*> \brief \b DSGT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D, * WORK, RESULT ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER ITYPE, LDA, LDB, LDZ, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ), * $ WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DDGT01 checks a decomposition of the form *> *> A Z = B Z D or *> A B Z = Z D or *> B A Z = Z D *> *> where A is a symmetric matrix, B is *> symmetric positive definite, Z is orthogonal, and D is diagonal. *> *> One of the following test ratios is computed: *> *> ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp ) *> *> ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp ) *> *> ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp ) *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> The form of the symmetric generalized eigenproblem. *> = 1: A*z = (lambda)*B*z *> = 2: A*B*z = (lambda)*z *> = 3: B*A*z = (lambda)*z *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrices A and B is stored. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of eigenvalues found. 0 <= M <= N. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> The original 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] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB, N) *> The original symmetric positive definite matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, M) *> The computed eigenvectors of the generalized eigenproblem. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= max(1,N). *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (M) *> The computed eigenvalues of the generalized eigenproblem. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N*N) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (1) *> The test ratio as described above. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2011 * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D, $ WORK, RESULT ) * * -- LAPACK test routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER ITYPE, LDA, LDB, LDZ, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ), $ WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION ANORM, ULP * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY EXTERNAL DLAMCH, DLANGE, DLANSY * .. * .. External Subroutines .. EXTERNAL DSCAL, DSYMM * .. * .. Executable Statements .. * RESULT( 1 ) = ZERO IF( N.LE.0 ) $ RETURN * ULP = DLAMCH( 'Epsilon' ) * * Compute product of 1-norms of A and Z. * ANORM = DLANSY( '1', UPLO, N, A, LDA, WORK )* $ DLANGE( '1', N, M, Z, LDZ, WORK ) IF( ANORM.EQ.ZERO ) $ ANORM = ONE * IF( ITYPE.EQ.1 ) THEN * * Norm of AZ - BZD * CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, $ WORK, N ) DO 10 I = 1, M CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 10 CONTINUE CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, -ONE, $ WORK, N ) * RESULT( 1 ) = ( DLANGE( '1', N, M, WORK, N, WORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.2 ) THEN * * Norm of ABZ - ZD * CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, ZERO, $ WORK, N ) DO 20 I = 1, M CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 20 CONTINUE CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, WORK, N, -ONE, Z, $ LDZ ) * RESULT( 1 ) = ( DLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.3 ) THEN * * Norm of BAZ - ZD * CALL DSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO, $ WORK, N ) DO 30 I = 1, M CALL DSCAL( N, D( I ), Z( 1, I ), 1 ) 30 CONTINUE CALL DSYMM( 'Left', UPLO, N, M, ONE, B, LDB, WORK, N, -ONE, Z, $ LDZ ) * RESULT( 1 ) = ( DLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) / $ ( N*ULP ) END IF * RETURN * * End of DDGT01 * END