SRC/dorbdb6.f(3)

NAME
SRC/dorbdb6.f

SYNOPSIS

  Functions/Subroutines
subroutine dorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
DORBDB6

Function/Subroutine Documentation

  subroutine dorbdb6 (integer m1, integer m2, integer n, double precision, dimension(*) x1, integer incx1, double precision, dimension(*) x2, integer incx2, double precision, dimension(ldq1,*) q1, integer ldq1, double precision, dimension(ldq2,*) q2, integer ldq2, double precision, dimension(*) work, integer lwork, integer info)

DORBDB6

Purpose:

     DORBDB6 orthogonalizes the column vector
          X = [ X1 ]
              [ X2 ]
     with respect to the columns of
          Q = [ Q1 ] .
              [ Q2 ]
     The columns of Q must be orthonormal. The orthogonalized vector will
     be zero if and only if it lies entirely in the range of Q.
     The projection is computed with at most two iterations of the
     classical Gram-Schmidt algorithm, see
     * L. Giraud, J. Langou, M. Rozložník. 'On the round-off error
       analysis of the Gram-Schmidt algorithm with reorthogonalization.'
       2002. CERFACS Technical Report No. TR/PA/02/33. URL:
       https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf

Parameters
    M1

              M1 is INTEGER
               The dimension of X1 and the number of rows in Q1. 0 <= M1.

    M2

              M2 is INTEGER
               The dimension of X2 and the number of rows in Q2. 0 <= M2.

    N

              N is INTEGER
               The number of columns in Q1 and Q2. 0 <= N.

    X1

              X1 is DOUBLE PRECISION array, dimension (M1)
               On entry, the top part of the vector to be orthogonalized.
               On exit, the top part of the projected vector.

    INCX1

              INCX1 is INTEGER
               Increment for entries of X1.

    X2

              X2 is DOUBLE PRECISION array, dimension (M2)
               On entry, the bottom part of the vector to be
               orthogonalized. On exit, the bottom part of the projected
               vector.

    INCX2

              INCX2 is INTEGER
               Increment for entries of X2.

    Q1

              Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
               The top part of the orthonormal basis matrix.

    LDQ1

              LDQ1 is INTEGER
               The leading dimension of Q1. LDQ1 >= M1.

    Q2

              Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
               The bottom part of the orthonormal basis matrix.

    LDQ2

              LDQ2 is INTEGER
               The leading dimension of Q2. LDQ2 >= M2.

    WORK

              WORK is DOUBLE PRECISION array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
               The dimension of the array WORK. LWORK >= N.

    INFO

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 157 of file dorbdb6.f.

Author

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