MB04XY

Applying the Householder transformations for bidiagonalization (stored in factored form) to specified one or two matrices, from the left

Purpose

  To apply the Householder transformations Pj stored in factored
  form into the columns of the array X, to the desired columns of
  the matrix U by premultiplication, and/or the Householder
  transformations Qj stored in factored form into the rows of the
  array X, to the desired columns of the matrix V by
  premultiplication. The Householder transformations Pj and Qj
  are stored as produced by LAPACK Library routine DGEBRD.

      SUBROUTINE MB04XY( JOBU, JOBV, M, N, X, LDX, TAUP, TAUQ, U,
     $                   LDU, V, LDV, INUL, INFO )
C     .. Scalar Arguments ..
      CHARACTER         JOBU, JOBV
      INTEGER           INFO, LDU, LDV, LDX, M, N
C     .. Array Arguments ..
      LOGICAL           INUL(*)
      DOUBLE PRECISION  TAUP(*), TAUQ(*), U(LDU,*), V(LDV,*),
     $                  X(LDX,*)

Mode Parameters

  JOBU    CHARACTER*1
          Specifies whether to transform the columns in U as
          follows:
          = 'N':  Do not transform the columns in U;
          = 'A':  Transform the columns in U (U has M columns);
          = 'S':  Transform the columns in U (U has min(M,N)
                  columns).

  JOBV    CHARACTER*1
          Specifies whether to transform the columns in V as
          follows:
          = 'N':  Do not transform the columns in V;
          = 'A':  Transform the columns in V (V has N columns);
          = 'S':  Transform the columns in V (V has min(M,N)
                  columns).

  M       (input) INTEGER
          The number of rows of the matrix X.  M >= 0.

  N       (input) INTEGER
          The number of columns of the matrix X.  N >= 0.

  X       (input) DOUBLE PRECISION array, dimension (LDX,N)
          The leading M-by-N part contains in the columns of its
          lower triangle the Householder transformations Pj, and
          in the rows of its upper triangle the Householder
          transformations Qj in factored form.
          X is modified by the routine but restored on exit.

  LDX     INTEGER
          The leading dimension of the array X.   LDX >= MAX(1,M).

  TAUP    (input) DOUBLE PRECISION array, dimension (MIN(M,N))
          The scalar factors of the Householder transformations Pj.

  TAUQ    (input) DOUBLE PRECISION array, dimension (MIN(M,N))
          The scalar factors of the Householder transformations Qj.

  U       (input/output) DOUBLE PRECISION array, dimension (LDU,*)
          On entry, U contains the M-by-M (if JOBU = 'A') or
          M-by-min(M,N) (if JOBU = 'S') matrix U.
          On exit, the Householder transformations Pj have been
          applied to each column i of U corresponding to a parameter
          INUL(i) = .TRUE.
          NOTE that U is not referenced if JOBU = 'N'.

  LDU     INTEGER
          The leading dimension of the array U.
          LDU >= MAX(1,M), if JOBU = 'A' or JOBU = 'S';
          LDU >= 1,        if JOBU = 'N'.

  V       (input/output) DOUBLE PRECISION array, dimension (LDV,*)
          On entry, V contains the N-by-N (if JOBV = 'A') or
          N-by-min(M,N) (if JOBV = 'S') matrix V.
          On exit, the Householder transformations Qj have been
          applied to each column i of V corresponding to a parameter
          INUL(i) = .TRUE.
          NOTE that V is not referenced if JOBV = 'N'.

  LDV     INTEGER
          The leading dimension of the array V.
          LDV >= MAX(1,M), if JOBV = 'A' or JOBV = 'S';
          LDV >= 1,        if JOBV = 'N'.

  INUL    (input) LOGICAL array, dimension (MAX(M,N))
          INUL(i) = .TRUE. if the i-th column of U and/or V is to be
          transformed, and INUL(i) = .FALSE., otherwise.
          (1 <= i <= MAX(M,N)).

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The Householder transformations Pj or Qj are applied to the
  columns of U or V indexed by I for which INUL(I) = .TRUE..

  The algorithm is backward stable.

  None

Program Text

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