sorbdb6.f - Man Page

subroutine sorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
SORBDB6

SORBDB6  

Purpose:

 SORBDB6 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sorbdb6.f.