NAME

SRC/sorbdb6.f

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sorbdb6 (integer m1, integer m2, integer n, real, dimension() x1, integer incx1, real, dimension() x2, integer incx2, real, dimension(ldq1,) q1, integer ldq1, real, dimension(ldq2,) q2, integer ldq2, real, dimension(*) work, integer lwork, integer info)

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 is INTEGER


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



          M2 is INTEGER


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



          N is INTEGER


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



          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 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 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 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.

Author