298 lines
8.4 KiB
Fortran
298 lines
8.4 KiB
Fortran
*> \brief \b DLATM7
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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 DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
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* RANK, INFO )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION COND
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* INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION D( * )
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* INTEGER ISEED( 4 )
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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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*> DLATM7 computes the entries of D as specified by MODE
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*> COND and IRSIGN. IDIST and ISEED determine the generation
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*> of random numbers. DLATM7 is called by DLATMT to generate
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*> random test matrices.
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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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*> \verbatim
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*> MODE - INTEGER
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*> On entry describes how D is to be computed:
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*> MODE = 0 means do not change D.
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*>
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*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND
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*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
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*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK
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*>
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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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*>
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*> COND - 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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*>
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*> IRSIGN - INTEGER
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*> On entry, if MODE neither -6, 0 nor 6, determines sign of
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*> entries of D
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*> 0 => leave entries of D unchanged
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*> 1 => multiply each entry of D by 1 or -1 with probability .5
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*>
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*> IDIST - CHARACTER*1
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*> On entry, IDIST specifies the type of distribution to be
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*> used to generate a random matrix .
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*> 1 => UNIFORM( 0, 1 )
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*> 2 => UNIFORM( -1, 1 )
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*> 3 => NORMAL( 0, 1 )
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*> Not modified.
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*>
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*> ISEED - INTEGER array, dimension ( 4 )
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*> On entry ISEED specifies the seed of the random number
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*> generator. The random number generator uses a
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*> 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 DLATM7
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*> to continue the same random number sequence.
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*> Changed on exit.
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*>
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*> D - DOUBLE PRECISION array, dimension ( MIN( M , N ) )
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*> Array to be computed according to MODE, COND and IRSIGN.
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*> May be changed on exit if MODE is nonzero.
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*>
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*> N - INTEGER
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*> Number of entries of D. Not modified.
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*>
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*> RANK - INTEGER
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*> The rank of matrix to be generated for modes 1,2,3 only.
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*> D( RANK+1:N ) = 0.
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*> Not modified.
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*>
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*> INFO - INTEGER
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*> 0 => normal termination
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*> -1 => if MODE not in range -6 to 6
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*> -2 => if MODE neither -6, 0 nor 6, and
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*> IRSIGN neither 0 nor 1
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*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1
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*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
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*> -7 => if N negative
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup double_matgen
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*
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* =====================================================================
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SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
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$ RANK, INFO )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION COND
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INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * )
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INTEGER ISEED( 4 )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D0 )
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D0 )
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DOUBLE PRECISION HALF
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PARAMETER ( HALF = 0.5D0 )
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION ALPHA, TEMP
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INTEGER I
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLARAN
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EXTERNAL DLARAN
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* ..
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* .. External Subroutines ..
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EXTERNAL DLARNV, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, EXP, LOG
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* ..
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* .. Executable Statements ..
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*
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* Decode and Test the input parameters. Initialize flags & seed.
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*
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INFO = 0
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Set INFO if an error
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*
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IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
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INFO = -1
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ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
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$ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN
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INFO = -2
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ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
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$ COND.LT.ONE ) THEN
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INFO = -3
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ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND.
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$ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN
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INFO = -4
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ELSE IF( N.LT.0 ) THEN
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INFO = -7
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DLATM7', -INFO )
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RETURN
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END IF
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*
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* Compute D according to COND and MODE
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*
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IF( MODE.NE.0 ) THEN
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GO TO ( 100, 130, 160, 190, 210, 230 )ABS( MODE )
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*
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* One large D value:
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*
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100 CONTINUE
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DO 110 I = 2, RANK
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D( I ) = ONE / COND
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110 CONTINUE
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DO 120 I = RANK + 1, N
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D( I ) = ZERO
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120 CONTINUE
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D( 1 ) = ONE
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GO TO 240
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*
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* One small D value:
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*
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130 CONTINUE
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DO 140 I = 1, RANK - 1
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D( I ) = ONE
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140 CONTINUE
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DO 150 I = RANK + 1, N
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D( I ) = ZERO
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150 CONTINUE
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D( RANK ) = ONE / COND
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GO TO 240
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*
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* Exponentially distributed D values:
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*
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160 CONTINUE
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D( 1 ) = ONE
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IF( N.GT.1 .AND. RANK.GT.1 ) THEN
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ALPHA = COND**( -ONE / DBLE( RANK-1 ) )
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DO 170 I = 2, RANK
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D( I ) = ALPHA**( I-1 )
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170 CONTINUE
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DO 180 I = RANK + 1, N
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D( I ) = ZERO
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180 CONTINUE
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END IF
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GO TO 240
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*
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* Arithmetically distributed D values:
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*
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190 CONTINUE
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D( 1 ) = ONE
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IF( N.GT.1 ) THEN
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TEMP = ONE / COND
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ALPHA = ( ONE-TEMP ) / DBLE( N-1 )
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DO 200 I = 2, N
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D( I ) = DBLE( N-I )*ALPHA + TEMP
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200 CONTINUE
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END IF
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GO TO 240
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*
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* Randomly distributed D values on ( 1/COND , 1):
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*
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210 CONTINUE
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ALPHA = LOG( ONE / COND )
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DO 220 I = 1, N
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D( I ) = EXP( ALPHA*DLARAN( ISEED ) )
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220 CONTINUE
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GO TO 240
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*
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* Randomly distributed D values from IDIST
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*
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230 CONTINUE
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CALL DLARNV( IDIST, ISEED, N, D )
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*
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240 CONTINUE
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*
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* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
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* random signs to D
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*
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IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
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$ IRSIGN.EQ.1 ) THEN
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DO 250 I = 1, N
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TEMP = DLARAN( ISEED )
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IF( TEMP.GT.HALF )
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$ D( I ) = -D( I )
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250 CONTINUE
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END IF
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*
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* Reverse if MODE < 0
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*
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IF( MODE.LT.0 ) THEN
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DO 260 I = 1, N / 2
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TEMP = D( I )
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D( I ) = D( N+1-I )
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D( N+1-I ) = TEMP
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260 CONTINUE
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END IF
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*
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END IF
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*
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RETURN
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*
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* End of DLATM7
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*
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END
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