# sorbdb6.f - Man Page

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

```          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.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sorbdb6(3) is an alias of sorbdb6.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK