numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/EIG/dsyl01.f | 11554B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311
*> \brief \b DSYL01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYL01( THRESH, NFAIL, RMAX, NINFO, KNT ) * * .. Scalar Arguments .. * INTEGER KNT * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * INTEGER NFAIL( 3 ), NINFO( 2 ) * DOUBLE PRECISION RMAX( 2 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYL01 tests DTRSYL and DTRSYL3, routines for solving the Sylvester matrix *> equation *> *> op(A)*X + ISGN*X*op(B) = scale*C, *> *> A and B are assumed to be in Schur canonical form, op() represents an *> optional transpose, and ISGN can be -1 or +1. Scale is an output *> less than or equal to 1, chosen to avoid overflow in X. *> *> The test code verifies that the following residual does not exceed *> the provided threshold: *> *> norm(op(A)*X + ISGN*X*op(B) - scale*C) / *> (EPS*max(norm(A),norm(B))*norm(X)) *> *> This routine complements DGET35 by testing with larger, *> random matrices, of which some require rescaling of X to avoid overflow. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] THRESH *> \verbatim *> THRESH is DOUBLE PRECISION *> A test will count as "failed" if the residual, computed as *> described above, exceeds THRESH. *> \endverbatim *> *> \param[out] NFAIL *> \verbatim *> NFAIL is INTEGER array, dimension (3) *> NFAIL(1) = No. of times residual DTRSYL exceeds threshold THRESH *> NFAIL(2) = No. of times residual DTRSYL3 exceeds threshold THRESH *> NFAIL(3) = No. of times DTRSYL3 and DTRSYL deviate *> \endverbatim *> *> \param[out] RMAX *> \verbatim *> RMAX is DOUBLE PRECISION, dimension (2) *> RMAX(1) = Value of the largest test ratio of DTRSYL *> RMAX(2) = Value of the largest test ratio of DTRSYL3 *> \endverbatim *> *> \param[out] NINFO *> \verbatim *> NINFO is INTEGER array, dimension (2) *> NINFO(1) = No. of times DTRSYL returns an expected INFO *> NINFO(2) = No. of times DTRSYL3 returns an expected INFO *> \endverbatim *> *> \param[out] KNT *> \verbatim *> KNT is INTEGER *> Total number of examples tested. *> \endverbatim * * -- LAPACK test routine -- SUBROUTINE DSYL01( THRESH, NFAIL, RMAX, NINFO, KNT ) 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 KNT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. INTEGER NFAIL( 3 ), NINFO( 2 ) DOUBLE PRECISION RMAX( 2 ) * .. * * ===================================================================== * .. * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) INTEGER MAXM, MAXN, LDSWORK PARAMETER ( MAXM = 245, MAXN = 192, LDSWORK = 36 ) * .. * .. Local Scalars .. CHARACTER TRANA, TRANB INTEGER I, INFO, IINFO, ISGN, ITRANA, ITRANB, J, KLA, $ KUA, KLB, KUB, LIWORK, M, N DOUBLE PRECISION ANRM, BNRM, BIGNUM, EPS, RES, RES1, RMUL, $ SCALE, SCALE3, SMLNUM, TNRM, XNRM * .. * .. Local Arrays .. DOUBLE PRECISION DUML( MAXM ), DUMR( MAXN ), $ D( MAX( MAXM, MAXN ) ), DUM( MAXN ), $ VM( 2 ) INTEGER ISEED( 4 ), IWORK( MAXM + MAXN + 2 ) * .. * .. Allocatable Arrays .. INTEGER AllocateStatus DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: A, B, C, CC, X, $ SWORK * .. * .. External Functions .. LOGICAL DISNAN DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DLATMR, DLACPY, DGEMM, DTRSYL, DTRSYL3 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX * .. * .. Allocate memory dynamically .. ALLOCATE ( A( MAXM, MAXM ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" ALLOCATE ( B( MAXN, MAXN ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" ALLOCATE ( C( MAXM, MAXN ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" ALLOCATE ( CC( MAXM, MAXN ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" ALLOCATE ( X( MAXM, MAXN ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" ALLOCATE ( SWORK( LDSWORK, 126 ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" * .. * .. Executable Statements .. * * Get machine parameters * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * VM( 1 ) = ONE VM( 2 ) = 0.000001D+0 * * Begin test loop * NINFO( 1 ) = 0 NINFO( 2 ) = 0 NFAIL( 1 ) = 0 NFAIL( 2 ) = 0 NFAIL( 3 ) = 0 RMAX( 1 ) = ZERO RMAX( 2 ) = ZERO KNT = 0 DO I = 1, 4 ISEED( I ) = 1 END DO SCALE = ONE SCALE3 = ONE LIWORK = MAXM + MAXN + 2 DO J = 1, 2 DO ISGN = -1, 1, 2 * Reset seed (overwritten by LATMR) DO I = 1, 4 ISEED( I ) = 1 END DO DO M = 32, MAXM, 71 KLA = 0 KUA = M - 1 CALL DLATMR( M, M, 'S', ISEED, 'N', D, $ 6, ONE, ONE, 'T', 'N', $ DUML, 1, ONE, DUMR, 1, ONE, $ 'N', IWORK, KLA, KUA, ZERO, $ ONE, 'NO', A, MAXM, IWORK, IINFO ) DO I = 1, M A( I, I ) = A( I, I ) * VM( J ) END DO ANRM = DLANGE( 'M', M, M, A, MAXM, DUM ) DO N = 51, MAXN, 47 KLB = 0 KUB = N - 1 CALL DLATMR( N, N, 'S', ISEED, 'N', D, $ 6, ONE, ONE, 'T', 'N', $ DUML, 1, ONE, DUMR, 1, ONE, $ 'N', IWORK, KLB, KUB, ZERO, $ ONE, 'NO', B, MAXN, IWORK, IINFO ) BNRM = DLANGE( 'M', N, N, B, MAXN, DUM ) TNRM = MAX( ANRM, BNRM ) CALL DLATMR( M, N, 'S', ISEED, 'N', D, $ 6, ONE, ONE, 'T', 'N', $ DUML, 1, ONE, DUMR, 1, ONE, $ 'N', IWORK, M, N, ZERO, ONE, $ 'NO', C, MAXM, IWORK, IINFO ) DO ITRANA = 1, 2 IF( ITRANA.EQ.1 ) THEN TRANA = 'N' END IF IF( ITRANA.EQ.2 ) THEN TRANA = 'T' END IF DO ITRANB = 1, 2 IF( ITRANB.EQ.1 ) THEN TRANB = 'N' END IF IF( ITRANB.EQ.2 ) THEN TRANB = 'T' END IF KNT = KNT + 1 * CALL DLACPY( 'All', M, N, C, MAXM, X, MAXM) CALL DLACPY( 'All', M, N, C, MAXM, CC, MAXM) CALL DTRSYL( TRANA, TRANB, ISGN, M, N, $ A, MAXM, B, MAXN, X, MAXM, $ SCALE, IINFO ) IF( IINFO.NE.0 ) $ NINFO( 1 ) = NINFO( 1 ) + 1 XNRM = DLANGE( 'M', M, N, X, MAXM, DUM ) RMUL = ONE IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN IF( XNRM.GT.BIGNUM / TNRM ) THEN RMUL = ONE / MAX( XNRM, TNRM ) END IF END IF CALL DGEMM( TRANA, 'N', M, N, M, RMUL, $ A, MAXM, X, MAXM, -SCALE*RMUL, $ CC, MAXM ) CALL DGEMM( 'N', TRANB, M, N, N, $ DBLE( ISGN )*RMUL, X, MAXM, B, $ MAXN, ONE, CC, MAXM ) RES1 = DLANGE( 'M', M, N, CC, MAXM, DUM ) RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM, $ ( ( RMUL*TNRM )*EPS )*XNRM ) IF( RES.GT.THRESH ) $ NFAIL( 1 ) = NFAIL( 1 ) + 1 IF( RES.GT.RMAX( 1 ) ) $ RMAX( 1 ) = RES * CALL DLACPY( 'All', M, N, C, MAXM, X, MAXM ) CALL DLACPY( 'All', M, N, C, MAXM, CC, MAXM ) CALL DTRSYL3( TRANA, TRANB, ISGN, M, N, $ A, MAXM, B, MAXN, X, MAXM, $ SCALE3, IWORK, LIWORK, $ SWORK, LDSWORK, INFO) IF( INFO.NE.0 ) $ NINFO( 2 ) = NINFO( 2 ) + 1 XNRM = DLANGE( 'M', M, N, X, MAXM, DUM ) RMUL = ONE IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN IF( XNRM.GT.BIGNUM / TNRM ) THEN RMUL = ONE / MAX( XNRM, TNRM ) END IF END IF CALL DGEMM( TRANA, 'N', M, N, M, RMUL, $ A, MAXM, X, MAXM, -SCALE3*RMUL, $ CC, MAXM ) CALL DGEMM( 'N', TRANB, M, N, N, $ DBLE( ISGN )*RMUL, X, MAXM, B, $ MAXN, ONE, CC, MAXM ) RES1 = DLANGE( 'M', M, N, CC, MAXM, DUM ) RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM, $ ( ( RMUL*TNRM )*EPS )*XNRM ) * Verify that TRSYL3 only flushes if TRSYL flushes (but * there may be cases where TRSYL3 avoid flushing). IF( SCALE3.EQ.ZERO .AND. SCALE.GT.ZERO .OR. $ IINFO.NE.INFO ) THEN NFAIL( 3 ) = NFAIL( 3 ) + 1 END IF IF( RES.GT.THRESH .OR. DISNAN( RES ) ) $ NFAIL( 2 ) = NFAIL( 2 ) + 1 IF( RES.GT.RMAX( 2 ) ) $ RMAX( 2 ) = RES END DO END DO END DO END DO END DO END DO * DEALLOCATE (A, STAT = AllocateStatus) DEALLOCATE (B, STAT = AllocateStatus) DEALLOCATE (C, STAT = AllocateStatus) DEALLOCATE (CC, STAT = AllocateStatus) DEALLOCATE (X, STAT = AllocateStatus) DEALLOCATE (SWORK, STAT = AllocateStatus) * RETURN * * End of DSYL01 * END