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*> \brief \b SGET54
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET54( 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
* REAL RESULT
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
* $ T( LDT, * ), U( LDU, * ), V( LDV, * ),
* $ WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET54 checks a generalized decomposition of the form
*>
*> A = U*S*V' and B = U*T* V'
*>
*> where ' means transpose and U and V are orthogonal.
*>
*> 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, SGET54 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (3*N**2)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL
*> 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 single_eig
*
* =====================================================================
SUBROUTINE SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
$ LDV, 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 ..
INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
REAL RESULT
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
$ WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
REAL ABNORM, ULP, UNFL, WNORM
* ..
* .. Local Arrays ..
REAL DUM( 1 )
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLACPY
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
RESULT = ZERO
IF( N.LE.0 )
$ RETURN
*
* Constants
*
UNFL = SLAMCH( 'Safe minimum' )
ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
*
* compute the norm of (A,B)
*
CALL SLACPY( 'Full', N, N, A, LDA, WORK, N )
CALL SLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
ABNORM = MAX( SLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
*
* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
*
CALL SLACPY( ' ', N, N, A, LDA, WORK, N )
CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, S, LDS, ZERO,
$ WORK( N*N+1 ), N )
*
CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( N*N+1 ), N, V, LDV,
$ ONE, WORK, N )
*
* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
*
CALL SLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, T, LDT, ZERO,
$ WORK( 2*N*N+1 ), N )
*
CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( 2*N*N+1 ), N, V, LDV,
$ ONE, WORK( N*N+1 ), N )
*
* Compute norm(W)/ ( ulp*norm((A,B)) )
*
WNORM = SLANGE( '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, REAL( 2*N ) ) / ( 2*N*ULP )
END IF
END IF
*
RETURN
*
* End of SGET54
*
END
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