642 lines
15 KiB
Fortran
642 lines
15 KiB
Fortran
*> \brief \b SLATB4
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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 SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
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* CNDNUM, DIST )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIST, TYPE
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* CHARACTER*3 PATH
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* INTEGER IMAT, KL, KU, M, MODE, N
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* REAL ANORM, CNDNUM
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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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*> SLATB4 sets parameters for the matrix generator based on the type of
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*> matrix to be generated.
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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] PATH
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*> \verbatim
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*> PATH is CHARACTER*3
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*> The LAPACK path name.
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*> \endverbatim
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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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows in the matrix to be generated.
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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 number of columns in the matrix to be generated.
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*> \endverbatim
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*>
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*> \param[out] TYPE
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*> \verbatim
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*> TYPE is CHARACTER*1
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*> The type of the matrix to be generated:
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*> = 'S': symmetric matrix
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*> = 'P': symmetric positive (semi)definite matrix
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*> = 'N': nonsymmetric matrix
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*> \endverbatim
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*>
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*> \param[out] KL
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*> \verbatim
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*> KL is INTEGER
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*> The lower band width of the matrix to be generated.
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*> \endverbatim
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*>
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*> \param[out] KU
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*> \verbatim
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*> KU is INTEGER
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*> The upper band width of the matrix to be generated.
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*> \endverbatim
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*>
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*> \param[out] ANORM
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*> \verbatim
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*> ANORM is REAL
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*> The desired norm of the matrix to be generated. The diagonal
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*> matrix of singular values or eigenvalues is scaled by this
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*> value.
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*> \endverbatim
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*>
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*> \param[out] MODE
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*> \verbatim
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*> MODE is INTEGER
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*> A key indicating how to choose the vector of eigenvalues.
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*> \endverbatim
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*>
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*> \param[out] CNDNUM
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*> \verbatim
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*> CNDNUM is REAL
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*> The desired condition number.
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*> \endverbatim
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*>
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*> \param[out] DIST
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*> \verbatim
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*> DIST is CHARACTER*1
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*> The type of distribution to be used by the random number
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*> generator.
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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 SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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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 DIST, TYPE
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CHARACTER*3 PATH
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INTEGER IMAT, KL, KU, M, MODE, N
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REAL ANORM, CNDNUM
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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 SHRINK, TENTH
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PARAMETER ( SHRINK = 0.25E0, TENTH = 0.1E+0 )
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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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REAL TWO
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PARAMETER ( TWO = 2.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL FIRST
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CHARACTER*2 C2
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INTEGER MAT
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REAL BADC1, BADC2, EPS, LARGE, SMALL
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* ..
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* .. External Functions ..
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LOGICAL LSAMEN
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REAL SLAMCH
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EXTERNAL LSAMEN, SLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, SQRT
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* ..
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* .. Save statement ..
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SAVE EPS, SMALL, LARGE, BADC1, BADC2, FIRST
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* ..
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* .. Data statements ..
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DATA FIRST / .TRUE. /
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* ..
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* .. Executable Statements ..
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*
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* Set some constants for use in the subroutine.
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*
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IF( FIRST ) THEN
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FIRST = .FALSE.
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EPS = SLAMCH( 'Precision' )
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BADC2 = TENTH / EPS
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BADC1 = SQRT( BADC2 )
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SMALL = SLAMCH( 'Safe minimum' )
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LARGE = ONE / SMALL
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SMALL = SHRINK*( SMALL / EPS )
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LARGE = ONE / SMALL
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END IF
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*
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C2 = PATH( 2: 3 )
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*
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* Set some parameters we don't plan to change.
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*
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DIST = 'S'
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MODE = 3
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*
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IF( LSAMEN( 2, C2, 'QR' ) .OR. LSAMEN( 2, C2, 'LQ' ) .OR.
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$ LSAMEN( 2, C2, 'QL' ) .OR. LSAMEN( 2, C2, 'RQ' ) ) THEN
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*
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* xQR, xLQ, xQL, xRQ: Set parameters to generate a general
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* M x N matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'N'
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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KU = 0
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ELSE IF( IMAT.EQ.2 ) THEN
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KL = 0
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KU = MAX( N-1, 0 )
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ELSE IF( IMAT.EQ.3 ) THEN
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KL = MAX( M-1, 0 )
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KU = 0
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ELSE
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KL = MAX( M-1, 0 )
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KU = MAX( N-1, 0 )
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END IF
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.5 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.6 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.7 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.8 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'QK' ) ) THEN
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*
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* xQK: truncated QR with pivoting.
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* Set parameters to generate a general
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* M x N matrix.
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*
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* Set TYPE, the type of matrix to be generated. 'N' is nonsymmetric.
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*
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TYPE = 'N'
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*
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* Set DIST, the type of distribution for the random
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* number generator. 'S' is
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*
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DIST = 'S'
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.2 ) THEN
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*
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* 2. Random, Diagonal, CNDNUM = 2
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*
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KL = 0
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KU = 0
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CNDNUM = TWO
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ANORM = ONE
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MODE = 3
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ELSE IF( IMAT.EQ.3 ) THEN
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*
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* 3. Random, Upper triangular, CNDNUM = 2
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*
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KL = 0
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KU = MAX( N-1, 0 )
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CNDNUM = TWO
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ANORM = ONE
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MODE = 3
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ELSE IF( IMAT.EQ.4 ) THEN
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*
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* 4. Random, Lower triangular, CNDNUM = 2
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*
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KL = MAX( M-1, 0 )
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KU = 0
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CNDNUM = TWO
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ANORM = ONE
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MODE = 3
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ELSE
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*
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* 5.-19. Rectangular matrix
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*
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KL = MAX( M-1, 0 )
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KU = MAX( N-1, 0 )
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*
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IF( IMAT.GE.5 .AND. IMAT.LE.14 ) THEN
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*
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* 5.-14. Random, CNDNUM = 2.
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*
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CNDNUM = TWO
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ANORM = ONE
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MODE = 3
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*
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ELSE IF( IMAT.EQ.15 ) THEN
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*
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* 15. Random, CNDNUM = sqrt(0.1/EPS)
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*
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CNDNUM = BADC1
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ANORM = ONE
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MODE = 3
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*
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ELSE IF( IMAT.EQ.16 ) THEN
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*
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* 16. Random, CNDNUM = 0.1/EPS
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*
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CNDNUM = BADC2
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ANORM = ONE
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MODE = 3
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*
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ELSE IF( IMAT.EQ.17 ) THEN
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*
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* 17. Random, CNDNUM = 0.1/EPS,
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* one small singular value S(N)=1/CNDNUM
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*
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CNDNUM = BADC2
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ANORM = ONE
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MODE = 2
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*
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ELSE IF( IMAT.EQ.18 ) THEN
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*
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* 18. Random, scaled near underflow
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*
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CNDNUM = TWO
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ANORM = SMALL
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MODE = 3
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*
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ELSE IF( IMAT.EQ.19 ) THEN
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*
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* 19. Random, scaled near overflow
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*
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CNDNUM = TWO
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ANORM = LARGE
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MODE = 3
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*
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END IF
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*
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'GE' ) ) THEN
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*
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* xGE: Set parameters to generate a general M x N matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'N'
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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KU = 0
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ELSE IF( IMAT.EQ.2 ) THEN
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KL = 0
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KU = MAX( N-1, 0 )
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ELSE IF( IMAT.EQ.3 ) THEN
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KL = MAX( M-1, 0 )
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KU = 0
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ELSE
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KL = MAX( M-1, 0 )
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KU = MAX( N-1, 0 )
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END IF
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.8 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.9 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.10 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.11 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN
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*
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* xGB: Set parameters to generate a general banded matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'N'
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.5 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.6 ) THEN
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CNDNUM = TENTH*BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.7 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.8 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'GT' ) ) THEN
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*
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* xGT: Set parameters to generate a general tridiagonal matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'N'
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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ELSE
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KL = 1
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END IF
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KU = KL
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.3 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.4 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.5 .OR. IMAT.EQ.11 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.6 .OR. IMAT.EQ.12 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'PP' ) ) THEN
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*
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* xPO, xPP, xSY, xSP: Set parameters to generate a
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* symmetric positive definite matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = C2( 1: 1 )
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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ELSE
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KL = MAX( N-1, 0 )
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END IF
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KU = KL
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.6 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.7 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.8 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.9 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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*
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ELSE IF( LSAMEN( 2, C2, 'SY' ) .OR. LSAMEN( 2, C2, 'SP' ) ) THEN
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*
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* xSY, xSP: Set parameters to generate a
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* symmetric matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = C2( 1: 1 )
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*
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* Set the lower and upper bandwidths.
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*
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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ELSE
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KL = MAX( N-1, 0 )
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END IF
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KU = KL
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.7 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.8 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.9 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.10 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'PB' ) ) THEN
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*
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* xPB: Set parameters to generate a symmetric band matrix.
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'P'
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*
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* Set the norm and condition number.
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*
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IF( IMAT.EQ.5 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.6 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.7 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.8 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'PT' ) ) THEN
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*
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* xPT: Set parameters to generate a symmetric positive definite
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* tridiagonal matrix.
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*
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TYPE = 'P'
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IF( IMAT.EQ.1 ) THEN
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KL = 0
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ELSE
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KL = 1
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END IF
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KU = KL
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*
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* Set the condition number and norm.
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*
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IF( IMAT.EQ.3 ) THEN
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CNDNUM = BADC1
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ELSE IF( IMAT.EQ.4 ) THEN
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CNDNUM = BADC2
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ELSE
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CNDNUM = TWO
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END IF
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*
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IF( IMAT.EQ.5 .OR. IMAT.EQ.11 ) THEN
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ANORM = SMALL
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ELSE IF( IMAT.EQ.6 .OR. IMAT.EQ.12 ) THEN
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ANORM = LARGE
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ELSE
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ANORM = ONE
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END IF
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*
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ELSE IF( LSAMEN( 2, C2, 'TR' ) .OR. LSAMEN( 2, C2, 'TP' ) ) THEN
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*
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* xTR, xTP: Set parameters to generate a triangular matrix
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*
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* Set TYPE, the type of matrix to be generated.
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*
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TYPE = 'N'
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*
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* Set the lower and upper bandwidths.
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*
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MAT = ABS( IMAT )
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IF( MAT.EQ.1 .OR. MAT.EQ.7 ) THEN
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KL = 0
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KU = 0
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ELSE IF( IMAT.LT.0 ) THEN
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KL = MAX( N-1, 0 )
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KU = 0
|
|
ELSE
|
|
KL = 0
|
|
KU = MAX( N-1, 0 )
|
|
END IF
|
|
*
|
|
* Set the condition number and norm.
|
|
*
|
|
IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
|
|
CNDNUM = BADC1
|
|
ELSE IF( MAT.EQ.4 ) THEN
|
|
CNDNUM = BADC2
|
|
ELSE IF( MAT.EQ.10 ) THEN
|
|
CNDNUM = BADC2
|
|
ELSE
|
|
CNDNUM = TWO
|
|
END IF
|
|
*
|
|
IF( MAT.EQ.5 ) THEN
|
|
ANORM = SMALL
|
|
ELSE IF( MAT.EQ.6 ) THEN
|
|
ANORM = LARGE
|
|
ELSE
|
|
ANORM = ONE
|
|
END IF
|
|
*
|
|
ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
|
|
*
|
|
* xTB: Set parameters to generate a triangular band matrix.
|
|
*
|
|
* Set TYPE, the type of matrix to be generated.
|
|
*
|
|
TYPE = 'N'
|
|
*
|
|
* Set the norm and condition number.
|
|
*
|
|
MAT = ABS( IMAT )
|
|
IF( MAT.EQ.2 .OR. MAT.EQ.8 ) THEN
|
|
CNDNUM = BADC1
|
|
ELSE IF( MAT.EQ.3 .OR. MAT.EQ.9 ) THEN
|
|
CNDNUM = BADC2
|
|
ELSE
|
|
CNDNUM = TWO
|
|
END IF
|
|
*
|
|
IF( MAT.EQ.4 ) THEN
|
|
ANORM = SMALL
|
|
ELSE IF( MAT.EQ.5 ) THEN
|
|
ANORM = LARGE
|
|
ELSE
|
|
ANORM = ONE
|
|
END IF
|
|
END IF
|
|
IF( N.LE.1 )
|
|
$ CNDNUM = ONE
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SLATB4
|
|
*
|
|
END
|