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00001 *> \brief \b ZCKCSD
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE ZCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
00012 *                          MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
00013 *                          WORK, RWORK, NIN, NOUT, INFO )
00014 * 
00015 *       .. Scalar Arguments ..
00016 *       INTEGER            INFO, NIN, NM, NMATS, MMAX, NOUT
00017 *       DOUBLE PRECISION   THRESH
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
00021 *      $                   QVAL( * )
00022 *       DOUBLE PRECISION   RWORK( * ), THETA( * )
00023 *       COMPLEX*16         U1( * ), U2( * ), V1T( * ), V2T( * ),
00024 *      $                   WORK( * ), X( * ), XF( * )
00025 *       ..
00026 *  
00027 *
00028 *> \par Purpose:
00029 *  =============
00030 *>
00031 *> \verbatim
00032 *>
00033 *> ZCKCSD tests ZUNCSD:
00034 *>        the CSD for an M-by-M unitary matrix X partitioned as
00035 *>        [ X11 X12; X21 X22 ]. X11 is P-by-Q.
00036 *> \endverbatim
00037 *
00038 *  Arguments:
00039 *  ==========
00040 *
00041 *> \param[in] NM
00042 *> \verbatim
00043 *>          NM is INTEGER
00044 *>          The number of values of M contained in the vector MVAL.
00045 *> \endverbatim
00046 *>
00047 *> \param[in] MVAL
00048 *> \verbatim
00049 *>          MVAL is INTEGER array, dimension (NM)
00050 *>          The values of the matrix row dimension M.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] PVAL
00054 *> \verbatim
00055 *>          PVAL is INTEGER array, dimension (NM)
00056 *>          The values of the matrix row dimension P.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] QVAL
00060 *> \verbatim
00061 *>          QVAL is INTEGER array, dimension (NM)
00062 *>          The values of the matrix column dimension Q.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] NMATS
00066 *> \verbatim
00067 *>          NMATS is INTEGER
00068 *>          The number of matrix types to be tested for each combination
00069 *>          of matrix dimensions.  If NMATS >= NTYPES (the maximum
00070 *>          number of matrix types), then all the different types are
00071 *>          generated for testing.  If NMATS < NTYPES, another input line
00072 *>          is read to get the numbers of the matrix types to be used.
00073 *> \endverbatim
00074 *>
00075 *> \param[in,out] ISEED
00076 *> \verbatim
00077 *>          ISEED is INTEGER array, dimension (4)
00078 *>          On entry, the seed of the random number generator.  The array
00079 *>          elements should be between 0 and 4095, otherwise they will be
00080 *>          reduced mod 4096, and ISEED(4) must be odd.
00081 *>          On exit, the next seed in the random number sequence after
00082 *>          all the test matrices have been generated.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] THRESH
00086 *> \verbatim
00087 *>          THRESH is DOUBLE PRECISION
00088 *>          The threshold value for the test ratios.  A result is
00089 *>          included in the output file if RESULT >= THRESH.  To have
00090 *>          every test ratio printed, use THRESH = 0.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] MMAX
00094 *> \verbatim
00095 *>          MMAX is INTEGER
00096 *>          The maximum value permitted for M, used in dimensioning the
00097 *>          work arrays.
00098 *> \endverbatim
00099 *>
00100 *> \param[out] X
00101 *> \verbatim
00102 *>          X is COMPLEX*16 array, dimension (MMAX*MMAX)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] XF
00106 *> \verbatim
00107 *>          XF is COMPLEX*16 array, dimension (MMAX*MMAX)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] U1
00111 *> \verbatim
00112 *>          U1 is COMPLEX*16 array, dimension (MMAX*MMAX)
00113 *> \endverbatim
00114 *>
00115 *> \param[out] U2
00116 *> \verbatim
00117 *>          U2 is COMPLEX*16 array, dimension (MMAX*MMAX)
00118 *> \endverbatim
00119 *>
00120 *> \param[out] V1T
00121 *> \verbatim
00122 *>          V1T is COMPLEX*16 array, dimension (MMAX*MMAX)
00123 *> \endverbatim
00124 *>
00125 *> \param[out] V2T
00126 *> \verbatim
00127 *>          V2T is COMPLEX*16 array, dimension (MMAX*MMAX)
00128 *> \endverbatim
00129 *>
00130 *> \param[out] THETA
00131 *> \verbatim
00132 *>          THETA is DOUBLE PRECISION array, dimension (MMAX)
00133 *> \endverbatim
00134 *>
00135 *> \param[out] IWORK
00136 *> \verbatim
00137 *>          IWORK is INTEGER array, dimension (MMAX)
00138 *> \endverbatim
00139 *>
00140 *> \param[out] WORK
00141 *> \verbatim
00142 *>          WORK is COMPLEX*16 array
00143 *> \endverbatim
00144 *>
00145 *> \param[out] RWORK
00146 *> \verbatim
00147 *>          RWORK is DOUBLE PRECISION array
00148 *> \endverbatim
00149 *>
00150 *> \param[in] NIN
00151 *> \verbatim
00152 *>          NIN is INTEGER
00153 *>          The unit number for input.
00154 *> \endverbatim
00155 *>
00156 *> \param[in] NOUT
00157 *> \verbatim
00158 *>          NOUT is INTEGER
00159 *>          The unit number for output.
00160 *> \endverbatim
00161 *>
00162 *> \param[out] INFO
00163 *> \verbatim
00164 *>          INFO is INTEGER
00165 *>          = 0 :  successful exit
00166 *>          > 0 :  If ZLAROR returns an error code, the absolute value
00167 *>                 of it is returned.
00168 *> \endverbatim
00169 *
00170 *  Authors:
00171 *  ========
00172 *
00173 *> \author Univ. of Tennessee 
00174 *> \author Univ. of California Berkeley 
00175 *> \author Univ. of Colorado Denver 
00176 *> \author NAG Ltd. 
00177 *
00178 *> \date November 2011
00179 *
00180 *> \ingroup complex16_eig
00181 *
00182 *  =====================================================================
00183       SUBROUTINE ZCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
00184      $                   MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK,
00185      $                   WORK, RWORK, NIN, NOUT, INFO )
00186 *
00187 *  -- LAPACK test routine (version 3.4.0) --
00188 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00189 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00190 *     November 2011
00191 *
00192 *     .. Scalar Arguments ..
00193       INTEGER            INFO, NIN, NM, NMATS, MMAX, NOUT
00194       DOUBLE PRECISION   THRESH
00195 *     ..
00196 *     .. Array Arguments ..
00197       INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
00198      $                   QVAL( * )
00199       DOUBLE PRECISION   RWORK( * ), THETA( * )
00200       COMPLEX*16         U1( * ), U2( * ), V1T( * ), V2T( * ),
00201      $                   WORK( * ), X( * ), XF( * )
00202 *     ..
00203 *
00204 *  =====================================================================
00205 *
00206 *     .. Parameters ..
00207       INTEGER            NTESTS
00208       PARAMETER          ( NTESTS = 9 )
00209       INTEGER            NTYPES
00210       PARAMETER          ( NTYPES = 3 )
00211       DOUBLE PRECISION   GAPDIGIT, ORTH, PIOVER2, TEN
00212       PARAMETER          ( GAPDIGIT = 18.0D0, ORTH = 1.0D-12,
00213      $                     PIOVER2 = 1.57079632679489662D0,
00214      $                     TEN = 10.0D0 )
00215       COMPLEX*16         ZERO, ONE
00216       PARAMETER          ( ZERO = (0.0D0,0.0D0), ONE = (1.0D0,0.0D0) )
00217 *     ..
00218 *     .. Local Scalars ..
00219       LOGICAL            FIRSTT
00220       CHARACTER*3        PATH
00221       INTEGER            I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T,
00222      $                   LDV2T, LDX, LWORK, M, NFAIL, NRUN, NT, P, Q, R
00223 *     ..
00224 *     .. Local Arrays ..
00225       LOGICAL            DOTYPE( NTYPES )
00226       DOUBLE PRECISION   RESULT( NTESTS )
00227 *     ..
00228 *     .. External Subroutines ..
00229       EXTERNAL           ALAHDG, ALAREQ, ALASUM, ZCSDTS, ZLACSG, ZLAROR,
00230      $                   ZLASET
00231 *     ..
00232 *     .. Intrinsic Functions ..
00233       INTRINSIC          ABS, MIN
00234 *     ..
00235 *     .. External Functions ..
00236       DOUBLE PRECISION   DLARND
00237       EXTERNAL           DLARND
00238 *     ..
00239 *     .. Executable Statements ..
00240 *
00241 *     Initialize constants and the random number seed.
00242 *
00243       PATH( 1: 3 ) = 'CSD'
00244       INFO = 0
00245       NRUN = 0
00246       NFAIL = 0
00247       FIRSTT = .TRUE.
00248       CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
00249       LDX = MMAX
00250       LDU1 = MMAX
00251       LDU2 = MMAX
00252       LDV1T = MMAX
00253       LDV2T = MMAX
00254       LWORK = MMAX*MMAX
00255 *
00256 *     Do for each value of M in MVAL.
00257 *
00258       DO 30 IM = 1, NM
00259          M = MVAL( IM )
00260          P = PVAL( IM )
00261          Q = QVAL( IM )
00262 *
00263          DO 20 IMAT = 1, NTYPES
00264 *
00265 *           Do the tests only if DOTYPE( IMAT ) is true.
00266 *
00267             IF( .NOT.DOTYPE( IMAT ) )
00268      $         GO TO 20
00269 *
00270 *           Generate X
00271 *
00272             IF( IMAT.EQ.1 ) THEN
00273                CALL ZLAROR( 'L', 'I', M, M, X, LDX, ISEED, WORK, IINFO )
00274                IF( M .NE. 0 .AND. IINFO .NE. 0 ) THEN
00275                   WRITE( NOUT, FMT = 9999 ) M, IINFO
00276                   INFO = ABS( IINFO )
00277                   GO TO 20
00278                END IF
00279             ELSE IF( IMAT.EQ.2 ) THEN
00280                R = MIN( P, M-P, Q, M-Q )
00281                DO I = 1, R
00282                   THETA(I) = PIOVER2 * DLARND( 1, ISEED )
00283                END DO
00284                CALL ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00285                DO I = 1, M
00286                   DO J = 1, M
00287                      X(I+(J-1)*LDX) = X(I+(J-1)*LDX) +
00288      $                                ORTH*DLARND(2,ISEED)
00289                   END DO
00290                END DO
00291             ELSE
00292                R = MIN( P, M-P, Q, M-Q )
00293                DO I = 1, R+1
00294                   THETA(I) = TEN**(-DLARND(1,ISEED)*GAPDIGIT)
00295                END DO
00296                DO I = 2, R+1
00297                   THETA(I) = THETA(I-1) + THETA(I)
00298                END DO
00299                DO I = 1, R
00300                   THETA(I) = PIOVER2 * THETA(I) / THETA(R+1)
00301                END DO
00302                CALL ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00303             END IF
00304 *
00305             NT = 9
00306 *
00307             CALL ZCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
00308      $                   LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
00309      $                   RWORK, RESULT )
00310 *
00311 *           Print information about the tests that did not
00312 *           pass the threshold.
00313 *
00314             DO 10 I = 1, NT
00315                IF( RESULT( I ).GE.THRESH ) THEN
00316                   IF( NFAIL.EQ.0 .AND. FIRSTT ) THEN
00317                      FIRSTT = .FALSE.
00318                      CALL ALAHDG( NOUT, PATH )
00319                   END IF
00320                   WRITE( NOUT, FMT = 9998 )M, P, Q, IMAT, I,
00321      $               RESULT( I )
00322                   NFAIL = NFAIL + 1
00323                END IF
00324    10       CONTINUE
00325             NRUN = NRUN + NT
00326    20    CONTINUE
00327    30 CONTINUE
00328 *
00329 *     Print a summary of the results.
00330 *
00331       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, 0 )
00332 *
00333  9999 FORMAT( ' ZLAROR in ZCKCSD: M = ', I5, ', INFO = ', I15 )
00334  9998 FORMAT( ' M=', I4, ' P=', I4, ', Q=', I4, ', type ', I2,
00335      $      ', test ', I2, ', ratio=', G13.6 )
00336       RETURN
00337 *
00338 *     End of ZCKCSD
00339 *
00340       END
00341 *
00342 *
00343 *
00344       SUBROUTINE ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00345       IMPLICIT NONE
00346 *
00347       INTEGER            LDX, M, P, Q
00348       INTEGER            ISEED( 4 )
00349       DOUBLE PRECISION   THETA( * )
00350       COMPLEX*16         WORK( * ), X( LDX, * )
00351 *
00352       COMPLEX*16         ONE, ZERO
00353       PARAMETER          ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) )
00354 *
00355       INTEGER            I, INFO, R
00356 *
00357       R = MIN( P, M-P, Q, M-Q )
00358 *
00359       CALL ZLASET( 'Full', M, M, ZERO, ZERO, X, LDX )
00360 *
00361       DO I = 1, MIN(P,Q)-R
00362          X(I,I) = ONE
00363       END DO
00364       DO I = 1, R
00365          X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) = DCMPLX( COS(THETA(I)), 0.0D0 )
00366       END DO
00367       DO I = 1, MIN(P,M-Q)-R
00368          X(P-I+1,M-I+1) = -ONE
00369       END DO
00370       DO I = 1, R
00371          X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) =
00372      $      DCMPLX( -SIN(THETA(R-I+1)), 0.0D0 )
00373       END DO
00374       DO I = 1, MIN(M-P,Q)-R
00375          X(M-I+1,Q-I+1) = ONE
00376       END DO
00377       DO I = 1, R
00378          X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) =
00379      $      DCMPLX( SIN(THETA(R-I+1)), 0.0D0 )
00380       END DO
00381       DO I = 1, MIN(M-P,M-Q)-R
00382          X(P+I,Q+I) = ONE
00383       END DO
00384       DO I = 1, R
00385          X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) =
00386      $      DCMPLX( COS(THETA(I)), 0.0D0 )
00387       END DO
00388       CALL ZLAROR( 'Left', 'No init', P, M, X, LDX, ISEED, WORK, INFO )
00389       CALL ZLAROR( 'Left', 'No init', M-P, M, X(P+1,1), LDX,
00390      $             ISEED, WORK, INFO )
00391       CALL ZLAROR( 'Right', 'No init', M, Q, X, LDX, ISEED,
00392      $             WORK, INFO )
00393       CALL ZLAROR( 'Right', 'No init', M, M-Q,
00394      $             X(1,Q+1), LDX, ISEED, WORK, INFO )
00395 *
00396       END
00397