testdata/lapack/TESTING/EIG/dget51.f
*> \brief \b DGET51
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RESULT )
*
* .. Scalar Arguments ..
* INTEGER ITYPE, LDA, LDB, LDU, LDV, N
* DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), U( LDU, * ),
* $ V( LDV, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET51 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 )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> ITYPE is 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 )
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, DGET51 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA, N)
*> The original (unfactored) matrix.
*> \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 DOUBLE PRECISION array, dimension (LDB, N)
*> The factored matrix.
*> \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] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension (LDU, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> Not referenced if ITYPE=2
*> \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 DOUBLE PRECISION array, dimension (LDV, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> Not referenced if ITYPE=2
*> \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 DOUBLE PRECISION array, dimension (2*N**2)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
$ RESULT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER ITYPE, LDA, LDB, LDU, LDV, N
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), U( LDU, * ),
$ V( LDV, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 )
* ..
* .. Local Scalars ..
INTEGER JCOL, JDIAG, JROW
DOUBLE PRECISION ANORM, ULP, UNFL, WNORM
* ..
* .. 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' )
*
* 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( DLANGE( '1', N, N, A, LDA, WORK ), UNFL )
*
IF( ITYPE.EQ.1 ) THEN
*
* ITYPE=1: Compute W = A - UBV'
*
CALL DLACPY( ' ', N, N, A, LDA, WORK, N )
CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, B, LDB, ZERO,
$ WORK( N**2+1 ), N )
*
CALL DGEMM( 'N', 'C', N, N, N, -ONE, WORK( N**2+1 ), N, V,
$ LDV, ONE, WORK, N )
*
ELSE
*
* ITYPE=2: Compute W = A - B
*
CALL DLACPY( ' ', 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 = DLANGE( '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, DBLE( N ) ) / ( N*ULP )
END IF
END IF
*
ELSE
*
* Tests not scaled by norm(A)
*
* ITYPE=3: Compute UU' - I
*
CALL DGEMM( '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( DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) ),
$ DBLE( N ) ) / ( N*ULP )
END IF
*
RETURN
*
* End of DGET51
*
END