dlaror.f

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      SUBROUTINE dlaror( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO )
*
*  -- LAPACK auxiliary test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          init, side
      INTEGER            info, lda, m, n
*     ..
*     .. Array Arguments ..
      INTEGER            iseed( 4 )
      DOUBLE PRECISION   a( lda, * ), x( * )
*     ..
*
*  Purpose
*  =======
*
*  DLAROR pre- or post-multiplies an M by N matrix A by a random
*  orthogonal matrix U, overwriting A.  A may optionally be initialized
*  to the identity matrix before multiplying by U.  U is generated using
*  the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409).
*
*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          Specifies whether A is multiplied on the left or right by U.
*          = 'L':         Multiply A on the left (premultiply) by U
*          = 'R':         Multiply A on the right (postmultiply) by U'
*          = 'C' or 'T':  Multiply A on the left by U and the right
*                          by U' (Here, U' means U-transpose.)
*
*  INIT    (input) CHARACTER*1
*          Specifies whether or not A should be initialized to the
*          identity matrix.
*          = 'I':  Initialize A to (a section of) the identity matrix
*                   before applying U.
*          = 'N':  No initialization.  Apply U to the input matrix A.
*
*          INIT = 'I' may be used to generate square or rectangular
*          orthogonal matrices:
*
*          For M = N and SIDE = 'L' or 'R', the rows will be orthogonal
*          to each other, as will the columns.
*
*          If M < N, SIDE = 'R' produces a dense matrix whose rows are
*          orthogonal and whose columns are not, while SIDE = 'L'
*          produces a matrix whose rows are orthogonal, and whose first
*          M columns are orthogonal, and whose remaining columns are
*          zero.
*
*          If M > N, SIDE = 'L' produces a dense matrix whose columns
*          are orthogonal and whose rows are not, while SIDE = 'R'
*          produces a matrix whose columns are orthogonal, and whose
*          first M rows are orthogonal, and whose remaining rows are
*          zero.
*
*  M       (input) INTEGER
*          The number of rows of A.
*
*  N       (input) INTEGER
*          The number of columns of A.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
*          On entry, the array A.
*          On exit, overwritten by U A ( if SIDE = 'L' ),
*           or by A U ( if SIDE = 'R' ),
*           or by U A U' ( if SIDE = 'C' or 'T').
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,M).
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry ISEED specifies the seed of the random number
*          generator. The array elements should be between 0 and 4095;
*          if not they will be reduced mod 4096.  Also, ISEED(4) must
*          be odd.  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 DLAROR to continue the same random number
*          sequence.
*
*  X       (workspace) DOUBLE PRECISION array, dimension (3*MAX( M, N ))
*          Workspace of length
*              2*M + N if SIDE = 'L',
*              2*N + M if SIDE = 'R',
*              3*N     if SIDE = 'C' or 'T'.
*
*  INFO    (output) INTEGER
*          An error flag.  It is set to:
*          = 0:  normal return
*          < 0:  if INFO = -k, the k-th argument had an illegal value
*          = 1:  if the random numbers generated by DLARND are bad.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one, toosml
      parameter( zero = 0.0d+0, one = 1.0d+0,
     $                   toosml = 1.0d-20 )
*     ..
*     .. Local Scalars ..
      INTEGER            irow, itype, ixfrm, j, jcol, kbeg, nxfrm
      DOUBLE PRECISION   factor, xnorm, xnorms
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      DOUBLE PRECISION   dlarnd, dnrm2
      EXTERNAL           lsame, dlarnd, dnrm2
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemv, dger, dlaset, dscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, sign
*     ..
*     .. Executable Statements ..
*
      IF( n.EQ.0 .OR. m.EQ.0 )
     $   return
*
      itype = 0
      IF( lsame( side, 'L' ) ) THEN
         itype = 1
      ELSE IF( lsame( side, 'R' ) ) THEN
         itype = 2
      ELSE IF( lsame( side, 'C' ) .OR. lsame( side, 'T' ) ) THEN
         itype = 3
      END IF
*
*     Check for argument errors.
*
      info = 0
      IF( itype.EQ.0 ) THEN
         info = -1
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 .OR. ( itype.EQ.3 .AND. n.NE.m ) ) THEN
         info = -4
      ELSE IF( lda.LT.m ) THEN
         info = -6
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DLAROR', -info )
         return
      END IF
*
      IF( itype.EQ.1 ) THEN
         nxfrm = m
      ELSE
         nxfrm = n
      END IF
*
*     Initialize A to the identity matrix if desired
*
      IF( lsame( init, 'I' ) )
     $   CALL dlaset( 'Full', m, n, zero, one, a, lda )
*
*     If no rotation possible, multiply by random +/-1
*
*     Compute rotation by computing Householder transformations
*     H(2), H(3), ..., H(nhouse)
*
      DO 10 j = 1, nxfrm
         x( j ) = zero
   10 continue
*
      DO 30 ixfrm = 2, nxfrm
         kbeg = nxfrm - ixfrm + 1
*
*        Generate independent normal( 0, 1 ) random numbers
*
         DO 20 j = kbeg, nxfrm
            x( j ) = dlarnd( 3, iseed )
   20    continue
*
*        Generate a Householder transformation from the random vector X
*
         xnorm = dnrm2( ixfrm, x( kbeg ), 1 )
         xnorms = sign( xnorm, x( kbeg ) )
         x( kbeg+nxfrm ) = sign( one, -x( kbeg ) )
         factor = xnorms*( xnorms+x( kbeg ) )
         IF( abs( factor ).LT.toosml ) THEN
            info = 1
            CALL xerbla( 'DLAROR', info )
            return
         ELSE
            factor = one / factor
         END IF
         x( kbeg ) = x( kbeg ) + xnorms
*
*        Apply Householder transformation to A
*
         IF( itype.EQ.1 .OR. itype.EQ.3 ) THEN
*
*           Apply H(k) from the left.
*
            CALL dgemv( 'T', ixfrm, n, one, a( kbeg, 1 ), lda,
     $                  x( kbeg ), 1, zero, x( 2*nxfrm+1 ), 1 )
            CALL dger( ixfrm, n, -factor, x( kbeg ), 1, x( 2*nxfrm+1 ),
     $                 1, a( kbeg, 1 ), lda )
*
         END IF
*
         IF( itype.EQ.2 .OR. itype.EQ.3 ) THEN
*
*           Apply H(k) from the right.
*
            CALL dgemv( 'N', m, ixfrm, one, a( 1, kbeg ), lda,
     $                  x( kbeg ), 1, zero, x( 2*nxfrm+1 ), 1 )
            CALL dger( m, ixfrm, -factor, x( 2*nxfrm+1 ), 1, x( kbeg ),
     $                 1, a( 1, kbeg ), lda )
*
         END IF
   30 continue
*
      x( 2*nxfrm ) = sign( one, dlarnd( 3, iseed ) )
*
*     Scale the matrix A by D.
*
      IF( itype.EQ.1 .OR. itype.EQ.3 ) THEN
         DO 40 irow = 1, m
            CALL dscal( n, x( nxfrm+irow ), a( irow, 1 ), lda )
   40    continue
      END IF
*
      IF( itype.EQ.2 .OR. itype.EQ.3 ) THEN
         DO 50 jcol = 1, n
            CALL dscal( m, x( nxfrm+jcol ), a( 1, jcol ), 1 )
   50    continue
      END IF
      return
*
*     End of DLAROR
*
      END