numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| .. | |||
| lapack/TESTING/LIN/csyt02.f | 5376B | -rw-r--r-- |
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*> \brief \b CSYT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CSYT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, * RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDB, LDX, N, NRHS * REAL RESID * .. * .. Array Arguments .. * REAL RWORK( * ) * COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSYT02 computes the residual for a solution to a complex symmetric *> system of linear equations A*x = b: *> *> RESID = norm(B - A*X) / ( norm(A) * norm(X) * 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 *> 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] NRHS *> \verbatim *> NRHS is INTEGER *> The number of columns of B, the matrix of right hand sides. *> NRHS >= 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] X *> \verbatim *> X is COMPLEX array, dimension (LDX,NRHS) *> The computed solution vectors for the system of linear *> equations. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,NRHS) *> On entry, the right hand side vectors for the system of *> linear equations. *> On exit, B is overwritten with the difference B - A*X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CSYT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, $ 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, LDB, LDX, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER J REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. REAL CLANSY, SCASUM, SLAMCH EXTERNAL CLANSY, SCASUM, SLAMCH * .. * .. External Subroutines .. EXTERNAL CSYMM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * IF( N.LE.0 .OR. NRHS.LE.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( 'Epsilon' ) ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X (or B - A'*X ) and store in B . * CALL CSYMM( 'Left', UPLO, N, NRHS, -CONE, A, LDA, X, LDX, CONE, B, $ LDB ) * * Compute the maximum over the number of right hand sides of * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) . * RESID = ZERO DO 10 J = 1, NRHS BNORM = SCASUM( N, B( 1, J ), 1 ) XNORM = SCASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS ) END IF 10 CONTINUE * RETURN * * End of CSYT02 * END