numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/EIG/csyl01.f | 11724B | -rw-r--r-- |
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*> \brief \b CSYL01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CSYL01( THRESH, NFAIL, RMAX, NINFO, KNT ) * * .. Scalar Arguments .. * INTEGER KNT * REAL THRESH * .. * .. Array Arguments .. * INTEGER NFAIL( 3 ), NINFO( 2 ) * REAL RMAX( 2 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSYL01 tests CTRSYL and CTRSYL3, routines for solving the Sylvester matrix *> equation *> *> op(A)*X + ISGN*X*op(B) = scale*C, *> *> where op(A) and op(B) are both upper triangular form, op() represents an *> optional conjugate 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 CGET35 by testing with larger, *> random matrices, of which some require rescaling of X to avoid overflow. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> 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 CTRSYL exceeds threshold THRESH *> NFAIL(2) = No. of times residual CTRSYL3 exceeds threshold THRESH *> NFAIL(3) = No. of times CTRSYL3 and CTRSYL deviate *> \endverbatim *> *> \param[out] RMAX *> \verbatim *> RMAX is DOUBLE PRECISION array, dimension (2) *> RMAX(1) = Value of the largest test ratio of CTRSYL *> RMAX(2) = Value of the largest test ratio of CTRSYL3 *> \endverbatim *> *> \param[out] NINFO *> \verbatim *> NINFO is INTEGER array, dimension (2) *> NINFO(1) = No. of times CTRSYL where INFO is nonzero *> NINFO(2) = No. of times CTRSYL3 where INFO is nonzero *> \endverbatim *> *> \param[out] KNT *> \verbatim *> KNT is INTEGER *> Total number of examples tested. *> \endverbatim * * -- LAPACK test routine -- SUBROUTINE CSYL01( 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 REAL THRESH * .. * .. Array Arguments .. INTEGER NFAIL( 3 ), NINFO( 2 ) REAL RMAX( 2 ) * .. * * ===================================================================== * .. * .. Parameters .. COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) REAL ONE, ZERO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) INTEGER MAXM, MAXN, LDSWORK PARAMETER ( MAXM = 101, MAXN = 138, LDSWORK = 18 ) * .. * .. Local Scalars .. CHARACTER TRANA, TRANB INTEGER I, INFO, IINFO, ISGN, ITRANA, ITRANB, J, KLA, $ KUA, KLB, KUB, M, N REAL ANRM, BNRM, BIGNUM, EPS, RES, RES1, $ SCALE, SCALE3, SMLNUM, TNRM, XNRM COMPLEX RMUL * .. * .. Local Arrays .. COMPLEX DUML( MAXM ), DUMR( MAXN ), $ D( MAX( MAXM, MAXN ) ) REAL DUM( MAXN ), VM( 2 ) INTEGER ISEED( 4 ), IWORK( MAXM + MAXN + 2 ) * .. * .. Allocatable Arrays .. INTEGER AllocateStatus COMPLEX, DIMENSION(:,:), ALLOCATABLE :: A, B, C, CC, X REAL, DIMENSION(:,:), ALLOCATABLE :: SWORK * .. * .. External Functions .. LOGICAL SISNAN REAL SLAMCH, CLANGE EXTERNAL SISNAN, SLAMCH, CLANGE * .. * .. External Subroutines .. EXTERNAL CLATMR, CLACPY, CGEMM, CTRSYL, CTRSYL3 * .. * .. Intrinsic Functions .. INTRINSIC ABS, REAL, 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, 54 ), STAT = AllocateStatus ) IF( AllocateStatus /= 0 ) STOP "*** Not enough memory ***" * .. * .. Executable Statements .. * * Get machine parameters * EPS = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * * Expect INFO = 0 VM( 1 ) = ONE * Expect INFO = 1 VM( 2 ) = 0.5E+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 ISEED( 1 ) = 1 ISEED( 2 ) = 1 ISEED( 3 ) = 1 ISEED( 4 ) = 1 SCALE = ONE SCALE3 = ONE DO J = 1, 2 DO ISGN = -1, 1, 2 * Reset seed (overwritten by LATMR) ISEED( 1 ) = 1 ISEED( 2 ) = 1 ISEED( 3 ) = 1 ISEED( 4 ) = 1 DO M = 32, MAXM, 23 KLA = 0 KUA = M - 1 CALL CLATMR( M, M, 'S', ISEED, 'N', D, $ 6, ONE, CONE, '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 = CLANGE( 'M', M, M, A, MAXM, DUM ) DO N = 51, MAXN, 29 KLB = 0 KUB = N - 1 CALL CLATMR( N, N, 'S', ISEED, 'N', D, $ 6, ONE, CONE, 'T', 'N', $ DUML, 1, ONE, DUMR, 1, ONE, $ 'N', IWORK, KLB, KUB, ZERO, $ ONE, 'NO', B, MAXN, IWORK, $ IINFO ) DO I = 1, N B( I, I ) = B( I, I ) * VM ( J ) END DO BNRM = CLANGE( 'M', N, N, B, MAXN, DUM ) TNRM = MAX( ANRM, BNRM ) CALL CLATMR( M, N, 'S', ISEED, 'N', D, $ 6, ONE, CONE, '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 ) $ TRANA = 'N' IF( ITRANA.EQ.2 ) $ TRANA = 'C' DO ITRANB = 1, 2 IF( ITRANB.EQ.1 ) $ TRANB = 'N' IF( ITRANB.EQ.2 ) $ TRANB = 'C' KNT = KNT + 1 * CALL CLACPY( 'All', M, N, C, MAXM, X, MAXM) CALL CLACPY( 'All', M, N, C, MAXM, CC, MAXM) CALL CTRSYL( TRANA, TRANB, ISGN, M, N, $ A, MAXM, B, MAXN, X, MAXM, $ SCALE, IINFO ) IF( IINFO.NE.0 ) $ NINFO( 1 ) = NINFO( 1 ) + 1 XNRM = CLANGE( 'M', M, N, X, MAXM, DUM ) RMUL = CONE IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN IF( XNRM.GT.BIGNUM / TNRM ) THEN RMUL = CONE / MAX( XNRM, TNRM ) END IF END IF CALL CGEMM( TRANA, 'N', M, N, M, RMUL, $ A, MAXM, X, MAXM, -SCALE*RMUL, $ CC, MAXM ) CALL CGEMM( 'N', TRANB, M, N, N, $ REAL( ISGN )*RMUL, X, MAXM, B, $ MAXN, CONE, CC, MAXM ) RES1 = CLANGE( 'M', M, N, CC, MAXM, DUM ) RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM, $ ( ( ABS( RMUL )*TNRM )*EPS )*XNRM ) IF( RES.GT.THRESH ) $ NFAIL( 1 ) = NFAIL( 1 ) + 1 IF( RES.GT.RMAX( 1 ) ) $ RMAX( 1 ) = RES * CALL CLACPY( 'All', M, N, C, MAXM, X, MAXM ) CALL CLACPY( 'All', M, N, C, MAXM, CC, MAXM ) CALL CTRSYL3( TRANA, TRANB, ISGN, M, N, $ A, MAXM, B, MAXN, X, MAXM, $ SCALE3, SWORK, LDSWORK, INFO) IF( INFO.NE.0 ) $ NINFO( 2 ) = NINFO( 2 ) + 1 XNRM = CLANGE( 'M', M, N, X, MAXM, DUM ) RMUL = CONE IF( XNRM.GT.ONE .AND. TNRM.GT.ONE ) THEN IF( XNRM.GT.BIGNUM / TNRM ) THEN RMUL = CONE / MAX( XNRM, TNRM ) END IF END IF CALL CGEMM( TRANA, 'N', M, N, M, RMUL, $ A, MAXM, X, MAXM, -SCALE3*RMUL, $ CC, MAXM ) CALL CGEMM( 'N', TRANB, M, N, N, $ REAL( ISGN )*RMUL, X, MAXM, B, $ MAXN, CONE, CC, MAXM ) RES1 = CLANGE( 'M', M, N, CC, MAXM, DUM ) RES = RES1 / MAX( SMLNUM, SMLNUM*XNRM, $ ( ( ABS( 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. SISNAN( 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 CSYL01 * END