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SUBROUTINE DGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
$ LDV, WORK, RESULT )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( LDS, * ),
$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
$ WORK( * )
* ..
*
* Purpose
* =======
*
* DGET54 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 )
*
* Arguments
* =========
*
* N (input) INTEGER
* The size of the matrix. If it is zero, DGET54 does nothing.
* It must be at least zero.
*
* A (input) DOUBLE PRECISION array, dimension (LDA, N)
* The original (unfactored) matrix A.
*
* LDA (input) INTEGER
* The leading dimension of A. It must be at least 1
* and at least N.
*
* B (input) DOUBLE PRECISION array, dimension (LDB, N)
* The original (unfactored) matrix B.
*
* LDB (input) INTEGER
* The leading dimension of B. It must be at least 1
* and at least N.
*
* S (input) DOUBLE PRECISION array, dimension (LDS, N)
* The factored matrix S.
*
* LDS (input) INTEGER
* The leading dimension of S. It must be at least 1
* and at least N.
*
* T (input) DOUBLE PRECISION array, dimension (LDT, N)
* The factored matrix T.
*
* LDT (input) INTEGER
* The leading dimension of T. It must be at least 1
* and at least N.
*
* U (input) DOUBLE PRECISION array, dimension (LDU, N)
* The orthogonal matrix on the left-hand side in the
* decomposition.
*
* LDU (input) INTEGER
* The leading dimension of U. LDU must be at least N and
* at least 1.
*
* V (input) DOUBLE PRECISION array, dimension (LDV, N)
* The orthogonal matrix on the left-hand side in the
* decomposition.
*
* LDV (input) INTEGER
* The leading dimension of V. LDV must be at least N and
* at least 1.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (3*N**2)
*
* RESULT (output) DOUBLE PRECISION
* The value RESULT, It is currently limited to 1/ulp, to
* avoid overflow. Errors are flagged by RESULT=10/ulp.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION ABNORM, ULP, UNFL, WNORM
* ..
* .. Local Arrays ..
DOUBLE PRECISION DUM( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE
EXTERNAL DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY
* ..
* .. 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 DLACPY( 'Full', N, N, A, LDA, WORK, N )
CALL DLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
ABNORM = MAX( DLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
*
* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
*
CALL DLACPY( ' ', N, N, A, LDA, WORK, N )
CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, S, LDS, ZERO,
$ WORK( N*N+1 ), N )
*
CALL DGEMM( '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 DLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, T, LDT, ZERO,
$ WORK( 2*N*N+1 ), N )
*
CALL DGEMM( '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 = DLANGE( '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 DGET54
*
END
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