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1225 lines
42 KiB
1225 lines
42 KiB
2 years ago
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*> \brief \b DLATMR
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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 DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
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* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
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* CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM,
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* PACK, A, LDA, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM
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* INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
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* DOUBLE PRECISION ANORM, COND, CONDL, CONDR, DMAX, SPARSE
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* ..
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* .. Array Arguments ..
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* INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * )
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* DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * )
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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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*> DLATMR generates random matrices of various types for testing
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*> LAPACK programs.
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*>
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*> DLATMR operates by applying the following sequence of
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*> operations:
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*>
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*> Generate a matrix A with random entries of distribution DIST
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*> which is symmetric if SYM='S', and nonsymmetric
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*> if SYM='N'.
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*>
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*> Set the diagonal to D, where D may be input or
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*> computed according to MODE, COND, DMAX and RSIGN
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*> as described below.
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*>
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*> Grade the matrix, if desired, from the left and/or right
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*> as specified by GRADE. The inputs DL, MODEL, CONDL, DR,
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*> MODER and CONDR also determine the grading as described
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*> below.
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*>
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*> Permute, if desired, the rows and/or columns as specified by
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*> PIVTNG and IPIVOT.
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*>
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*> Set random entries to zero, if desired, to get a random sparse
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*> matrix as specified by SPARSE.
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*>
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*> Make A a band matrix, if desired, by zeroing out the matrix
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*> outside a band of lower bandwidth KL and upper bandwidth KU.
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*>
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*> Scale A, if desired, to have maximum entry ANORM.
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*>
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*> Pack the matrix if desired. Options specified by PACK are:
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*> no packing
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*> zero out upper half (if symmetric)
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*> zero out lower half (if symmetric)
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*> store the upper half columnwise (if symmetric or
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*> square upper triangular)
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*> store the lower half columnwise (if symmetric or
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*> square lower triangular)
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*> same as upper half rowwise if symmetric
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*> store the lower triangle in banded format (if symmetric)
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*> store the upper triangle in banded format (if symmetric)
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*> store the entire matrix in banded format
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*>
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*> Note: If two calls to DLATMR differ only in the PACK parameter,
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*> they will generate mathematically equivalent matrices.
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*>
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*> If two calls to DLATMR both have full bandwidth (KL = M-1
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*> and KU = N-1), and differ only in the PIVTNG and PACK
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*> parameters, then the matrices generated will differ only
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*> in the order of the rows and/or columns, and otherwise
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*> contain the same data. This consistency cannot be and
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*> is not maintained with less than full bandwidth.
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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] M
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*> \verbatim
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*> M is INTEGER
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*> Number of rows of A. Not modified.
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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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*> Number of columns of A. Not modified.
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*> \endverbatim
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*>
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*> \param[in] DIST
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*> \verbatim
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*> DIST is CHARACTER*1
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*> On entry, DIST specifies the type of distribution to be used
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*> to generate a random matrix .
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*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
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*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
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*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal )
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*> Not modified.
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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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*> On entry ISEED specifies the seed of the random number
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*> generator. They should lie between 0 and 4095 inclusive,
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*> and ISEED(4) should be odd. The random number generator
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*> uses a linear congruential sequence limited to small
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*> integers, and so should produce machine independent
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*> random numbers. The values of ISEED are changed on
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*> exit, and can be used in the next call to DLATMR
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*> to continue the same random number sequence.
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*> Changed on exit.
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*> \endverbatim
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*>
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*> \param[in] SYM
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*> \verbatim
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*> SYM is CHARACTER*1
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*> If SYM='S' or 'H', generated matrix is symmetric.
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*> If SYM='N', generated matrix is nonsymmetric.
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (min(M,N))
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*> On entry this array specifies the diagonal entries
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*> of the diagonal of A. D may either be specified
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*> on entry, or set according to MODE and COND as described
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*> below. May be changed on exit if MODE is nonzero.
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*> \endverbatim
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*>
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*> \param[in] MODE
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*> \verbatim
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*> MODE is INTEGER
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*> On entry describes how D is to be used:
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*> MODE = 0 means use D as input
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*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
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*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
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*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
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*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
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*> MODE = 5 sets D to random numbers in the range
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*> ( 1/COND , 1 ) such that their logarithms
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*> are uniformly distributed.
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*> MODE = 6 set D to random numbers from same distribution
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*> as the rest of the matrix.
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*> MODE < 0 has the same meaning as ABS(MODE), except that
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*> the order of the elements of D is reversed.
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*> Thus if MODE is positive, D has entries ranging from
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*> 1 to 1/COND, if negative, from 1/COND to 1,
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in] COND
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*> \verbatim
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*> COND is DOUBLE PRECISION
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*> On entry, used as described under MODE above.
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*> If used, it must be >= 1. Not modified.
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*> \endverbatim
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*>
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*> \param[in] DMAX
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*> \verbatim
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*> DMAX is DOUBLE PRECISION
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*> If MODE neither -6, 0 nor 6, the diagonal is scaled by
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*> DMAX / max(abs(D(i))), so that maximum absolute entry
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*> of diagonal is abs(DMAX). If DMAX is negative (or zero),
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*> diagonal will be scaled by a negative number (or zero).
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*> \endverbatim
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*>
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*> \param[in] RSIGN
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*> \verbatim
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*> RSIGN is CHARACTER*1
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*> If MODE neither -6, 0 nor 6, specifies sign of diagonal
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*> as follows:
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*> 'T' => diagonal entries are multiplied by 1 or -1
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*> with probability .5
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*> 'F' => diagonal unchanged
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in] GRADE
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*> \verbatim
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*> GRADE is CHARACTER*1
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*> Specifies grading of matrix as follows:
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*> 'N' => no grading
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*> 'L' => matrix premultiplied by diag( DL )
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*> (only if matrix nonsymmetric)
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*> 'R' => matrix postmultiplied by diag( DR )
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*> (only if matrix nonsymmetric)
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*> 'B' => matrix premultiplied by diag( DL ) and
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*> postmultiplied by diag( DR )
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*> (only if matrix nonsymmetric)
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*> 'S' or 'H' => matrix premultiplied by diag( DL ) and
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*> postmultiplied by diag( DL )
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*> ('S' for symmetric, or 'H' for Hermitian)
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*> 'E' => matrix premultiplied by diag( DL ) and
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*> postmultiplied by inv( diag( DL ) )
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*> ( 'E' for eigenvalue invariance)
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*> (only if matrix nonsymmetric)
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*> Note: if GRADE='E', then M must equal N.
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in,out] DL
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*> \verbatim
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*> DL is DOUBLE PRECISION array, dimension (M)
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*> If MODEL=0, then on entry this array specifies the diagonal
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*> entries of a diagonal matrix used as described under GRADE
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*> above. If MODEL is not zero, then DL will be set according
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*> to MODEL and CONDL, analogous to the way D is set according
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*> to MODE and COND (except there is no DMAX parameter for DL).
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*> If GRADE='E', then DL cannot have zero entries.
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*> Not referenced if GRADE = 'N' or 'R'. Changed on exit.
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*> \endverbatim
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*>
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*> \param[in] MODEL
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*> \verbatim
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*> MODEL is INTEGER
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*> This specifies how the diagonal array DL is to be computed,
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*> just as MODE specifies how D is to be computed.
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in] CONDL
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*> \verbatim
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*> CONDL is DOUBLE PRECISION
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*> When MODEL is not zero, this specifies the condition number
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*> of the computed DL. Not modified.
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*> \endverbatim
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*>
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*> \param[in,out] DR
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*> \verbatim
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*> DR is DOUBLE PRECISION array, dimension (N)
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*> If MODER=0, then on entry this array specifies the diagonal
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*> entries of a diagonal matrix used as described under GRADE
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*> above. If MODER is not zero, then DR will be set according
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*> to MODER and CONDR, analogous to the way D is set according
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*> to MODE and COND (except there is no DMAX parameter for DR).
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*> Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'.
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*> Changed on exit.
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*> \endverbatim
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*>
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*> \param[in] MODER
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*> \verbatim
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*> MODER is INTEGER
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*> This specifies how the diagonal array DR is to be computed,
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*> just as MODE specifies how D is to be computed.
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in] CONDR
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*> \verbatim
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*> CONDR is DOUBLE PRECISION
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*> When MODER is not zero, this specifies the condition number
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*> of the computed DR. Not modified.
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*> \endverbatim
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*>
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*> \param[in] PIVTNG
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*> \verbatim
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*> PIVTNG is CHARACTER*1
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*> On entry specifies pivoting permutations as follows:
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*> 'N' or ' ' => none.
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*> 'L' => left or row pivoting (matrix must be nonsymmetric).
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*> 'R' => right or column pivoting (matrix must be
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*> nonsymmetric).
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*> 'B' or 'F' => both or full pivoting, i.e., on both sides.
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*> In this case, M must equal N
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*>
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*> If two calls to DLATMR both have full bandwidth (KL = M-1
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*> and KU = N-1), and differ only in the PIVTNG and PACK
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*> parameters, then the matrices generated will differ only
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*> in the order of the rows and/or columns, and otherwise
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*> contain the same data. This consistency cannot be
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*> maintained with less than full bandwidth.
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*> \endverbatim
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*>
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*> \param[in] IPIVOT
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*> \verbatim
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*> IPIVOT is INTEGER array, dimension (N or M)
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*> This array specifies the permutation used. After the
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*> basic matrix is generated, the rows, columns, or both
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*> are permuted. If, say, row pivoting is selected, DLATMR
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*> starts with the *last* row and interchanges the M-th and
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*> IPIVOT(M)-th rows, then moves to the next-to-last row,
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*> interchanging the (M-1)-th and the IPIVOT(M-1)-th rows,
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*> and so on. In terms of "2-cycles", the permutation is
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*> (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M))
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*> where the rightmost cycle is applied first. This is the
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*> *inverse* of the effect of pivoting in LINPACK. The idea
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*> is that factoring (with pivoting) an identity matrix
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*> which has been inverse-pivoted in this way should
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*> result in a pivot vector identical to IPIVOT.
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*> Not referenced if PIVTNG = 'N'. Not modified.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> On entry specifies the lower bandwidth of the matrix. For
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*> example, KL=0 implies upper triangular, KL=1 implies upper
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*> Hessenberg, and KL at least M-1 implies the matrix is not
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*> banded. Must equal KU if matrix is symmetric.
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*> Not modified.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> On entry specifies the upper bandwidth of the matrix. For
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*> example, KU=0 implies lower triangular, KU=1 implies lower
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*> Hessenberg, and KU at least N-1 implies the matrix is not
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*> banded. Must equal KL if matrix is symmetric.
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*> Not modified.
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*> \endverbatim
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||
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*>
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*> \param[in] SPARSE
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*> \verbatim
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*> SPARSE is DOUBLE PRECISION
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||
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*> On entry specifies the sparsity of the matrix if a sparse
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||
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*> matrix is to be generated. SPARSE should lie between
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*> 0 and 1. To generate a sparse matrix, for each matrix entry
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*> a uniform ( 0, 1 ) random number x is generated and
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*> compared to SPARSE; if x is larger the matrix entry
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*> is unchanged and if x is smaller the entry is set
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*> to zero. Thus on the average a fraction SPARSE of the
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*> entries will be set to zero.
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*> Not modified.
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*> \endverbatim
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||
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*>
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||
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*> \param[in] ANORM
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*> \verbatim
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||
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*> ANORM is DOUBLE PRECISION
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||
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*> On entry specifies maximum entry of output matrix
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||
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*> (output matrix will by multiplied by a constant so that
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*> its largest absolute entry equal ANORM)
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||
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*> if ANORM is nonnegative. If ANORM is negative no scaling
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*> is done. Not modified.
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||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] PACK
|
||
|
|
*> \verbatim
|
||
|
|
*> PACK is CHARACTER*1
|
||
|
|
*> On entry specifies packing of matrix as follows:
|
||
|
|
*> 'N' => no packing
|
||
|
|
*> 'U' => zero out all subdiagonal entries (if symmetric)
|
||
|
|
*> 'L' => zero out all superdiagonal entries (if symmetric)
|
||
|
|
*> 'C' => store the upper triangle columnwise
|
||
|
|
*> (only if matrix symmetric or square upper triangular)
|
||
|
|
*> 'R' => store the lower triangle columnwise
|
||
|
|
*> (only if matrix symmetric or square lower triangular)
|
||
|
|
*> (same as upper half rowwise if symmetric)
|
||
|
|
*> 'B' => store the lower triangle in band storage scheme
|
||
|
|
*> (only if matrix symmetric)
|
||
|
|
*> 'Q' => store the upper triangle in band storage scheme
|
||
|
|
*> (only if matrix symmetric)
|
||
|
|
*> 'Z' => store the entire matrix in band storage scheme
|
||
|
|
*> (pivoting can be provided for by using this
|
||
|
|
*> option to store A in the trailing rows of
|
||
|
|
*> the allocated storage)
|
||
|
|
*>
|
||
|
|
*> Using these options, the various LAPACK packed and banded
|
||
|
|
*> storage schemes can be obtained:
|
||
|
|
*> GB - use 'Z'
|
||
|
|
*> PB, SB or TB - use 'B' or 'Q'
|
||
|
|
*> PP, SP or TP - use 'C' or 'R'
|
||
|
|
*>
|
||
|
|
*> If two calls to DLATMR differ only in the PACK parameter,
|
||
|
|
*> they will generate mathematically equivalent matrices.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is DOUBLE PRECISION array, dimension (LDA,N)
|
||
|
|
*> On exit A is the desired test matrix. Only those
|
||
|
|
*> entries of A which are significant on output
|
||
|
|
*> will be referenced (even if A is in packed or band
|
||
|
|
*> storage format). The 'unoccupied corners' of A in
|
||
|
|
*> band format will be zeroed out.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> on entry LDA specifies the first dimension of A as
|
||
|
|
*> declared in the calling program.
|
||
|
|
*> If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ).
|
||
|
|
*> If PACK='C' or 'R', LDA must be at least 1.
|
||
|
|
*> If PACK='B', or 'Q', LDA must be MIN ( KU+1, N )
|
||
|
|
*> If PACK='Z', LDA must be at least KUU+KLL+1, where
|
||
|
|
*> KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, M-1 )
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] IWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> IWORK is INTEGER array, dimension ( N or M)
|
||
|
|
*> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] INFO
|
||
|
|
*> \verbatim
|
||
|
|
*> INFO is INTEGER
|
||
|
|
*> Error parameter on exit:
|
||
|
|
*> 0 => normal return
|
||
|
|
*> -1 => M negative or unequal to N and SYM='S' or 'H'
|
||
|
|
*> -2 => N negative
|
||
|
|
*> -3 => DIST illegal string
|
||
|
|
*> -5 => SYM illegal string
|
||
|
|
*> -7 => MODE not in range -6 to 6
|
||
|
|
*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6
|
||
|
|
*> -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string
|
||
|
|
*> -11 => GRADE illegal string, or GRADE='E' and
|
||
|
|
*> M not equal to N, or GRADE='L', 'R', 'B' or 'E' and
|
||
|
|
*> SYM = 'S' or 'H'
|
||
|
|
*> -12 => GRADE = 'E' and DL contains zero
|
||
|
|
*> -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H',
|
||
|
|
*> 'S' or 'E'
|
||
|
|
*> -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E',
|
||
|
|
*> and MODEL neither -6, 0 nor 6
|
||
|
|
*> -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B'
|
||
|
|
*> -17 => CONDR less than 1.0, GRADE='R' or 'B', and
|
||
|
|
*> MODER neither -6, 0 nor 6
|
||
|
|
*> -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and
|
||
|
|
*> M not equal to N, or PIVTNG='L' or 'R' and SYM='S'
|
||
|
|
*> or 'H'
|
||
|
|
*> -19 => IPIVOT contains out of range number and
|
||
|
|
*> PIVTNG not equal to 'N'
|
||
|
|
*> -20 => KL negative
|
||
|
|
*> -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL
|
||
|
|
*> -22 => SPARSE not in range 0. to 1.
|
||
|
|
*> -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q'
|
||
|
|
*> and SYM='N', or PACK='C' and SYM='N' and either KL
|
||
|
|
*> not equal to 0 or N not equal to M, or PACK='R' and
|
||
|
|
*> SYM='N', and either KU not equal to 0 or N not equal
|
||
|
|
*> to M
|
||
|
|
*> -26 => LDA too small
|
||
|
|
*> 1 => Error return from DLATM1 (computing D)
|
||
|
|
*> 2 => Cannot scale diagonal to DMAX (max. entry is 0)
|
||
|
|
*> 3 => Error return from DLATM1 (computing DL)
|
||
|
|
*> 4 => Error return from DLATM1 (computing DR)
|
||
|
|
*> 5 => ANORM is positive, but matrix constructed prior to
|
||
|
|
*> attempting to scale it to have norm ANORM, is zero
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup double_matgen
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
|
||
|
|
$ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
|
||
|
|
$ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM,
|
||
|
|
$ PACK, A, LDA, IWORK, INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK computational routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM
|
||
|
|
INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
|
||
|
|
DOUBLE PRECISION ANORM, COND, CONDL, CONDR, DMAX, SPARSE
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * )
|
||
|
|
DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
DOUBLE PRECISION ZERO
|
||
|
|
PARAMETER ( ZERO = 0.0D0 )
|
||
|
|
DOUBLE PRECISION ONE
|
||
|
|
PARAMETER ( ONE = 1.0D0 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL BADPVT, DZERO, FULBND
|
||
|
|
INTEGER I, IDIST, IGRADE, IISUB, IPACK, IPVTNG, IRSIGN,
|
||
|
|
$ ISUB, ISYM, J, JJSUB, JSUB, K, KLL, KUU, MNMIN,
|
||
|
|
$ MNSUB, MXSUB, NPVTS
|
||
|
|
DOUBLE PRECISION ALPHA, ONORM, TEMP
|
||
|
|
* ..
|
||
|
|
* .. Local Arrays ..
|
||
|
|
DOUBLE PRECISION TEMPA( 1 )
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
DOUBLE PRECISION DLANGB, DLANGE, DLANSB, DLANSP, DLANSY, DLATM2,
|
||
|
|
$ DLATM3
|
||
|
|
EXTERNAL LSAME, DLANGB, DLANGE, DLANSB, DLANSP, DLANSY,
|
||
|
|
$ DLATM2, DLATM3
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL DLATM1, DSCAL, XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC ABS, MAX, MIN, MOD
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* 1) Decode and Test the input parameters.
|
||
|
|
* Initialize flags & seed.
|
||
|
|
*
|
||
|
|
INFO = 0
|
||
|
|
*
|
||
|
|
* Quick return if possible
|
||
|
|
*
|
||
|
|
IF( M.EQ.0 .OR. N.EQ.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
* Decode DIST
|
||
|
|
*
|
||
|
|
IF( LSAME( DIST, 'U' ) ) THEN
|
||
|
|
IDIST = 1
|
||
|
|
ELSE IF( LSAME( DIST, 'S' ) ) THEN
|
||
|
|
IDIST = 2
|
||
|
|
ELSE IF( LSAME( DIST, 'N' ) ) THEN
|
||
|
|
IDIST = 3
|
||
|
|
ELSE
|
||
|
|
IDIST = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode SYM
|
||
|
|
*
|
||
|
|
IF( LSAME( SYM, 'S' ) ) THEN
|
||
|
|
ISYM = 0
|
||
|
|
ELSE IF( LSAME( SYM, 'N' ) ) THEN
|
||
|
|
ISYM = 1
|
||
|
|
ELSE IF( LSAME( SYM, 'H' ) ) THEN
|
||
|
|
ISYM = 0
|
||
|
|
ELSE
|
||
|
|
ISYM = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode RSIGN
|
||
|
|
*
|
||
|
|
IF( LSAME( RSIGN, 'F' ) ) THEN
|
||
|
|
IRSIGN = 0
|
||
|
|
ELSE IF( LSAME( RSIGN, 'T' ) ) THEN
|
||
|
|
IRSIGN = 1
|
||
|
|
ELSE
|
||
|
|
IRSIGN = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode PIVTNG
|
||
|
|
*
|
||
|
|
IF( LSAME( PIVTNG, 'N' ) ) THEN
|
||
|
|
IPVTNG = 0
|
||
|
|
ELSE IF( LSAME( PIVTNG, ' ' ) ) THEN
|
||
|
|
IPVTNG = 0
|
||
|
|
ELSE IF( LSAME( PIVTNG, 'L' ) ) THEN
|
||
|
|
IPVTNG = 1
|
||
|
|
NPVTS = M
|
||
|
|
ELSE IF( LSAME( PIVTNG, 'R' ) ) THEN
|
||
|
|
IPVTNG = 2
|
||
|
|
NPVTS = N
|
||
|
|
ELSE IF( LSAME( PIVTNG, 'B' ) ) THEN
|
||
|
|
IPVTNG = 3
|
||
|
|
NPVTS = MIN( N, M )
|
||
|
|
ELSE IF( LSAME( PIVTNG, 'F' ) ) THEN
|
||
|
|
IPVTNG = 3
|
||
|
|
NPVTS = MIN( N, M )
|
||
|
|
ELSE
|
||
|
|
IPVTNG = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode GRADE
|
||
|
|
*
|
||
|
|
IF( LSAME( GRADE, 'N' ) ) THEN
|
||
|
|
IGRADE = 0
|
||
|
|
ELSE IF( LSAME( GRADE, 'L' ) ) THEN
|
||
|
|
IGRADE = 1
|
||
|
|
ELSE IF( LSAME( GRADE, 'R' ) ) THEN
|
||
|
|
IGRADE = 2
|
||
|
|
ELSE IF( LSAME( GRADE, 'B' ) ) THEN
|
||
|
|
IGRADE = 3
|
||
|
|
ELSE IF( LSAME( GRADE, 'E' ) ) THEN
|
||
|
|
IGRADE = 4
|
||
|
|
ELSE IF( LSAME( GRADE, 'H' ) .OR. LSAME( GRADE, 'S' ) ) THEN
|
||
|
|
IGRADE = 5
|
||
|
|
ELSE
|
||
|
|
IGRADE = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode PACK
|
||
|
|
*
|
||
|
|
IF( LSAME( PACK, 'N' ) ) THEN
|
||
|
|
IPACK = 0
|
||
|
|
ELSE IF( LSAME( PACK, 'U' ) ) THEN
|
||
|
|
IPACK = 1
|
||
|
|
ELSE IF( LSAME( PACK, 'L' ) ) THEN
|
||
|
|
IPACK = 2
|
||
|
|
ELSE IF( LSAME( PACK, 'C' ) ) THEN
|
||
|
|
IPACK = 3
|
||
|
|
ELSE IF( LSAME( PACK, 'R' ) ) THEN
|
||
|
|
IPACK = 4
|
||
|
|
ELSE IF( LSAME( PACK, 'B' ) ) THEN
|
||
|
|
IPACK = 5
|
||
|
|
ELSE IF( LSAME( PACK, 'Q' ) ) THEN
|
||
|
|
IPACK = 6
|
||
|
|
ELSE IF( LSAME( PACK, 'Z' ) ) THEN
|
||
|
|
IPACK = 7
|
||
|
|
ELSE
|
||
|
|
IPACK = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set certain internal parameters
|
||
|
|
*
|
||
|
|
MNMIN = MIN( M, N )
|
||
|
|
KLL = MIN( KL, M-1 )
|
||
|
|
KUU = MIN( KU, N-1 )
|
||
|
|
*
|
||
|
|
* If inv(DL) is used, check to see if DL has a zero entry.
|
||
|
|
*
|
||
|
|
DZERO = .FALSE.
|
||
|
|
IF( IGRADE.EQ.4 .AND. MODEL.EQ.0 ) THEN
|
||
|
|
DO 10 I = 1, M
|
||
|
|
IF( DL( I ).EQ.ZERO )
|
||
|
|
$ DZERO = .TRUE.
|
||
|
|
10 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Check values in IPIVOT
|
||
|
|
*
|
||
|
|
BADPVT = .FALSE.
|
||
|
|
IF( IPVTNG.GT.0 ) THEN
|
||
|
|
DO 20 J = 1, NPVTS
|
||
|
|
IF( IPIVOT( J ).LE.0 .OR. IPIVOT( J ).GT.NPVTS )
|
||
|
|
$ BADPVT = .TRUE.
|
||
|
|
20 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set INFO if an error
|
||
|
|
*
|
||
|
|
IF( M.LT.0 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( M.NE.N .AND. ISYM.EQ.0 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( N.LT.0 ) THEN
|
||
|
|
INFO = -2
|
||
|
|
ELSE IF( IDIST.EQ.-1 ) THEN
|
||
|
|
INFO = -3
|
||
|
|
ELSE IF( ISYM.EQ.-1 ) THEN
|
||
|
|
INFO = -5
|
||
|
|
ELSE IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
|
||
|
|
INFO = -7
|
||
|
|
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
|
||
|
|
$ COND.LT.ONE ) THEN
|
||
|
|
INFO = -8
|
||
|
|
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
|
||
|
|
$ IRSIGN.EQ.-1 ) THEN
|
||
|
|
INFO = -10
|
||
|
|
ELSE IF( IGRADE.EQ.-1 .OR. ( IGRADE.EQ.4 .AND. M.NE.N ) .OR.
|
||
|
|
$ ( ( IGRADE.GE.1 .AND. IGRADE.LE.4 ) .AND. ISYM.EQ.0 ) )
|
||
|
|
$ THEN
|
||
|
|
INFO = -11
|
||
|
|
ELSE IF( IGRADE.EQ.4 .AND. DZERO ) THEN
|
||
|
|
INFO = -12
|
||
|
|
ELSE IF( ( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR.
|
||
|
|
$ IGRADE.EQ.5 ) .AND. ( MODEL.LT.-6 .OR. MODEL.GT.6 ) )
|
||
|
|
$ THEN
|
||
|
|
INFO = -13
|
||
|
|
ELSE IF( ( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR.
|
||
|
|
$ IGRADE.EQ.5 ) .AND. ( MODEL.NE.-6 .AND. MODEL.NE.0 .AND.
|
||
|
|
$ MODEL.NE.6 ) .AND. CONDL.LT.ONE ) THEN
|
||
|
|
INFO = -14
|
||
|
|
ELSE IF( ( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) .AND.
|
||
|
|
$ ( MODER.LT.-6 .OR. MODER.GT.6 ) ) THEN
|
||
|
|
INFO = -16
|
||
|
|
ELSE IF( ( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) .AND.
|
||
|
|
$ ( MODER.NE.-6 .AND. MODER.NE.0 .AND. MODER.NE.6 ) .AND.
|
||
|
|
$ CONDR.LT.ONE ) THEN
|
||
|
|
INFO = -17
|
||
|
|
ELSE IF( IPVTNG.EQ.-1 .OR. ( IPVTNG.EQ.3 .AND. M.NE.N ) .OR.
|
||
|
|
$ ( ( IPVTNG.EQ.1 .OR. IPVTNG.EQ.2 ) .AND. ISYM.EQ.0 ) )
|
||
|
|
$ THEN
|
||
|
|
INFO = -18
|
||
|
|
ELSE IF( IPVTNG.NE.0 .AND. BADPVT ) THEN
|
||
|
|
INFO = -19
|
||
|
|
ELSE IF( KL.LT.0 ) THEN
|
||
|
|
INFO = -20
|
||
|
|
ELSE IF( KU.LT.0 .OR. ( ISYM.EQ.0 .AND. KL.NE.KU ) ) THEN
|
||
|
|
INFO = -21
|
||
|
|
ELSE IF( SPARSE.LT.ZERO .OR. SPARSE.GT.ONE ) THEN
|
||
|
|
INFO = -22
|
||
|
|
ELSE IF( IPACK.EQ.-1 .OR. ( ( IPACK.EQ.1 .OR. IPACK.EQ.2 .OR.
|
||
|
|
$ IPACK.EQ.5 .OR. IPACK.EQ.6 ) .AND. ISYM.EQ.1 ) .OR.
|
||
|
|
$ ( IPACK.EQ.3 .AND. ISYM.EQ.1 .AND. ( KL.NE.0 .OR. M.NE.
|
||
|
|
$ N ) ) .OR. ( IPACK.EQ.4 .AND. ISYM.EQ.1 .AND. ( KU.NE.
|
||
|
|
$ 0 .OR. M.NE.N ) ) ) THEN
|
||
|
|
INFO = -24
|
||
|
|
ELSE IF( ( ( IPACK.EQ.0 .OR. IPACK.EQ.1 .OR. IPACK.EQ.2 ) .AND.
|
||
|
|
$ LDA.LT.MAX( 1, M ) ) .OR. ( ( IPACK.EQ.3 .OR. IPACK.EQ.
|
||
|
|
$ 4 ) .AND. LDA.LT.1 ) .OR. ( ( IPACK.EQ.5 .OR. IPACK.EQ.
|
||
|
|
$ 6 ) .AND. LDA.LT.KUU+1 ) .OR.
|
||
|
|
$ ( IPACK.EQ.7 .AND. LDA.LT.KLL+KUU+1 ) ) THEN
|
||
|
|
INFO = -26
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'DLATMR', -INFO )
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decide if we can pivot consistently
|
||
|
|
*
|
||
|
|
FULBND = .FALSE.
|
||
|
|
IF( KUU.EQ.N-1 .AND. KLL.EQ.M-1 )
|
||
|
|
$ FULBND = .TRUE.
|
||
|
|
*
|
||
|
|
* Initialize random number generator
|
||
|
|
*
|
||
|
|
DO 30 I = 1, 4
|
||
|
|
ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 )
|
||
|
|
30 CONTINUE
|
||
|
|
*
|
||
|
|
ISEED( 4 ) = 2*( ISEED( 4 ) / 2 ) + 1
|
||
|
|
*
|
||
|
|
* 2) Set up D, DL, and DR, if indicated.
|
||
|
|
*
|
||
|
|
* Compute D according to COND and MODE
|
||
|
|
*
|
||
|
|
CALL DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
INFO = 1
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
IF( MODE.NE.0 .AND. MODE.NE.-6 .AND. MODE.NE.6 ) THEN
|
||
|
|
*
|
||
|
|
* Scale by DMAX
|
||
|
|
*
|
||
|
|
TEMP = ABS( D( 1 ) )
|
||
|
|
DO 40 I = 2, MNMIN
|
||
|
|
TEMP = MAX( TEMP, ABS( D( I ) ) )
|
||
|
|
40 CONTINUE
|
||
|
|
IF( TEMP.EQ.ZERO .AND. DMAX.NE.ZERO ) THEN
|
||
|
|
INFO = 2
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
IF( TEMP.NE.ZERO ) THEN
|
||
|
|
ALPHA = DMAX / TEMP
|
||
|
|
ELSE
|
||
|
|
ALPHA = ONE
|
||
|
|
END IF
|
||
|
|
DO 50 I = 1, MNMIN
|
||
|
|
D( I ) = ALPHA*D( I )
|
||
|
|
50 CONTINUE
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute DL if grading set
|
||
|
|
*
|
||
|
|
IF( IGRADE.EQ.1 .OR. IGRADE.EQ.3 .OR. IGRADE.EQ.4 .OR. IGRADE.EQ.
|
||
|
|
$ 5 ) THEN
|
||
|
|
CALL DLATM1( MODEL, CONDL, 0, IDIST, ISEED, DL, M, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
INFO = 3
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute DR if grading set
|
||
|
|
*
|
||
|
|
IF( IGRADE.EQ.2 .OR. IGRADE.EQ.3 ) THEN
|
||
|
|
CALL DLATM1( MODER, CONDR, 0, IDIST, ISEED, DR, N, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
INFO = 4
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 3) Generate IWORK if pivoting
|
||
|
|
*
|
||
|
|
IF( IPVTNG.GT.0 ) THEN
|
||
|
|
DO 60 I = 1, NPVTS
|
||
|
|
IWORK( I ) = I
|
||
|
|
60 CONTINUE
|
||
|
|
IF( FULBND ) THEN
|
||
|
|
DO 70 I = 1, NPVTS
|
||
|
|
K = IPIVOT( I )
|
||
|
|
J = IWORK( I )
|
||
|
|
IWORK( I ) = IWORK( K )
|
||
|
|
IWORK( K ) = J
|
||
|
|
70 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 80 I = NPVTS, 1, -1
|
||
|
|
K = IPIVOT( I )
|
||
|
|
J = IWORK( I )
|
||
|
|
IWORK( I ) = IWORK( K )
|
||
|
|
IWORK( K ) = J
|
||
|
|
80 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 4) Generate matrices for each kind of PACKing
|
||
|
|
* Always sweep matrix columnwise (if symmetric, upper
|
||
|
|
* half only) so that matrix generated does not depend
|
||
|
|
* on PACK
|
||
|
|
*
|
||
|
|
IF( FULBND ) THEN
|
||
|
|
*
|
||
|
|
* Use DLATM3 so matrices generated with differing PIVOTing only
|
||
|
|
* differ only in the order of their rows and/or columns.
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.0 ) THEN
|
||
|
|
IF( ISYM.EQ.0 ) THEN
|
||
|
|
DO 100 J = 1, N
|
||
|
|
DO 90 I = 1, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
A( ISUB, JSUB ) = TEMP
|
||
|
|
A( JSUB, ISUB ) = TEMP
|
||
|
|
90 CONTINUE
|
||
|
|
100 CONTINUE
|
||
|
|
ELSE IF( ISYM.EQ.1 ) THEN
|
||
|
|
DO 120 J = 1, N
|
||
|
|
DO 110 I = 1, M
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
A( ISUB, JSUB ) = TEMP
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
DO 140 J = 1, N
|
||
|
|
DO 130 I = 1, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
|
||
|
|
$ SPARSE )
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
A( MNSUB, MXSUB ) = TEMP
|
||
|
|
IF( MNSUB.NE.MXSUB )
|
||
|
|
$ A( MXSUB, MNSUB ) = ZERO
|
||
|
|
130 CONTINUE
|
||
|
|
140 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.2 ) THEN
|
||
|
|
*
|
||
|
|
DO 160 J = 1, N
|
||
|
|
DO 150 I = 1, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
|
||
|
|
$ SPARSE )
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
A( MXSUB, MNSUB ) = TEMP
|
||
|
|
IF( MNSUB.NE.MXSUB )
|
||
|
|
$ A( MNSUB, MXSUB ) = ZERO
|
||
|
|
150 CONTINUE
|
||
|
|
160 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.3 ) THEN
|
||
|
|
*
|
||
|
|
DO 180 J = 1, N
|
||
|
|
DO 170 I = 1, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
|
||
|
|
$ SPARSE )
|
||
|
|
*
|
||
|
|
* Compute K = location of (ISUB,JSUB) entry in packed
|
||
|
|
* array
|
||
|
|
*
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
K = MXSUB*( MXSUB-1 ) / 2 + MNSUB
|
||
|
|
*
|
||
|
|
* Convert K to (IISUB,JJSUB) location
|
||
|
|
*
|
||
|
|
JJSUB = ( K-1 ) / LDA + 1
|
||
|
|
IISUB = K - LDA*( JJSUB-1 )
|
||
|
|
*
|
||
|
|
A( IISUB, JJSUB ) = TEMP
|
||
|
|
170 CONTINUE
|
||
|
|
180 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
DO 200 J = 1, N
|
||
|
|
DO 190 I = 1, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
|
||
|
|
$ SPARSE )
|
||
|
|
*
|
||
|
|
* Compute K = location of (I,J) entry in packed array
|
||
|
|
*
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
IF( MNSUB.EQ.1 ) THEN
|
||
|
|
K = MXSUB
|
||
|
|
ELSE
|
||
|
|
K = N*( N+1 ) / 2 - ( N-MNSUB+1 )*( N-MNSUB+2 ) /
|
||
|
|
$ 2 + MXSUB - MNSUB + 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Convert K to (IISUB,JJSUB) location
|
||
|
|
*
|
||
|
|
JJSUB = ( K-1 ) / LDA + 1
|
||
|
|
IISUB = K - LDA*( JJSUB-1 )
|
||
|
|
*
|
||
|
|
A( IISUB, JJSUB ) = TEMP
|
||
|
|
190 CONTINUE
|
||
|
|
200 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.5 ) THEN
|
||
|
|
*
|
||
|
|
DO 220 J = 1, N
|
||
|
|
DO 210 I = J - KUU, J
|
||
|
|
IF( I.LT.1 ) THEN
|
||
|
|
A( J-I+1, I+N ) = ZERO
|
||
|
|
ELSE
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
A( MXSUB-MNSUB+1, MNSUB ) = TEMP
|
||
|
|
END IF
|
||
|
|
210 CONTINUE
|
||
|
|
220 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.6 ) THEN
|
||
|
|
*
|
||
|
|
DO 240 J = 1, N
|
||
|
|
DO 230 I = J - KUU, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
|
||
|
|
$ SPARSE )
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP
|
||
|
|
230 CONTINUE
|
||
|
|
240 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.7 ) THEN
|
||
|
|
*
|
||
|
|
IF( ISYM.EQ.0 ) THEN
|
||
|
|
DO 260 J = 1, N
|
||
|
|
DO 250 I = J - KUU, J
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
MNSUB = MIN( ISUB, JSUB )
|
||
|
|
MXSUB = MAX( ISUB, JSUB )
|
||
|
|
A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP
|
||
|
|
IF( I.LT.1 )
|
||
|
|
$ A( J-I+1+KUU, I+N ) = ZERO
|
||
|
|
IF( I.GE.1 .AND. MNSUB.NE.MXSUB )
|
||
|
|
$ A( MXSUB-MNSUB+1+KUU, MNSUB ) = TEMP
|
||
|
|
250 CONTINUE
|
||
|
|
260 CONTINUE
|
||
|
|
ELSE IF( ISYM.EQ.1 ) THEN
|
||
|
|
DO 280 J = 1, N
|
||
|
|
DO 270 I = J - KUU, J + KLL
|
||
|
|
TEMP = DLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
A( ISUB-JSUB+KUU+1, JSUB ) = TEMP
|
||
|
|
270 CONTINUE
|
||
|
|
280 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Use DLATM2
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.0 ) THEN
|
||
|
|
IF( ISYM.EQ.0 ) THEN
|
||
|
|
DO 300 J = 1, N
|
||
|
|
DO 290 I = 1, J
|
||
|
|
A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
A( J, I ) = A( I, J )
|
||
|
|
290 CONTINUE
|
||
|
|
300 CONTINUE
|
||
|
|
ELSE IF( ISYM.EQ.1 ) THEN
|
||
|
|
DO 320 J = 1, N
|
||
|
|
DO 310 I = 1, M
|
||
|
|
A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
310 CONTINUE
|
||
|
|
320 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
DO 340 J = 1, N
|
||
|
|
DO 330 I = 1, J
|
||
|
|
A( I, J ) = DLATM2( M, N, I, J, KL, KU, IDIST, ISEED,
|
||
|
|
$ D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
|
||
|
|
IF( I.NE.J )
|
||
|
|
$ A( J, I ) = ZERO
|
||
|
|
330 CONTINUE
|
||
|
|
340 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.2 ) THEN
|
||
|
|
*
|
||
|
|
DO 360 J = 1, N
|
||
|
|
DO 350 I = 1, J
|
||
|
|
A( J, I ) = DLATM2( M, N, I, J, KL, KU, IDIST, ISEED,
|
||
|
|
$ D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
|
||
|
|
IF( I.NE.J )
|
||
|
|
$ A( I, J ) = ZERO
|
||
|
|
350 CONTINUE
|
||
|
|
360 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.3 ) THEN
|
||
|
|
*
|
||
|
|
ISUB = 0
|
||
|
|
JSUB = 1
|
||
|
|
DO 380 J = 1, N
|
||
|
|
DO 370 I = 1, J
|
||
|
|
ISUB = ISUB + 1
|
||
|
|
IF( ISUB.GT.LDA ) THEN
|
||
|
|
ISUB = 1
|
||
|
|
JSUB = JSUB + 1
|
||
|
|
END IF
|
||
|
|
A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
370 CONTINUE
|
||
|
|
380 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
IF( ISYM.EQ.0 ) THEN
|
||
|
|
DO 400 J = 1, N
|
||
|
|
DO 390 I = 1, J
|
||
|
|
*
|
||
|
|
* Compute K = location of (I,J) entry in packed array
|
||
|
|
*
|
||
|
|
IF( I.EQ.1 ) THEN
|
||
|
|
K = J
|
||
|
|
ELSE
|
||
|
|
K = N*( N+1 ) / 2 - ( N-I+1 )*( N-I+2 ) / 2 +
|
||
|
|
$ J - I + 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Convert K to (ISUB,JSUB) location
|
||
|
|
*
|
||
|
|
JSUB = ( K-1 ) / LDA + 1
|
||
|
|
ISUB = K - LDA*( JSUB-1 )
|
||
|
|
*
|
||
|
|
A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR,
|
||
|
|
$ IPVTNG, IWORK, SPARSE )
|
||
|
|
390 CONTINUE
|
||
|
|
400 CONTINUE
|
||
|
|
ELSE
|
||
|
|
ISUB = 0
|
||
|
|
JSUB = 1
|
||
|
|
DO 420 J = 1, N
|
||
|
|
DO 410 I = J, M
|
||
|
|
ISUB = ISUB + 1
|
||
|
|
IF( ISUB.GT.LDA ) THEN
|
||
|
|
ISUB = 1
|
||
|
|
JSUB = JSUB + 1
|
||
|
|
END IF
|
||
|
|
A( ISUB, JSUB ) = DLATM2( M, N, I, J, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL, DR,
|
||
|
|
$ IPVTNG, IWORK, SPARSE )
|
||
|
|
410 CONTINUE
|
||
|
|
420 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.5 ) THEN
|
||
|
|
*
|
||
|
|
DO 440 J = 1, N
|
||
|
|
DO 430 I = J - KUU, J
|
||
|
|
IF( I.LT.1 ) THEN
|
||
|
|
A( J-I+1, I+N ) = ZERO
|
||
|
|
ELSE
|
||
|
|
A( J-I+1, I ) = DLATM2( M, N, I, J, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
END IF
|
||
|
|
430 CONTINUE
|
||
|
|
440 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.6 ) THEN
|
||
|
|
*
|
||
|
|
DO 460 J = 1, N
|
||
|
|
DO 450 I = J - KUU, J
|
||
|
|
A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU, IDIST,
|
||
|
|
$ ISEED, D, IGRADE, DL, DR, IPVTNG,
|
||
|
|
$ IWORK, SPARSE )
|
||
|
|
450 CONTINUE
|
||
|
|
460 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.7 ) THEN
|
||
|
|
*
|
||
|
|
IF( ISYM.EQ.0 ) THEN
|
||
|
|
DO 480 J = 1, N
|
||
|
|
DO 470 I = J - KUU, J
|
||
|
|
A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL,
|
||
|
|
$ DR, IPVTNG, IWORK, SPARSE )
|
||
|
|
IF( I.LT.1 )
|
||
|
|
$ A( J-I+1+KUU, I+N ) = ZERO
|
||
|
|
IF( I.GE.1 .AND. I.NE.J )
|
||
|
|
$ A( J-I+1+KUU, I ) = A( I-J+KUU+1, J )
|
||
|
|
470 CONTINUE
|
||
|
|
480 CONTINUE
|
||
|
|
ELSE IF( ISYM.EQ.1 ) THEN
|
||
|
|
DO 500 J = 1, N
|
||
|
|
DO 490 I = J - KUU, J + KLL
|
||
|
|
A( I-J+KUU+1, J ) = DLATM2( M, N, I, J, KL, KU,
|
||
|
|
$ IDIST, ISEED, D, IGRADE, DL,
|
||
|
|
$ DR, IPVTNG, IWORK, SPARSE )
|
||
|
|
490 CONTINUE
|
||
|
|
500 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 5) Scaling the norm
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.0 ) THEN
|
||
|
|
ONORM = DLANGE( 'M', M, N, A, LDA, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.1 ) THEN
|
||
|
|
ONORM = DLANSY( 'M', 'U', N, A, LDA, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.2 ) THEN
|
||
|
|
ONORM = DLANSY( 'M', 'L', N, A, LDA, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.3 ) THEN
|
||
|
|
ONORM = DLANSP( 'M', 'U', N, A, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.4 ) THEN
|
||
|
|
ONORM = DLANSP( 'M', 'L', N, A, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.5 ) THEN
|
||
|
|
ONORM = DLANSB( 'M', 'L', N, KLL, A, LDA, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.6 ) THEN
|
||
|
|
ONORM = DLANSB( 'M', 'U', N, KUU, A, LDA, TEMPA )
|
||
|
|
ELSE IF( IPACK.EQ.7 ) THEN
|
||
|
|
ONORM = DLANGB( 'M', N, KLL, KUU, A, LDA, TEMPA )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( ANORM.GE.ZERO ) THEN
|
||
|
|
*
|
||
|
|
IF( ANORM.GT.ZERO .AND. ONORM.EQ.ZERO ) THEN
|
||
|
|
*
|
||
|
|
* Desired scaling impossible
|
||
|
|
*
|
||
|
|
INFO = 5
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
ELSE IF( ( ANORM.GT.ONE .AND. ONORM.LT.ONE ) .OR.
|
||
|
|
$ ( ANORM.LT.ONE .AND. ONORM.GT.ONE ) ) THEN
|
||
|
|
*
|
||
|
|
* Scale carefully to avoid over / underflow
|
||
|
|
*
|
||
|
|
IF( IPACK.LE.2 ) THEN
|
||
|
|
DO 510 J = 1, N
|
||
|
|
CALL DSCAL( M, ONE / ONORM, A( 1, J ), 1 )
|
||
|
|
CALL DSCAL( M, ANORM, A( 1, J ), 1 )
|
||
|
|
510 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
CALL DSCAL( N*( N+1 ) / 2, ONE / ONORM, A, 1 )
|
||
|
|
CALL DSCAL( N*( N+1 ) / 2, ANORM, A, 1 )
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.GE.5 ) THEN
|
||
|
|
*
|
||
|
|
DO 520 J = 1, N
|
||
|
|
CALL DSCAL( KLL+KUU+1, ONE / ONORM, A( 1, J ), 1 )
|
||
|
|
CALL DSCAL( KLL+KUU+1, ANORM, A( 1, J ), 1 )
|
||
|
|
520 CONTINUE
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Scale straightforwardly
|
||
|
|
*
|
||
|
|
IF( IPACK.LE.2 ) THEN
|
||
|
|
DO 530 J = 1, N
|
||
|
|
CALL DSCAL( M, ANORM / ONORM, A( 1, J ), 1 )
|
||
|
|
530 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
CALL DSCAL( N*( N+1 ) / 2, ANORM / ONORM, A, 1 )
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.GE.5 ) THEN
|
||
|
|
*
|
||
|
|
DO 540 J = 1, N
|
||
|
|
CALL DSCAL( KLL+KUU+1, ANORM / ONORM, A( 1, J ), 1 )
|
||
|
|
540 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* End of DLATMR
|
||
|
|
*
|
||
|
|
END
|