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SUBROUTINE SGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
$ RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
INTEGER ITYPE, LDA, LDB, LDU, LDV, N
REAL RESULT
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), U( LDU, * ),
$ V( LDV, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SGET51 generally checks a decomposition of the form
*
* A = U B V'
*
* where ' means transpose and U and V are orthogonal.
*
* Specifically, if ITYPE=1
*
* RESULT = | A - U B V' | / ( |A| n ulp )
*
* If ITYPE=2, then:
*
* RESULT = | A - B | / ( |A| n ulp )
*
* If ITYPE=3, then:
*
* RESULT = | I - UU' | / ( n ulp )
*
* Arguments
* =========
*
* ITYPE (input) INTEGER
* Specifies the type of tests to be performed.
* =1: RESULT = | A - U B V' | / ( |A| n ulp )
* =2: RESULT = | A - B | / ( |A| n ulp )
* =3: RESULT = | I - UU' | / ( n ulp )
*
* N (input) INTEGER
* The size of the matrix. If it is zero, SGET51 does nothing.
* It must be at least zero.
*
* A (input) REAL array, dimension (LDA, N)
* The original (unfactored) matrix.
*
* LDA (input) INTEGER
* The leading dimension of A. It must be at least 1
* and at least N.
*
* B (input) REAL array, dimension (LDB, N)
* The factored matrix.
*
* LDB (input) INTEGER
* The leading dimension of B. It must be at least 1
* and at least N.
*
* U (input) REAL array, dimension (LDU, N)
* The orthogonal matrix on the left-hand side in the
* decomposition.
* Not referenced if ITYPE=2
*
* LDU (input) INTEGER
* The leading dimension of U. LDU must be at least N and
* at least 1.
*
* V (input) REAL array, dimension (LDV, N)
* The orthogonal matrix on the left-hand side in the
* decomposition.
* Not referenced if ITYPE=2
*
* LDV (input) INTEGER
* The leading dimension of V. LDV must be at least N and
* at least 1.
*
* WORK (workspace) REAL array, dimension (2*N**2)
*
* RESULT (output) REAL
* The values computed by the test specified by ITYPE. The
* value is currently limited to 1/ulp, to avoid overflow.
* Errors are flagged by RESULT=10/ulp.
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0, ONE = 1.0E0, TEN = 10.0E0 )
* ..
* .. Local Scalars ..
INTEGER JCOL, JDIAG, JROW
REAL ANORM, ULP, UNFL, WNORM
* ..
* .. 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' )
*
* Some Error Checks
*
IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
RESULT = TEN / ULP
RETURN
END IF
*
IF( ITYPE.LE.2 ) THEN
*
* Tests scaled by the norm(A)
*
ANORM = MAX( SLANGE( '1', N, N, A, LDA, WORK ), UNFL )
*
IF( ITYPE.EQ.1 ) THEN
*
* ITYPE=1: Compute W = A - UBV'
*
CALL SLACPY( ' ', N, N, A, LDA, WORK, N )
CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, B, LDB, ZERO,
$ WORK( N**2+1 ), N )
*
CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( N**2+1 ), N, V,
$ LDV, ONE, WORK, N )
*
ELSE
*
* ITYPE=2: Compute W = A - B
*
CALL SLACPY( ' ', N, N, B, LDB, WORK, N )
*
DO 20 JCOL = 1, N
DO 10 JROW = 1, N
WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
$ - A( JROW, JCOL )
10 CONTINUE
20 CONTINUE
END IF
*
* Compute norm(W)/ ( ulp*norm(A) )
*
WNORM = SLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) )
*
IF( ANORM.GT.WNORM ) THEN
RESULT = ( WNORM / ANORM ) / ( N*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
ELSE
RESULT = MIN( WNORM / ANORM, REAL( N ) ) / ( N*ULP )
END IF
END IF
*
ELSE
*
* Tests not scaled by norm(A)
*
* ITYPE=3: Compute UU' - I
*
CALL SGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
$ N )
*
DO 30 JDIAG = 1, N
WORK( ( N+1 )*( JDIAG-1 )+1 ) = WORK( ( N+1 )*( JDIAG-1 )+
$ 1 ) - ONE
30 CONTINUE
*
RESULT = MIN( SLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) ),
$ REAL( N ) ) / ( N*ULP )
END IF
*
RETURN
*
* End of SGET51
*
END
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