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*> \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( * )
* ..
*
* Purpose
* =======
*
*>\details \b 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.
*
*> \date November 2011
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
$ LDV, WORK, RESULT )
*
* -- LAPACK test routine (version 3.1) --
* -- 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 ..
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
|
