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|
*> \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 December 2016
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
$ WORK, RESULT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. 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
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