243 lines
6.2 KiB
Fortran
243 lines
6.2 KiB
Fortran
*> \brief \b SSGT01
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SSGT01( 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 ..
|
|
* REAL A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ),
|
|
* $ WORK( * ), Z( LDZ, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SSGT01 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M)
|
|
*> The computed eigenvalues of the generalized eigenproblem.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension (N*N)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RESULT
|
|
*> \verbatim
|
|
*> RESULT is REAL 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.
|
|
*
|
|
*> \ingroup single_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
|
|
$ WORK, RESULT )
|
|
*
|
|
* -- 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 ITYPE, LDA, LDB, LDZ, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ),
|
|
$ WORK( * ), Z( LDZ, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I
|
|
REAL ANORM, ULP
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH, SLANGE, SLANSY
|
|
EXTERNAL SLAMCH, SLANGE, SLANSY
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SSCAL, SSYMM
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
RESULT( 1 ) = ZERO
|
|
IF( N.LE.0 )
|
|
$ RETURN
|
|
*
|
|
ULP = SLAMCH( 'Epsilon' )
|
|
*
|
|
* Compute product of 1-norms of A and Z.
|
|
*
|
|
ANORM = SLANSY( '1', UPLO, N, A, LDA, WORK )*
|
|
$ SLANGE( '1', N, M, Z, LDZ, WORK )
|
|
IF( ANORM.EQ.ZERO )
|
|
$ ANORM = ONE
|
|
*
|
|
IF( ITYPE.EQ.1 ) THEN
|
|
*
|
|
* Norm of AZ - BZD
|
|
*
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO,
|
|
$ WORK, N )
|
|
DO 10 I = 1, M
|
|
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
|
|
10 CONTINUE
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, -ONE,
|
|
$ WORK, N )
|
|
*
|
|
RESULT( 1 ) = ( SLANGE( '1', N, M, WORK, N, WORK ) / ANORM ) /
|
|
$ ( N*ULP )
|
|
*
|
|
ELSE IF( ITYPE.EQ.2 ) THEN
|
|
*
|
|
* Norm of ABZ - ZD
|
|
*
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, ZERO,
|
|
$ WORK, N )
|
|
DO 20 I = 1, M
|
|
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
|
|
20 CONTINUE
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, WORK, N, -ONE, Z,
|
|
$ LDZ )
|
|
*
|
|
RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) /
|
|
$ ( N*ULP )
|
|
*
|
|
ELSE IF( ITYPE.EQ.3 ) THEN
|
|
*
|
|
* Norm of BAZ - ZD
|
|
*
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO,
|
|
$ WORK, N )
|
|
DO 30 I = 1, M
|
|
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
|
|
30 CONTINUE
|
|
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, WORK, N, -ONE, Z,
|
|
$ LDZ )
|
|
*
|
|
RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) /
|
|
$ ( N*ULP )
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SSGT01
|
|
*
|
|
END
|