LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sckcsd.f
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00001 *> \brief \b SCKCSD
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 SCKCSD( 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 *       REAL               THRESH
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
00021 *      $                   QVAL( * )
00022 *       REAL               RWORK( * ), THETA( * )
00023 *       REAL               U1( * ), U2( * ), V1T( * ), V2T( * ),
00024 *      $                   WORK( * ), X( * ), XF( * )
00025 *       ..
00026 *  
00027 *
00028 *> \par Purpose:
00029 *  =============
00030 *>
00031 *> \verbatim
00032 *>
00033 *> SCKCSD tests SORCSD:
00034 *>        the CSD for an M-by-M orthogonal 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 REAL
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 REAL array, dimension (MMAX*MMAX)
00103 *> \endverbatim
00104 *>
00105 *> \param[out] XF
00106 *> \verbatim
00107 *>          XF is REAL array, dimension (MMAX*MMAX)
00108 *> \endverbatim
00109 *>
00110 *> \param[out] U1
00111 *> \verbatim
00112 *>          U1 is REAL array, dimension (MMAX*MMAX)
00113 *> \endverbatim
00114 *>
00115 *> \param[out] U2
00116 *> \verbatim
00117 *>          U2 is REAL array, dimension (MMAX*MMAX)
00118 *> \endverbatim
00119 *>
00120 *> \param[out] V1T
00121 *> \verbatim
00122 *>          V1T is REAL array, dimension (MMAX*MMAX)
00123 *> \endverbatim
00124 *>
00125 *> \param[out] V2T
00126 *> \verbatim
00127 *>          V2T is REAL array, dimension (MMAX*MMAX)
00128 *> \endverbatim
00129 *>
00130 *> \param[out] THETA
00131 *> \verbatim
00132 *>          THETA is REAL 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 REAL array
00143 *> \endverbatim
00144 *>
00145 *> \param[out] RWORK
00146 *> \verbatim
00147 *>          RWORK is REAL 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 SLAROR 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 single_eig
00181 *
00182 *  =====================================================================
00183       SUBROUTINE SCKCSD( 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       REAL               THRESH
00195 *     ..
00196 *     .. Array Arguments ..
00197       INTEGER            ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ),
00198      $                   QVAL( * )
00199       REAL               RWORK( * ), THETA( * )
00200       REAL               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       REAL               GAPDIGIT, ORTH, PIOVER2, TEN
00212       PARAMETER          ( GAPDIGIT = 10.0E0, ORTH = 1.0E-4,
00213      $                     PIOVER2 = 1.57079632679489662E0,
00214      $                     TEN = 10.0D0 )
00215 *     ..
00216 *     .. Local Scalars ..
00217       LOGICAL            FIRSTT
00218       CHARACTER*3        PATH
00219       INTEGER            I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T,
00220      $                   LDV2T, LDX, LWORK, M, NFAIL, NRUN, NT, P, Q, R
00221 *     ..
00222 *     .. Local Arrays ..
00223       LOGICAL            DOTYPE( NTYPES )
00224       REAL               RESULT( NTESTS )
00225 *     ..
00226 *     .. External Subroutines ..
00227       EXTERNAL           ALAHDG, ALAREQ, ALASUM, SCSDTS, SLACSG, SLAROR,
00228      $                   SLASET
00229 *     ..
00230 *     .. Intrinsic Functions ..
00231       INTRINSIC          ABS, MIN
00232 *     ..
00233 *     .. External Functions ..
00234       REAL               SLARND
00235       EXTERNAL           SLARND
00236 *     ..
00237 *     .. Executable Statements ..
00238 *
00239 *     Initialize constants and the random number seed.
00240 *
00241       PATH( 1: 3 ) = 'CSD'
00242       INFO = 0
00243       NRUN = 0
00244       NFAIL = 0
00245       FIRSTT = .TRUE.
00246       CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT )
00247       LDX = MMAX
00248       LDU1 = MMAX
00249       LDU2 = MMAX
00250       LDV1T = MMAX
00251       LDV2T = MMAX
00252       LWORK = MMAX*MMAX
00253 *
00254 *     Do for each value of M in MVAL.
00255 *
00256       DO 30 IM = 1, NM
00257          M = MVAL( IM )
00258          P = PVAL( IM )
00259          Q = QVAL( IM )
00260 *
00261          DO 20 IMAT = 1, NTYPES
00262 *
00263 *           Do the tests only if DOTYPE( IMAT ) is true.
00264 *
00265             IF( .NOT.DOTYPE( IMAT ) )
00266      $         GO TO 20
00267 *
00268 *           Generate X
00269 *
00270             IF( IMAT.EQ.1 ) THEN
00271                CALL SLAROR( 'L', 'I', M, M, X, LDX, ISEED, WORK, IINFO )
00272                IF( M .NE. 0 .AND. IINFO .NE. 0 ) THEN
00273                   WRITE( NOUT, FMT = 9999 ) M, IINFO
00274                   INFO = ABS( IINFO )
00275                   GO TO 20
00276                END IF
00277             ELSE IF( IMAT.EQ.2 ) THEN
00278                R = MIN( P, M-P, Q, M-Q )
00279                DO I = 1, R
00280                   THETA(I) = PIOVER2 * SLARND( 1, ISEED )
00281                END DO
00282                CALL SLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00283                DO I = 1, M
00284                   DO J = 1, M
00285                      X(I+(J-1)*LDX) = X(I+(J-1)*LDX) +
00286      $                                ORTH*SLARND(2,ISEED)
00287                   END DO
00288                END DO
00289             ELSE
00290                R = MIN( P, M-P, Q, M-Q )
00291                DO I = 1, R+1
00292                   THETA(I) = TEN**(-SLARND(1,ISEED)*GAPDIGIT)
00293                END DO
00294                DO I = 2, R+1
00295                   THETA(I) = THETA(I-1) + THETA(I)
00296                END DO
00297                DO I = 1, R
00298                   THETA(I) = PIOVER2 * THETA(I) / THETA(R+1)
00299                END DO
00300                CALL SLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00301             END IF
00302 *
00303             NT = 9
00304 *
00305             CALL SCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
00306      $                   LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
00307      $                   RWORK, RESULT )
00308 *
00309 *           Print information about the tests that did not
00310 *           pass the threshold.
00311 *
00312             DO 10 I = 1, NT
00313                IF( RESULT( I ).GE.THRESH ) THEN
00314                   IF( NFAIL.EQ.0 .AND. FIRSTT ) THEN
00315                      FIRSTT = .FALSE.
00316                      CALL ALAHDG( NOUT, PATH )
00317                   END IF
00318                   WRITE( NOUT, FMT = 9998 )M, P, Q, IMAT, I,
00319      $               RESULT( I )
00320                   NFAIL = NFAIL + 1
00321                END IF
00322    10       CONTINUE
00323             NRUN = NRUN + NT
00324    20    CONTINUE
00325    30 CONTINUE
00326 *
00327 *     Print a summary of the results.
00328 *
00329       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, 0 )
00330 *
00331  9999 FORMAT( ' SLAROR in SCKCSD: M = ', I5, ', INFO = ', I15 )
00332  9998 FORMAT( ' M=', I4, ' P=', I4, ', Q=', I4, ', type ', I2,
00333      $      ', test ', I2, ', ratio=', G13.6 )
00334       RETURN
00335 *
00336 *     End of SCKCSD
00337 *
00338       END
00339 *
00340 *
00341 *
00342       SUBROUTINE SLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK )
00343       IMPLICIT NONE
00344 *
00345       INTEGER            LDX, M, P, Q
00346       INTEGER            ISEED( 4 )
00347       REAL               THETA( * )
00348       REAL               WORK( * ), X( LDX, * )
00349 *
00350       REAL               ONE, ZERO
00351       PARAMETER          ( ONE = 1.0E0, ZERO = 0.0E0 )
00352 *
00353       INTEGER            I, INFO, R
00354 *
00355       R = MIN( P, M-P, Q, M-Q )
00356 *
00357       CALL SLASET( 'Full', M, M, ZERO, ZERO, X, LDX )
00358 *
00359       DO I = 1, MIN(P,Q)-R
00360          X(I,I) = ONE
00361       END DO
00362       DO I = 1, R
00363          X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) = COS(THETA(I))
00364       END DO
00365       DO I = 1, MIN(P,M-Q)-R
00366          X(P-I+1,M-I+1) = -ONE
00367       END DO
00368       DO I = 1, R
00369          X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) =
00370      $      -SIN(THETA(R-I+1))
00371       END DO
00372       DO I = 1, MIN(M-P,Q)-R
00373          X(M-I+1,Q-I+1) = ONE
00374       END DO
00375       DO I = 1, R
00376          X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) =
00377      $      SIN(THETA(R-I+1))
00378       END DO
00379       DO I = 1, MIN(M-P,M-Q)-R
00380          X(P+I,Q+I) = ONE
00381       END DO
00382       DO I = 1, R
00383          X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) =
00384      $      COS(THETA(I))
00385       END DO
00386       CALL SLAROR( 'Left', 'No init', P, M, X, LDX, ISEED, WORK, INFO )
00387       CALL SLAROR( 'Left', 'No init', M-P, M, X(P+1,1), LDX,
00388      $             ISEED, WORK, INFO )
00389       CALL SLAROR( 'Right', 'No init', M, Q, X, LDX, ISEED,
00390      $             WORK, INFO )
00391       CALL SLAROR( 'Right', 'No init', M, M-Q,
00392      $             X(1,Q+1), LDX, ISEED, WORK, INFO )
00393 *
00394       END
00395 
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