAMEN( 2, P2, 'LQ' ) ) THEN
*
@ -1147,6 +1159,11 @@
* What we do next
*
9949 FORMAT( ' ==> Doing only the condition estimate for this case' )
*
* SUBNAM, INFO, M, N, NB, IMAT
*
9930 FORMAT( ' *** Error code from ', A, '=', I5, / ' ==> M =', I5,
$ ', N =', I5, ', NX =', I5, ', NB =', I4, ', type ', I2 )
*
RETURN
*

62
lapack-netlib/TESTING/LIN/alahd.f
View File

@ -584,13 +584,27 @@
*
* QR decomposition with column pivoting
*
WRITE( IOUNIT, FMT = 9986 )PATH
WRITE( IOUNIT, FMT = 8006 )PATH
WRITE( IOUNIT, FMT = 9969 )
WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
WRITE( IOUNIT, FMT = 9940 )1
WRITE( IOUNIT, FMT = 9939 )2
WRITE( IOUNIT, FMT = 9938 )3
WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
ELSE IF( LSAMEN( 2, P2, 'QK' ) ) THEN
*
* truncated QR decomposition with column pivoting
*
WRITE( IOUNIT, FMT = 8006 )PATH
WRITE( IOUNIT, FMT = 9871 )
WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
WRITE( IOUNIT, FMT = 8060 )1
WRITE( IOUNIT, FMT = 8061 )2
WRITE( IOUNIT, FMT = 8062 )3
WRITE( IOUNIT, FMT = 8063 )4
WRITE( IOUNIT, FMT = 8064 )5
WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
*
ELSE IF( LSAMEN( 2, P2, 'TZ' ) ) THEN
*
@ -779,6 +793,8 @@
$ 'tall-skinny or short-wide matrices' )
8005 FORMAT( / 1X, A3, ': Householder reconstruction from TSQR',
$ ' factorization output ', /,' for tall-skinny matrices.' )
8006 FORMAT( / 1X, A3, ': truncated QR factorization',
$ ' with column pivoting' )
*
* GE matrix types
*
@ -922,6 +938,36 @@
$ / 4X, '3. Geometric distribution', 10X,
$ '6. Every second column fixed' )
*
* QK matrix types
*
9871 FORMAT( 4X, ' 1. Zero matrix', /
$ 4X, ' 2. Random, Diagonal, CNDNUM = 2', /
$ 4X, ' 3. Random, Upper triangular, CNDNUM = 2', /
$ 4X, ' 4. Random, Lower triangular, CNDNUM = 2', /
$ 4X, ' 5. Random, First column is zero, CNDNUM = 2', /
$ 4X, ' 6. Random, Last MINMN column is zero, CNDNUM = 2', /
$ 4X, ' 7. Random, Last N column is zero, CNDNUM = 2', /
$ 4X, ' 8. Random, Middle column in MINMN is zero,',
$ ' CNDNUM = 2', /
$ 4X, ' 9. Random, First half of MINMN columns are zero,',
$ ' CNDNUM = 2', /
$ 4X, '10. Random, Last columns are zero starting from',
$ ' MINMN/2+1, CNDNUM = 2', /
$ 4X, '11. Random, Half MINMN columns in the middle are',
$ ' zero starting from MINMN/2-(MINMN/2)/2+1,'
$ ' CNDNUM = 2', /
$ 4X, '12. Random, Odd columns are ZERO, CNDNUM = 2', /
$ 4X, '13. Random, Even columns are ZERO, CNDNUM = 2', /
$ 4X, '14. Random, CNDNUM = 2', /
$ 4X, '15. Random, CNDNUM = sqrt(0.1/EPS)', /
$ 4X, '16. Random, CNDNUM = 0.1/EPS', /
$ 4X, '17. Random, CNDNUM = 0.1/EPS,',
$ ' one small singular value S(N)=1/CNDNUM', /
$ 4X, '18. Random, CNDNUM = 2, scaled near underflow,',
$ ' NORM = SMALL = SAFMIN', /
$ 4X, '19. Random, CNDNUM = 2, scaled near overflow,',
$ ' NORM = LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) )' )
*
* TZ matrix types
*
9968 FORMAT( ' Matrix types (2-3 have condition 1/EPS):', / 4X,
@ -1030,9 +1076,8 @@
$ ' * norm(C) * EPS )' )
9940 FORMAT( 3X, I2, ': norm(svd(A) - svd(R)) / ',
$ '( M * norm(svd(R)) * EPS )' )
9939 FORMAT( 3X, I2, ': norm( A*P - Q*R ) / ( M * norm(A) * EPS )'
$ )
9938 FORMAT( 3X, I2, ': norm( I - Q''*Q ) / ( M * EPS )' )
9939 FORMAT( 3X, I2, ': norm( A*P - Q*R ) / ( M * norm(A) * EPS )')
9938 FORMAT( 3X, I2, ': norm( I - Q''*Q ) / ( M * EPS )' )
9937 FORMAT( 3X, I2, ': norm( A - R*Q ) / ( M * norm(A) * EPS )'
$ )
9935 FORMAT( 3X, I2, ': norm( B - A * X ) / ',
@ -1105,6 +1150,15 @@
8054 FORMAT(3X,I2,': norm( C*Q - C*Q ) / ( M * norm(C) * EPS )' )
8055 FORMAT(3X,I2,': norm( C*Q'' - C*Q'' ) / ( M * norm(C) * EPS )')
8060 FORMAT( 3X, I2, ': 2-norm(svd(A) - svd(R)) / ',
$ '( max(M,N) * 2-norm(svd(R)) * EPS )' )
8061 FORMAT( 3X, I2, ': 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A)',
$ ' * EPS )')
8062 FORMAT( 3X, I2, ': 1-norm( I - Q''*Q ) / ( M * EPS )' )
8063 FORMAT( 3X, I2, ': Returns 1.0D+100, if abs(R(K+1,K+1))',
$ ' > abs(R(K,K)), where K=1:KFACT-1' )
8064 FORMAT( 3X, I2, ': 1-norm(Q**T * B - Q**T * B ) / ( M * EPS )')
*
RETURN
*

6
lapack-netlib/TESTING/LIN/alareq.f
View File

@ -28,12 +28,12 @@
*> to evaluate the input line which requested NMATS matrix types for
*> PATH. The flow of control is as follows:
*>
*> If NMATS = NTYPES then
*> IF NMATS = NTYPES THEN
*> DOTYPE(1:NTYPES) = .TRUE.
*> else
*> ELSE
*> Read the next input line for NMATS matrix types
*> Set DOTYPE(I) = .TRUE. for each valid type I
*> endif
*> END IF
*> \endverbatim
*
* Arguments:

43
lapack-netlib/TESTING/LIN/cchkaa.F
View File

@ -69,6 +69,7 @@
*> CLQ 8 List types on next line if 0 < NTYPES < 8
*> CQL 8 List types on next line if 0 < NTYPES < 8
*> CQP 6 List types on next line if 0 < NTYPES < 6
*> ZQK 19 List types on next line if 0 < NTYPES < 19
*> CTZ 3 List types on next line if 0 < NTYPES < 3
*> CLS 6 List types on next line if 0 < NTYPES < 6
*> CEQ
@ -153,12 +154,11 @@
$ NBVAL( MAXIN ), NBVAL2( MAXIN ),
$ NSVAL( MAXIN ), NVAL( MAXIN ), NXVAL( MAXIN ),
$ RANKVAL( MAXIN ), PIV( NMAX )
REAL S( 2*NMAX )
COMPLEX E( NMAX )
* ..
* .. Allocatable Arrays ..
INTEGER AllocateStatus
REAL, DIMENSION(:), ALLOCATABLE :: RWORK
REAL, DIMENSION(:), ALLOCATABLE :: RWORK, S
COMPLEX, DIMENSION(:), ALLOCATABLE :: E
COMPLEX, DIMENSION(:,:), ALLOCATABLE :: A, B, WORK
* ..
* .. External Functions ..
@ -170,14 +170,14 @@
EXTERNAL ALAREQ, CCHKEQ, CCHKGB, CCHKGE, CCHKGT, CCHKHE,
$ CCHKHE_ROOK, CCHKHE_RK, CCHKHE_AA, CCHKHP,
$ CCHKLQ, CCHKUNHR_COL, CCHKPB, CCHKPO, CCHKPS,
$ CCHKPP, CCHKPT, CCHKQ3, CCHKQL, CCHKQR, CCHKRQ,
$ CCHKSP, CCHKSY, CCHKSY_ROOK, CCHKSY_RK,
$ CCHKSY_AA, CCHKTB, CCHKTP, CCHKTR, CCHKTZ,
$ CDRVGB, CDRVGE, CDRVGT, CDRVHE, CDRVHE_ROOK,
$ CDRVHE_RK, CDRVHE_AA, CDRVHP, CDRVLS, CDRVPB,
$ CDRVPO, CDRVPP, CDRVPT, CDRVSP, CDRVSY,
$ CDRVSY_ROOK, CDRVSY_RK, CDRVSY_AA, ILAVER,
$ CCHKQRT, CCHKQRTP
$ CCHKPP, CCHKPT, CCHKQ3, CCHKQP3RK, CCHKQL,
$ CCHKQR, CCHKRQ, CCHKSP, CCHKSY, CCHKSY_ROOK,
$ CCHKSY_RK, CCHKSY_AA, CCHKTB, CCHKTP, CCHKTR,
$ CCHKTZ, CDRVGB, CDRVGE, CDRVGT, CDRVHE,
$ CDRVHE_ROOK, CDRVHE_RK, CDRVHE_AA, CDRVHP,
$ CDRVLS, CDRVPB, CDRVPO, CDRVPP, CDRVPT, CDRVSP,
$ CDRVSY, CDRVSY_ROOK, CDRVSY_RK, CDRVSY_AA,
$ ILAVER, CCHKQRT, CCHKQRTP
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
@ -203,6 +203,10 @@
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( WORK( NMAX, NMAX+MAXRHS+10 ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( E( NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( S( 2*NMAX ), STAT = AllocateStatus)
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( RWORK( 150*NMAX+2*MAXRHS ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
* ..
@ -1109,6 +1113,23 @@
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* QK: truncated QR factorization with pivoting
*
NTYPES = 19
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
IF( TSTCHK ) THEN
CALL CCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A( 1, 1 ),
$ A( 1, 2 ), B( 1, 1 ), B( 1, 2 ),
$ S( 1 ), B( 1, 4 ),
$ WORK, RWORK, IWORK, NOUT )
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'LS' ) ) THEN
*

836
lapack-netlib/TESTING/LIN/cchkqp3rk.f Normal file
View File

@ -0,0 +1,836 @@
*> \brief \b CCHKQP3RK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
* $ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
* $ B, COPYB, S, TAU,
* $ WORK, RWORK, IWORK, NOUT )
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* INTEGER NM, NN, NNB, NOUT
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
* $ NXVAL( * )
* REAL S( * ), RWORK( * )
* COMPLEX A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CCHKQP3RK tests CGEQP3RK.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*> NM is INTEGER
*> The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB and NX contained in the
*> vectors NBVAL and NXVAL. The blocking parameters are used
*> in pairs (NB,NX).
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NXVAL
*> \verbatim
*> NXVAL is INTEGER array, dimension (NNB)
*> The values of the crossover point NX.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX array, dimension (MMAX*NMAX)
*> where MMAX is the maximum value of M in MVAL and NMAX is the
*> maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] COPYA
*> \verbatim
*> COPYA is COMPLEX array, dimension (MMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX array, dimension (MMAX*NSMAX)
*> where MMAX is the maximum value of M in MVAL and NSMAX is the
*> maximum value of NRHS in NSVAL.
*> \endverbatim
*>
*> \param[out] COPYB
*> \verbatim
*> COPYB is COMPLEX array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is REAL array, dimension
*> (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (MMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (max(M*max(M,N) + 4*min(M,N) + max(M,N)))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (4*NMAX)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
$ B, COPYB, S, TAU,
$ WORK, RWORK, IWORK, NOUT )
IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER NM, NN, NNB, NNS, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
$ NSVAL( * ), NXVAL( * )
REAL S( * ), RWORK( * )
COMPLEX A( * ), COPYA( * ), B( * ), COPYB( * ),
$ TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPES
PARAMETER ( NTYPES = 19 )
INTEGER NTESTS
PARAMETER ( NTESTS = 5 )
REAL ONE, ZERO, BIGNUM
COMPLEX CONE, CZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0,
$ CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ),
$ BIGNUM = 1.0E+38 )
* ..
* .. Local Scalars ..
CHARACTER DIST, TYPE
CHARACTER*3 PATH
INTEGER I, IHIGH, ILOW, IM, IMAT, IN, INC_ZERO,
$ INB, IND_OFFSET_GEN,
$ IND_IN, IND_OUT, INS, INFO,
$ ISTEP, J, J_INC, J_FIRST_NZ, JB_ZERO,
$ KFACT, KL, KMAX, KU, LDA, LW, LWORK,
$ LWORK_MQR, M, MINMN, MINMNB_GEN, MODE, N,
$ NB, NB_ZERO, NERRS, NFAIL, NB_GEN, NRHS,
$ NRUN, NX, T
REAL ANORM, CNDNUM, EPS, ABSTOL, RELTOL,
$ DTEMP, MAXC2NRMK, RELMAXC2NRMK
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
REAL RESULT( NTESTS ), RDUMMY( 1 )
* ..
* .. External Functions ..
REAL SLAMCH, CQPT01, CQRT11, CQRT12, CLANGE
EXTERNAL SLAMCH, CQPT01, CQRT11, CQRT12, CLANGE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, SLAORD, ICOPY, CAXPY,
$ XLAENV, CGEQP3RK, CLACPY, CLASET, CLATB4,
$ CLATMS, CUNMQR, CSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD, REAL
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT, CUNMQR_LWORK
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Complex precision'
PATH( 2: 3 ) = 'QK'
NRUN = 0
NFAIL = 0
NERRS = 0
DO I = 1, 4
ISEED( I ) = ISEEDY( I )
END DO
EPS = SLAMCH( 'Epsilon' )
INFOT = 0
*
DO IM = 1, NM
*
* Do for each value of M in MVAL.
*
M = MVAL( IM )
LDA = MAX( 1, M )
*
DO IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
MINMN = MIN( M, N )
LWORK = MAX( 1, M*MAX( M, N )+4*MINMN+MAX( M, N ),
$ M*N + 2*MINMN + 4*N )
*
DO INS = 1, NNS
NRHS = NSVAL( INS )
*
* Set up parameters with CLATB4 and generate
* M-by-NRHS B matrix with CLATMS.
* IMAT = 14:
* Random matrix, CNDNUM = 2, NORM = ONE,
* MODE = 3 (geometric distribution of singular values).
*
CALL CLATB4( PATH, 14, M, NRHS, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'CLATMS'
CALL CLATMS( M, NRHS, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYB, LDA, WORK, INFO )
*
* Check error code from CLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', M,
$ NRHS, -1, -1, -1, 6, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
DO IMAT = 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ CYCLE
*
* The type of distribution used to generate the random
* eigen-/singular values:
* ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 )
*
* Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE
* 1. Zero matrix
* 2. Random, Diagonal, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 3. Random, Upper triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 4. Random, Lower triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 5. Random, First column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 6. Random, Last MINMN column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 7. Random, Last N column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 8. Random, Middle column in MINMN is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 9. Random, First half of MINMN columns are zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 10. Random, Last columns are zero starting from MINMN/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 11. Random, Half MINMN columns in the middle are zero starting
* from MINMN/2-(MINMN/2)/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 12. Random, Odd columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 13. Random, Even columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 14. Random, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) ONE 3 ( geometric distribution of singular values )
* 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS ONE 3 ( geometric distribution of singular values )
* 17. Random, CNDNUM = 0.1/EPS, CNDNUM = BADC2 = 0.1/EPS ONE 2 ( one small singular value, S(N)=1/CNDNUM )
* one small singular value S(N)=1/CNDNUM
* 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN
* 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values )
*
IF( IMAT.EQ.1 ) THEN
*
* Matrix 1: Zero matrix
*
CALL CLASET( 'Full', M, N, CZERO, CZERO, COPYA, LDA )
DO I = 1, MINMN
S( I ) = ZERO
END DO
*
ELSE IF( (IMAT.GE.2 .AND. IMAT.LE.4 )
$ .OR. (IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN
*
* Matrices 2-5.
*
* Set up parameters with DLATB4 and generate a test
* matrix with CLATMS.
*
CALL CLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'CLATMS'
CALL CLATMS( M, N, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA, LDA, WORK, INFO )
*
* Check error code from CLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', M, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
CALL SLAORD( 'Decreasing', MINMN, S, 1 )
*
ELSE IF( MINMN.GE.2
$ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN
*
* Rectangular matrices 5-13 that contain zero columns,
* only for matrices MINMN >=2.
*
* JB_ZERO is the column index of ZERO block.
* NB_ZERO is the column block size of ZERO block.
* NB_GEN is the column blcok size of the
* generated block.
* J_INC in the non_zero column index increment
* for matrix 12 and 13.
* J_FIRS_NZ is the index of the first non-zero
* column.
*
IF( IMAT.EQ.5 ) THEN
*
* First column is zero.
*
JB_ZERO = 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.6 ) THEN
*
* Last column MINMN is zero.
*
JB_ZERO = MINMN
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.7 ) THEN
*
* Last column N is zero.
*
JB_ZERO = N
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.8 ) THEN
*
* Middle column in MINMN is zero.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.9 ) THEN
*
* First half of MINMN columns is zero.
*
JB_ZERO = 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.10 ) THEN
*
* Last columns are zero columns,
* starting from (MINMN / 2 + 1) column.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = N - JB_ZERO + 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.11 ) THEN
*
* Half of the columns in the middle of MINMN
* columns is zero, starting from
* MINMN/2 - (MINMN/2)/2 + 1 column.
*
JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.12 ) THEN
*
* Odd-numbered columns are zero,
*
NB_GEN = N / 2
NB_ZERO = N - NB_GEN
J_INC = 2
J_FIRST_NZ = 2
*
ELSE IF( IMAT.EQ.13 ) THEN
*
* Even-numbered columns are zero.
*
NB_ZERO = N / 2
NB_GEN = N - NB_ZERO
J_INC = 2
J_FIRST_NZ = 1
*
END IF
*
*
* 1) Set the first NB_ZERO columns in COPYA(1:M,1:N)
* to zero.
*
CALL CLASET( 'Full', M, NB_ZERO, CZERO, CZERO,
$ COPYA, LDA )
*
* 2) Generate an M-by-(N-NB_ZERO) matrix with the
* chosen singular value distribution
* in COPYA(1:M,NB_ZERO+1:N).
*
CALL CLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU,
$ ANORM, MODE, CNDNUM, DIST )
*
SRNAMT = 'CLATMS'
*
IND_OFFSET_GEN = NB_ZERO * LDA
*
CALL CLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA( IND_OFFSET_GEN + 1 ), LDA,
$ WORK, INFO )
*
* Check error code from CLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', M,
$ NB_GEN, -1, -1, -1, IMAT, NFAIL,
$ NERRS, NOUT )
CYCLE
END IF
*
* 3) Swap the gererated colums from the right side
* NB_GEN-size block in COPYA into correct column
* positions.
*
IF( IMAT.EQ.6
$ .OR. IMAT.EQ.7
$ .OR. IMAT.EQ.8
$ .OR. IMAT.EQ.10
$ .OR. IMAT.EQ.11 ) THEN
*
* Move by swapping the generated columns
* from the right NB_GEN-size block from
* (NB_ZERO+1:NB_ZERO+JB_ZERO)
* into columns (1:JB_ZERO-1).
*
DO J = 1, JB_ZERO-1, 1
CALL CSWAP( M,
$ COPYA( ( NB_ZERO+J-1)*LDA+1), 1,
$ COPYA( (J-1)*LDA + 1 ), 1 )
END DO
*
ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN
*
* ( IMAT = 12, Odd-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the even zero colums in the
* left NB_ZERO-size block.
*
* ( IMAT = 13, Even-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the odd zero colums in the
* left NB_ZERO-size block.
*
DO J = 1, NB_GEN, 1
IND_OUT = ( NB_ZERO+J-1 )*LDA + 1
IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA
$ + 1
CALL CSWAP( M,
$ COPYA( IND_OUT ), 1,
$ COPYA( IND_IN), 1 )
END DO
*
END IF
*
* 5) Order the singular values generated by
* DLAMTS in decreasing order and add trailing zeros
* that correspond to zero columns.
* The total number of singular values is MINMN.
*
MINMNB_GEN = MIN( M, NB_GEN )
*
CALL SLAORD( 'Decreasing', MINMNB_GEN, S, 1 )
DO I = MINMNB_GEN+1, MINMN
S( I ) = ZERO
END DO
*
ELSE
*
* IF(MINMN.LT.2) skip this size for this matrix type.
*
CYCLE
END IF
*
* Initialize a copy array for a pivot array for DGEQP3RK.
*
DO I = 1, N
IWORK( I ) = 0
END DO
*
DO INB = 1, NNB
*
* Do for each pair of values (NB,NX) in NBVAL and NXVAL.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
*
* We do MIN(M,N)+1 because we need a test for KMAX > N,
* when KMAX is larger than MIN(M,N), KMAX should be
* KMAX = MIN(M,N)
*
DO KMAX = 0, MIN(M,N)+1
*
* Get a working copy of COPYA into A( 1:M,1:N ).
* Get a working copy of COPYB into A( 1:M, (N+1):NRHS ).
* Get a working copy of COPYB into into B( 1:M, 1:NRHS ).
* Get a working copy of IWORK(1:N) awith zeroes into
* which is going to be used as pivot array IWORK( N+1:2N ).
* NOTE: IWORK(2N+1:3N) is going to be used as a WORK array
* for the routine.
*
CALL CLACPY( 'All', M, N, COPYA, LDA, A, LDA )
CALL CLACPY( 'All', M, NRHS, COPYB, LDA,
$ A( LDA*N + 1 ), LDA )
CALL CLACPY( 'All', M, NRHS, COPYB, LDA,
$ B, LDA )
CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 )
*
ABSTOL = -1.0
RELTOl = -1.0
*
* Compute the QR factorization with pivoting of A
*
LW = MAX( 1, MAX( 2*N + NB*( N+NRHS+1 ),
$ 3*N + NRHS - 1 ) )
*
* Compute CGEQP3RK factorization of A.
*
SRNAMT = 'CGEQP3RK'
CALL CGEQP3RK( M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ A, LDA, KFACT, MAXC2NRMK,
$ RELMAXC2NRMK, IWORK( N+1 ), TAU,
$ WORK, LW, RWORK, IWORK( 2*N+1 ),
$ INFO )
*
* Check error code from CGEQP3RK.
*
IF( INFO.LT.0 )
$ CALL ALAERH( PATH, 'CGEQP3RK', INFO, 0, ' ',
$ M, N, NX, -1, NB, IMAT,
$ NFAIL, NERRS, NOUT )
*
IF( KFACT.EQ.MINMN ) THEN
*
* Compute test 1:
*
* This test in only for the full rank factorization of
* the matrix A.
*
* Array S(1:min(M,N)) contains svd(A) the sigular values
* of the original matrix A in decreasing absolute value
* order. The test computes svd(R), the vector sigular
* values of the upper trapezoid of A(1:M,1:N) that
* contains the factor R, in decreasing order. The test
* returns the ratio:
*
* 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS )
*
RESULT( 1 ) = CQRT12( M, N, A, LDA, S, WORK,
$ LWORK , RWORK )
*
DO T = 1, 1
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'CGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL, NB, NX,
$ IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 1
*
END IF
* Compute test 2:
*
* The test returns the ratio:
*
* 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS )
*
RESULT( 2 ) = CQPT01( M, N, KFACT, COPYA, A, LDA, TAU,
$ IWORK( N+1 ), WORK, LWORK )
*
* Compute test 3:
*
* The test returns the ratio:
*
* 1-norm( Q**T * Q - I ) / ( M * EPS )
*
RESULT( 3 ) = CQRT11( M, KFACT, A, LDA, TAU, WORK,
$ LWORK )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 2, 3
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'CGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 2
*
* Compute test 4:
*
* This test is only for the factorizations with the
* rank greater than 2.
* The elements on the diagonal of R should be non-
* increasing.
*
* The test returns the ratio:
*
* Returns 1.0D+100 if abs(R(K+1,K+1)) > abs(R(K,K)),
* K=1:KFACT-1
*
IF( MIN(KFACT, MINMN).GE.2 ) THEN
*
DO J = 1, KFACT-1, 1
*
DTEMP = (( ABS( A( (J-1)*M+J ) ) -
$ ABS( A( (J)*M+J+1 ) ) ) /
$ ABS( A(1) ) )
*
IF( DTEMP.LT.ZERO ) THEN
RESULT( 4 ) = BIGNUM
END IF
*
END DO
*
* Print information about the tests that did not
* pass the threshold.
*
DO T = 4, 4
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'CGEQP3RK',
$ M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T,
$ RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 4.
*
END IF
*
* Compute test 5:
*
* This test in only for matrix A with min(M,N) > 0.
*
* The test returns the ratio:
*
* 1-norm(Q**T * B - Q**T * B ) /
* ( M * EPS )
*
* (1) Compute B:=Q**T * B in the matrix B.
*
IF( MINMN.GT.0 ) THEN
*
LWORK_MQR = MAX(1, NRHS)
CALL CUNMQR( 'Left', 'Conjugate transpose',
$ M, NRHS, KFACT, A, LDA, TAU, B, LDA,
$ WORK, LWORK_MQR, INFO )
*
DO I = 1, NRHS
*
* Compare N+J-th column of A and J-column of B.
*
CALL CAXPY( M, -CONE, A( ( N+I-1 )*LDA+1 ), 1,
$ B( ( I-1 )*LDA+1 ), 1 )
END DO
*
RESULT( 5 ) =
$ ABS(
$ CLANGE( 'One-norm', M, NRHS, B, LDA, RDUMMY ) /
$ ( REAL( M )*SLAMCH( 'Epsilon' ) )
$ )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 5, 5
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'CGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End compute test 5.
*
END IF
*
* END DO KMAX = 1, MIN(M,N)+1
*
END DO
*
* END DO for INB = 1, NNB
*
END DO
*
* END DO for IMAT = 1, NTYPES
*
END DO
*
* END DO for INS = 1, NNS
*
END DO
*
* END DO for IN = 1, NN
*
END DO
*
* END DO for IM = 1, NM
*
END DO
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NRHS =', I5,
$ ', KMAX =', I5, ', ABSTOL =', G12.5,
$ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4,
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
*
* End of CCHKQP3RK
*
END

121
lapack-netlib/TESTING/LIN/clatb4.f
View File

@ -154,9 +154,6 @@
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. External Subroutines ..
EXTERNAL SLABAD
* ..
* .. Save statement ..
SAVE EPS, SMALL, LARGE, BADC1, BADC2, FIRST
* ..
@ -174,11 +171,6 @@
BADC1 = SQRT( BADC2 )
SMALL = SLAMCH( 'Safe minimum' )
LARGE = ONE / SMALL
*
* If it looks like we're on a Cray, take the square root of
* SMALL and LARGE to avoid overflow and underflow problems.
*
CALL SLABAD( SMALL, LARGE )
SMALL = SHRINK*( SMALL / EPS )
LARGE = ONE / SMALL
END IF
@ -233,6 +225,110 @@
ELSE
ANORM = ONE
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* xQK: truncated QR with pivoting.
* Set parameters to generate a general
* M x N matrix.
*
* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
*
TYPE = 'N'
*
* Set DIST, the type of distribution for the random
* number generator. 'S' is
*
DIST = 'S'
*
* Set the lower and upper bandwidths.
*
IF( IMAT.EQ.2 ) THEN
*
* 2. Random, Diagonal, CNDNUM = 2
*
KL = 0
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.3 ) THEN
*
* 3. Random, Upper triangular, CNDNUM = 2
*
KL = 0
KU = MAX( N-1, 0 )
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.4 ) THEN
*
* 4. Random, Lower triangular, CNDNUM = 2
*
KL = MAX( M-1, 0 )
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE
*
* 5.-19. Rectangular matrix
*
KL = MAX( M-1, 0 )
KU = MAX( N-1, 0 )
*
IF( IMAT.GE.5 .AND. IMAT.LE.14 ) THEN
*
* 5.-14. Random, CNDNUM = 2.
*
CNDNUM = TWO
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.15 ) THEN
*
* 15. Random, CNDNUM = sqrt(0.1/EPS)
*
CNDNUM = BADC1
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.16 ) THEN
*
* 16. Random, CNDNUM = 0.1/EPS
*
CNDNUM = BADC2
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.17 ) THEN
*
* 17. Random, CNDNUM = 0.1/EPS,
* one small singular value S(N)=1/CNDNUM
*
CNDNUM = BADC2
ANORM = ONE
MODE = 2
*
ELSE IF( IMAT.EQ.18 ) THEN
*
* 18. Random, scaled near underflow
*
CNDNUM = TWO
ANORM = SMALL
MODE = 3
*
ELSE IF( IMAT.EQ.19 ) THEN
*
* 19. Random, scaled near overflow
*
CNDNUM = TWO
ANORM = LARGE
MODE = 3
*
END IF
*
END IF
*
ELSE IF( LSAMEN( 2, C2, 'GE' ) ) THEN
*
@ -517,17 +613,18 @@
*
* Set the norm and condition number.
*
IF( IMAT.EQ.2 .OR. IMAT.EQ.8 ) THEN
MAT = ABS( IMAT )
IF( MAT.EQ.2 .OR. MAT.EQ.8 ) THEN
CNDNUM = BADC1
ELSE IF( IMAT.EQ.3 .OR. IMAT.EQ.9 ) THEN
ELSE IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
CNDNUM = BADC2
ELSE
CNDNUM = TWO
END IF
*
IF( IMAT.EQ.4 ) THEN
IF( MAT.EQ.4 ) THEN
ANORM = SMALL
ELSE IF( IMAT.EQ.5 ) THEN
ELSE IF( MAT.EQ.5 ) THEN
ANORM = LARGE
ELSE
ANORM = ONE

23
lapack-netlib/TESTING/LIN/cqpt01.f
View File

@ -33,7 +33,8 @@
*> Householder vectors, and the rest of AF contains a partially updated
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
*> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
*> where || . || is matrix one norm.
*> \endverbatim
*
* Arguments:
@ -172,28 +173,28 @@
*
NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
DO 30 J = 1, K
DO 10 I = 1, MIN( J, M )
DO J = 1, K
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
DO 20 I = J + 1, M
END DO
DO I = J + 1, M
WORK( ( J-1 )*M+I ) = ZERO
20 CONTINUE
30 CONTINUE
DO 40 J = K + 1, N
END DO
END DO
DO J = K + 1, N
CALL CCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
40 CONTINUE
END DO
*
CALL CUNMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
DO 50 J = 1, N
DO J = 1, N
*
* Compare i-th column of QR and jpvt(i)-th column of A
*
CALL CAXPY( M, CMPLX( -ONE ), A( 1, JPVT( J ) ), 1,
$ WORK( ( J-1 )*M+1 ), 1 )
50 CONTINUE
END DO
*
CQPT01 = CLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
$ ( REAL( MAX( M, N ) )*SLAMCH( 'Epsilon' ) )

4
lapack-netlib/TESTING/LIN/cqrt11.f
View File

@ -157,9 +157,9 @@
CALL CUNM2R( 'Left', 'Conjugate transpose', M, M, K, A, LDA, TAU,
$ WORK, M, WORK( M*M+1 ), INFO )
*
DO 10 J = 1, M
DO J = 1, M
WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
10 CONTINUE
END DO
*
CQRT11 = CLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
$ ( REAL( M )*SLAMCH( 'Epsilon' ) )

19
lapack-netlib/TESTING/LIN/cqrt12.f
View File

@ -28,7 +28,7 @@
*> CQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
*> || svlues -s ||/( ||s||*eps*max(M,N) )
*> \endverbatim
*
* Arguments:
@ -125,8 +125,8 @@
EXTERNAL CLANGE, SASUM, SLAMCH, SNRM2
* ..
* .. External Subroutines ..
EXTERNAL CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLABAD,
$ SLASCL, XERBLA
EXTERNAL CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLASCL,
$ XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, MIN, REAL
@ -153,17 +153,16 @@
* Copy upper triangle of A into work
*
CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M )
DO 20 J = 1, N
DO 10 I = 1, MIN( J, M )
DO J = 1, N
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = A( I, J )
10 CONTINUE
20 CONTINUE
END DO
END DO
*
* Get machine parameters
*
SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* Scale work if max entry outside range [SMLNUM,BIGNUM]
*
@ -207,9 +206,9 @@
*
ELSE
*
DO 30 I = 1, MN
DO I = 1, MN
RWORK( I ) = ZERO
30 CONTINUE
END DO
END IF
*
* Compare s and singular values of work

48
lapack-netlib/TESTING/LIN/dchkaa.F
View File

@ -63,6 +63,7 @@
*> DLQ 8 List types on next line if 0 < NTYPES < 8
*> DQL 8 List types on next line if 0 < NTYPES < 8
*> DQP 6 List types on next line if 0 < NTYPES < 6
*> DQK 19 List types on next line if 0 < NTYPES < 19
*> DTZ 3 List types on next line if 0 < NTYPES < 3
*> DLS 6 List types on next line if 0 < NTYPES < 6
*> DEQ
@ -149,12 +150,12 @@
$ NBVAL( MAXIN ), NBVAL2( MAXIN ),
$ NSVAL( MAXIN ), NVAL( MAXIN ), NXVAL( MAXIN ),
$ RANKVAL( MAXIN ), PIV( NMAX )
DOUBLE PRECISION E( NMAX ), S( 2*NMAX )
* ..
* .. Allocatable Arrays ..
INTEGER AllocateStatus
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: RWORK
DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: A, B, WORK
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: RWORK, S
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: E
DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: A, B, WORK
* ..
* .. External Functions ..
LOGICAL LSAME, LSAMEN
@ -164,13 +165,13 @@
* .. External Subroutines ..
EXTERNAL ALAREQ, DCHKEQ, DCHKGB, DCHKGE, DCHKGT, DCHKLQ,
$ DCHKORHR_COL, DCHKPB, DCHKPO, DCHKPS, DCHKPP,
$ DCHKPT, DCHKQ3, DCHKQL, DCHKQR, DCHKRQ, DCHKSP,
$ DCHKSY, DCHKSY_ROOK, DCHKSY_RK, DCHKSY_AA,
$ DCHKTB, DCHKTP, DCHKTR, DCHKTZ, DDRVGB, DDRVGE,
$ DDRVGT, DDRVLS, DDRVPB, DDRVPO, DDRVPP, DDRVPT,
$ DDRVSP, DDRVSY, DDRVSY_ROOK, DDRVSY_RK,
$ DDRVSY_AA, ILAVER, DCHKLQTP, DCHKQRT, DCHKQRTP,
$ DCHKLQT,DCHKTSQR
$ DCHKPT, DCHKQ3, DCHKQP3RK, DCHKQL, DCHKQR,
$ DCHKRQ, DCHKSP, DCHKSY, DCHKSY_ROOK, DCHKSY_RK,
$ DCHKSY_AA, DCHKTB, DCHKTP, DCHKTR, DCHKTZ,
$ DDRVGB, DDRVGE, DDRVGT, DDRVLS, DDRVPB, DDRVPO,
$ DDRVPP, DDRVPT, DDRVSP, DDRVSY, DDRVSY_ROOK,
$ DDRVSY_RK, DDRVSY_AA, ILAVER, DCHKLQTP, DCHKQRT,
$ DCHKQRTP, DCHKLQT,DCHKTSQR
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
@ -197,6 +198,10 @@
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( WORK( NMAX, 3*NMAX+MAXRHS+30 ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( E( NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( S( 2*NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( RWORK( 5*NMAX+2*MAXRHS ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
*
@ -919,9 +924,26 @@
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
IF( TSTCHK ) THEN
CALL DCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
$ THRESH, A( 1, 1 ), A( 1, 2 ), B( 1, 1 ),
$ B( 1, 3 ), WORK, IWORK, NOUT )
CALL DCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL,
$ NXVAL, THRESH, A( 1, 1 ), A( 1, 2 ),
$ B( 1, 1 ), B( 1, 3 ), WORK, IWORK, NOUT )
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* QK: truncated QR factorization with pivoting
*
NTYPES = 19
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
IF( TSTCHK ) THEN
CALL DCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A( 1, 1 ),
$ A( 1, 2 ), B( 1, 1 ), B( 1, 2 ),
$ B( 1, 3 ), B( 1, 4 ),
$ WORK, IWORK, NOUT )
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF

2
lapack-netlib/TESTING/LIN/dchkq3.f
View File

@ -30,7 +30,7 @@
*>
*> \verbatim
*>
*> DCHKQ3 tests DGEQP3.
*> DCHKQ3 tests DGEQP3.
*> \endverbatim
*
* Arguments:

832
lapack-netlib/TESTING/LIN/dchkqp3rk.f Normal file
View File

@ -0,0 +1,832 @@
*> \brief \b DCHKQP3RK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
* $ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
* $ B, COPYB, S, TAU,
* $ WORK, IWORK, NOUT )
* IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
* INTEGER NM, NN, NNS, NNB, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
* $ NVAL( * ), NXVAL( * )
* DOUBLE PRECISION A( * ), COPYA( * ), B( * ), COPYB( * ),
* $ S( * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCHKQP3RK tests DGEQP3RK.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*> NM is INTEGER
*> The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB and NX contained in the
*> vectors NBVAL and NXVAL. The blocking parameters are used
*> in pairs (NB,NX).
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NXVAL
*> \verbatim
*> NXVAL is INTEGER array, dimension (NNB)
*> The values of the crossover point NX.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is DOUBLE PRECISION
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (MMAX*NMAX)
*> where MMAX is the maximum value of M in MVAL and NMAX is the
*> maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] COPYA
*> \verbatim
*> COPYA is DOUBLE PRECISION array, dimension (MMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
*> where MMAX is the maximum value of M in MVAL and NSMAX is the
*> maximum value of NRHS in NSVAL.
*> \endverbatim
*>
*> \param[out] COPYB
*> \verbatim
*> COPYB is DOUBLE PRECISION array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is DOUBLE PRECISION array, dimension
*> (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (MMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension
*> (MMAX*NMAX + 4*NMAX + MMAX)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
$ B, COPYB, S, TAU,
$ WORK, IWORK, NOUT )
IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER NM, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
$ NSVAL( * ), NXVAL( * )
DOUBLE PRECISION A( * ), COPYA( * ), B( * ), COPYB( * ),
$ S( * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPES
PARAMETER ( NTYPES = 19 )
INTEGER NTESTS
PARAMETER ( NTESTS = 5 )
DOUBLE PRECISION ONE, ZERO, BIGNUM
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0,
$ BIGNUM = 1.0D+38 )
* ..
* .. Local Scalars ..
CHARACTER DIST, TYPE
CHARACTER*3 PATH
INTEGER I, IHIGH, ILOW, IM, IMAT, IN, INC_ZERO,
$ INB, IND_OFFSET_GEN,
$ IND_IN, IND_OUT, INS, INFO,
$ ISTEP, J, J_INC, J_FIRST_NZ, JB_ZERO,
$ KFACT, KL, KMAX, KU, LDA, LW, LWORK,
$ LWORK_MQR, M, MINMN, MINMNB_GEN, MODE, N,
$ NB, NB_ZERO, NERRS, NFAIL, NB_GEN, NRHS,
$ NRUN, NX, T
DOUBLE PRECISION ANORM, CNDNUM, EPS, ABSTOL, RELTOL,
$ DTEMP, MAXC2NRMK, RELMAXC2NRMK
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), RDUMMY( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DQPT01, DQRT11, DQRT12, DLANGE,
$ DLAPY2
EXTERNAL DLAMCH, DQPT01, DQRT11, DQRT12, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, DAXPY, DGEQP3RK,
$ DLACPY, DLAORD, DLASET, DLATB4, DLATMS,
$ DORMQR, DSWAP, ICOPY, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, MOD
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'QK'
NRUN = 0
NFAIL = 0
NERRS = 0
DO I = 1, 4
ISEED( I ) = ISEEDY( I )
END DO
EPS = DLAMCH( 'Epsilon' )
INFOT = 0
*
DO IM = 1, NM
*
* Do for each value of M in MVAL.
*
M = MVAL( IM )
LDA = MAX( 1, M )
*
DO IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
MINMN = MIN( M, N )
LWORK = MAX( 1, M*MAX( M, N )+4*MINMN+MAX( M, N ),
$ M*N + 2*MINMN + 4*N )
*
DO INS = 1, NNS
NRHS = NSVAL( INS )
*
* Set up parameters with DLATB4 and generate
* M-by-NRHS B matrix with DLATMS.
* IMAT = 14:
* Random matrix, CNDNUM = 2, NORM = ONE,
* MODE = 3 (geometric distribution of singular values).
*
CALL DLATB4( PATH, 14, M, NRHS, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'DLATMS'
CALL DLATMS( M, NRHS, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYB, LDA, WORK, INFO )
*
* Check error code from DLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', M,
$ NRHS, -1, -1, -1, 6, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
DO IMAT = 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ CYCLE
*
* The type of distribution used to generate the random
* eigen-/singular values:
* ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 )
*
* Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE
* 1. Zero matrix
* 2. Random, Diagonal, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 3. Random, Upper triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 4. Random, Lower triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 5. Random, First column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 6. Random, Last MINMN column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 7. Random, Last N column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 8. Random, Middle column in MINMN is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 9. Random, First half of MINMN columns are zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 10. Random, Last columns are zero starting from MINMN/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 11. Random, Half MINMN columns in the middle are zero starting
* from MINMN/2-(MINMN/2)/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 12. Random, Odd columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 13. Random, Even columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 14. Random, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) ONE 3 ( geometric distribution of singular values )
* 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS ONE 3 ( geometric distribution of singular values )
* 17. Random, CNDNUM = 0.1/EPS, CNDNUM = BADC2 = 0.1/EPS ONE 2 ( one small singular value, S(N)=1/CNDNUM )
* one small singular value S(N)=1/CNDNUM
* 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN
* 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values )
*
IF( IMAT.EQ.1 ) THEN
*
* Matrix 1: Zero matrix
*
CALL DLASET( 'Full', M, N, ZERO, ZERO, COPYA, LDA )
DO I = 1, MINMN
S( I ) = ZERO
END DO
*
ELSE IF( (IMAT.GE.2 .AND. IMAT.LE.4 )
$ .OR. (IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN
*
* Matrices 2-5.
*
* Set up parameters with DLATB4 and generate a test
* matrix with DLATMS.
*
CALL DLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'DLATMS'
CALL DLATMS( M, N, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA, LDA, WORK, INFO )
*
* Check error code from DLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', M, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
CALL DLAORD( 'Decreasing', MINMN, S, 1 )
*
ELSE IF( MINMN.GE.2
$ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN
*
* Rectangular matrices 5-13 that contain zero columns,
* only for matrices MINMN >=2.
*
* JB_ZERO is the column index of ZERO block.
* NB_ZERO is the column block size of ZERO block.
* NB_GEN is the column blcok size of the
* generated block.
* J_INC in the non_zero column index increment
* for matrix 12 and 13.
* J_FIRS_NZ is the index of the first non-zero
* column.
*
IF( IMAT.EQ.5 ) THEN
*
* First column is zero.
*
JB_ZERO = 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.6 ) THEN
*
* Last column MINMN is zero.
*
JB_ZERO = MINMN
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.7 ) THEN
*
* Last column N is zero.
*
JB_ZERO = N
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.8 ) THEN
*
* Middle column in MINMN is zero.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.9 ) THEN
*
* First half of MINMN columns is zero.
*
JB_ZERO = 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.10 ) THEN
*
* Last columns are zero columns,
* starting from (MINMN / 2 + 1) column.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = N - JB_ZERO + 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.11 ) THEN
*
* Half of the columns in the middle of MINMN
* columns is zero, starting from
* MINMN/2 - (MINMN/2)/2 + 1 column.
*
JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.12 ) THEN
*
* Odd-numbered columns are zero,
*
NB_GEN = N / 2
NB_ZERO = N - NB_GEN
J_INC = 2
J_FIRST_NZ = 2
*
ELSE IF( IMAT.EQ.13 ) THEN
*
* Even-numbered columns are zero.
*
NB_ZERO = N / 2
NB_GEN = N - NB_ZERO
J_INC = 2
J_FIRST_NZ = 1
*
END IF
*
*
* 1) Set the first NB_ZERO columns in COPYA(1:M,1:N)
* to zero.
*
CALL DLASET( 'Full', M, NB_ZERO, ZERO, ZERO,
$ COPYA, LDA )
*
* 2) Generate an M-by-(N-NB_ZERO) matrix with the
* chosen singular value distribution
* in COPYA(1:M,NB_ZERO+1:N).
*
CALL DLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU,
$ ANORM, MODE, CNDNUM, DIST )
*
SRNAMT = 'DLATMS'
*
IND_OFFSET_GEN = NB_ZERO * LDA
*
CALL DLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA( IND_OFFSET_GEN + 1 ), LDA,
$ WORK, INFO )
*
* Check error code from DLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', M,
$ NB_GEN, -1, -1, -1, IMAT, NFAIL,
$ NERRS, NOUT )
CYCLE
END IF
*
* 3) Swap the gererated colums from the right side
* NB_GEN-size block in COPYA into correct column
* positions.
*
IF( IMAT.EQ.6
$ .OR. IMAT.EQ.7
$ .OR. IMAT.EQ.8
$ .OR. IMAT.EQ.10
$ .OR. IMAT.EQ.11 ) THEN
*
* Move by swapping the generated columns
* from the right NB_GEN-size block from
* (NB_ZERO+1:NB_ZERO+JB_ZERO)
* into columns (1:JB_ZERO-1).
*
DO J = 1, JB_ZERO-1, 1
CALL DSWAP( M,
$ COPYA( ( NB_ZERO+J-1)*LDA+1), 1,
$ COPYA( (J-1)*LDA + 1 ), 1 )
END DO
*
ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN
*
* ( IMAT = 12, Odd-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the even zero colums in the
* left NB_ZERO-size block.
*
* ( IMAT = 13, Even-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the odd zero colums in the
* left NB_ZERO-size block.
*
DO J = 1, NB_GEN, 1
IND_OUT = ( NB_ZERO+J-1 )*LDA + 1
IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA
$ + 1
CALL DSWAP( M,
$ COPYA( IND_OUT ), 1,
$ COPYA( IND_IN), 1 )
END DO
*
END IF
*
* 5) Order the singular values generated by
* DLAMTS in decreasing order and add trailing zeros
* that correspond to zero columns.
* The total number of singular values is MINMN.
*
MINMNB_GEN = MIN( M, NB_GEN )
*
DO I = MINMNB_GEN+1, MINMN
S( I ) = ZERO
END DO
*
ELSE
*
* IF(MINMN.LT.2) skip this size for this matrix type.
*
CYCLE
END IF
*
* Initialize a copy array for a pivot array for DGEQP3RK.
*
DO I = 1, N
IWORK( I ) = 0
END DO
*
DO INB = 1, NNB
*
* Do for each pair of values (NB,NX) in NBVAL and NXVAL.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
*
* We do MIN(M,N)+1 because we need a test for KMAX > N,
* when KMAX is larger than MIN(M,N), KMAX should be
* KMAX = MIN(M,N)
*
DO KMAX = 0, MIN(M,N)+1
*
* Get a working copy of COPYA into A( 1:M,1:N ).
* Get a working copy of COPYB into A( 1:M, (N+1):NRHS ).
* Get a working copy of COPYB into into B( 1:M, 1:NRHS ).
* Get a working copy of IWORK(1:N) awith zeroes into
* which is going to be used as pivot array IWORK( N+1:2N ).
* NOTE: IWORK(2N+1:3N) is going to be used as a WORK array
* for the routine.
*
CALL DLACPY( 'All', M, N, COPYA, LDA, A, LDA )
CALL DLACPY( 'All', M, NRHS, COPYB, LDA,
$ A( LDA*N + 1 ), LDA )
CALL DLACPY( 'All', M, NRHS, COPYB, LDA,
$ B, LDA )
CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 )
*
ABSTOL = -1.0
RELTOL = -1.0
*
* Compute the QR factorization with pivoting of A
*
LW = MAX( 1, MAX( 2*N + NB*( N+NRHS+1 ),
$ 3*N + NRHS - 1 ) )
*
* Compute DGEQP3RK factorization of A.
*
SRNAMT = 'DGEQP3RK'
CALL DGEQP3RK( M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ A, LDA, KFACT, MAXC2NRMK,
$ RELMAXC2NRMK, IWORK( N+1 ), TAU,
$ WORK, LW, IWORK( 2*N+1 ), INFO )
*
* Check error code from DGEQP3RK.
*
IF( INFO.LT.0 )
$ CALL ALAERH( PATH, 'DGEQP3RK', INFO, 0, ' ',
$ M, N, NX, -1, NB, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Compute test 1:
*
* This test in only for the full rank factorization of
* the matrix A.
*
* Array S(1:min(M,N)) contains svd(A) the sigular values
* of the original matrix A in decreasing absolute value
* order. The test computes svd(R), the vector sigular
* values of the upper trapezoid of A(1:M,1:N) that
* contains the factor R, in decreasing order. The test
* returns the ratio:
*
* 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS )
*
IF( KFACT.EQ.MINMN ) THEN
*
RESULT( 1 ) = DQRT12( M, N, A, LDA, S, WORK,
$ LWORK )
*
DO T = 1, 1
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'DGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL, NB, NX,
$ IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 1
*
END IF
*
* Compute test 2:
*
* The test returns the ratio:
*
* 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS )
*
RESULT( 2 ) = DQPT01( M, N, KFACT, COPYA, A, LDA, TAU,
$ IWORK( N+1 ), WORK, LWORK )
*
* Compute test 3:
*
* The test returns the ratio:
*
* 1-norm( Q**T * Q - I ) / ( M * EPS )
*
RESULT( 3 ) = DQRT11( M, KFACT, A, LDA, TAU, WORK,
$ LWORK )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 2, 3
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'DGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 2
*
* Compute test 4:
*
* This test is only for the factorizations with the
* rank greater than 2.
* The elements on the diagonal of R should be non-
* increasing.
*
* The test returns the ratio:
*
* Returns 1.0D+100 if abs(R(K+1,K+1)) > abs(R(K,K)),
* K=1:KFACT-1
*
IF( MIN(KFACT, MINMN).GE.2 ) THEN
*
DO J = 1, KFACT-1, 1
DTEMP = (( ABS( A( (J-1)*M+J ) ) -
$ ABS( A( (J)*M+J+1 ) ) ) /
$ ABS( A(1) ) )
*
IF( DTEMP.LT.ZERO ) THEN
RESULT( 4 ) = BIGNUM
END IF
*
END DO
*
* Print information about the tests that did not
* pass the threshold.
*
DO T = 4, 4
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'DGEQP3RK',
$ M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T,
$ RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 4.
*
END IF
*
* Compute test 5:
*
* This test in only for matrix A with min(M,N) > 0.
*
* The test returns the ratio:
*
* 1-norm(Q**T * B - Q**T * B ) /
* ( M * EPS )
*
* (1) Compute B:=Q**T * B in the matrix B.
*
IF( MINMN.GT.0 ) THEN
*
LWORK_MQR = MAX(1, NRHS)
CALL DORMQR( 'Left', 'Transpose',
$ M, NRHS, KFACT, A, LDA, TAU, B, LDA,
$ WORK, LWORK_MQR, INFO )
*
DO I = 1, NRHS
*
* Compare N+J-th column of A and J-column of B.
*
CALL DAXPY( M, -ONE, A( ( N+I-1 )*LDA+1 ), 1,
$ B( ( I-1 )*LDA+1 ), 1 )
END DO
*
RESULT( 5 ) =
$ ABS(
$ DLANGE( 'One-norm', M, NRHS, B, LDA, RDUMMY ) /
$ ( DBLE( M )*DLAMCH( 'Epsilon' ) )
$ )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 5, 5
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'DGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End compute test 5.
*
END IF
*
* END DO KMAX = 1, MIN(M,N)+1
*
END DO
*
* END DO for INB = 1, NNB
*
END DO
*
* END DO for IMAT = 1, NTYPES
*
END DO
*
* END DO for INS = 1, NNS
*
END DO
*
* END DO for IN = 1, NN
*
END DO
*
* END DO for IM = 1, NM
*
END DO
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NRHS =', I5,
$ ', KMAX =', I5, ', ABSTOL =', G12.5,
$ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4,
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
*
* End of DCHKQP3RK
*
END

123
lapack-netlib/TESTING/LIN/dlatb4.f
View File

@ -133,7 +133,7 @@
*
* .. Parameters ..
DOUBLE PRECISION SHRINK, TENTH
PARAMETER ( SHRINK = 0.25D0, TENTH = 0.1D+0 )
PARAMETER ( SHRINK = 0.25D+0, TENTH = 0.1D+0 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
DOUBLE PRECISION TWO
@ -153,9 +153,6 @@
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. External Subroutines ..
EXTERNAL DLABAD
* ..
* .. Save statement ..
SAVE EPS, SMALL, LARGE, BADC1, BADC2, FIRST
* ..
@ -173,11 +170,6 @@
BADC1 = SQRT( BADC2 )
SMALL = DLAMCH( 'Safe minimum' )
LARGE = ONE / SMALL
*
* If it looks like we're on a Cray, take the square root of
* SMALL and LARGE to avoid overflow and underflow problems.
*
CALL DLABAD( SMALL, LARGE )
SMALL = SHRINK*( SMALL / EPS )
LARGE = ONE / SMALL
END IF
@ -232,6 +224,110 @@
ELSE
ANORM = ONE
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* xQK: truncated QR with pivoting.
* Set parameters to generate a general
* M x N matrix.
*
* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
*
TYPE = 'N'
*
* Set DIST, the type of distribution for the random
* number generator. 'S' is
*
DIST = 'S'
*
* Set the lower and upper bandwidths.
*
IF( IMAT.EQ.2 ) THEN
*
* 2. Random, Diagonal, CNDNUM = 2
*
KL = 0
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.3 ) THEN
*
* 3. Random, Upper triangular, CNDNUM = 2
*
KL = 0
KU = MAX( N-1, 0 )
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.4 ) THEN
*
* 4. Random, Lower triangular, CNDNUM = 2
*
KL = MAX( M-1, 0 )
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE
*
* 5.-19. Rectangular matrix
*
KL = MAX( M-1, 0 )
KU = MAX( N-1, 0 )
*
IF( IMAT.GE.5 .AND. IMAT.LE.14 ) THEN
*
* 5.-14. Random, CNDNUM = 2.
*
CNDNUM = TWO
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.15 ) THEN
*
* 15. Random, CNDNUM = sqrt(0.1/EPS)
*
CNDNUM = BADC1
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.16 ) THEN
*
* 16. Random, CNDNUM = 0.1/EPS
*
CNDNUM = BADC2
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.17 ) THEN
*
* 17. Random, CNDNUM = 0.1/EPS,
* one small singular value S(N)=1/CNDNUM
*
CNDNUM = BADC2
ANORM = ONE
MODE = 2
*
ELSE IF( IMAT.EQ.18 ) THEN
*
* 18. Random, scaled near underflow
*
CNDNUM = TWO
ANORM = SMALL
MODE = 3
*
ELSE IF( IMAT.EQ.19 ) THEN
*
* 19. Random, scaled near overflow
*
CNDNUM = TWO
ANORM = LARGE
MODE = 3
*
END IF
*
END IF
*
ELSE IF( LSAMEN( 2, C2, 'GE' ) ) THEN
*
@ -518,17 +614,18 @@
*
* Set the norm and condition number.
*
IF( IMAT.EQ.2 .OR. IMAT.EQ.8 ) THEN
MAT = ABS( IMAT )
IF( MAT.EQ.2 .OR. MAT.EQ.8 ) THEN
CNDNUM = BADC1
ELSE IF( IMAT.EQ.3 .OR. IMAT.EQ.9 ) THEN
ELSE IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
CNDNUM = BADC2
ELSE
CNDNUM = TWO
END IF
*
IF( IMAT.EQ.4 ) THEN
IF( MAT.EQ.4 ) THEN
ANORM = SMALL
ELSE IF( IMAT.EQ.5 ) THEN
ELSE IF( MAT.EQ.5 ) THEN
ANORM = LARGE
ELSE
ANORM = ONE

42
lapack-netlib/TESTING/LIN/dqpt01.f
View File

@ -28,12 +28,13 @@
*>
*> DQPT01 tests the QR-factorization with pivoting of a matrix A. The
*> array AF contains the (possibly partial) QR-factorization of A, where
*> the upper triangle of AF(1:k,1:k) is a partial triangular factor,
*> the entries below the diagonal in the first k columns are the
*> the upper triangle of AF(1:K,1:K) is a partial triangular factor,
*> the entries below the diagonal in the first K columns are the
*> Householder vectors, and the rest of AF contains a partially updated
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
*> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) ),
*> where || . || is matrix one norm.
*> \endverbatim
*
* Arguments:
@ -172,28 +173,41 @@
*
NORMA = DLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
DO 30 J = 1, K
DO 10 I = 1, MIN( J, M )
DO J = 1, K
*
* Copy the upper triangular part of the factor R stored
* in AF(1:K,1:K) into the work array WORK.
*
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
DO 20 I = J + 1, M
END DO
*
* Zero out the elements below the diagonal in the work array.
*
DO I = J + 1, M
WORK( ( J-1 )*M+I ) = ZERO
20 CONTINUE
30 CONTINUE
DO 40 J = K + 1, N
END DO
END DO
*
* Copy columns (K+1,N) from AF into the work array WORK.
* AF(1:K,K+1:N) contains the rectangular block of the upper trapezoidal
* factor R, AF(K+1:M,K+1:N) contains the partially updated residual
* matrix of R.
*
DO J = K + 1, N
CALL DCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
40 CONTINUE
END DO
*
CALL DORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
DO 50 J = 1, N
DO J = 1, N
*
* Compare i-th column of QR and jpvt(i)-th column of A
* Compare J-th column of QR and JPVT(J)-th column of A.
*
CALL DAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ),
$ 1 )
50 CONTINUE
END DO
*
DQPT01 = DLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
$ ( DBLE( MAX( M, N ) )*DLAMCH( 'Epsilon' ) )

4
lapack-netlib/TESTING/LIN/dqrt11.f
View File

@ -157,9 +157,9 @@
CALL DORM2R( 'Left', 'Transpose', M, M, K, A, LDA, TAU, WORK, M,
$ WORK( M*M+1 ), INFO )
*
DO 10 J = 1, M
DO J = 1, M
WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
10 CONTINUE
END DO
*
DQRT11 = DLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
$ ( DBLE( M )*DLAMCH( 'Epsilon' ) )

22
lapack-netlib/TESTING/LIN/dqrt12.f
View File

@ -26,7 +26,7 @@
*> DQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
*> || svlues - s ||/(||s||*eps*max(M,N))
*> \endverbatim
*
* Arguments:
@ -113,8 +113,7 @@
EXTERNAL DASUM, DLAMCH, DLANGE, DNRM2
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DBDSQR, DGEBD2, DLABAD, DLASCL, DLASET,
$ XERBLA
EXTERNAL DAXPY, DBDSQR, DGEBD2, DLASCL, DLASET, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
@ -145,17 +144,16 @@
* Copy upper triangle of A into work
*
CALL DLASET( 'Full', M, N, ZERO, ZERO, WORK, M )
DO 20 J = 1, N
DO 10 I = 1, MIN( J, M )
DO J = 1, N
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = A( I, J )
10 CONTINUE
20 CONTINUE
END DO
END DO
*
* Get machine parameters
*
SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* Scale work if max entry outside range [SMLNUM,BIGNUM]
*
@ -199,16 +197,18 @@
*
ELSE
*
DO 30 I = 1, MN
DO I = 1, MN
WORK( M*N+I ) = ZERO
30 CONTINUE
END DO
END IF
*
* Compare s and singular values of work
*
CALL DAXPY( MN, -ONE, S, 1, WORK( M*N+1 ), 1 )
*
DQRT12 = DASUM( MN, WORK( M*N+1 ), 1 ) /
$ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
$ ( DLAMCH('Epsilon') * DBLE( MAX( M, N ) ) )
*
IF( NRMSVL.NE.ZERO )
$ DQRT12 = DQRT12 / NRMSVL
*

48
lapack-netlib/TESTING/LIN/schkaa.F
View File

@ -63,6 +63,7 @@
*> SLQ 8 List types on next line if 0 < NTYPES < 8
*> SQL 8 List types on next line if 0 < NTYPES < 8
*> SQP 6 List types on next line if 0 < NTYPES < 6
*> DQK 19 List types on next line if 0 < NTYPES < 19
*> STZ 3 List types on next line if 0 < NTYPES < 3
*> SLS 6 List types on next line if 0 < NTYPES < 6
*> SEQ
@ -147,11 +148,11 @@
$ NBVAL( MAXIN ), NBVAL2( MAXIN ),
$ NSVAL( MAXIN ), NVAL( MAXIN ), NXVAL( MAXIN ),
$ RANKVAL( MAXIN ), PIV( NMAX )
REAL E( NMAX ), S( 2*NMAX )
* ..
* .. Allocatable Arrays ..
INTEGER AllocateStatus
REAL, DIMENSION(:), ALLOCATABLE :: RWORK
REAL, DIMENSION(:), ALLOCATABLE :: RWORK, S
REAL, DIMENSION(:), ALLOCATABLE :: E
REAL, DIMENSION(:,:), ALLOCATABLE :: A, B, WORK
* ..
* .. External Functions ..
@ -162,13 +163,13 @@
* .. External Subroutines ..
EXTERNAL ALAREQ, SCHKEQ, SCHKGB, SCHKGE, SCHKGT, SCHKLQ,
$ SCHKORHR_COL, SCHKPB, SCHKPO, SCHKPS, SCHKPP,
$ SCHKPT, SCHKQ3, SCHKQL, SCHKQR, SCHKRQ, SCHKSP,
$ SCHKSY, SCHKSY_ROOK, SCHKSY_RK, SCHKSY_AA,
$ SCHKTB, SCHKTP, SCHKTR, SCHKTZ, SDRVGB, SDRVGE,
$ SDRVGT, SDRVLS, SDRVPB, SDRVPO, SDRVPP, SDRVPT,
$ SDRVSP, SDRVSY, SDRVSY_ROOK, SDRVSY_RK,
$ SDRVSY_AA, ILAVER, SCHKLQTP, SCHKQRT, SCHKQRTP,
$ SCHKLQT, SCHKTSQR
$ SCHKPT, SCHKQ3, SCHKQP3RK, SCHKQL, SCHKQR,
$ SCHKRQ, SCHKSP, SCHKSY, SCHKSY_ROOK, SCHKSY_RK,
$ SCHKSY_AA, SCHKTB, SCHKTP, SCHKTR, SCHKTZ,
$ SDRVGB, SDRVGE, SDRVGT, SDRVLS, SDRVPB, SDRVPO,
$ SDRVPP, SDRVPT, SDRVSP, SDRVSY, SDRVSY_ROOK,
$ SDRVSY_RK, SDRVSY_AA, ILAVER, SCHKLQTP, SCHKQRT,
$ SCHKQRTP, SCHKLQT, SCHKTSQR
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
@ -188,13 +189,17 @@
* ..
* .. Allocate memory dynamically ..
*
ALLOCATE (A( ( KDMAX+1 )*NMAX, 7 ), STAT = AllocateStatus )
ALLOCATE ( A( ( KDMAX+1 )*NMAX, 7 ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (B( NMAX*MAXRHS, 4 ), STAT = AllocateStatus )
ALLOCATE ( B( NMAX*MAXRHS, 4 ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (WORK( NMAX, NMAX+MAXRHS+30 ) , STAT = AllocateStatus )
ALLOCATE ( WORK( NMAX, 3*NMAX+MAXRHS+30 ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (RWORK( 5*NMAX+2*MAXRHS ), STAT = AllocateStatus )
ALLOCATE ( E( NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( S( 2*NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( RWORK( 5*NMAX+2*MAXRHS ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
* ..
* .. Executable Statements ..
@ -920,6 +925,23 @@
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* QK: truncated QR factorization with pivoting
*
NTYPES = 19
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
IF( TSTCHK ) THEN
CALL SCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A( 1, 1 ),
$ A( 1, 2 ), B( 1, 1 ), B( 1, 2 ),
$ B( 1, 3 ), B( 1, 4 ),
$ WORK, IWORK, NOUT )
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'TZ' ) ) THEN
*

831
lapack-netlib/TESTING/LIN/schkqp3rk.f Normal file
View File

@ -0,0 +1,831 @@
*> \brief \b SCHKQP3RK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
* $ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
* $ B, COPYB, S, TAU,
* $ WORK, IWORK, NOUT )
* IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
* INTEGER NM, NN, NNS, NNB, NOUT
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
* $ NVAL( * ), NXVAL( * )
* REAL A( * ), COPYA( * ), B( * ), COPYB( * ),
* $ S( * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SCHKQP3RK tests SGEQP3RK.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*> NM is INTEGER
*> The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB and NX contained in the
*> vectors NBVAL and NXVAL. The blocking parameters are used
*> in pairs (NB,NX).
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NXVAL
*> \verbatim
*> NXVAL is INTEGER array, dimension (NNB)
*> The values of the crossover point NX.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is REAL array, dimension (MMAX*NMAX)
*> where MMAX is the maximum value of M in MVAL and NMAX is the
*> maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] COPYA
*> \verbatim
*> COPYA is REAL array, dimension (MMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is REAL array, dimension (MMAX*NSMAX)
*> where MMAX is the maximum value of M in MVAL and NSMAX is the
*> maximum value of NRHS in NSVAL.
*> \endverbatim
*>
*> \param[out] COPYB
*> \verbatim
*> COPYB is REAL array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is REAL array, dimension
*> (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is REAL array, dimension (MMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension
*> (MMAX*NMAX + 4*NMAX + MMAX)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
$ B, COPYB, S, TAU,
$ WORK, IWORK, NOUT )
IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER NM, NN, NNB, NNS, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
$ NSVAL( * ), NXVAL( * )
REAL A( * ), COPYA( * ), B( * ), COPYB( * ),
$ S( * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPES
PARAMETER ( NTYPES = 19 )
INTEGER NTESTS
PARAMETER ( NTESTS = 5 )
REAL ONE, ZERO, BIGNUM
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0,
$ BIGNUM = 1.0E+38 )
* ..
* .. Local Scalars ..
CHARACTER DIST, TYPE
CHARACTER*3 PATH
INTEGER I, IHIGH, ILOW, IM, IMAT, IN, INC_ZERO,
$ INB, IND_OFFSET_GEN,
$ IND_IN, IND_OUT, INS, INFO,
$ ISTEP, J, J_INC, J_FIRST_NZ, JB_ZERO,
$ KFACT, KL, KMAX, KU, LDA, LW, LWORK,
$ LWORK_MQR, M, MINMN, MINMNB_GEN, MODE, N,
$ NB, NB_ZERO, NERRS, NFAIL, NB_GEN, NRHS,
$ NRUN, NX, T
REAL ANORM, CNDNUM, EPS, ABSTOL, RELTOL,
$ DTEMP, MAXC2NRMK, RELMAXC2NRMK
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
REAL RESULT( NTESTS ), RDUMMY( 1 )
* ..
* .. External Functions ..
REAL SLAMCH, SQPT01, SQRT11, SQRT12, SLANGE
EXTERNAL SLAMCH, SQPT01, SQRT11, SQRT12, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, SAXPY, SGEQP3RK,
$ SLACPY, SLAORD, SLASET, SLATB4, SLATMS,
$ SORMQR, SSWAP, ICOPY, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD, REAL
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'QK'
NRUN = 0
NFAIL = 0
NERRS = 0
DO I = 1, 4
ISEED( I ) = ISEEDY( I )
END DO
EPS = SLAMCH( 'Epsilon' )
INFOT = 0
*
DO IM = 1, NM
*
* Do for each value of M in MVAL.
*
M = MVAL( IM )
LDA = MAX( 1, M )
*
DO IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
MINMN = MIN( M, N )
LWORK = MAX( 1, M*MAX( M, N )+4*MINMN+MAX( M, N ),
$ M*N + 2*MINMN + 4*N )
*
DO INS = 1, NNS
NRHS = NSVAL( INS )
*
* Set up parameters with SLATB4 and generate
* M-by-NRHS B matrix with SLATMS.
* IMAT = 14:
* Random matrix, CNDNUM = 2, NORM = ONE,
* MODE = 3 (geometric distribution of singular values).
*
CALL SLATB4( PATH, 14, M, NRHS, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'SLATMS'
CALL SLATMS( M, NRHS, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYB, LDA, WORK, INFO )
*
* Check error code from SLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M,
$ NRHS, -1, -1, -1, 6, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
DO IMAT = 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ CYCLE
*
* The type of distribution used to generate the random
* eigen-/singular values:
* ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 )
*
* Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE
* 1. Zero matrix
* 2. Random, Diagonal, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 3. Random, Upper triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 4. Random, Lower triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 5. Random, First column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 6. Random, Last MINMN column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 7. Random, Last N column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 8. Random, Middle column in MINMN is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 9. Random, First half of MINMN columns are zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 10. Random, Last columns are zero starting from MINMN/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 11. Random, Half MINMN columns in the middle are zero starting
* from MINMN/2-(MINMN/2)/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 12. Random, Odd columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 13. Random, Even columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 14. Random, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) ONE 3 ( geometric distribution of singular values )
* 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS ONE 3 ( geometric distribution of singular values )
* 17. Random, CNDNUM = 0.1/EPS, CNDNUM = BADC2 = 0.1/EPS ONE 2 ( one small singular value, S(N)=1/CNDNUM )
* one small singular value S(N)=1/CNDNUM
* 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN
* 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values )
*
IF( IMAT.EQ.1 ) THEN
*
* Matrix 1: Zero matrix
*
CALL SLASET( 'Full', M, N, ZERO, ZERO, COPYA, LDA )
DO I = 1, MINMN
S( I ) = ZERO
END DO
*
ELSE IF( (IMAT.GE.2 .AND. IMAT.LE.4 )
$ .OR. (IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN
*
* Matrices 2-5.
*
* Set up parameters with SLATB4 and generate a test
* matrix with SLATMS.
*
CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'SLATMS'
CALL SLATMS( M, N, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA, LDA, WORK, INFO )
*
* Check error code from SLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
CALL SLAORD( 'Decreasing', MINMN, S, 1 )
*
ELSE IF( MINMN.GE.2
$ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN
*
* Rectangular matrices 5-13 that contain zero columns,
* only for matrices MINMN >=2.
*
* JB_ZERO is the column index of ZERO block.
* NB_ZERO is the column block size of ZERO block.
* NB_GEN is the column blcok size of the
* generated block.
* J_INC in the non_zero column index increment
* for matrix 12 and 13.
* J_FIRS_NZ is the index of the first non-zero
* column.
*
IF( IMAT.EQ.5 ) THEN
*
* First column is zero.
*
JB_ZERO = 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.6 ) THEN
*
* Last column MINMN is zero.
*
JB_ZERO = MINMN
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.7 ) THEN
*
* Last column N is zero.
*
JB_ZERO = N
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.8 ) THEN
*
* Middle column in MINMN is zero.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.9 ) THEN
*
* First half of MINMN columns is zero.
*
JB_ZERO = 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.10 ) THEN
*
* Last columns are zero columns,
* starting from (MINMN / 2 + 1) column.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = N - JB_ZERO + 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.11 ) THEN
*
* Half of the columns in the middle of MINMN
* columns is zero, starting from
* MINMN/2 - (MINMN/2)/2 + 1 column.
*
JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.12 ) THEN
*
* Odd-numbered columns are zero,
*
NB_GEN = N / 2
NB_ZERO = N - NB_GEN
J_INC = 2
J_FIRST_NZ = 2
*
ELSE IF( IMAT.EQ.13 ) THEN
*
* Even-numbered columns are zero.
*
NB_ZERO = N / 2
NB_GEN = N - NB_ZERO
J_INC = 2
J_FIRST_NZ = 1
*
END IF
*
*
* 1) Set the first NB_ZERO columns in COPYA(1:M,1:N)
* to zero.
*
CALL SLASET( 'Full', M, NB_ZERO, ZERO, ZERO,
$ COPYA, LDA )
*
* 2) Generate an M-by-(N-NB_ZERO) matrix with the
* chosen singular value distribution
* in COPYA(1:M,NB_ZERO+1:N).
*
CALL SLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU,
$ ANORM, MODE, CNDNUM, DIST )
*
SRNAMT = 'SLATMS'
*
IND_OFFSET_GEN = NB_ZERO * LDA
*
CALL SLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA( IND_OFFSET_GEN + 1 ), LDA,
$ WORK, INFO )
*
* Check error code from SLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M,
$ NB_GEN, -1, -1, -1, IMAT, NFAIL,
$ NERRS, NOUT )
CYCLE
END IF
*
* 3) Swap the gererated colums from the right side
* NB_GEN-size block in COPYA into correct column
* positions.
*
IF( IMAT.EQ.6
$ .OR. IMAT.EQ.7
$ .OR. IMAT.EQ.8
$ .OR. IMAT.EQ.10
$ .OR. IMAT.EQ.11 ) THEN
*
* Move by swapping the generated columns
* from the right NB_GEN-size block from
* (NB_ZERO+1:NB_ZERO+JB_ZERO)
* into columns (1:JB_ZERO-1).
*
DO J = 1, JB_ZERO-1, 1
CALL SSWAP( M,
$ COPYA( ( NB_ZERO+J-1)*LDA+1), 1,
$ COPYA( (J-1)*LDA + 1 ), 1 )
END DO
*
ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN
*
* ( IMAT = 12, Odd-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the even zero colums in the
* left NB_ZERO-size block.
*
* ( IMAT = 13, Even-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the odd zero colums in the
* left NB_ZERO-size block.
*
DO J = 1, NB_GEN, 1
IND_OUT = ( NB_ZERO+J-1 )*LDA + 1
IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA
$ + 1
CALL SSWAP( M,
$ COPYA( IND_OUT ), 1,
$ COPYA( IND_IN), 1 )
END DO
*
END IF
*
* 5) Order the singular values generated by
* DLAMTS in decreasing order and add trailing zeros
* that correspond to zero columns.
* The total number of singular values is MINMN.
*
MINMNB_GEN = MIN( M, NB_GEN )
*
DO I = MINMNB_GEN+1, MINMN
S( I ) = ZERO
END DO
*
ELSE
*
* IF(MINMN.LT.2) skip this size for this matrix type.
*
CYCLE
END IF
*
* Initialize a copy array for a pivot array for SGEQP3RK.
*
DO I = 1, N
IWORK( I ) = 0
END DO
*
DO INB = 1, NNB
*
* Do for each pair of values (NB,NX) in NBVAL and NXVAL.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
*
* We do MIN(M,N)+1 because we need a test for KMAX > N,
* when KMAX is larger than MIN(M,N), KMAX should be
* KMAX = MIN(M,N)
*
DO KMAX = 0, MIN(M,N)+1
*
* Get a working copy of COPYA into A( 1:M,1:N ).
* Get a working copy of COPYB into A( 1:M, (N+1):NRHS ).
* Get a working copy of COPYB into into B( 1:M, 1:NRHS ).
* Get a working copy of IWORK(1:N) awith zeroes into
* which is going to be used as pivot array IWORK( N+1:2N ).
* NOTE: IWORK(2N+1:3N) is going to be used as a WORK array
* for the routine.
*
CALL SLACPY( 'All', M, N, COPYA, LDA, A, LDA )
CALL SLACPY( 'All', M, NRHS, COPYB, LDA,
$ A( LDA*N + 1 ), LDA )
CALL SLACPY( 'All', M, NRHS, COPYB, LDA,
$ B, LDA )
CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 )
*
ABSTOL = -1.0
RELTOL = -1.0
*
* Compute the QR factorization with pivoting of A
*
LW = MAX( 1, MAX( 2*N + NB*( N+NRHS+1 ),
$ 3*N + NRHS - 1 ) )
*
* Compute SGEQP3RK factorization of A.
*
SRNAMT = 'SGEQP3RK'
CALL SGEQP3RK( M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ A, LDA, KFACT, MAXC2NRMK,
$ RELMAXC2NRMK, IWORK( N+1 ), TAU,
$ WORK, LW, IWORK( 2*N+1 ), INFO )
*
* Check error code from SGEQP3RK.
*
IF( INFO.LT.0 )
$ CALL ALAERH( PATH, 'SGEQP3RK', INFO, 0, ' ',
$ M, N, NX, -1, NB, IMAT,
$ NFAIL, NERRS, NOUT )
*
* Compute test 1:
*
* This test in only for the full rank factorization of
* the matrix A.
*
* Array S(1:min(M,N)) contains svd(A) the sigular values
* of the original matrix A in decreasing absolute value
* order. The test computes svd(R), the vector sigular
* values of the upper trapezoid of A(1:M,1:N) that
* contains the factor R, in decreasing order. The test
* returns the ratio:
*
* 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS )
*
IF( KFACT.EQ.MINMN ) THEN
*
RESULT( 1 ) = SQRT12( M, N, A, LDA, S, WORK,
$ LWORK )
*
DO T = 1, 1
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'SGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL, NB, NX,
$ IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 1
*
END IF
*
* Compute test 2:
*
* The test returns the ratio:
*
* 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS )
*
RESULT( 2 ) = SQPT01( M, N, KFACT, COPYA, A, LDA, TAU,
$ IWORK( N+1 ), WORK, LWORK )
*
* Compute test 3:
*
* The test returns the ratio:
*
* 1-norm( Q**T * Q - I ) / ( M * EPS )
*
RESULT( 3 ) = SQRT11( M, KFACT, A, LDA, TAU, WORK,
$ LWORK )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 2, 3
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'SGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 2
*
* Compute test 4:
*
* This test is only for the factorizations with the
* rank greater than 2.
* The elements on the diagonal of R should be non-
* increasing.
*
* The test returns the ratio:
*
* Returns 1.0D+100 if abs(R(K+1,K+1)) > abs(R(K,K)),
* K=1:KFACT-1
*
IF( MIN(KFACT, MINMN).GE.2 ) THEN
*
DO J = 1, KFACT-1, 1
DTEMP = (( ABS( A( (J-1)*M+J ) ) -
$ ABS( A( (J)*M+J+1 ) ) ) /
$ ABS( A(1) ) )
*
IF( DTEMP.LT.ZERO ) THEN
RESULT( 4 ) = BIGNUM
END IF
*
END DO
*
* Print information about the tests that did not
* pass the threshold.
*
DO T = 4, 4
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'SGEQP3RK',
$ M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T,
$ RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 4.
*
END IF
*
* Compute test 5:
*
* This test in only for matrix A with min(M,N) > 0.
*
* The test returns the ratio:
*
* 1-norm(Q**T * B - Q**T * B ) /
* ( M * EPS )
*
* (1) Compute B:=Q**T * B in the matrix B.
*
IF( MINMN.GT.0 ) THEN
*
LWORK_MQR = MAX(1, NRHS)
CALL SORMQR( 'Left', 'Transpose',
$ M, NRHS, KFACT, A, LDA, TAU, B, LDA,
$ WORK, LWORK_MQR, INFO )
*
DO I = 1, NRHS
*
* Compare N+J-th column of A and J-column of B.
*
CALL SAXPY( M, -ONE, A( ( N+I-1 )*LDA+1 ), 1,
$ B( ( I-1 )*LDA+1 ), 1 )
END DO
*
RESULT( 5 ) =
$ ABS(
$ SLANGE( 'One-norm', M, NRHS, B, LDA, RDUMMY ) /
$ ( REAL( M )*SLAMCH( 'Epsilon' ) )
$ )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 5, 5
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'SGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End compute test 5.
*
END IF
*
* END DO KMAX = 1, MIN(M,N)+1
*
END DO
*
* END DO for INB = 1, NNB
*
END DO
*
* END DO for IMAT = 1, NTYPES
*
END DO
*
* END DO for INS = 1, NNS
*
END DO
*
* END DO for IN = 1, NN
*
END DO
*
* END DO for IM = 1, NM
*
END DO
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NRHS =', I5,
$ ', KMAX =', I5, ', ABSTOL =', G12.5,
$ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4,
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
*
* End of SCHKQP3RK
*
END

121
lapack-netlib/TESTING/LIN/slatb4.f
View File

@ -153,9 +153,6 @@
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. External Subroutines ..
EXTERNAL SLABAD
* ..
* .. Save statement ..
SAVE EPS, SMALL, LARGE, BADC1, BADC2, FIRST
* ..
@ -173,11 +170,6 @@
BADC1 = SQRT( BADC2 )
SMALL = SLAMCH( 'Safe minimum' )
LARGE = ONE / SMALL
*
* If it looks like we're on a Cray, take the square root of
* SMALL and LARGE to avoid overflow and underflow problems.
*
CALL SLABAD( SMALL, LARGE )
SMALL = SHRINK*( SMALL / EPS )
LARGE = ONE / SMALL
END IF
@ -232,6 +224,110 @@
ELSE
ANORM = ONE
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* xQK: truncated QR with pivoting.
* Set parameters to generate a general
* M x N matrix.
*
* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
*
TYPE = 'N'
*
* Set DIST, the type of distribution for the random
* number generator. 'S' is
*
DIST = 'S'
*
* Set the lower and upper bandwidths.
*
IF( IMAT.EQ.2 ) THEN
*
* 2. Random, Diagonal, CNDNUM = 2
*
KL = 0
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.3 ) THEN
*
* 3. Random, Upper triangular, CNDNUM = 2
*
KL = 0
KU = MAX( N-1, 0 )
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.4 ) THEN
*
* 4. Random, Lower triangular, CNDNUM = 2
*
KL = MAX( M-1, 0 )
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE
*
* 5.-19. Rectangular matrix
*
KL = MAX( M-1, 0 )
KU = MAX( N-1, 0 )
*
IF( IMAT.GE.5 .AND. IMAT.LE.14 ) THEN
*
* 5.-14. Random, CNDNUM = 2.
*
CNDNUM = TWO
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.15 ) THEN
*
* 15. Random, CNDNUM = sqrt(0.1/EPS)
*
CNDNUM = BADC1
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.16 ) THEN
*
* 16. Random, CNDNUM = 0.1/EPS
*
CNDNUM = BADC2
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.17 ) THEN
*
* 17. Random, CNDNUM = 0.1/EPS,
* one small singular value S(N)=1/CNDNUM
*
CNDNUM = BADC2
ANORM = ONE
MODE = 2
*
ELSE IF( IMAT.EQ.18 ) THEN
*
* 18. Random, scaled near underflow
*
CNDNUM = TWO
ANORM = SMALL
MODE = 3
*
ELSE IF( IMAT.EQ.19 ) THEN
*
* 19. Random, scaled near overflow
*
CNDNUM = TWO
ANORM = LARGE
MODE = 3
*
END IF
*
END IF
*
ELSE IF( LSAMEN( 2, C2, 'GE' ) ) THEN
*
@ -518,17 +614,18 @@
*
* Set the norm and condition number.
*
IF( IMAT.EQ.2 .OR. IMAT.EQ.8 ) THEN
MAT = ABS( IMAT )
IF( MAT.EQ.2 .OR. MAT.EQ.8 ) THEN
CNDNUM = BADC1
ELSE IF( IMAT.EQ.3 .OR. IMAT.EQ.9 ) THEN
ELSE IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
CNDNUM = BADC2
ELSE
CNDNUM = TWO
END IF
*
IF( IMAT.EQ.4 ) THEN
IF( MAT.EQ.4 ) THEN
ANORM = SMALL
ELSE IF( IMAT.EQ.5 ) THEN
ELSE IF( MAT.EQ.5 ) THEN
ANORM = LARGE
ELSE
ANORM = ONE

23
lapack-netlib/TESTING/LIN/sqpt01.f
View File

@ -33,7 +33,8 @@
*> Householder vectors, and the rest of AF contains a partially updated
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
*> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
*> where || . || is matrix one norm.
*> \endverbatim
*
* Arguments:
@ -172,28 +173,28 @@
*
NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
DO 30 J = 1, K
DO 10 I = 1, MIN( J, M )
DO J = 1, K
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
DO 20 I = J + 1, M
END DO
DO I = J + 1, M
WORK( ( J-1 )*M+I ) = ZERO
20 CONTINUE
30 CONTINUE
DO 40 J = K + 1, N
END DO
END DO
DO J = K + 1, N
CALL SCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
40 CONTINUE
END DO
*
CALL SORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
DO 50 J = 1, N
DO J = 1, N
*
* Compare i-th column of QR and jpvt(i)-th column of A
*
CALL SAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ),
$ 1 )
50 CONTINUE
END DO
*
SQPT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
$ ( REAL( MAX( M, N ) )*SLAMCH( 'Epsilon' ) )

4
lapack-netlib/TESTING/LIN/sqrt11.f
View File

@ -157,9 +157,9 @@
CALL SORM2R( 'Left', 'Transpose', M, M, K, A, LDA, TAU, WORK, M,
$ WORK( M*M+1 ), INFO )
*
DO 10 J = 1, M
DO J = 1, M
WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
10 CONTINUE
END DO
*
SQRT11 = SLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
$ ( REAL( M )*SLAMCH( 'Epsilon' ) )

18
lapack-netlib/TESTING/LIN/sqrt12.f
View File

@ -26,7 +26,7 @@
*> SQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
*> || svlues - s ||/(||s||*eps*max(M,N))
*> \endverbatim
*
* Arguments:
@ -113,8 +113,7 @@
EXTERNAL SASUM, SLAMCH, SLANGE, SNRM2
* ..
* .. External Subroutines ..
EXTERNAL SAXPY, SBDSQR, SGEBD2, SLABAD, SLASCL, SLASET,
$ XERBLA
EXTERNAL SAXPY, SBDSQR, SGEBD2, SLASCL, SLASET, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
@ -145,17 +144,16 @@
* Copy upper triangle of A into work
*
CALL SLASET( 'Full', M, N, ZERO, ZERO, WORK, M )
DO 20 J = 1, N
DO 10 I = 1, MIN( J, M )
DO J = 1, N
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = A( I, J )
10 CONTINUE
20 CONTINUE
END DO
END DO
*
* Get machine parameters
*
SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* Scale work if max entry outside range [SMLNUM,BIGNUM]
*
@ -199,9 +197,9 @@
*
ELSE
*
DO 30 I = 1, MN
DO I = 1, MN
WORK( M*N+I ) = ZERO
30 CONTINUE
END DO
END IF
*
* Compare s and singular values of work

59
lapack-netlib/TESTING/LIN/zchkaa.F
View File

@ -69,6 +69,7 @@
*> ZLQ 8 List types on next line if 0 < NTYPES < 8
*> ZQL 8 List types on next line if 0 < NTYPES < 8
*> ZQP 6 List types on next line if 0 < NTYPES < 6
*> ZQK 19 List types on next line if 0 < NTYPES < 19
*> ZTZ 3 List types on next line if 0 < NTYPES < 3
*> ZLS 6 List types on next line if 0 < NTYPES < 6
*> ZEQ
@ -153,12 +154,11 @@
$ NBVAL( MAXIN ), NBVAL2( MAXIN ),
$ NSVAL( MAXIN ), NVAL( MAXIN ), NXVAL( MAXIN ),
$ RANKVAL( MAXIN ), PIV( NMAX )
DOUBLE PRECISION S( 2*NMAX )
COMPLEX*16 E( NMAX )
*
* .. Allocatable Arrays ..
* ..
* .. Allocatable Arrays ..
INTEGER AllocateStatus
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE:: RWORK
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE:: RWORK, S
COMPLEX*16, DIMENSION(:), ALLOCATABLE :: E
COMPLEX*16, DIMENSION(:,:), ALLOCATABLE:: A, B, WORK
* ..
* .. External Functions ..
@ -170,15 +170,16 @@
EXTERNAL ALAREQ, ZCHKEQ, ZCHKGB, ZCHKGE, ZCHKGT, ZCHKHE,
$ ZCHKHE_ROOK, ZCHKHE_RK, ZCHKHE_AA, ZCHKHP,
$ ZCHKLQ, ZCHKUNHR_COL, ZCHKPB, ZCHKPO, ZCHKPS,
$ ZCHKPP, ZCHKPT, ZCHKQ3, ZCHKQL, ZCHKQR, ZCHKRQ,
$ ZCHKSP, ZCHKSY, ZCHKSY_ROOK, ZCHKSY_RK,
$ ZCHKSY_AA, ZCHKTB, ZCHKTP, ZCHKTR, ZCHKTZ,
$ ZDRVGB, ZDRVGE, ZDRVGT, ZDRVHE, ZDRVHE_ROOK,
$ ZDRVHE_RK, ZDRVHE_AA, ZDRVHE_AA_2STAGE, ZDRVHP,
$ ZDRVLS, ZDRVPB, ZDRVPO, ZDRVPP, ZDRVPT,
$ ZDRVSP, ZDRVSY, ZDRVSY_ROOK, ZDRVSY_RK,
$ ZDRVSY_AA, ZDRVSY_AA_2STAGE, ILAVER, ZCHKQRT,
$ ZCHKQRTP, ZCHKLQT, ZCHKLQTP, ZCHKTSQR
$ ZCHKPP, ZCHKPT, ZCHKQ3, ZCHKQP3RK, ZCHKQL,
$ ZCHKQR, ZCHKRQ, ZCHKSP, ZCHKSY, ZCHKSY_ROOK,
$ ZCHKSY_RK, ZCHKSY_AA, ZCHKTB, ZCHKTP, ZCHKTR,
$ ZCHKTZ, ZDRVGB, ZDRVGE, ZDRVGT, ZDRVHE,
$ ZDRVHE_ROOK, ZDRVHE_RK, ZDRVHE_AA,
$ ZDRVHE_AA_2STAGE, ZDRVHP, ZDRVLS, ZDRVPB,
$ ZDRVPO, ZDRVPP, ZDRVPT, ZDRVSP, ZDRVSY,
$ ZDRVSY_ROOK, ZDRVSY_RK, ZDRVSY_AA,
$ ZDRVSY_AA_2STAGE, ILAVER, ZCHKQRT, ZCHKQRTP,
$ ZCHKLQT, ZCHKLQTP, ZCHKTSQR
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
@ -197,13 +198,18 @@
DATA THREQ / 2.0D0 / , INTSTR / '0123456789' /
*
* .. Allocate memory dynamically ..
ALLOCATE (RWORK( 150*NMAX+2*MAXRHS ), STAT = AllocateStatus)
*
ALLOCATE ( A ( (KDMAX+1) * NMAX, 7 ), STAT = AllocateStatus)
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (A ((KDMAX+1) * NMAX, 7), STAT = AllocateStatus)
ALLOCATE ( B ( NMAX * MAXRHS, 4 ), STAT = AllocateStatus)
IF (AllocateStatus /= 0 ) STOP "*** Not enough memory ***"
ALLOCATE ( WORK ( NMAX, NMAX+MAXRHS+10 ), STAT = AllocateStatus)
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (B (NMAX * MAXRHS, 4), STAT = AllocateStatus)
ALLOCATE ( E( NMAX ), STAT = AllocateStatus )
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE (WORK (NMAX, NMAX+MAXRHS+10), STAT = AllocateStatus)
ALLOCATE ( S( 2*NMAX ), STAT = AllocateStatus)
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
ALLOCATE ( RWORK( 150*NMAX+2*MAXRHS ), STAT = AllocateStatus)
IF (AllocateStatus /= 0) STOP "*** Not enough memory ***"
* ..
* .. Executable Statements ..
@ -1109,6 +1115,23 @@
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* QK: truncated QR factorization with pivoting
*
NTYPES = 19
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
*
IF( TSTCHK ) THEN
CALL ZCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A( 1, 1 ),
$ A( 1, 2 ), B( 1, 1 ), B( 1, 2 ),
$ S( 1 ), B( 1, 4 ),
$ WORK, RWORK, IWORK, NOUT )
ELSE
WRITE( NOUT, FMT = 9989 )PATH
END IF
*
ELSE IF( LSAMEN( 2, C2, 'LS' ) ) THEN
*

836
lapack-netlib/TESTING/LIN/zchkqp3rk.f Normal file
View File

@ -0,0 +1,836 @@
*> \brief \b ZCHKQP3RK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
* $ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
* $ B, COPYB, S, TAU,
* $ WORK, RWORK, IWORK, NOUT )
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* INTEGER NM, NN, NNB, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
* $ NXVAL( * )
* DOUBLE PRECISION S( * ), RWORK( * )
* COMPLEX*16 A( * ), COPYA( * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCHKQP3RK tests ZGEQP3RK.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*> NM is INTEGER
*> The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB and NX contained in the
*> vectors NBVAL and NXVAL. The blocking parameters are used
*> in pairs (NB,NX).
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NXVAL
*> \verbatim
*> NXVAL is INTEGER array, dimension (NNB)
*> The values of the crossover point NX.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is DOUBLE PRECISION
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (MMAX*NMAX)
*> where MMAX is the maximum value of M in MVAL and NMAX is the
*> maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] COPYA
*> \verbatim
*> COPYA is COMPLEX*16 array, dimension (MMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (MMAX*NSMAX)
*> where MMAX is the maximum value of M in MVAL and NSMAX is the
*> maximum value of NRHS in NSVAL.
*> \endverbatim
*>
*> \param[out] COPYB
*> \verbatim
*> COPYB is COMPLEX*16 array, dimension (MMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is DOUBLE PRECISION array, dimension
*> (min(MMAX,NMAX))
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (MMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension
*> (max(M*max(M,N) + 4*min(M,N) + max(M,N)))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (4*NMAX)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL,
$ NNB, NBVAL, NXVAL, THRESH, A, COPYA,
$ B, COPYB, S, TAU,
$ WORK, RWORK, IWORK, NOUT )
IMPLICIT NONE
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER NM, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ),
$ NSVAL( * ), NXVAL( * )
DOUBLE PRECISION S( * ), RWORK( * )
COMPLEX*16 A( * ), COPYA( * ), B( * ), COPYB( * ),
$ TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPES
PARAMETER ( NTYPES = 19 )
INTEGER NTESTS
PARAMETER ( NTESTS = 5 )
DOUBLE PRECISION ONE, ZERO, BIGNUM
COMPLEX*16 CONE, CZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0,
$ CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ),
$ BIGNUM = 1.0D+38 )
* ..
* .. Local Scalars ..
CHARACTER DIST, TYPE
CHARACTER*3 PATH
INTEGER I, IHIGH, ILOW, IM, IMAT, IN, INC_ZERO,
$ INB, IND_OFFSET_GEN,
$ IND_IN, IND_OUT, INS, INFO,
$ ISTEP, J, J_INC, J_FIRST_NZ, JB_ZERO,
$ KFACT, KL, KMAX, KU, LDA, LW, LWORK,
$ LWORK_MQR, M, MINMN, MINMNB_GEN, MODE, N,
$ NB, NB_ZERO, NERRS, NFAIL, NB_GEN, NRHS,
$ NRUN, NX, T
DOUBLE PRECISION ANORM, CNDNUM, EPS, ABSTOL, RELTOL,
$ DTEMP, MAXC2NRMK, RELMAXC2NRMK
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), RDUMMY( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZQPT01, ZQRT11, ZQRT12, ZLANGE
EXTERNAL DLAMCH, ZQPT01, ZQRT11, ZQRT12, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, DLAORD, ICOPY, ZAXPY,
$ XLAENV, ZGEQP3RK, ZLACPY, ZLASET, ZLATB4,
$ ZLATMS, ZUNMQR, ZSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, MOD
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT, ZUNMQR_LWORK
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'QK'
NRUN = 0
NFAIL = 0
NERRS = 0
DO I = 1, 4
ISEED( I ) = ISEEDY( I )
END DO
EPS = DLAMCH( 'Epsilon' )
INFOT = 0
*
DO IM = 1, NM
*
* Do for each value of M in MVAL.
*
M = MVAL( IM )
LDA = MAX( 1, M )
*
DO IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
MINMN = MIN( M, N )
LWORK = MAX( 1, M*MAX( M, N )+4*MINMN+MAX( M, N ),
$ M*N + 2*MINMN + 4*N )
*
DO INS = 1, NNS
NRHS = NSVAL( INS )
*
* Set up parameters with ZLATB4 and generate
* M-by-NRHS B matrix with ZLATMS.
* IMAT = 14:
* Random matrix, CNDNUM = 2, NORM = ONE,
* MODE = 3 (geometric distribution of singular values).
*
CALL ZLATB4( PATH, 14, M, NRHS, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( M, NRHS, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYB, LDA, WORK, INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', M,
$ NRHS, -1, -1, -1, 6, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
DO IMAT = 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ CYCLE
*
* The type of distribution used to generate the random
* eigen-/singular values:
* ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 )
*
* Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE
* 1. Zero matrix
* 2. Random, Diagonal, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 3. Random, Upper triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 4. Random, Lower triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 5. Random, First column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 6. Random, Last MINMN column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 7. Random, Last N column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 8. Random, Middle column in MINMN is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 9. Random, First half of MINMN columns are zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 10. Random, Last columns are zero starting from MINMN/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 11. Random, Half MINMN columns in the middle are zero starting
* from MINMN/2-(MINMN/2)/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 12. Random, Odd columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 13. Random, Even columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 14. Random, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values )
* 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) ONE 3 ( geometric distribution of singular values )
* 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS ONE 3 ( geometric distribution of singular values )
* 17. Random, CNDNUM = 0.1/EPS, CNDNUM = BADC2 = 0.1/EPS ONE 2 ( one small singular value, S(N)=1/CNDNUM )
* one small singular value S(N)=1/CNDNUM
* 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN
* 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values )
*
IF( IMAT.EQ.1 ) THEN
*
* Matrix 1: Zero matrix
*
CALL ZLASET( 'Full', M, N, CZERO, CZERO, COPYA, LDA )
DO I = 1, MINMN
S( I ) = ZERO
END DO
*
ELSE IF( (IMAT.GE.2 .AND. IMAT.LE.4 )
$ .OR. (IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN
*
* Matrices 2-5.
*
* Set up parameters with DLATB4 and generate a test
* matrix with ZLATMS.
*
CALL ZLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( M, N, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA, LDA, WORK, INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', M, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS,
$ NOUT )
CYCLE
END IF
*
CALL DLAORD( 'Decreasing', MINMN, S, 1 )
*
ELSE IF( MINMN.GE.2
$ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN
*
* Rectangular matrices 5-13 that contain zero columns,
* only for matrices MINMN >=2.
*
* JB_ZERO is the column index of ZERO block.
* NB_ZERO is the column block size of ZERO block.
* NB_GEN is the column blcok size of the
* generated block.
* J_INC in the non_zero column index increment
* for matrix 12 and 13.
* J_FIRS_NZ is the index of the first non-zero
* column.
*
IF( IMAT.EQ.5 ) THEN
*
* First column is zero.
*
JB_ZERO = 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.6 ) THEN
*
* Last column MINMN is zero.
*
JB_ZERO = MINMN
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.7 ) THEN
*
* Last column N is zero.
*
JB_ZERO = N
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.8 ) THEN
*
* Middle column in MINMN is zero.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.9 ) THEN
*
* First half of MINMN columns is zero.
*
JB_ZERO = 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.10 ) THEN
*
* Last columns are zero columns,
* starting from (MINMN / 2 + 1) column.
*
JB_ZERO = MINMN / 2 + 1
NB_ZERO = N - JB_ZERO + 1
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.11 ) THEN
*
* Half of the columns in the middle of MINMN
* columns is zero, starting from
* MINMN/2 - (MINMN/2)/2 + 1 column.
*
JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1
NB_ZERO = MINMN / 2
NB_GEN = N - NB_ZERO
*
ELSE IF( IMAT.EQ.12 ) THEN
*
* Odd-numbered columns are zero,
*
NB_GEN = N / 2
NB_ZERO = N - NB_GEN
J_INC = 2
J_FIRST_NZ = 2
*
ELSE IF( IMAT.EQ.13 ) THEN
*
* Even-numbered columns are zero.
*
NB_ZERO = N / 2
NB_GEN = N - NB_ZERO
J_INC = 2
J_FIRST_NZ = 1
*
END IF
*
*
* 1) Set the first NB_ZERO columns in COPYA(1:M,1:N)
* to zero.
*
CALL ZLASET( 'Full', M, NB_ZERO, CZERO, CZERO,
$ COPYA, LDA )
*
* 2) Generate an M-by-(N-NB_ZERO) matrix with the
* chosen singular value distribution
* in COPYA(1:M,NB_ZERO+1:N).
*
CALL ZLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU,
$ ANORM, MODE, CNDNUM, DIST )
*
SRNAMT = 'ZLATMS'
*
IND_OFFSET_GEN = NB_ZERO * LDA
*
CALL ZLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE,
$ CNDNUM, ANORM, KL, KU, 'No packing',
$ COPYA( IND_OFFSET_GEN + 1 ), LDA,
$ WORK, INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', M,
$ NB_GEN, -1, -1, -1, IMAT, NFAIL,
$ NERRS, NOUT )
CYCLE
END IF
*
* 3) Swap the gererated colums from the right side
* NB_GEN-size block in COPYA into correct column
* positions.
*
IF( IMAT.EQ.6
$ .OR. IMAT.EQ.7
$ .OR. IMAT.EQ.8
$ .OR. IMAT.EQ.10
$ .OR. IMAT.EQ.11 ) THEN
*
* Move by swapping the generated columns
* from the right NB_GEN-size block from
* (NB_ZERO+1:NB_ZERO+JB_ZERO)
* into columns (1:JB_ZERO-1).
*
DO J = 1, JB_ZERO-1, 1
CALL ZSWAP( M,
$ COPYA( ( NB_ZERO+J-1)*LDA+1), 1,
$ COPYA( (J-1)*LDA + 1 ), 1 )
END DO
*
ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN
*
* ( IMAT = 12, Odd-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the even zero colums in the
* left NB_ZERO-size block.
*
* ( IMAT = 13, Even-numbered ZERO columns. )
* Swap the generated columns from the right
* NB_GEN-size block into the odd zero colums in the
* left NB_ZERO-size block.
*
DO J = 1, NB_GEN, 1
IND_OUT = ( NB_ZERO+J-1 )*LDA + 1
IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA
$ + 1
CALL ZSWAP( M,
$ COPYA( IND_OUT ), 1,
$ COPYA( IND_IN), 1 )
END DO
*
END IF
*
* 5) Order the singular values generated by
* DLAMTS in decreasing order and add trailing zeros
* that correspond to zero columns.
* The total number of singular values is MINMN.
*
MINMNB_GEN = MIN( M, NB_GEN )
*
CALL DLAORD( 'Decreasing', MINMNB_GEN, S, 1 )
DO I = MINMNB_GEN+1, MINMN
S( I ) = ZERO
END DO
*
ELSE
*
* IF(MINMN.LT.2) skip this size for this matrix type.
*
CYCLE
END IF
*
* Initialize a copy array for a pivot array for DGEQP3RK.
*
DO I = 1, N
IWORK( I ) = 0
END DO
*
DO INB = 1, NNB
*
* Do for each pair of values (NB,NX) in NBVAL and NXVAL.
*
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
*
* We do MIN(M,N)+1 because we need a test for KMAX > N,
* when KMAX is larger than MIN(M,N), KMAX should be
* KMAX = MIN(M,N)
*
DO KMAX = 0, MIN(M,N)+1
*
* Get a working copy of COPYA into A( 1:M,1:N ).
* Get a working copy of COPYB into A( 1:M, (N+1):NRHS ).
* Get a working copy of COPYB into into B( 1:M, 1:NRHS ).
* Get a working copy of IWORK(1:N) awith zeroes into
* which is going to be used as pivot array IWORK( N+1:2N ).
* NOTE: IWORK(2N+1:3N) is going to be used as a WORK array
* for the routine.
*
CALL ZLACPY( 'All', M, N, COPYA, LDA, A, LDA )
CALL ZLACPY( 'All', M, NRHS, COPYB, LDA,
$ A( LDA*N + 1 ), LDA )
CALL ZLACPY( 'All', M, NRHS, COPYB, LDA,
$ B, LDA )
CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 )
*
ABSTOL = -1.0
RELTOl = -1.0
*
* Compute the QR factorization with pivoting of A
*
LW = MAX( 1, MAX( 2*N + NB*( N+NRHS+1 ),
$ 3*N + NRHS - 1 ) )
*
* Compute ZGEQP3RK factorization of A.
*
SRNAMT = 'ZGEQP3RK'
CALL ZGEQP3RK( M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ A, LDA, KFACT, MAXC2NRMK,
$ RELMAXC2NRMK, IWORK( N+1 ), TAU,
$ WORK, LW, RWORK, IWORK( 2*N+1 ),
$ INFO )
*
* Check error code from ZGEQP3RK.
*
IF( INFO.LT.0 )
$ CALL ALAERH( PATH, 'ZGEQP3RK', INFO, 0, ' ',
$ M, N, NX, -1, NB, IMAT,
$ NFAIL, NERRS, NOUT )
*
IF( KFACT.EQ.MINMN ) THEN
*
* Compute test 1:
*
* This test in only for the full rank factorization of
* the matrix A.
*
* Array S(1:min(M,N)) contains svd(A) the sigular values
* of the original matrix A in decreasing absolute value
* order. The test computes svd(R), the vector sigular
* values of the upper trapezoid of A(1:M,1:N) that
* contains the factor R, in decreasing order. The test
* returns the ratio:
*
* 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS )
*
RESULT( 1 ) = ZQRT12( M, N, A, LDA, S, WORK,
$ LWORK , RWORK )
*
DO T = 1, 1
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'ZGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL, NB, NX,
$ IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 1
*
END IF
* Compute test 2:
*
* The test returns the ratio:
*
* 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS )
*
RESULT( 2 ) = ZQPT01( M, N, KFACT, COPYA, A, LDA, TAU,
$ IWORK( N+1 ), WORK, LWORK )
*
* Compute test 3:
*
* The test returns the ratio:
*
* 1-norm( Q**T * Q - I ) / ( M * EPS )
*
RESULT( 3 ) = ZQRT11( M, KFACT, A, LDA, TAU, WORK,
$ LWORK )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 2, 3
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'ZGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 2
*
* Compute test 4:
*
* This test is only for the factorizations with the
* rank greater than 2.
* The elements on the diagonal of R should be non-
* increasing.
*
* The test returns the ratio:
*
* Returns 1.0D+100 if abs(R(K+1,K+1)) > abs(R(K,K)),
* K=1:KFACT-1
*
IF( MIN(KFACT, MINMN).GE.2 ) THEN
*
DO J = 1, KFACT-1, 1
*
DTEMP = (( ABS( A( (J-1)*M+J ) ) -
$ ABS( A( (J)*M+J+1 ) ) ) /
$ ABS( A(1) ) )
*
IF( DTEMP.LT.ZERO ) THEN
RESULT( 4 ) = BIGNUM
END IF
*
END DO
*
* Print information about the tests that did not
* pass the threshold.
*
DO T = 4, 4
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'ZGEQP3RK',
$ M, N, NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T,
$ RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End test 4.
*
END IF
*
* Compute test 5:
*
* This test in only for matrix A with min(M,N) > 0.
*
* The test returns the ratio:
*
* 1-norm(Q**T * B - Q**T * B ) /
* ( M * EPS )
*
* (1) Compute B:=Q**T * B in the matrix B.
*
IF( MINMN.GT.0 ) THEN
*
LWORK_MQR = MAX(1, NRHS)
CALL ZUNMQR( 'Left', 'Conjugate transpose',
$ M, NRHS, KFACT, A, LDA, TAU, B, LDA,
$ WORK, LWORK_MQR, INFO )
*
DO I = 1, NRHS
*
* Compare N+J-th column of A and J-column of B.
*
CALL ZAXPY( M, -CONE, A( ( N+I-1 )*LDA+1 ), 1,
$ B( ( I-1 )*LDA+1 ), 1 )
END DO
*
RESULT( 5 ) =
$ ABS(
$ ZLANGE( 'One-norm', M, NRHS, B, LDA, RDUMMY ) /
$ ( DBLE( M )*DLAMCH( 'Epsilon' ) )
$ )
*
* Print information about the tests that did not pass
* the threshold.
*
DO T = 5, 5
IF( RESULT( T ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 ) 'ZGEQP3RK', M, N,
$ NRHS, KMAX, ABSTOL, RELTOL,
$ NB, NX, IMAT, T, RESULT( T )
NFAIL = NFAIL + 1
END IF
END DO
NRUN = NRUN + 1
*
* End compute test 5.
*
END IF
*
* END DO KMAX = 1, MIN(M,N)+1
*
END DO
*
* END DO for INB = 1, NNB
*
END DO
*
* END DO for IMAT = 1, NTYPES
*
END DO
*
* END DO for INS = 1, NNS
*
END DO
*
* END DO for IN = 1, NN
*
END DO
*
* END DO for IM = 1, NM
*
END DO
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NRHS =', I5,
$ ', KMAX =', I5, ', ABSTOL =', G12.5,
$ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4,
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
*
* End of ZCHKQP3RK
*
END

121
lapack-netlib/TESTING/LIN/zlatb4.f
View File

@ -154,9 +154,6 @@
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. External Subroutines ..
EXTERNAL DLABAD
* ..
* .. Save statement ..
SAVE EPS, SMALL, LARGE, BADC1, BADC2, FIRST
* ..
@ -174,11 +171,6 @@
BADC1 = SQRT( BADC2 )
SMALL = DLAMCH( 'Safe minimum' )
LARGE = ONE / SMALL
*
* If it looks like we're on a Cray, take the square root of
* SMALL and LARGE to avoid overflow and underflow problems.
*
CALL DLABAD( SMALL, LARGE )
SMALL = SHRINK*( SMALL / EPS )
LARGE = ONE / SMALL
END IF
@ -233,6 +225,110 @@
ELSE
ANORM = ONE
END IF
*
ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
*
* xQK: truncated QR with pivoting.
* Set parameters to generate a general
* M x N matrix.
*
* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
*
TYPE = 'N'
*
* Set DIST, the type of distribution for the random
* number generator. 'S' is
*
DIST = 'S'
*
* Set the lower and upper bandwidths.
*
IF( IMAT.EQ.2 ) THEN
*
* 2. Random, Diagonal, CNDNUM = 2
*
KL = 0
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.3 ) THEN
*
* 3. Random, Upper triangular, CNDNUM = 2
*
KL = 0
KU = MAX( N-1, 0 )
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE IF( IMAT.EQ.4 ) THEN
*
* 4. Random, Lower triangular, CNDNUM = 2
*
KL = MAX( M-1, 0 )
KU = 0
CNDNUM = TWO
ANORM = ONE
MODE = 3
ELSE
*
* 5.-19. Rectangular matrix
*
KL = MAX( M-1, 0 )
KU = MAX( N-1, 0 )
*
IF( IMAT.GE.5 .AND. IMAT.LE.14 ) THEN
*
* 5.-14. Random, CNDNUM = 2.
*
CNDNUM = TWO
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.15 ) THEN
*
* 15. Random, CNDNUM = sqrt(0.1/EPS)
*
CNDNUM = BADC1
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.16 ) THEN
*
* 16. Random, CNDNUM = 0.1/EPS
*
CNDNUM = BADC2
ANORM = ONE
MODE = 3
*
ELSE IF( IMAT.EQ.17 ) THEN
*
* 17. Random, CNDNUM = 0.1/EPS,
* one small singular value S(N)=1/CNDNUM
*
CNDNUM = BADC2
ANORM = ONE
MODE = 2
*
ELSE IF( IMAT.EQ.18 ) THEN
*
* 18. Random, scaled near underflow
*
CNDNUM = TWO
ANORM = SMALL
MODE = 3
*
ELSE IF( IMAT.EQ.19 ) THEN
*
* 19. Random, scaled near overflow
*
CNDNUM = TWO
ANORM = LARGE
MODE = 3
*
END IF
*
END IF
*
ELSE IF( LSAMEN( 2, C2, 'GE' ) ) THEN
*
@ -517,17 +613,18 @@
*
* Set the norm and condition number.
*
IF( IMAT.EQ.2 .OR. IMAT.EQ.8 ) THEN
MAT = ABS( IMAT )
IF( MAT.EQ.2 .OR. MAT.EQ.8 ) THEN
CNDNUM = BADC1
ELSE IF( IMAT.EQ.3 .OR. IMAT.EQ.9 ) THEN
ELSE IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
CNDNUM = BADC2
ELSE
CNDNUM = TWO
END IF
*
IF( IMAT.EQ.4 ) THEN
IF( MAT.EQ.4 ) THEN
ANORM = SMALL
ELSE IF( IMAT.EQ.5 ) THEN
ELSE IF( MAT.EQ.5 ) THEN
ANORM = LARGE
ELSE
ANORM = ONE

22
lapack-netlib/TESTING/LIN/zqpt01.f
View File

@ -33,7 +33,7 @@
*> Householder vectors, and the rest of AF contains a partially updated
*> matrix.
*>
*> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
*> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
*> \endverbatim
*
* Arguments:
@ -172,28 +172,28 @@
*
NORMA = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
DO 30 J = 1, K
DO 10 I = 1, MIN( J, M )
DO J = 1, K
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
DO 20 I = J + 1, M
END DO
DO I = J + 1, M
WORK( ( J-1 )*M+I ) = ZERO
20 CONTINUE
30 CONTINUE
DO 40 J = K + 1, N
END DO
END DO
DO J = K + 1, N
CALL ZCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 )
40 CONTINUE
END DO
*
CALL ZUNMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK,
$ M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
DO 50 J = 1, N
DO J = 1, N
*
* Compare i-th column of QR and jpvt(i)-th column of A
*
CALL ZAXPY( M, DCMPLX( -ONE ), A( 1, JPVT( J ) ), 1,
$ WORK( ( J-1 )*M+1 ), 1 )
50 CONTINUE
END DO
*
ZQPT01 = ZLANGE( 'One-norm', M, N, WORK, M, RWORK ) /
$ ( DBLE( MAX( M, N ) )*DLAMCH( 'Epsilon' ) )

4
lapack-netlib/TESTING/LIN/zqrt11.f
View File

@ -158,9 +158,9 @@
CALL ZUNM2R( 'Left', 'Conjugate transpose', M, M, K, A, LDA, TAU,
$ WORK, M, WORK( M*M+1 ), INFO )
*
DO 10 J = 1, M
DO J = 1, M
WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
10 CONTINUE
END DO
*
ZQRT11 = ZLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
$ ( DBLE( M )*DLAMCH( 'Epsilon' ) )

20
lapack-netlib/TESTING/LIN/zqrt12.f
View File

@ -28,7 +28,7 @@
*> ZQRT12 computes the singular values `svlues' of the upper trapezoid
*> of A(1:M,1:N) and returns the ratio
*>
*> || s - svlues||/(||svlues||*eps*max(M,N))
*> || svlues - s||/(||s||*eps*max(M,N))
*> \endverbatim
*
* Arguments:
@ -125,8 +125,8 @@
EXTERNAL DASUM, DLAMCH, DNRM2, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DBDSQR, DLABAD, DLASCL, XERBLA, ZGEBD2,
$ ZLASCL, ZLASET
EXTERNAL DAXPY, DBDSQR, DLASCL, XERBLA, ZGEBD2, ZLASCL,
$ ZLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX, MIN
@ -154,17 +154,16 @@
*
CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK,
$ M )
DO 20 J = 1, N
DO 10 I = 1, MIN( J, M )
DO J = 1, N
DO I = 1, MIN( J, M )
WORK( ( J-1 )*M+I ) = A( I, J )
10 CONTINUE
20 CONTINUE
END DO
END DO
*
* Get machine parameters
*
SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* Scale work if max entry outside range [SMLNUM,BIGNUM]
*
@ -208,9 +207,9 @@
*
ELSE
*
DO 30 I = 1, MN
DO I = 1, MN
RWORK( I ) = ZERO
30 CONTINUE
END DO
END IF
*
* Compare s and singular values of work
@ -218,6 +217,7 @@
CALL DAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 )
ZQRT12 = DASUM( MN, RWORK( 1 ), 1 ) /
$ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
*
IF( NRMSVL.NE.ZERO )
$ ZQRT12 = ZQRT12 / NRMSVL
*