LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ sorbdb6()

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

Download SORBDB6 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SORBDB6 orthogonalizes the column vector
      X = [ X1 ]
          [ X2 ]
 with respect to the columns of
      Q = [ Q1 ] .
          [ Q2 ]
 The Euclidean norm of X must be one and 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
[in]M1
          M1 is INTEGER
           The dimension of X1 and the number of rows in Q1. 0 <= M1.
[in]M2
          M2 is INTEGER
           The dimension of X2 and the number of rows in Q2. 0 <= M2.
[in]N
          N is INTEGER
           The number of columns in Q1 and Q2. 0 <= N.
[in,out]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.
[in]INCX1
          INCX1 is INTEGER
           Increment for entries of X1.
[in,out]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.
[in]INCX2
          INCX2 is INTEGER
           Increment for entries of X2.
[in]Q1
          Q1 is REAL array, dimension (LDQ1, N)
           The top part of the orthonormal basis matrix.
[in]LDQ1
          LDQ1 is INTEGER
           The leading dimension of Q1. LDQ1 >= M1.
[in]Q2
          Q2 is REAL array, dimension (LDQ2, N)
           The bottom part of the orthonormal basis matrix.
[in]LDQ2
          LDQ2 is INTEGER
           The leading dimension of Q2. LDQ2 >= M2.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
           The dimension of the array WORK. LWORK >= N.
[out]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.