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718 lines
22 KiB
718 lines
22 KiB
2 years ago
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*> \brief \b SLATTR
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
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* WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, TRANS, UPLO
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* INTEGER IMAT, INFO, LDA, N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* REAL A( LDA, * ), B( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLATTR generates a triangular test matrix.
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*> IMAT and UPLO uniquely specify the properties of the test
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*> matrix, which is returned in the array A.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] IMAT
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*> \verbatim
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*> IMAT is INTEGER
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*> An integer key describing which matrix to generate for this
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*> path.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the matrix A will be upper or lower
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*> triangular.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies whether the matrix or its transpose will be used.
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*> = 'N': No transpose
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*> = 'T': Transpose
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*> = 'C': Conjugate transpose (= Transpose)
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*> \endverbatim
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*>
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*> \param[out] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the matrix A is unit triangular.
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*> = 'N': Non-unit triangular
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*> = 'U': Unit triangular
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> The seed vector for the random number generator (used in
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*> SLATMS). Modified on exit.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix to be generated.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The triangular matrix A. If UPLO = 'U', the leading n by n
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*> upper triangular part of the array A contains the upper
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*> triangular matrix, and the strictly lower triangular part of
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*> A is not referenced. If UPLO = 'L', the leading n by n lower
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*> triangular part of the array A contains the lower triangular
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*> matrix, and the strictly upper triangular part of A is not
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*> referenced. If DIAG = 'U', the diagonal elements of A are
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*> set so that A(k,k) = k for 1 <= k <= n.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is REAL array, dimension (N)
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*> The right hand side vector, if IMAT > 10.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (3*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -k, the k-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B,
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$ WORK, INFO )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, TRANS, UPLO
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INTEGER IMAT, INFO, LDA, N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL A( LDA, * ), B( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, TWO, ZERO
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PARAMETER ( ONE = 1.0E+0, TWO = 2.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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CHARACTER DIST, TYPE
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CHARACTER*3 PATH
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INTEGER I, IY, J, JCOUNT, KL, KU, MODE
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REAL ANORM, BIGNUM, BNORM, BSCAL, C, CNDNUM, PLUS1,
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$ PLUS2, RA, RB, REXP, S, SFAC, SMLNUM, STAR1,
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$ TEXP, TLEFT, TSCAL, ULP, UNFL, X, Y, Z
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ISAMAX
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REAL SLAMCH, SLARND
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EXTERNAL LSAME, ISAMAX, SLAMCH, SLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SLARNV, SLATB4, SLATMS, SROT,
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$ SROTG, SSCAL, SSWAP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, REAL, SIGN, SQRT
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* ..
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* .. Executable Statements ..
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*
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PATH( 1: 1 ) = 'Single precision'
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PATH( 2: 3 ) = 'TR'
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UNFL = SLAMCH( 'Safe minimum' )
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ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
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SMLNUM = UNFL
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BIGNUM = ( ONE-ULP ) / SMLNUM
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IF( ( IMAT.GE.7 .AND. IMAT.LE.10 ) .OR. IMAT.EQ.18 ) THEN
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DIAG = 'U'
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ELSE
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DIAG = 'N'
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END IF
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INFO = 0
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*
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* Quick return if N.LE.0.
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*
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IF( N.LE.0 )
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$ RETURN
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*
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* Call SLATB4 to set parameters for SLATMS.
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*
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UPPER = LSAME( UPLO, 'U' )
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IF( UPPER ) THEN
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CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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ELSE
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CALL SLATB4( PATH, -IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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END IF
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*
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* IMAT <= 6: Non-unit triangular matrix
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*
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IF( IMAT.LE.6 ) THEN
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CALL SLATMS( N, N, DIST, ISEED, TYPE, B, MODE, CNDNUM, ANORM,
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$ KL, KU, 'No packing', A, LDA, WORK, INFO )
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*
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* IMAT > 6: Unit triangular matrix
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* The diagonal is deliberately set to something other than 1.
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*
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* IMAT = 7: Matrix is the identity
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*
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ELSE IF( IMAT.EQ.7 ) THEN
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IF( UPPER ) THEN
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DO 20 J = 1, N
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DO 10 I = 1, J - 1
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A( I, J ) = ZERO
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10 CONTINUE
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A( J, J ) = J
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20 CONTINUE
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ELSE
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DO 40 J = 1, N
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A( J, J ) = J
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DO 30 I = J + 1, N
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A( I, J ) = ZERO
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30 CONTINUE
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40 CONTINUE
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END IF
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*
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* IMAT > 7: Non-trivial unit triangular matrix
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*
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* Generate a unit triangular matrix T with condition CNDNUM by
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* forming a triangular matrix with known singular values and
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* filling in the zero entries with Givens rotations.
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*
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ELSE IF( IMAT.LE.10 ) THEN
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IF( UPPER ) THEN
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DO 60 J = 1, N
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DO 50 I = 1, J - 1
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A( I, J ) = ZERO
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50 CONTINUE
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A( J, J ) = J
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60 CONTINUE
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ELSE
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DO 80 J = 1, N
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A( J, J ) = J
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DO 70 I = J + 1, N
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A( I, J ) = ZERO
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70 CONTINUE
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80 CONTINUE
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END IF
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*
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* Since the trace of a unit triangular matrix is 1, the product
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* of its singular values must be 1. Let s = sqrt(CNDNUM),
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* x = sqrt(s) - 1/sqrt(s), y = sqrt(2/(n-2))*x, and z = x**2.
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* The following triangular matrix has singular values s, 1, 1,
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* ..., 1, 1/s:
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*
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* 1 y y y ... y y z
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* 1 0 0 ... 0 0 y
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* 1 0 ... 0 0 y
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* . ... . . .
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* . . . .
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* 1 0 y
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* 1 y
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* 1
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*
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* To fill in the zeros, we first multiply by a matrix with small
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* condition number of the form
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*
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* 1 0 0 0 0 ...
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* 1 + * 0 0 ...
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* 1 + 0 0 0
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* 1 + * 0 0
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* 1 + 0 0
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* ...
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* 1 + 0
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* 1 0
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* 1
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*
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* Each element marked with a '*' is formed by taking the product
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* of the adjacent elements marked with '+'. The '*'s can be
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* chosen freely, and the '+'s are chosen so that the inverse of
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* T will have elements of the same magnitude as T. If the *'s in
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* both T and inv(T) have small magnitude, T is well conditioned.
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* The two offdiagonals of T are stored in WORK.
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*
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* The product of these two matrices has the form
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*
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* 1 y y y y y . y y z
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* 1 + * 0 0 . 0 0 y
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* 1 + 0 0 . 0 0 y
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* 1 + * . . . .
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* 1 + . . . .
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* . . . . .
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* . . . .
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* 1 + y
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* 1 y
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* 1
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*
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* Now we multiply by Givens rotations, using the fact that
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*
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* [ c s ] [ 1 w ] [ -c -s ] = [ 1 -w ]
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* [ -s c ] [ 0 1 ] [ s -c ] [ 0 1 ]
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* and
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* [ -c -s ] [ 1 0 ] [ c s ] = [ 1 0 ]
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* [ s -c ] [ w 1 ] [ -s c ] [ -w 1 ]
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*
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* where c = w / sqrt(w**2+4) and s = 2 / sqrt(w**2+4).
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*
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STAR1 = 0.25
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SFAC = 0.5
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PLUS1 = SFAC
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DO 90 J = 1, N, 2
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PLUS2 = STAR1 / PLUS1
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WORK( J ) = PLUS1
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WORK( N+J ) = STAR1
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IF( J+1.LE.N ) THEN
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WORK( J+1 ) = PLUS2
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WORK( N+J+1 ) = ZERO
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PLUS1 = STAR1 / PLUS2
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REXP = SLARND( 2, ISEED )
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STAR1 = STAR1*( SFAC**REXP )
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IF( REXP.LT.ZERO ) THEN
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STAR1 = -SFAC**( ONE-REXP )
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ELSE
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STAR1 = SFAC**( ONE+REXP )
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END IF
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END IF
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90 CONTINUE
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*
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X = SQRT( CNDNUM ) - 1 / SQRT( CNDNUM )
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IF( N.GT.2 ) THEN
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Y = SQRT( 2. / ( N-2 ) )*X
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ELSE
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Y = ZERO
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END IF
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Z = X*X
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*
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IF( UPPER ) THEN
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IF( N.GT.3 ) THEN
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CALL SCOPY( N-3, WORK, 1, A( 2, 3 ), LDA+1 )
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IF( N.GT.4 )
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$ CALL SCOPY( N-4, WORK( N+1 ), 1, A( 2, 4 ), LDA+1 )
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END IF
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DO 100 J = 2, N - 1
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A( 1, J ) = Y
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A( J, N ) = Y
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100 CONTINUE
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A( 1, N ) = Z
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ELSE
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IF( N.GT.3 ) THEN
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CALL SCOPY( N-3, WORK, 1, A( 3, 2 ), LDA+1 )
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IF( N.GT.4 )
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$ CALL SCOPY( N-4, WORK( N+1 ), 1, A( 4, 2 ), LDA+1 )
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END IF
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DO 110 J = 2, N - 1
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A( J, 1 ) = Y
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A( N, J ) = Y
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110 CONTINUE
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A( N, 1 ) = Z
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END IF
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*
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* Fill in the zeros using Givens rotations.
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*
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IF( UPPER ) THEN
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DO 120 J = 1, N - 1
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RA = A( J, J+1 )
|
||
|
|
RB = 2.0
|
||
|
|
CALL SROTG( RA, RB, C, S )
|
||
|
|
*
|
||
|
|
* Multiply by [ c s; -s c] on the left.
|
||
|
|
*
|
||
|
|
IF( N.GT.J+1 )
|
||
|
|
$ CALL SROT( N-J-1, A( J, J+2 ), LDA, A( J+1, J+2 ),
|
||
|
|
$ LDA, C, S )
|
||
|
|
*
|
||
|
|
* Multiply by [-c -s; s -c] on the right.
|
||
|
|
*
|
||
|
|
IF( J.GT.1 )
|
||
|
|
$ CALL SROT( J-1, A( 1, J+1 ), 1, A( 1, J ), 1, -C, -S )
|
||
|
|
*
|
||
|
|
* Negate A(J,J+1).
|
||
|
|
*
|
||
|
|
A( J, J+1 ) = -A( J, J+1 )
|
||
|
|
120 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 130 J = 1, N - 1
|
||
|
|
RA = A( J+1, J )
|
||
|
|
RB = 2.0
|
||
|
|
CALL SROTG( RA, RB, C, S )
|
||
|
|
*
|
||
|
|
* Multiply by [ c -s; s c] on the right.
|
||
|
|
*
|
||
|
|
IF( N.GT.J+1 )
|
||
|
|
$ CALL SROT( N-J-1, A( J+2, J+1 ), 1, A( J+2, J ), 1, C,
|
||
|
|
$ -S )
|
||
|
|
*
|
||
|
|
* Multiply by [-c s; -s -c] on the left.
|
||
|
|
*
|
||
|
|
IF( J.GT.1 )
|
||
|
|
$ CALL SROT( J-1, A( J, 1 ), LDA, A( J+1, 1 ), LDA, -C,
|
||
|
|
$ S )
|
||
|
|
*
|
||
|
|
* Negate A(J+1,J).
|
||
|
|
*
|
||
|
|
A( J+1, J ) = -A( J+1, J )
|
||
|
|
130 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* IMAT > 10: Pathological test cases. These triangular matrices
|
||
|
|
* are badly scaled or badly conditioned, so when used in solving a
|
||
|
|
* triangular system they may cause overflow in the solution vector.
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.11 ) THEN
|
||
|
|
*
|
||
|
|
* Type 11: Generate a triangular matrix with elements between
|
||
|
|
* -1 and 1. Give the diagonal norm 2 to make it well-conditioned.
|
||
|
|
* Make the right hand side large so that it requires scaling.
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 140 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
||
|
|
A( J, J ) = SIGN( TWO, A( J, J ) )
|
||
|
|
140 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 150 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, N-J+1, A( J, J ) )
|
||
|
|
A( J, J ) = SIGN( TWO, A( J, J ) )
|
||
|
|
150 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set the right hand side so that the largest value is BIGNUM.
|
||
|
|
*
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
IY = ISAMAX( N, B, 1 )
|
||
|
|
BNORM = ABS( B( IY ) )
|
||
|
|
BSCAL = BIGNUM / MAX( ONE, BNORM )
|
||
|
|
CALL SSCAL( N, BSCAL, B, 1 )
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.12 ) THEN
|
||
|
|
*
|
||
|
|
* Type 12: Make the first diagonal element in the solve small to
|
||
|
|
* cause immediate overflow when dividing by T(j,j).
|
||
|
|
* In type 12, the offdiagonal elements are small (CNORM(j) < 1).
|
||
|
|
*
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
TSCAL = ONE / MAX( ONE, REAL( N-1 ) )
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 160 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
||
|
|
CALL SSCAL( J-1, TSCAL, A( 1, J ), 1 )
|
||
|
|
A( J, J ) = SIGN( ONE, A( J, J ) )
|
||
|
|
160 CONTINUE
|
||
|
|
A( N, N ) = SMLNUM*A( N, N )
|
||
|
|
ELSE
|
||
|
|
DO 170 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, N-J+1, A( J, J ) )
|
||
|
|
IF( N.GT.J )
|
||
|
|
$ CALL SSCAL( N-J, TSCAL, A( J+1, J ), 1 )
|
||
|
|
A( J, J ) = SIGN( ONE, A( J, J ) )
|
||
|
|
170 CONTINUE
|
||
|
|
A( 1, 1 ) = SMLNUM*A( 1, 1 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.13 ) THEN
|
||
|
|
*
|
||
|
|
* Type 13: Make the first diagonal element in the solve small to
|
||
|
|
* cause immediate overflow when dividing by T(j,j).
|
||
|
|
* In type 13, the offdiagonal elements are O(1) (CNORM(j) > 1).
|
||
|
|
*
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 180 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
||
|
|
A( J, J ) = SIGN( ONE, A( J, J ) )
|
||
|
|
180 CONTINUE
|
||
|
|
A( N, N ) = SMLNUM*A( N, N )
|
||
|
|
ELSE
|
||
|
|
DO 190 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, N-J+1, A( J, J ) )
|
||
|
|
A( J, J ) = SIGN( ONE, A( J, J ) )
|
||
|
|
190 CONTINUE
|
||
|
|
A( 1, 1 ) = SMLNUM*A( 1, 1 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.14 ) THEN
|
||
|
|
*
|
||
|
|
* Type 14: T is diagonal with small numbers on the diagonal to
|
||
|
|
* make the growth factor underflow, but a small right hand side
|
||
|
|
* chosen so that the solution does not overflow.
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
JCOUNT = 1
|
||
|
|
DO 210 J = N, 1, -1
|
||
|
|
DO 200 I = 1, J - 1
|
||
|
|
A( I, J ) = ZERO
|
||
|
|
200 CONTINUE
|
||
|
|
IF( JCOUNT.LE.2 ) THEN
|
||
|
|
A( J, J ) = SMLNUM
|
||
|
|
ELSE
|
||
|
|
A( J, J ) = ONE
|
||
|
|
END IF
|
||
|
|
JCOUNT = JCOUNT + 1
|
||
|
|
IF( JCOUNT.GT.4 )
|
||
|
|
$ JCOUNT = 1
|
||
|
|
210 CONTINUE
|
||
|
|
ELSE
|
||
|
|
JCOUNT = 1
|
||
|
|
DO 230 J = 1, N
|
||
|
|
DO 220 I = J + 1, N
|
||
|
|
A( I, J ) = ZERO
|
||
|
|
220 CONTINUE
|
||
|
|
IF( JCOUNT.LE.2 ) THEN
|
||
|
|
A( J, J ) = SMLNUM
|
||
|
|
ELSE
|
||
|
|
A( J, J ) = ONE
|
||
|
|
END IF
|
||
|
|
JCOUNT = JCOUNT + 1
|
||
|
|
IF( JCOUNT.GT.4 )
|
||
|
|
$ JCOUNT = 1
|
||
|
|
230 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set the right hand side alternately zero and small.
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
B( 1 ) = ZERO
|
||
|
|
DO 240 I = N, 2, -2
|
||
|
|
B( I ) = ZERO
|
||
|
|
B( I-1 ) = SMLNUM
|
||
|
|
240 CONTINUE
|
||
|
|
ELSE
|
||
|
|
B( N ) = ZERO
|
||
|
|
DO 250 I = 1, N - 1, 2
|
||
|
|
B( I ) = ZERO
|
||
|
|
B( I+1 ) = SMLNUM
|
||
|
|
250 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.15 ) THEN
|
||
|
|
*
|
||
|
|
* Type 15: Make the diagonal elements small to cause gradual
|
||
|
|
* overflow when dividing by T(j,j). To control the amount of
|
||
|
|
* scaling needed, the matrix is bidiagonal.
|
||
|
|
*
|
||
|
|
TEXP = ONE / MAX( ONE, REAL( N-1 ) )
|
||
|
|
TSCAL = SMLNUM**TEXP
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 270 J = 1, N
|
||
|
|
DO 260 I = 1, J - 2
|
||
|
|
A( I, J ) = 0.
|
||
|
|
260 CONTINUE
|
||
|
|
IF( J.GT.1 )
|
||
|
|
$ A( J-1, J ) = -ONE
|
||
|
|
A( J, J ) = TSCAL
|
||
|
|
270 CONTINUE
|
||
|
|
B( N ) = ONE
|
||
|
|
ELSE
|
||
|
|
DO 290 J = 1, N
|
||
|
|
DO 280 I = J + 2, N
|
||
|
|
A( I, J ) = 0.
|
||
|
|
280 CONTINUE
|
||
|
|
IF( J.LT.N )
|
||
|
|
$ A( J+1, J ) = -ONE
|
||
|
|
A( J, J ) = TSCAL
|
||
|
|
290 CONTINUE
|
||
|
|
B( 1 ) = ONE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.16 ) THEN
|
||
|
|
*
|
||
|
|
* Type 16: One zero diagonal element.
|
||
|
|
*
|
||
|
|
IY = N / 2 + 1
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 300 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
||
|
|
IF( J.NE.IY ) THEN
|
||
|
|
A( J, J ) = SIGN( TWO, A( J, J ) )
|
||
|
|
ELSE
|
||
|
|
A( J, J ) = ZERO
|
||
|
|
END IF
|
||
|
|
300 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 310 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, N-J+1, A( J, J ) )
|
||
|
|
IF( J.NE.IY ) THEN
|
||
|
|
A( J, J ) = SIGN( TWO, A( J, J ) )
|
||
|
|
ELSE
|
||
|
|
A( J, J ) = ZERO
|
||
|
|
END IF
|
||
|
|
310 CONTINUE
|
||
|
|
END IF
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
CALL SSCAL( N, TWO, B, 1 )
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.17 ) THEN
|
||
|
|
*
|
||
|
|
* Type 17: Make the offdiagonal elements large to cause overflow
|
||
|
|
* when adding a column of T. In the non-transposed case, the
|
||
|
|
* matrix is constructed to cause overflow when adding a column in
|
||
|
|
* every other step.
|
||
|
|
*
|
||
|
|
TSCAL = UNFL / ULP
|
||
|
|
TSCAL = ( ONE-ULP ) / TSCAL
|
||
|
|
DO 330 J = 1, N
|
||
|
|
DO 320 I = 1, N
|
||
|
|
A( I, J ) = 0.
|
||
|
|
320 CONTINUE
|
||
|
|
330 CONTINUE
|
||
|
|
TEXP = ONE
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 340 J = N, 2, -2
|
||
|
|
A( 1, J ) = -TSCAL / REAL( N+1 )
|
||
|
|
A( J, J ) = ONE
|
||
|
|
B( J ) = TEXP*( ONE-ULP )
|
||
|
|
A( 1, J-1 ) = -( TSCAL / REAL( N+1 ) ) / REAL( N+2 )
|
||
|
|
A( J-1, J-1 ) = ONE
|
||
|
|
B( J-1 ) = TEXP*REAL( N*N+N-1 )
|
||
|
|
TEXP = TEXP*2.
|
||
|
|
340 CONTINUE
|
||
|
|
B( 1 ) = ( REAL( N+1 ) / REAL( N+2 ) )*TSCAL
|
||
|
|
ELSE
|
||
|
|
DO 350 J = 1, N - 1, 2
|
||
|
|
A( N, J ) = -TSCAL / REAL( N+1 )
|
||
|
|
A( J, J ) = ONE
|
||
|
|
B( J ) = TEXP*( ONE-ULP )
|
||
|
|
A( N, J+1 ) = -( TSCAL / REAL( N+1 ) ) / REAL( N+2 )
|
||
|
|
A( J+1, J+1 ) = ONE
|
||
|
|
B( J+1 ) = TEXP*REAL( N*N+N-1 )
|
||
|
|
TEXP = TEXP*2.
|
||
|
|
350 CONTINUE
|
||
|
|
B( N ) = ( REAL( N+1 ) / REAL( N+2 ) )*TSCAL
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.18 ) THEN
|
||
|
|
*
|
||
|
|
* Type 18: Generate a unit triangular matrix with elements
|
||
|
|
* between -1 and 1, and make the right hand side large so that it
|
||
|
|
* requires scaling.
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 360 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J-1, A( 1, J ) )
|
||
|
|
A( J, J ) = ZERO
|
||
|
|
360 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 370 J = 1, N
|
||
|
|
IF( J.LT.N )
|
||
|
|
$ CALL SLARNV( 2, ISEED, N-J, A( J+1, J ) )
|
||
|
|
A( J, J ) = ZERO
|
||
|
|
370 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set the right hand side so that the largest value is BIGNUM.
|
||
|
|
*
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
IY = ISAMAX( N, B, 1 )
|
||
|
|
BNORM = ABS( B( IY ) )
|
||
|
|
BSCAL = BIGNUM / MAX( ONE, BNORM )
|
||
|
|
CALL SSCAL( N, BSCAL, B, 1 )
|
||
|
|
*
|
||
|
|
ELSE IF( IMAT.EQ.19 ) THEN
|
||
|
|
*
|
||
|
|
* Type 19: Generate a triangular matrix with elements between
|
||
|
|
* BIGNUM/(n-1) and BIGNUM so that at least one of the column
|
||
|
|
* norms will exceed BIGNUM.
|
||
|
|
* 1/3/91: SLATRS no longer can handle this case
|
||
|
|
*
|
||
|
|
TLEFT = BIGNUM / MAX( ONE, REAL( N-1 ) )
|
||
|
|
TSCAL = BIGNUM*( REAL( N-1 ) / MAX( ONE, REAL( N ) ) )
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 390 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, J, A( 1, J ) )
|
||
|
|
DO 380 I = 1, J
|
||
|
|
A( I, J ) = SIGN( TLEFT, A( I, J ) ) + TSCAL*A( I, J )
|
||
|
|
380 CONTINUE
|
||
|
|
390 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 410 J = 1, N
|
||
|
|
CALL SLARNV( 2, ISEED, N-J+1, A( J, J ) )
|
||
|
|
DO 400 I = J, N
|
||
|
|
A( I, J ) = SIGN( TLEFT, A( I, J ) ) + TSCAL*A( I, J )
|
||
|
|
400 CONTINUE
|
||
|
|
410 CONTINUE
|
||
|
|
END IF
|
||
|
|
CALL SLARNV( 2, ISEED, N, B )
|
||
|
|
CALL SSCAL( N, TWO, B, 1 )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Flip the matrix if the transpose will be used.
|
||
|
|
*
|
||
|
|
IF( .NOT.LSAME( TRANS, 'N' ) ) THEN
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
DO 420 J = 1, N / 2
|
||
|
|
CALL SSWAP( N-2*J+1, A( J, J ), LDA, A( J+1, N-J+1 ),
|
||
|
|
$ -1 )
|
||
|
|
420 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 430 J = 1, N / 2
|
||
|
|
CALL SSWAP( N-2*J+1, A( J, J ), 1, A( N-J+1, J+1 ),
|
||
|
|
$ -LDA )
|
||
|
|
430 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SLATTR
|
||
|
|
*
|
||
|
|
END
|