SRC/dorbdb6.f(3)           Library Functions Manual           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. Rozloznik. '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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/dorbdb6.f(3)