You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
250 lines
6.6 KiB
250 lines
6.6 KiB
2 years ago
|
*> \brief \b ZGET54
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE ZGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
|
||
|
|
* LDV, WORK, RESULT )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
|
||
|
|
* DOUBLE PRECISION RESULT
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* COMPLEX*16 A( LDA, * ), B( LDB, * ), S( LDS, * ),
|
||
|
|
* $ T( LDT, * ), U( LDU, * ), V( LDV, * ),
|
||
|
|
* $ WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> ZGET54 checks a generalized decomposition of the form
|
||
|
|
*>
|
||
|
|
*> A = U*S*V' and B = U*T* V'
|
||
|
|
*>
|
||
|
|
*> where ' means conjugate transpose and U and V are unitary.
|
||
|
|
*>
|
||
|
|
*> Specifically,
|
||
|
|
*>
|
||
|
|
*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The size of the matrix. If it is zero, DGET54 does nothing.
|
||
|
|
*> It must be at least zero.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is COMPLEX*16 array, dimension (LDA, N)
|
||
|
|
*> The original (unfactored) matrix A.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of A. It must be at least 1
|
||
|
|
*> and at least N.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is COMPLEX*16 array, dimension (LDB, N)
|
||
|
|
*> The original (unfactored) matrix B.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDB
|
||
|
|
*> \verbatim
|
||
|
|
*> LDB is INTEGER
|
||
|
|
*> The leading dimension of B. It must be at least 1
|
||
|
|
*> and at least N.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] S
|
||
|
|
*> \verbatim
|
||
|
|
*> S is COMPLEX*16 array, dimension (LDS, N)
|
||
|
|
*> The factored matrix S.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDS
|
||
|
|
*> \verbatim
|
||
|
|
*> LDS is INTEGER
|
||
|
|
*> The leading dimension of S. It must be at least 1
|
||
|
|
*> and at least N.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] T
|
||
|
|
*> \verbatim
|
||
|
|
*> T is COMPLEX*16 array, dimension (LDT, N)
|
||
|
|
*> The factored matrix T.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDT
|
||
|
|
*> \verbatim
|
||
|
|
*> LDT is INTEGER
|
||
|
|
*> The leading dimension of T. It must be at least 1
|
||
|
|
*> and at least N.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] U
|
||
|
|
*> \verbatim
|
||
|
|
*> U is COMPLEX*16 array, dimension (LDU, N)
|
||
|
|
*> The orthogonal matrix on the left-hand side in the
|
||
|
|
*> decomposition.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDU
|
||
|
|
*> \verbatim
|
||
|
|
*> LDU is INTEGER
|
||
|
|
*> The leading dimension of U. LDU must be at least N and
|
||
|
|
*> at least 1.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] V
|
||
|
|
*> \verbatim
|
||
|
|
*> V is COMPLEX*16 array, dimension (LDV, N)
|
||
|
|
*> The orthogonal matrix on the left-hand side in the
|
||
|
|
*> decomposition.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDV
|
||
|
|
*> \verbatim
|
||
|
|
*> LDV is INTEGER
|
||
|
|
*> The leading dimension of V. LDV must be at least N and
|
||
|
|
*> at least 1.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] WORK
|
||
|
|
*> \verbatim
|
||
|
|
*> WORK is COMPLEX*16 array, dimension (3*N**2)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] RESULT
|
||
|
|
*> \verbatim
|
||
|
|
*> RESULT is DOUBLE PRECISION
|
||
|
|
*> The value RESULT, It is currently limited to 1/ulp, to
|
||
|
|
*> avoid overflow. Errors are flagged by RESULT=10/ulp.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complex16_eig
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE ZGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
|
||
|
|
$ LDV, 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 ..
|
||
|
|
INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
|
||
|
|
DOUBLE PRECISION RESULT
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
COMPLEX*16 A( LDA, * ), B( LDB, * ), S( LDS, * ),
|
||
|
|
$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
|
||
|
|
$ WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
DOUBLE PRECISION ZERO, ONE
|
||
|
|
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
|
||
|
|
COMPLEX*16 CZERO, CONE
|
||
|
|
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
|
||
|
|
$ CONE = ( 1.0D+0, 0.0D+0 ) )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
DOUBLE PRECISION ABNORM, ULP, UNFL, WNORM
|
||
|
|
* ..
|
||
|
|
* .. Local Arrays ..
|
||
|
|
DOUBLE PRECISION DUM( 1 )
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
DOUBLE PRECISION DLAMCH, ZLANGE
|
||
|
|
EXTERNAL DLAMCH, ZLANGE
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL ZGEMM, ZLACPY
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC DBLE, MAX, MIN
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
RESULT = ZERO
|
||
|
|
IF( N.LE.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
* Constants
|
||
|
|
*
|
||
|
|
UNFL = DLAMCH( 'Safe minimum' )
|
||
|
|
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
|
||
|
|
*
|
||
|
|
* compute the norm of (A,B)
|
||
|
|
*
|
||
|
|
CALL ZLACPY( 'Full', N, N, A, LDA, WORK, N )
|
||
|
|
CALL ZLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
|
||
|
|
ABNORM = MAX( ZLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
|
||
|
|
*
|
||
|
|
* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
|
||
|
|
*
|
||
|
|
CALL ZLACPY( ' ', N, N, A, LDA, WORK, N )
|
||
|
|
CALL ZGEMM( 'N', 'N', N, N, N, CONE, U, LDU, S, LDS, CZERO,
|
||
|
|
$ WORK( N*N+1 ), N )
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'N', 'C', N, N, N, -CONE, WORK( N*N+1 ), N, V, LDV,
|
||
|
|
$ CONE, WORK, N )
|
||
|
|
*
|
||
|
|
* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
|
||
|
|
*
|
||
|
|
CALL ZLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
|
||
|
|
CALL ZGEMM( 'N', 'N', N, N, N, CONE, U, LDU, T, LDT, CZERO,
|
||
|
|
$ WORK( 2*N*N+1 ), N )
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'N', 'C', N, N, N, -CONE, WORK( 2*N*N+1 ), N, V, LDV,
|
||
|
|
$ CONE, WORK( N*N+1 ), N )
|
||
|
|
*
|
||
|
|
* Compute norm(W)/ ( ulp*norm((A,B)) )
|
||
|
|
*
|
||
|
|
WNORM = ZLANGE( '1', N, 2*N, WORK, N, DUM )
|
||
|
|
*
|
||
|
|
IF( ABNORM.GT.WNORM ) THEN
|
||
|
|
RESULT = ( WNORM / ABNORM ) / ( 2*N*ULP )
|
||
|
|
ELSE
|
||
|
|
IF( ABNORM.LT.ONE ) THEN
|
||
|
|
RESULT = ( MIN( WNORM, 2*N*ABNORM ) / ABNORM ) / ( 2*N*ULP )
|
||
|
|
ELSE
|
||
|
|
RESULT = MIN( WNORM / ABNORM, DBLE( 2*N ) ) / ( 2*N*ULP )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZGET54
|
||
|
|
*
|
||
|
|
END
|