You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1126 lines
39 KiB
1126 lines
39 KiB
2 years ago
|
*> \brief \b DLATMS
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
|
||
|
|
* KL, KU, PACK, A, LDA, WORK, INFO )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER DIST, PACK, SYM
|
||
|
|
* INTEGER INFO, KL, KU, LDA, M, MODE, N
|
||
|
|
* DOUBLE PRECISION COND, DMAX
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* INTEGER ISEED( 4 )
|
||
|
|
* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> DLATMS generates random matrices with specified singular values
|
||
|
|
*> (or symmetric/hermitian with specified eigenvalues)
|
||
|
|
*> for testing LAPACK programs.
|
||
|
|
*>
|
||
|
|
*> DLATMS operates by applying the following sequence of
|
||
|
|
*> operations:
|
||
|
|
*>
|
||
|
|
*> Set the diagonal to D, where D may be input or
|
||
|
|
*> computed according to MODE, COND, DMAX, and SYM
|
||
|
|
*> as described below.
|
||
|
|
*>
|
||
|
|
*> Generate a matrix with the appropriate band structure, by one
|
||
|
|
*> of two methods:
|
||
|
|
*>
|
||
|
|
*> Method A:
|
||
|
|
*> Generate a dense M x N matrix by multiplying D on the left
|
||
|
|
*> and the right by random unitary matrices, then:
|
||
|
|
*>
|
||
|
|
*> Reduce the bandwidth according to KL and KU, using
|
||
|
|
*> Householder transformations.
|
||
|
|
*>
|
||
|
|
*> Method B:
|
||
|
|
*> Convert the bandwidth-0 (i.e., diagonal) matrix to a
|
||
|
|
*> bandwidth-1 matrix using Givens rotations, "chasing"
|
||
|
|
*> out-of-band elements back, much as in QR; then
|
||
|
|
*> convert the bandwidth-1 to a bandwidth-2 matrix, etc.
|
||
|
|
*> Note that for reasonably small bandwidths (relative to
|
||
|
|
*> M and N) this requires less storage, as a dense matrix
|
||
|
|
*> is not generated. Also, for symmetric matrices, only
|
||
|
|
*> one triangle is generated.
|
||
|
|
*>
|
||
|
|
*> Method A is chosen if the bandwidth is a large fraction of the
|
||
|
|
*> order of the matrix, and LDA is at least M (so a dense
|
||
|
|
*> matrix can be stored.) Method B is chosen if the bandwidth
|
||
|
|
*> is small (< 1/2 N for symmetric, < .3 N+M for
|
||
|
|
*> non-symmetric), or LDA is less than M and not less than the
|
||
|
|
*> bandwidth.
|
||
|
|
*>
|
||
|
|
*> Pack the matrix if desired. Options specified by PACK are:
|
||
|
|
*> no packing
|
||
|
|
*> zero out upper half (if symmetric)
|
||
|
|
*> zero out lower half (if symmetric)
|
||
|
|
*> store the upper half columnwise (if symmetric or upper
|
||
|
|
*> triangular)
|
||
|
|
*> store the lower half columnwise (if symmetric or lower
|
||
|
|
*> triangular)
|
||
|
|
*> store the lower triangle in banded format (if symmetric
|
||
|
|
*> or lower triangular)
|
||
|
|
*> store the upper triangle in banded format (if symmetric
|
||
|
|
*> or upper triangular)
|
||
|
|
*> store the entire matrix in banded format
|
||
|
|
*> If Method B is chosen, and band format is specified, then the
|
||
|
|
*> matrix will be generated in the band format, so no repacking
|
||
|
|
*> will be necessary.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] M
|
||
|
|
*> \verbatim
|
||
|
|
*> M is INTEGER
|
||
|
|
*> The number of rows of A. Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The number of columns of A. Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] DIST
|
||
|
|
*> \verbatim
|
||
|
|
*> DIST is CHARACTER*1
|
||
|
|
*> On entry, DIST specifies the type of distribution to be used
|
||
|
|
*> to generate the random eigen-/singular values.
|
||
|
|
*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
|
||
|
|
*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
|
||
|
|
*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal )
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] ISEED
|
||
|
|
*> \verbatim
|
||
|
|
*> ISEED is INTEGER array, dimension ( 4 )
|
||
|
|
*> On entry ISEED specifies the seed of the random number
|
||
|
|
*> generator. They should lie between 0 and 4095 inclusive,
|
||
|
|
*> and ISEED(4) should be odd. The random number generator
|
||
|
|
*> uses a linear congruential sequence limited to small
|
||
|
|
*> integers, and so should produce machine independent
|
||
|
|
*> random numbers. The values of ISEED are changed on
|
||
|
|
*> exit, and can be used in the next call to DLATMS
|
||
|
|
*> to continue the same random number sequence.
|
||
|
|
*> Changed on exit.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] SYM
|
||
|
|
*> \verbatim
|
||
|
|
*> SYM is CHARACTER*1
|
||
|
|
*> If SYM='S' or 'H', the generated matrix is symmetric, with
|
||
|
|
*> eigenvalues specified by D, COND, MODE, and DMAX; they
|
||
|
|
*> may be positive, negative, or zero.
|
||
|
|
*> If SYM='P', the generated matrix is symmetric, with
|
||
|
|
*> eigenvalues (= singular values) specified by D, COND,
|
||
|
|
*> MODE, and DMAX; they will not be negative.
|
||
|
|
*> If SYM='N', the generated matrix is nonsymmetric, with
|
||
|
|
*> singular values specified by D, COND, MODE, and DMAX;
|
||
|
|
*> they will not be negative.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] D
|
||
|
|
*> \verbatim
|
||
|
|
*> D is DOUBLE PRECISION array, dimension ( MIN( M , N ) )
|
||
|
|
*> This array is used to specify the singular values or
|
||
|
|
*> eigenvalues of A (see SYM, above.) If MODE=0, then D is
|
||
|
|
*> assumed to contain the singular/eigenvalues, otherwise
|
||
|
|
*> they will be computed according to MODE, COND, and DMAX,
|
||
|
|
*> and placed in D.
|
||
|
|
*> Modified if MODE is nonzero.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] MODE
|
||
|
|
*> \verbatim
|
||
|
|
*> MODE is INTEGER
|
||
|
|
*> On entry this describes how the singular/eigenvalues are to
|
||
|
|
*> be specified:
|
||
|
|
*> MODE = 0 means use D as input
|
||
|
|
*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
|
||
|
|
*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
|
||
|
|
*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
|
||
|
|
*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
|
||
|
|
*> MODE = 5 sets D to random numbers in the range
|
||
|
|
*> ( 1/COND , 1 ) such that their logarithms
|
||
|
|
*> are uniformly distributed.
|
||
|
|
*> MODE = 6 set D to random numbers from same distribution
|
||
|
|
*> as the rest of the matrix.
|
||
|
|
*> MODE < 0 has the same meaning as ABS(MODE), except that
|
||
|
|
*> the order of the elements of D is reversed.
|
||
|
|
*> Thus if MODE is positive, D has entries ranging from
|
||
|
|
*> 1 to 1/COND, if negative, from 1/COND to 1,
|
||
|
|
*> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then
|
||
|
|
*> the elements of D will also be multiplied by a random
|
||
|
|
*> sign (i.e., +1 or -1.)
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] COND
|
||
|
|
*> \verbatim
|
||
|
|
*> COND is DOUBLE PRECISION
|
||
|
|
*> On entry, this is used as described under MODE above.
|
||
|
|
*> If used, it must be >= 1. Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] DMAX
|
||
|
|
*> \verbatim
|
||
|
|
*> DMAX is DOUBLE PRECISION
|
||
|
|
*> If MODE is neither -6, 0 nor 6, the contents of D, as
|
||
|
|
*> computed according to MODE and COND, will be scaled by
|
||
|
|
*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or
|
||
|
|
*> singular value (which is to say the norm) will be abs(DMAX).
|
||
|
|
*> Note that DMAX need not be positive: if DMAX is negative
|
||
|
|
*> (or zero), D will be scaled by a negative number (or zero).
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] KL
|
||
|
|
*> \verbatim
|
||
|
|
*> KL is INTEGER
|
||
|
|
*> This specifies the lower bandwidth of the matrix. For
|
||
|
|
*> example, KL=0 implies upper triangular, KL=1 implies upper
|
||
|
|
*> Hessenberg, and KL being at least M-1 means that the matrix
|
||
|
|
*> has full lower bandwidth. KL must equal KU if the matrix
|
||
|
|
*> is symmetric.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] KU
|
||
|
|
*> \verbatim
|
||
|
|
*> KU is INTEGER
|
||
|
|
*> This specifies the upper bandwidth of the matrix. For
|
||
|
|
*> example, KU=0 implies lower triangular, KU=1 implies lower
|
||
|
|
*> Hessenberg, and KU being at least N-1 means that the matrix
|
||
|
|
*> has full upper bandwidth. KL must equal KU if the matrix
|
||
|
|
*> is symmetric.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] PACK
|
||
|
|
*> \verbatim
|
||
|
|
*> PACK is CHARACTER*1
|
||
|
|
*> This 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 the matrix is symmetric or upper triangular)
|
||
|
|
*> 'R' => store the lower triangle columnwise
|
||
|
|
*> (only if the matrix is symmetric or lower triangular)
|
||
|
|
*> 'B' => store the lower triangle in band storage scheme
|
||
|
|
*> (only if matrix symmetric or lower triangular)
|
||
|
|
*> 'Q' => store the upper triangle in band storage scheme
|
||
|
|
*> (only if matrix symmetric or upper triangular)
|
||
|
|
*> '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 DLATMS differ only in the PACK parameter,
|
||
|
|
*> they will generate mathematically equivalent matrices.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is DOUBLE PRECISION array, dimension ( LDA, N )
|
||
|
|
*> On exit A is the desired test matrix. A is first generated
|
||
|
|
*> in full (unpacked) form, and then packed, if so specified
|
||
|
|
*> by PACK. Thus, the first M elements of the first N
|
||
|
|
*> columns will always be modified. If PACK specifies a
|
||
|
|
*> packed or banded storage scheme, all LDA elements of the
|
||
|
|
*> first N columns will be modified; the elements of the
|
||
|
|
*> array which do not correspond to elements of the generated
|
||
|
|
*> matrix are set to zero.
|
||
|
|
*> Modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> LDA specifies the first dimension of A as declared in the
|
||
|
|
*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then
|
||
|
|
*> LDA must be at least M. If PACK='B' or 'Q', then LDA must
|
||
|
|
*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)).
|
||
|
|
*> If PACK='Z', LDA must be large enough to hold the packed
|
||
|
|
*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1.
|
||
|
|
*> Not modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] WORK
|
||
|
|
*> \verbatim
|
||
|
|
*> WORK is DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) )
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] INFO
|
||
|
|
*> \verbatim
|
||
|
|
*> INFO is INTEGER
|
||
|
|
*> Error code. On exit, INFO will be set to one of the
|
||
|
|
*> following values:
|
||
|
|
*> 0 => normal return
|
||
|
|
*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P'
|
||
|
|
*> -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 => KL negative
|
||
|
|
*> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL
|
||
|
|
*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N';
|
||
|
|
*> or PACK='C' or 'Q' and SYM='N' and KL is not zero;
|
||
|
|
*> or PACK='R' or 'B' and SYM='N' and KU is not zero;
|
||
|
|
*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not
|
||
|
|
*> N.
|
||
|
|
*> -14 => LDA is less than M, or PACK='Z' and LDA is less than
|
||
|
|
*> MIN(KU,N-1) + MIN(KL,M-1) + 1.
|
||
|
|
*> 1 => Error return from DLATM1
|
||
|
|
*> 2 => Cannot scale to DMAX (max. sing. value is 0)
|
||
|
|
*> 3 => Error return from DLAGGE or SLAGSY
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup double_matgen
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
|
||
|
|
$ KL, KU, PACK, A, LDA, WORK, 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, PACK, SYM
|
||
|
|
INTEGER INFO, KL, KU, LDA, M, MODE, N
|
||
|
|
DOUBLE PRECISION COND, DMAX
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
INTEGER ISEED( 4 )
|
||
|
|
DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
DOUBLE PRECISION ZERO
|
||
|
|
PARAMETER ( ZERO = 0.0D0 )
|
||
|
|
DOUBLE PRECISION ONE
|
||
|
|
PARAMETER ( ONE = 1.0D0 )
|
||
|
|
DOUBLE PRECISION TWOPI
|
||
|
|
PARAMETER ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL GIVENS, ILEXTR, ILTEMP, TOPDWN
|
||
|
|
INTEGER I, IC, ICOL, IDIST, IENDCH, IINFO, IL, ILDA,
|
||
|
|
$ IOFFG, IOFFST, IPACK, IPACKG, IR, IR1, IR2,
|
||
|
|
$ IROW, IRSIGN, ISKEW, ISYM, ISYMPK, J, JC, JCH,
|
||
|
|
$ JKL, JKU, JR, K, LLB, MINLDA, MNMIN, MR, NC,
|
||
|
|
$ UUB
|
||
|
|
DOUBLE PRECISION ALPHA, ANGLE, C, DUMMY, EXTRA, S, TEMP
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
DOUBLE PRECISION DLARND
|
||
|
|
EXTERNAL LSAME, DLARND
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL DCOPY, DLAGGE, DLAGSY, DLAROT, DLARTG, DLASET,
|
||
|
|
$ DLATM1, DSCAL, XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC ABS, COS, DBLE, MAX, MIN, MOD, SIN
|
||
|
|
* ..
|
||
|
|
* .. 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, 'N' ) ) THEN
|
||
|
|
ISYM = 1
|
||
|
|
IRSIGN = 0
|
||
|
|
ELSE IF( LSAME( SYM, 'P' ) ) THEN
|
||
|
|
ISYM = 2
|
||
|
|
IRSIGN = 0
|
||
|
|
ELSE IF( LSAME( SYM, 'S' ) ) THEN
|
||
|
|
ISYM = 2
|
||
|
|
IRSIGN = 1
|
||
|
|
ELSE IF( LSAME( SYM, 'H' ) ) THEN
|
||
|
|
ISYM = 2
|
||
|
|
IRSIGN = 1
|
||
|
|
ELSE
|
||
|
|
ISYM = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Decode PACK
|
||
|
|
*
|
||
|
|
ISYMPK = 0
|
||
|
|
IF( LSAME( PACK, 'N' ) ) THEN
|
||
|
|
IPACK = 0
|
||
|
|
ELSE IF( LSAME( PACK, 'U' ) ) THEN
|
||
|
|
IPACK = 1
|
||
|
|
ISYMPK = 1
|
||
|
|
ELSE IF( LSAME( PACK, 'L' ) ) THEN
|
||
|
|
IPACK = 2
|
||
|
|
ISYMPK = 1
|
||
|
|
ELSE IF( LSAME( PACK, 'C' ) ) THEN
|
||
|
|
IPACK = 3
|
||
|
|
ISYMPK = 2
|
||
|
|
ELSE IF( LSAME( PACK, 'R' ) ) THEN
|
||
|
|
IPACK = 4
|
||
|
|
ISYMPK = 3
|
||
|
|
ELSE IF( LSAME( PACK, 'B' ) ) THEN
|
||
|
|
IPACK = 5
|
||
|
|
ISYMPK = 3
|
||
|
|
ELSE IF( LSAME( PACK, 'Q' ) ) THEN
|
||
|
|
IPACK = 6
|
||
|
|
ISYMPK = 2
|
||
|
|
ELSE IF( LSAME( PACK, 'Z' ) ) THEN
|
||
|
|
IPACK = 7
|
||
|
|
ELSE
|
||
|
|
IPACK = -1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set certain internal parameters
|
||
|
|
*
|
||
|
|
MNMIN = MIN( M, N )
|
||
|
|
LLB = MIN( KL, M-1 )
|
||
|
|
UUB = MIN( KU, N-1 )
|
||
|
|
MR = MIN( M, N+LLB )
|
||
|
|
NC = MIN( N, M+UUB )
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.5 .OR. IPACK.EQ.6 ) THEN
|
||
|
|
MINLDA = UUB + 1
|
||
|
|
ELSE IF( IPACK.EQ.7 ) THEN
|
||
|
|
MINLDA = LLB + UUB + 1
|
||
|
|
ELSE
|
||
|
|
MINLDA = M
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Use Givens rotation method if bandwidth small enough,
|
||
|
|
* or if LDA is too small to store the matrix unpacked.
|
||
|
|
*
|
||
|
|
GIVENS = .FALSE.
|
||
|
|
IF( ISYM.EQ.1 ) THEN
|
||
|
|
IF( DBLE( LLB+UUB ).LT.0.3D0*DBLE( MAX( 1, MR+NC ) ) )
|
||
|
|
$ GIVENS = .TRUE.
|
||
|
|
ELSE
|
||
|
|
IF( 2*LLB.LT.M )
|
||
|
|
$ GIVENS = .TRUE.
|
||
|
|
END IF
|
||
|
|
IF( LDA.LT.M .AND. LDA.GE.MINLDA )
|
||
|
|
$ GIVENS = .TRUE.
|
||
|
|
*
|
||
|
|
* Set INFO if an error
|
||
|
|
*
|
||
|
|
IF( M.LT.0 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( M.NE.N .AND. ISYM.NE.1 ) 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( ABS( MODE ).GT.6 ) THEN
|
||
|
|
INFO = -7
|
||
|
|
ELSE IF( ( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) .AND. COND.LT.ONE )
|
||
|
|
$ THEN
|
||
|
|
INFO = -8
|
||
|
|
ELSE IF( KL.LT.0 ) THEN
|
||
|
|
INFO = -10
|
||
|
|
ELSE IF( KU.LT.0 .OR. ( ISYM.NE.1 .AND. KL.NE.KU ) ) THEN
|
||
|
|
INFO = -11
|
||
|
|
ELSE IF( IPACK.EQ.-1 .OR. ( ISYMPK.EQ.1 .AND. ISYM.EQ.1 ) .OR.
|
||
|
|
$ ( ISYMPK.EQ.2 .AND. ISYM.EQ.1 .AND. KL.GT.0 ) .OR.
|
||
|
|
$ ( ISYMPK.EQ.3 .AND. ISYM.EQ.1 .AND. KU.GT.0 ) .OR.
|
||
|
|
$ ( ISYMPK.NE.0 .AND. M.NE.N ) ) THEN
|
||
|
|
INFO = -12
|
||
|
|
ELSE IF( LDA.LT.MAX( 1, MINLDA ) ) THEN
|
||
|
|
INFO = -14
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'DLATMS', -INFO )
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Initialize random number generator
|
||
|
|
*
|
||
|
|
DO 10 I = 1, 4
|
||
|
|
ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 )
|
||
|
|
10 CONTINUE
|
||
|
|
*
|
||
|
|
IF( MOD( ISEED( 4 ), 2 ).NE.1 )
|
||
|
|
$ ISEED( 4 ) = ISEED( 4 ) + 1
|
||
|
|
*
|
||
|
|
* 2) Set up D if indicated.
|
||
|
|
*
|
||
|
|
* Compute D according to COND and MODE
|
||
|
|
*
|
||
|
|
CALL DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, IINFO )
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
INFO = 1
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Choose Top-Down if D is (apparently) increasing,
|
||
|
|
* Bottom-Up if D is (apparently) decreasing.
|
||
|
|
*
|
||
|
|
IF( ABS( D( 1 ) ).LE.ABS( D( MNMIN ) ) ) THEN
|
||
|
|
TOPDWN = .TRUE.
|
||
|
|
ELSE
|
||
|
|
TOPDWN = .FALSE.
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( MODE.NE.0 .AND. ABS( MODE ).NE.6 ) THEN
|
||
|
|
*
|
||
|
|
* Scale by DMAX
|
||
|
|
*
|
||
|
|
TEMP = ABS( D( 1 ) )
|
||
|
|
DO 20 I = 2, MNMIN
|
||
|
|
TEMP = MAX( TEMP, ABS( D( I ) ) )
|
||
|
|
20 CONTINUE
|
||
|
|
*
|
||
|
|
IF( TEMP.GT.ZERO ) THEN
|
||
|
|
ALPHA = DMAX / TEMP
|
||
|
|
ELSE
|
||
|
|
INFO = 2
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL DSCAL( MNMIN, ALPHA, D, 1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 3) Generate Banded Matrix using Givens rotations.
|
||
|
|
* Also the special case of UUB=LLB=0
|
||
|
|
*
|
||
|
|
* Compute Addressing constants to cover all
|
||
|
|
* storage formats. Whether GE, SY, GB, or SB,
|
||
|
|
* upper or lower triangle or both,
|
||
|
|
* the (i,j)-th element is in
|
||
|
|
* A( i - ISKEW*j + IOFFST, j )
|
||
|
|
*
|
||
|
|
IF( IPACK.GT.4 ) THEN
|
||
|
|
ILDA = LDA - 1
|
||
|
|
ISKEW = 1
|
||
|
|
IF( IPACK.GT.5 ) THEN
|
||
|
|
IOFFST = UUB + 1
|
||
|
|
ELSE
|
||
|
|
IOFFST = 1
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
ILDA = LDA
|
||
|
|
ISKEW = 0
|
||
|
|
IOFFST = 0
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* IPACKG is the format that the matrix is generated in. If this is
|
||
|
|
* different from IPACK, then the matrix must be repacked at the
|
||
|
|
* end. It also signals how to compute the norm, for scaling.
|
||
|
|
*
|
||
|
|
IPACKG = 0
|
||
|
|
CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
|
||
|
|
*
|
||
|
|
* Diagonal Matrix -- We are done, unless it
|
||
|
|
* is to be stored SP/PP/TP (PACK='R' or 'C')
|
||
|
|
*
|
||
|
|
IF( LLB.EQ.0 .AND. UUB.EQ.0 ) THEN
|
||
|
|
CALL DCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 )
|
||
|
|
IF( IPACK.LE.2 .OR. IPACK.GE.5 )
|
||
|
|
$ IPACKG = IPACK
|
||
|
|
*
|
||
|
|
ELSE IF( GIVENS ) THEN
|
||
|
|
*
|
||
|
|
* Check whether to use Givens rotations,
|
||
|
|
* Householder transformations, or nothing.
|
||
|
|
*
|
||
|
|
IF( ISYM.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Non-symmetric -- A = U D V
|
||
|
|
*
|
||
|
|
IF( IPACK.GT.4 ) THEN
|
||
|
|
IPACKG = IPACK
|
||
|
|
ELSE
|
||
|
|
IPACKG = 0
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL DCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 )
|
||
|
|
*
|
||
|
|
IF( TOPDWN ) THEN
|
||
|
|
JKL = 0
|
||
|
|
DO 50 JKU = 1, UUB
|
||
|
|
*
|
||
|
|
* Transform from bandwidth JKL, JKU-1 to JKL, JKU
|
||
|
|
*
|
||
|
|
* Last row actually rotated is M
|
||
|
|
* Last column actually rotated is MIN( M+JKU, N )
|
||
|
|
*
|
||
|
|
DO 40 JR = 1, MIN( M+JKU, N ) + JKL - 1
|
||
|
|
EXTRA = ZERO
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = SIN( ANGLE )
|
||
|
|
ICOL = MAX( 1, JR-JKL )
|
||
|
|
IF( JR.LT.M ) THEN
|
||
|
|
IL = MIN( N, JR+JKU ) + 1 - ICOL
|
||
|
|
CALL DLAROT( .TRUE., JR.GT.JKL, .FALSE., IL, C,
|
||
|
|
$ S, A( JR-ISKEW*ICOL+IOFFST, ICOL ),
|
||
|
|
$ ILDA, EXTRA, DUMMY )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Chase "EXTRA" back up
|
||
|
|
*
|
||
|
|
IR = JR
|
||
|
|
IC = ICOL
|
||
|
|
DO 30 JCH = JR - JKL, 1, -JKL - JKU
|
||
|
|
IF( IR.LT.M ) THEN
|
||
|
|
CALL DLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
|
||
|
|
$ IC+1 ), EXTRA, C, S, DUMMY )
|
||
|
|
END IF
|
||
|
|
IROW = MAX( 1, JCH-JKU )
|
||
|
|
IL = IR + 2 - IROW
|
||
|
|
TEMP = ZERO
|
||
|
|
ILTEMP = JCH.GT.JKU
|
||
|
|
CALL DLAROT( .FALSE., ILTEMP, .TRUE., IL, C, -S,
|
||
|
|
$ A( IROW-ISKEW*IC+IOFFST, IC ),
|
||
|
|
$ ILDA, TEMP, EXTRA )
|
||
|
|
IF( ILTEMP ) THEN
|
||
|
|
CALL DLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST,
|
||
|
|
$ IC+1 ), TEMP, C, S, DUMMY )
|
||
|
|
ICOL = MAX( 1, JCH-JKU-JKL )
|
||
|
|
IL = IC + 2 - ICOL
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .TRUE., JCH.GT.JKU+JKL, .TRUE.,
|
||
|
|
$ IL, C, -S, A( IROW-ISKEW*ICOL+
|
||
|
|
$ IOFFST, ICOL ), ILDA, EXTRA,
|
||
|
|
$ TEMP )
|
||
|
|
IC = ICOL
|
||
|
|
IR = IROW
|
||
|
|
END IF
|
||
|
|
30 CONTINUE
|
||
|
|
40 CONTINUE
|
||
|
|
50 CONTINUE
|
||
|
|
*
|
||
|
|
JKU = UUB
|
||
|
|
DO 80 JKL = 1, LLB
|
||
|
|
*
|
||
|
|
* Transform from bandwidth JKL-1, JKU to JKL, JKU
|
||
|
|
*
|
||
|
|
DO 70 JC = 1, MIN( N+JKL, M ) + JKU - 1
|
||
|
|
EXTRA = ZERO
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = SIN( ANGLE )
|
||
|
|
IROW = MAX( 1, JC-JKU )
|
||
|
|
IF( JC.LT.N ) THEN
|
||
|
|
IL = MIN( M, JC+JKL ) + 1 - IROW
|
||
|
|
CALL DLAROT( .FALSE., JC.GT.JKU, .FALSE., IL, C,
|
||
|
|
$ S, A( IROW-ISKEW*JC+IOFFST, JC ),
|
||
|
|
$ ILDA, EXTRA, DUMMY )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Chase "EXTRA" back up
|
||
|
|
*
|
||
|
|
IC = JC
|
||
|
|
IR = IROW
|
||
|
|
DO 60 JCH = JC - JKU, 1, -JKL - JKU
|
||
|
|
IF( IC.LT.N ) THEN
|
||
|
|
CALL DLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
|
||
|
|
$ IC+1 ), EXTRA, C, S, DUMMY )
|
||
|
|
END IF
|
||
|
|
ICOL = MAX( 1, JCH-JKL )
|
||
|
|
IL = IC + 2 - ICOL
|
||
|
|
TEMP = ZERO
|
||
|
|
ILTEMP = JCH.GT.JKL
|
||
|
|
CALL DLAROT( .TRUE., ILTEMP, .TRUE., IL, C, -S,
|
||
|
|
$ A( IR-ISKEW*ICOL+IOFFST, ICOL ),
|
||
|
|
$ ILDA, TEMP, EXTRA )
|
||
|
|
IF( ILTEMP ) THEN
|
||
|
|
CALL DLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST,
|
||
|
|
$ ICOL+1 ), TEMP, C, S, DUMMY )
|
||
|
|
IROW = MAX( 1, JCH-JKL-JKU )
|
||
|
|
IL = IR + 2 - IROW
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .FALSE., JCH.GT.JKL+JKU, .TRUE.,
|
||
|
|
$ IL, C, -S, A( IROW-ISKEW*ICOL+
|
||
|
|
$ IOFFST, ICOL ), ILDA, EXTRA,
|
||
|
|
$ TEMP )
|
||
|
|
IC = ICOL
|
||
|
|
IR = IROW
|
||
|
|
END IF
|
||
|
|
60 CONTINUE
|
||
|
|
70 CONTINUE
|
||
|
|
80 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Bottom-Up -- Start at the bottom right.
|
||
|
|
*
|
||
|
|
JKL = 0
|
||
|
|
DO 110 JKU = 1, UUB
|
||
|
|
*
|
||
|
|
* Transform from bandwidth JKL, JKU-1 to JKL, JKU
|
||
|
|
*
|
||
|
|
* First row actually rotated is M
|
||
|
|
* First column actually rotated is MIN( M+JKU, N )
|
||
|
|
*
|
||
|
|
IENDCH = MIN( M, N+JKL ) - 1
|
||
|
|
DO 100 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1
|
||
|
|
EXTRA = ZERO
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = SIN( ANGLE )
|
||
|
|
IROW = MAX( 1, JC-JKU+1 )
|
||
|
|
IF( JC.GT.0 ) THEN
|
||
|
|
IL = MIN( M, JC+JKL+1 ) + 1 - IROW
|
||
|
|
CALL DLAROT( .FALSE., .FALSE., JC+JKL.LT.M, IL,
|
||
|
|
$ C, S, A( IROW-ISKEW*JC+IOFFST,
|
||
|
|
$ JC ), ILDA, DUMMY, EXTRA )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Chase "EXTRA" back down
|
||
|
|
*
|
||
|
|
IC = JC
|
||
|
|
DO 90 JCH = JC + JKL, IENDCH, JKL + JKU
|
||
|
|
ILEXTR = IC.GT.0
|
||
|
|
IF( ILEXTR ) THEN
|
||
|
|
CALL DLARTG( A( JCH-ISKEW*IC+IOFFST, IC ),
|
||
|
|
$ EXTRA, C, S, DUMMY )
|
||
|
|
END IF
|
||
|
|
IC = MAX( 1, IC )
|
||
|
|
ICOL = MIN( N-1, JCH+JKU )
|
||
|
|
ILTEMP = JCH + JKU.LT.N
|
||
|
|
TEMP = ZERO
|
||
|
|
CALL DLAROT( .TRUE., ILEXTR, ILTEMP, ICOL+2-IC,
|
||
|
|
$ C, S, A( JCH-ISKEW*IC+IOFFST, IC ),
|
||
|
|
$ ILDA, EXTRA, TEMP )
|
||
|
|
IF( ILTEMP ) THEN
|
||
|
|
CALL DLARTG( A( JCH-ISKEW*ICOL+IOFFST,
|
||
|
|
$ ICOL ), TEMP, C, S, DUMMY )
|
||
|
|
IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .FALSE., .TRUE.,
|
||
|
|
$ JCH+JKL+JKU.LE.IENDCH, IL, C, S,
|
||
|
|
$ A( JCH-ISKEW*ICOL+IOFFST,
|
||
|
|
$ ICOL ), ILDA, TEMP, EXTRA )
|
||
|
|
IC = ICOL
|
||
|
|
END IF
|
||
|
|
90 CONTINUE
|
||
|
|
100 CONTINUE
|
||
|
|
110 CONTINUE
|
||
|
|
*
|
||
|
|
JKU = UUB
|
||
|
|
DO 140 JKL = 1, LLB
|
||
|
|
*
|
||
|
|
* Transform from bandwidth JKL-1, JKU to JKL, JKU
|
||
|
|
*
|
||
|
|
* First row actually rotated is MIN( N+JKL, M )
|
||
|
|
* First column actually rotated is N
|
||
|
|
*
|
||
|
|
IENDCH = MIN( N, M+JKU ) - 1
|
||
|
|
DO 130 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1
|
||
|
|
EXTRA = ZERO
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = SIN( ANGLE )
|
||
|
|
ICOL = MAX( 1, JR-JKL+1 )
|
||
|
|
IF( JR.GT.0 ) THEN
|
||
|
|
IL = MIN( N, JR+JKU+1 ) + 1 - ICOL
|
||
|
|
CALL DLAROT( .TRUE., .FALSE., JR+JKU.LT.N, IL,
|
||
|
|
$ C, S, A( JR-ISKEW*ICOL+IOFFST,
|
||
|
|
$ ICOL ), ILDA, DUMMY, EXTRA )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Chase "EXTRA" back down
|
||
|
|
*
|
||
|
|
IR = JR
|
||
|
|
DO 120 JCH = JR + JKU, IENDCH, JKL + JKU
|
||
|
|
ILEXTR = IR.GT.0
|
||
|
|
IF( ILEXTR ) THEN
|
||
|
|
CALL DLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ),
|
||
|
|
$ EXTRA, C, S, DUMMY )
|
||
|
|
END IF
|
||
|
|
IR = MAX( 1, IR )
|
||
|
|
IROW = MIN( M-1, JCH+JKL )
|
||
|
|
ILTEMP = JCH + JKL.LT.M
|
||
|
|
TEMP = ZERO
|
||
|
|
CALL DLAROT( .FALSE., ILEXTR, ILTEMP, IROW+2-IR,
|
||
|
|
$ C, S, A( IR-ISKEW*JCH+IOFFST,
|
||
|
|
$ JCH ), ILDA, EXTRA, TEMP )
|
||
|
|
IF( ILTEMP ) THEN
|
||
|
|
CALL DLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ),
|
||
|
|
$ TEMP, C, S, DUMMY )
|
||
|
|
IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .TRUE., .TRUE.,
|
||
|
|
$ JCH+JKL+JKU.LE.IENDCH, IL, C, S,
|
||
|
|
$ A( IROW-ISKEW*JCH+IOFFST, JCH ),
|
||
|
|
$ ILDA, TEMP, EXTRA )
|
||
|
|
IR = IROW
|
||
|
|
END IF
|
||
|
|
120 CONTINUE
|
||
|
|
130 CONTINUE
|
||
|
|
140 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Symmetric -- A = U D U'
|
||
|
|
*
|
||
|
|
IPACKG = IPACK
|
||
|
|
IOFFG = IOFFST
|
||
|
|
*
|
||
|
|
IF( TOPDWN ) THEN
|
||
|
|
*
|
||
|
|
* Top-Down -- Generate Upper triangle only
|
||
|
|
*
|
||
|
|
IF( IPACK.GE.5 ) THEN
|
||
|
|
IPACKG = 6
|
||
|
|
IOFFG = UUB + 1
|
||
|
|
ELSE
|
||
|
|
IPACKG = 1
|
||
|
|
END IF
|
||
|
|
CALL DCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 )
|
||
|
|
*
|
||
|
|
DO 170 K = 1, UUB
|
||
|
|
DO 160 JC = 1, N - 1
|
||
|
|
IROW = MAX( 1, JC-K )
|
||
|
|
IL = MIN( JC+1, K+2 )
|
||
|
|
EXTRA = ZERO
|
||
|
|
TEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 )
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = SIN( ANGLE )
|
||
|
|
CALL DLAROT( .FALSE., JC.GT.K, .TRUE., IL, C, S,
|
||
|
|
$ A( IROW-ISKEW*JC+IOFFG, JC ), ILDA,
|
||
|
|
$ EXTRA, TEMP )
|
||
|
|
CALL DLAROT( .TRUE., .TRUE., .FALSE.,
|
||
|
|
$ MIN( K, N-JC )+1, C, S,
|
||
|
|
$ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
|
||
|
|
$ TEMP, DUMMY )
|
||
|
|
*
|
||
|
|
* Chase EXTRA back up the matrix
|
||
|
|
*
|
||
|
|
ICOL = JC
|
||
|
|
DO 150 JCH = JC - K, 1, -K
|
||
|
|
CALL DLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG,
|
||
|
|
$ ICOL+1 ), EXTRA, C, S, DUMMY )
|
||
|
|
TEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 )
|
||
|
|
CALL DLAROT( .TRUE., .TRUE., .TRUE., K+2, C, -S,
|
||
|
|
$ A( ( 1-ISKEW )*JCH+IOFFG, JCH ),
|
||
|
|
$ ILDA, TEMP, EXTRA )
|
||
|
|
IROW = MAX( 1, JCH-K )
|
||
|
|
IL = MIN( JCH+1, K+2 )
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .FALSE., JCH.GT.K, .TRUE., IL, C,
|
||
|
|
$ -S, A( IROW-ISKEW*JCH+IOFFG, JCH ),
|
||
|
|
$ ILDA, EXTRA, TEMP )
|
||
|
|
ICOL = JCH
|
||
|
|
150 CONTINUE
|
||
|
|
160 CONTINUE
|
||
|
|
170 CONTINUE
|
||
|
|
*
|
||
|
|
* If we need lower triangle, copy from upper. Note that
|
||
|
|
* the order of copying is chosen to work for 'q' -> 'b'
|
||
|
|
*
|
||
|
|
IF( IPACK.NE.IPACKG .AND. IPACK.NE.3 ) THEN
|
||
|
|
DO 190 JC = 1, N
|
||
|
|
IROW = IOFFST - ISKEW*JC
|
||
|
|
DO 180 JR = JC, MIN( N, JC+UUB )
|
||
|
|
A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
|
||
|
|
180 CONTINUE
|
||
|
|
190 CONTINUE
|
||
|
|
IF( IPACK.EQ.5 ) THEN
|
||
|
|
DO 210 JC = N - UUB + 1, N
|
||
|
|
DO 200 JR = N + 2 - JC, UUB + 1
|
||
|
|
A( JR, JC ) = ZERO
|
||
|
|
200 CONTINUE
|
||
|
|
210 CONTINUE
|
||
|
|
END IF
|
||
|
|
IF( IPACKG.EQ.6 ) THEN
|
||
|
|
IPACKG = IPACK
|
||
|
|
ELSE
|
||
|
|
IPACKG = 0
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Bottom-Up -- Generate Lower triangle only
|
||
|
|
*
|
||
|
|
IF( IPACK.GE.5 ) THEN
|
||
|
|
IPACKG = 5
|
||
|
|
IF( IPACK.EQ.6 )
|
||
|
|
$ IOFFG = 1
|
||
|
|
ELSE
|
||
|
|
IPACKG = 2
|
||
|
|
END IF
|
||
|
|
CALL DCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 )
|
||
|
|
*
|
||
|
|
DO 240 K = 1, UUB
|
||
|
|
DO 230 JC = N - 1, 1, -1
|
||
|
|
IL = MIN( N+1-JC, K+2 )
|
||
|
|
EXTRA = ZERO
|
||
|
|
TEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC )
|
||
|
|
ANGLE = TWOPI*DLARND( 1, ISEED )
|
||
|
|
C = COS( ANGLE )
|
||
|
|
S = -SIN( ANGLE )
|
||
|
|
CALL DLAROT( .FALSE., .TRUE., N-JC.GT.K, IL, C, S,
|
||
|
|
$ A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
|
||
|
|
$ TEMP, EXTRA )
|
||
|
|
ICOL = MAX( 1, JC-K+1 )
|
||
|
|
CALL DLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL, C,
|
||
|
|
$ S, A( JC-ISKEW*ICOL+IOFFG, ICOL ),
|
||
|
|
$ ILDA, DUMMY, TEMP )
|
||
|
|
*
|
||
|
|
* Chase EXTRA back down the matrix
|
||
|
|
*
|
||
|
|
ICOL = JC
|
||
|
|
DO 220 JCH = JC + K, N - 1, K
|
||
|
|
CALL DLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
|
||
|
|
$ EXTRA, C, S, DUMMY )
|
||
|
|
TEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH )
|
||
|
|
CALL DLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S,
|
||
|
|
$ A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
|
||
|
|
$ ILDA, EXTRA, TEMP )
|
||
|
|
IL = MIN( N+1-JCH, K+2 )
|
||
|
|
EXTRA = ZERO
|
||
|
|
CALL DLAROT( .FALSE., .TRUE., N-JCH.GT.K, IL, C,
|
||
|
|
$ S, A( ( 1-ISKEW )*JCH+IOFFG, JCH ),
|
||
|
|
$ ILDA, TEMP, EXTRA )
|
||
|
|
ICOL = JCH
|
||
|
|
220 CONTINUE
|
||
|
|
230 CONTINUE
|
||
|
|
240 CONTINUE
|
||
|
|
*
|
||
|
|
* If we need upper triangle, copy from lower. Note that
|
||
|
|
* the order of copying is chosen to work for 'b' -> 'q'
|
||
|
|
*
|
||
|
|
IF( IPACK.NE.IPACKG .AND. IPACK.NE.4 ) THEN
|
||
|
|
DO 260 JC = N, 1, -1
|
||
|
|
IROW = IOFFST - ISKEW*JC
|
||
|
|
DO 250 JR = JC, MAX( 1, JC-UUB ), -1
|
||
|
|
A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
|
||
|
|
250 CONTINUE
|
||
|
|
260 CONTINUE
|
||
|
|
IF( IPACK.EQ.6 ) THEN
|
||
|
|
DO 280 JC = 1, UUB
|
||
|
|
DO 270 JR = 1, UUB + 1 - JC
|
||
|
|
A( JR, JC ) = ZERO
|
||
|
|
270 CONTINUE
|
||
|
|
280 CONTINUE
|
||
|
|
END IF
|
||
|
|
IF( IPACKG.EQ.5 ) THEN
|
||
|
|
IPACKG = IPACK
|
||
|
|
ELSE
|
||
|
|
IPACKG = 0
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* 4) Generate Banded Matrix by first
|
||
|
|
* Rotating by random Unitary matrices,
|
||
|
|
* then reducing the bandwidth using Householder
|
||
|
|
* transformations.
|
||
|
|
*
|
||
|
|
* Note: we should get here only if LDA .ge. N
|
||
|
|
*
|
||
|
|
IF( ISYM.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Non-symmetric -- A = U D V
|
||
|
|
*
|
||
|
|
CALL DLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK,
|
||
|
|
$ IINFO )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Symmetric -- A = U D U'
|
||
|
|
*
|
||
|
|
CALL DLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
IF( IINFO.NE.0 ) THEN
|
||
|
|
INFO = 3
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* 5) Pack the matrix
|
||
|
|
*
|
||
|
|
IF( IPACK.NE.IPACKG ) THEN
|
||
|
|
IF( IPACK.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* 'U' -- Upper triangular, not packed
|
||
|
|
*
|
||
|
|
DO 300 J = 1, M
|
||
|
|
DO 290 I = J + 1, M
|
||
|
|
A( I, J ) = ZERO
|
||
|
|
290 CONTINUE
|
||
|
|
300 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.2 ) THEN
|
||
|
|
*
|
||
|
|
* 'L' -- Lower triangular, not packed
|
||
|
|
*
|
||
|
|
DO 320 J = 2, M
|
||
|
|
DO 310 I = 1, J - 1
|
||
|
|
A( I, J ) = ZERO
|
||
|
|
310 CONTINUE
|
||
|
|
320 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.3 ) THEN
|
||
|
|
*
|
||
|
|
* 'C' -- Upper triangle packed Columnwise.
|
||
|
|
*
|
||
|
|
ICOL = 1
|
||
|
|
IROW = 0
|
||
|
|
DO 340 J = 1, M
|
||
|
|
DO 330 I = 1, J
|
||
|
|
IROW = IROW + 1
|
||
|
|
IF( IROW.GT.LDA ) THEN
|
||
|
|
IROW = 1
|
||
|
|
ICOL = ICOL + 1
|
||
|
|
END IF
|
||
|
|
A( IROW, ICOL ) = A( I, J )
|
||
|
|
330 CONTINUE
|
||
|
|
340 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.EQ.4 ) THEN
|
||
|
|
*
|
||
|
|
* 'R' -- Lower triangle packed Columnwise.
|
||
|
|
*
|
||
|
|
ICOL = 1
|
||
|
|
IROW = 0
|
||
|
|
DO 360 J = 1, M
|
||
|
|
DO 350 I = J, M
|
||
|
|
IROW = IROW + 1
|
||
|
|
IF( IROW.GT.LDA ) THEN
|
||
|
|
IROW = 1
|
||
|
|
ICOL = ICOL + 1
|
||
|
|
END IF
|
||
|
|
A( IROW, ICOL ) = A( I, J )
|
||
|
|
350 CONTINUE
|
||
|
|
360 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.GE.5 ) THEN
|
||
|
|
*
|
||
|
|
* 'B' -- The lower triangle is packed as a band matrix.
|
||
|
|
* 'Q' -- The upper triangle is packed as a band matrix.
|
||
|
|
* 'Z' -- The whole matrix is packed as a band matrix.
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.5 )
|
||
|
|
$ UUB = 0
|
||
|
|
IF( IPACK.EQ.6 )
|
||
|
|
$ LLB = 0
|
||
|
|
*
|
||
|
|
DO 380 J = 1, UUB
|
||
|
|
DO 370 I = MIN( J+LLB, M ), 1, -1
|
||
|
|
A( I-J+UUB+1, J ) = A( I, J )
|
||
|
|
370 CONTINUE
|
||
|
|
380 CONTINUE
|
||
|
|
*
|
||
|
|
DO 400 J = UUB + 2, N
|
||
|
|
DO 390 I = J - UUB, MIN( J+LLB, M )
|
||
|
|
A( I-J+UUB+1, J ) = A( I, J )
|
||
|
|
390 CONTINUE
|
||
|
|
400 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* If packed, zero out extraneous elements.
|
||
|
|
*
|
||
|
|
* Symmetric/Triangular Packed --
|
||
|
|
* zero out everything after A(IROW,ICOL)
|
||
|
|
*
|
||
|
|
IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN
|
||
|
|
DO 420 JC = ICOL, M
|
||
|
|
DO 410 JR = IROW + 1, LDA
|
||
|
|
A( JR, JC ) = ZERO
|
||
|
|
410 CONTINUE
|
||
|
|
IROW = 0
|
||
|
|
420 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( IPACK.GE.5 ) THEN
|
||
|
|
*
|
||
|
|
* Packed Band --
|
||
|
|
* 1st row is now in A( UUB+2-j, j), zero above it
|
||
|
|
* m-th row is now in A( M+UUB-j,j), zero below it
|
||
|
|
* last non-zero diagonal is now in A( UUB+LLB+1,j ),
|
||
|
|
* zero below it, too.
|
||
|
|
*
|
||
|
|
IR1 = UUB + LLB + 2
|
||
|
|
IR2 = UUB + M + 2
|
||
|
|
DO 450 JC = 1, N
|
||
|
|
DO 430 JR = 1, UUB + 1 - JC
|
||
|
|
A( JR, JC ) = ZERO
|
||
|
|
430 CONTINUE
|
||
|
|
DO 440 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA
|
||
|
|
A( JR, JC ) = ZERO
|
||
|
|
440 CONTINUE
|
||
|
|
450 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DLATMS
|
||
|
|
*
|
||
|
|
END
|