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SUBROUTINE CCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
$ MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
$ WORK, RWORK, NIN, NOUT, INFO )
IMPLICIT NONE
*
* Originally CCKGSV
* -- LAPACK test routine (version 3.3.0) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2010
*
* Adapted to CCKCSD
* July 2010
*
* .. Scalar Arguments ..
INTEGER INFO, NIN, NM, NMATS, MMAX, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
$ QVAL( * )
REAL RWORK( * ), THETA( * )
COMPLEX U1( * ), U2( * ), V1T( * ), V2T( * ),
$ WORK( * ), X( * ), XF( * )
* ..
*
* Purpose
* =======
*
* CCKCSD tests CUNCSD:
* the CSD for an M-by-M unitary matrix X partitioned as
* [ X11 X12; X21 X22 ]. X11 is P-by-Q.
*
* Arguments
* =========
*
* NM (input) INTEGER
* The number of values of M contained in the vector MVAL.
*
* MVAL (input) INTEGER array, dimension (NM)
* The values of the matrix row dimension M.
*
* PVAL (input) INTEGER array, dimension (NM)
* The values of the matrix row dimension P.
*
* QVAL (input) INTEGER array, dimension (NM)
* The values of the matrix column dimension Q.
*
* NMATS (input) INTEGER
* The number of matrix types to be tested for each combination
* of matrix dimensions. If NMATS >= NTYPES (the maximum
* number of matrix types), then all the different types are
* generated for testing. If NMATS < NTYPES, another input line
* is read to get the numbers of the matrix types to be used.
*
* ISEED (input/output) INTEGER array, dimension (4)
* On entry, the seed of the random number generator. The array
* elements should be between 0 and 4095, otherwise they will be
* reduced mod 4096, and ISEED(4) must be odd.
* On exit, the next seed in the random number sequence after
* all the test matrices have been generated.
*
* THRESH (input) 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.
*
* MMAX (input) INTEGER
* The maximum value permitted for M, used in dimensioning the
* work arrays.
*
* X (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* XF (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* U1 (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* U2 (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* V1T (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* V2T (workspace) COMPLEX array, dimension (MMAX*MMAX)
*
* THETA (workspace) REAL array, dimension (MMAX)
*
* IWORK (workspace) INTEGER array, dimension (MMAX)
*
* WORK (workspace) COMPLEX array
*
* RWORK (workspace) REAL array
*
* NIN (input) INTEGER
* The unit number for input.
*
* NOUT (input) INTEGER
* The unit number for output.
*
* INFO (output) INTEGER
* = 0 : successful exit
* > 0 : If CLAROR returns an error code, the absolute value
* of it is returned.
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTESTS
PARAMETER ( NTESTS = 9 )
INTEGER NTYPES
PARAMETER ( NTYPES = 3 )
REAL GAPDIGIT, ORTH, PIOVER2, TEN
PARAMETER ( GAPDIGIT = 10.0E0, ORTH = 1.0E-4,
$ PIOVER2 = 1.57079632679489662E0,
$ TEN = 10.0D0 )
COMPLEX ZERO, ONE
PARAMETER ( ZERO = (0.0E0,0.0E0), ONE = (1.0E0,0.0E0) )
* ..
* .. Local Scalars ..
LOGICAL FIRSTT
CHARACTER*3 PATH
INTEGER I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T,
$ LDV2T, LDX, LWORK, M, NFAIL, NRUN, NT, P, Q, R
* ..
* .. Local Arrays ..
LOGICAL DOTYPE( NTYPES )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Subroutines ..
EXTERNAL ALAHDG, ALAREQ, ALASUM, CCSDTS, CLACSG, CLAROR,
$ CLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, COS, MIN, SIN
* ..
* .. External Functions ..
REAL CLANGE, SLARND
EXTERNAL CLANGE, SLARND
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 3 ) = 'CSD'
INFO = 0
NRUN = 0
NFAIL = 0
FIRSTT = .TRUE.
CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
LDX = MMAX
LDU1 = MMAX
LDU2 = MMAX
LDV1T = MMAX
LDV2T = MMAX
LWORK = MMAX*MMAX
*
* Do for each value of M in MVAL.
*
DO 30 IM = 1, NM
M = MVAL( IM )
P = PVAL( IM )
Q = QVAL( IM )
*
DO 20 IMAT = 1, NTYPES
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 20
*
* Generate X
*
IF( IMAT.EQ.1 ) THEN
CALL CLAROR( 'L', 'I', M, M, X, LDX, ISEED, WORK, IINFO )
IF( M .NE. 0 .AND. IINFO .NE. 0 ) THEN
WRITE( NOUT, FMT = 9999 ) M, IINFO
INFO = ABS( IINFO )
GO TO 20
END IF
ELSE IF( IMAT.EQ.2 ) THEN
R = MIN( P, M-P, Q, M-Q )
DO I = 1, R
THETA(I) = PIOVER2 * SLARND( 1, ISEED )
END DO
CALL CLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
DO I = 1, M
DO J = 1, M
X(I+(J-1)*LDX) = X(I+(J-1)*LDX) +
$ ORTH*SLARND(2,ISEED)
END DO
END DO
ELSE
R = MIN( P, M-P, Q, M-Q )
DO I = 1, R+1
THETA(I) = TEN**(-SLARND(1,ISEED)*GAPDIGIT)
END DO
DO I = 2, R+1
THETA(I) = THETA(I-1) + THETA(I)
END DO
DO I = 1, R
THETA(I) = PIOVER2 * THETA(I) / THETA(R+1)
END DO
CALL CLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
END IF
*
NT = 9
*
CALL CCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
$ LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
$ RWORK, RESULT )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 10 I = 1, NT
IF( RESULT( I ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. FIRSTT ) THEN
FIRSTT = .FALSE.
CALL ALAHDG( NOUT, PATH )
END IF
WRITE( NOUT, FMT = 9998 )M, P, Q, IMAT, I,
$ RESULT( I )
NFAIL = NFAIL + 1
END IF
10 CONTINUE
NRUN = NRUN + NT
20 CONTINUE
30 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, 0 )
*
9999 FORMAT( ' CLAROR in CCKCSD: M = ', I5, ', INFO = ', I15 )
9998 FORMAT( ' M=', I4, ' P=', I4, ', Q=', I4, ', type ', I2,
$ ', test ', I2, ', ratio=', G13.6 )
RETURN
*
* End of CCKCSD
*
END
*
*
*
SUBROUTINE CLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
IMPLICIT NONE
*
INTEGER LDX, M, P, Q
INTEGER ISEED( 4 )
REAL THETA( * )
COMPLEX WORK( * ), X( LDX, * )
*
COMPLEX ONE, ZERO
PARAMETER ( ONE = (1.0E0,0.0E0), ZERO = (0.0E0,0.0E0) )
*
INTEGER I, INFO, R
*
R = MIN( P, M-P, Q, M-Q )
*
CALL CLASET( 'Full', M, M, ZERO, ZERO, X, LDX )
*
DO I = 1, MIN(P,Q)-R
X(I,I) = ONE
END DO
DO I = 1, R
X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) = CMPLX ( COS(THETA(I)), 0.0E0 )
END DO
DO I = 1, MIN(P,M-Q)-R
X(P-I+1,M-I+1) = -ONE
END DO
DO I = 1, R
X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) =
$ CMPLX( -SIN(THETA(R-I+1)), 0.0E0 )
END DO
DO I = 1, MIN(M-P,Q)-R
X(M-I+1,Q-I+1) = ONE
END DO
DO I = 1, R
X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) =
$ CMPLX( SIN(THETA(R-I+1)), 0.0E0 )
END DO
DO I = 1, MIN(M-P,M-Q)-R
X(P+I,Q+I) = ONE
END DO
DO I = 1, R
X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) =
$ CMPLX( COS(THETA(I)), 0.0E0 )
END DO
CALL CLAROR( 'Left', 'No init', P, M, X, LDX, ISEED, WORK, INFO )
CALL CLAROR( 'Left', 'No init', M-P, M, X(P+1,1), LDX,
$ ISEED, WORK, INFO )
CALL CLAROR( 'Right', 'No init', M, Q, X, LDX, ISEED,
$ WORK, INFO )
CALL CLAROR( 'Right', 'No init', M, M-Q,
$ X(1,Q+1), LDX, ISEED, WORK, INFO )
*
END
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