dlatm1.f

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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 ( 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.
*
*> \ingroup double_matgen
*
*  =====================================================================
      SUBROUTINE dlatm1( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
     $                   INFO )
*
*  -- 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
*
      SUBROUTINE dlatm1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, …
      END