dlatm1()

subroutine dlatm1	(	integer	mode,
		double precision	cond,
		integer	irsign,
		integer	idist,
		integer, dimension( 4 )	iseed,
		double precision, dimension( * )	d,
		integer	n,
		integer	info
	)

DLATM1

Purpose:

    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.

Parameters

[in]	MODE	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.
[in]	COND	COND is DOUBLE PRECISION On entry, used as described under MODE above. If used, it must be >= 1. Not modified.
[in]	IRSIGN	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
[in]	IDIST	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.
[in,out]	ISEED	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.
[in,out]	D	D is DOUBLE PRECISION array, dimension ( N ) Array to be computed according to MODE, COND and IRSIGN. May be changed on exit if MODE is nonzero.
[in]	N	N is INTEGER Number of entries of D. Not modified.
[out]	INFO	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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file dlatm1.f.

*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. 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
*

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