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*> \brief \b DLATM1
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* .. Scalar Arguments ..
* INTEGER IDIST, INFO, IRSIGN, MODE, N
* DOUBLE PRECISION COND
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* DOUBLE PRECISION D( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLATM1 computes the entries of D(1..N) as specified by
*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. DLATM1 is called by DLATMR to generate
*> random test matrices for LAPACK programs.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] MODE
*> \verbatim
*> MODE is INTEGER
*> On entry describes how D is to be computed:
*> MODE = 0 means do not change D.
*> 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,
*> Not modified.
*> \endverbatim
*>
*> \param[in] COND
*> \verbatim
*> COND is DOUBLE PRECISION
*> On entry, used as described under MODE above.
*> If used, it must be >= 1. Not modified.
*> \endverbatim
*>
*> \param[in] IRSIGN
*> \verbatim
*> IRSIGN is INTEGER
*> On entry, if MODE neither -6, 0 nor 6, determines sign of
*> entries of D
*> 0 => leave entries of D unchanged
*> 1 => multiply each entry of D by 1 or -1 with probability .5
*> \endverbatim
*>
*> \param[in] IDIST
*> \verbatim
*> IDIST is INTEGER
*> On entry, IDIST specifies the type of distribution to be
*> used to generate a random matrix .
*> 1 => UNIFORM( 0, 1 )
*> 2 => UNIFORM( -1, 1 )
*> 3 => NORMAL( 0, 1 )
*> 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. 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 DLATM1
*> to continue the same random number sequence.
*> Changed on exit.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension ( MIN( M , N ) )
*> Array to be computed according to MODE, COND and IRSIGN.
*> May be changed on exit if MODE is nonzero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> Number of entries of D. Not modified.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> 0 => normal termination
*> -1 => if MODE not in range -6 to 6
*> -2 => if MODE neither -6, 0 nor 6, and
*> IRSIGN neither 0 nor 1
*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_matgen
*
* =====================================================================
SUBROUTINE DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER IDIST, INFO, IRSIGN, MODE, N
DOUBLE PRECISION COND
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
DOUBLE PRECISION D( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
DOUBLE PRECISION HALF
PARAMETER ( HALF = 0.5D0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION ALPHA, TEMP
* ..
* .. External Functions ..
DOUBLE PRECISION DLARAN
EXTERNAL DLARAN
* ..
* .. External Subroutines ..
EXTERNAL DLARNV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, EXP, LOG
* ..
* .. Executable Statements ..
*
* Decode and Test the input parameters. Initialize flags & seed.
*
INFO = 0
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Set INFO if an error
*
IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
INFO = -1
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN
INFO = -2
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ COND.LT.ONE ) THEN
INFO = -3
ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND.
$ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -7
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLATM1', -INFO )
RETURN
END IF
*
* Compute D according to COND and MODE
*
IF( MODE.NE.0 ) THEN
GO TO ( 10, 30, 50, 70, 90, 110 )ABS( MODE )
*
* One large D value:
*
10 CONTINUE
DO 20 I = 1, N
D( I ) = ONE / COND
20 CONTINUE
D( 1 ) = ONE
GO TO 120
*
* One small D value:
*
30 CONTINUE
DO 40 I = 1, N
D( I ) = ONE
40 CONTINUE
D( N ) = ONE / COND
GO TO 120
*
* Exponentially distributed D values:
*
50 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 ) THEN
ALPHA = COND**( -ONE / DBLE( N-1 ) )
DO 60 I = 2, N
D( I ) = ALPHA**( I-1 )
60 CONTINUE
END IF
GO TO 120
*
* Arithmetically distributed D values:
*
70 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 ) THEN
TEMP = ONE / COND
ALPHA = ( ONE-TEMP ) / DBLE( N-1 )
DO 80 I = 2, N
D( I ) = DBLE( N-I )*ALPHA + TEMP
80 CONTINUE
END IF
GO TO 120
*
* Randomly distributed D values on ( 1/COND , 1):
*
90 CONTINUE
ALPHA = LOG( ONE / COND )
DO 100 I = 1, N
D( I ) = EXP( ALPHA*DLARAN( ISEED ) )
100 CONTINUE
GO TO 120
*
* Randomly distributed D values from IDIST
*
110 CONTINUE
CALL DLARNV( IDIST, ISEED, N, D )
*
120 CONTINUE
*
* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
* random signs to D
*
IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ IRSIGN.EQ.1 ) THEN
DO 130 I = 1, N
TEMP = DLARAN( ISEED )
IF( TEMP.GT.HALF )
$ D( I ) = -D( I )
130 CONTINUE
END IF
*
* Reverse if MODE < 0
*
IF( MODE.LT.0 ) THEN
DO 140 I = 1, N / 2
TEMP = D( I )
D( I ) = D( N+1-I )
D( N+1-I ) = TEMP
140 CONTINUE
END IF
*
END IF
*
RETURN
*
* End of DLATM1
*
END
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