numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/csyt03.f | 6141B | -rw-r--r-- |
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*> \brief \b CSYT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CSYT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, * RWORK, RCOND, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDAINV, LDWORK, N * REAL RCOND, RESID * .. * .. Array Arguments .. * REAL RWORK( * ) * COMPLEX A( LDA, * ), AINV( LDAINV, * ), * $ WORK( LDWORK, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSYT03 computes the residual for a complex symmetric matrix times *> its inverse: *> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ) *> where EPS is the machine epsilon. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> complex symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The original complex symmetric matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N) *> \endverbatim *> *> \param[in,out] AINV *> \verbatim *> AINV is COMPLEX array, dimension (LDAINV,N) *> On entry, the inverse of the matrix A, stored as a symmetric *> matrix in the same format as A. *> In this version, AINV is expanded into a full matrix and *> multiplied by A, so the opposing triangle of AINV will be *> changed; i.e., if the upper triangular part of AINV is *> stored, the lower triangular part will be used as work space. *> \endverbatim *> *> \param[in] LDAINV *> \verbatim *> LDAINV is INTEGER *> The leading dimension of the array AINV. LDAINV >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (LDWORK,N) *> \endverbatim *> *> \param[in] LDWORK *> \verbatim *> LDWORK is INTEGER *> The leading dimension of the array WORK. LDWORK >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is REAL *> The reciprocal of the condition number of A, computed as *> RCOND = 1/ (norm(A) * norm(AINV)). *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CSYT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, $ RWORK, RCOND, RESID ) * * -- 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 .. CHARACTER UPLO INTEGER LDA, LDAINV, LDWORK, N REAL RCOND, RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX A( LDA, * ), AINV( LDAINV, * ), $ WORK( LDWORK, * ) * .. * * ===================================================================== * * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, J REAL AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, CLANSY, SLAMCH EXTERNAL LSAME, CLANGE, CLANSY, SLAMCH * .. * .. External Subroutines .. EXTERNAL CSYMM * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. Executable Statements .. * * Quick exit if N = 0 * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = SLAMCH( 'Epsilon' ) ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK ) AINVNM = CLANSY( '1', UPLO, N, AINV, LDAINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE/ANORM ) / AINVNM * * Expand AINV into a full matrix and call CSYMM to multiply * AINV on the left by A (store the result in WORK). * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J - 1 AINV( J, I ) = AINV( I, J ) 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J + 1, N AINV( J, I ) = AINV( I, J ) 30 CONTINUE 40 CONTINUE END IF CALL CSYMM( 'Left', UPLO, N, N, -CONE, A, LDA, AINV, LDAINV, $ CZERO, WORK, LDWORK ) * * Add the identity matrix to WORK . * DO 50 I = 1, N WORK( I, I ) = WORK( I, I ) + CONE 50 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = CLANGE( '1', N, N, WORK, LDWORK, RWORK ) * RESID = ( ( RESID*RCOND )/EPS ) / REAL( N ) * RETURN * * End of CSYT03 * END