dlatm7()

subroutine dlatm7	(	integer	mode,
		double precision	cond,
		integer	irsign,
		integer	idist,
		integer, dimension( 4 )	iseed,
		double precision, dimension( * )	d,
		integer	n,
		integer	rank,
		integer	info
	)

DLATM7

Purpose:

    DLATM7 computes the entries of D as specified by MODE
    COND and IRSIGN. IDIST and ISEED determine the generation
    of random numbers. DLATM7 is called by DLATMT to generate
    random test matrices.

  MODE   - 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:RANK)=1.0/COND
           MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
           MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK

           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.

  COND   - DOUBLE PRECISION
           On entry, used as described under MODE above.
           If used, it must be >= 1. Not modified.

  IRSIGN - 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

  IDIST  - CHARACTER*1
           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.

  ISEED  - 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 DLATM7
           to continue the same random number sequence.
           Changed on exit.

  D      - 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.

  N      - INTEGER
           Number of entries of D. Not modified.

  RANK   - INTEGER
           The rank of matrix to be generated for modes 1,2,3 only.
           D( RANK+1:N ) = 0.
           Not modified.

  INFO   - 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 120 of file dlatm7.f.

*
*  -- 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 ..
      DOUBLE PRECISION   COND
      INTEGER            IDIST, INFO, IRSIGN, MODE, N, RANK
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * )
      INTEGER            ISEED( 4 )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d0 )
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d0 )
      DOUBLE PRECISION   HALF
      parameter( half = 0.5d0 )
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION   ALPHA, TEMP
      INTEGER            I
*     ..
*     .. 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( 'DLATM7', -info )
         RETURN
      END IF
*
*     Compute D according to COND and MODE
*
      IF( mode.NE.0 ) THEN
         GO TO ( 100, 130, 160, 190, 210, 230 )abs( mode )
*
*        One large D value:
*
  100    CONTINUE
         DO 110 i = 2, rank
            d( i ) = one / cond
  110    CONTINUE
         DO 120 i = rank + 1, n
            d( i ) = zero
  120    CONTINUE
         d( 1 ) = one
         GO TO 240
*
*        One small D value:
*
  130    CONTINUE
         DO 140 i = 1, rank - 1
            d( i ) = one
  140    CONTINUE
         DO 150 i = rank + 1, n
            d( i ) = zero
  150    CONTINUE
         d( rank ) = one / cond
         GO TO 240
*
*        Exponentially distributed D values:
*
  160    CONTINUE
         d( 1 ) = one
         IF( n.GT.1 .AND. rank.GT.1 ) THEN
            alpha = cond**( -one / dble( rank-1 ) )
            DO 170 i = 2, rank
               d( i ) = alpha**( i-1 )
  170       CONTINUE
            DO 180 i = rank + 1, n
               d( i ) = zero
  180       CONTINUE
         END IF
         GO TO 240
*
*        Arithmetically distributed D values:
*
  190    CONTINUE
         d( 1 ) = one
         IF( n.GT.1 ) THEN
            temp = one / cond
            alpha = ( one-temp ) / dble( n-1 )
            DO 200 i = 2, n
               d( i ) = dble( n-i )*alpha + temp
  200       CONTINUE
         END IF
         GO TO 240
*
*        Randomly distributed D values on ( 1/COND , 1):
*
  210    CONTINUE
         alpha = log( one / cond )
         DO 220 i = 1, n
            d( i ) = exp( alpha*dlaran( iseed ) )
  220    CONTINUE
         GO TO 240
*
*        Randomly distributed D values from IDIST
*
  230    CONTINUE
         CALL dlarnv( idist, iseed, n, d )
*
  240    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 250 i = 1, n
               temp = dlaran( iseed )
               IF( temp.GT.half )
     $            d( i ) = -d( i )
  250       CONTINUE
         END IF
*
*        Reverse if MODE < 0
*
         IF( mode.LT.0 ) THEN
            DO 260 i = 1, n / 2
               temp = d( i )
               d( i ) = d( n+1-i )
               d( n+1-i ) = temp
  260       CONTINUE
         END IF
*
      END IF
*
      RETURN
*
*     End of DLATM7
*

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