# sqlt02.f - Man Page

TESTING/LIN/sqlt02.f

## Synopsis

### Functions/Subroutines

subroutine sqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
SQLT02

## Function/Subroutine Documentation

### subroutine sqlt02 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) l, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SQLT02

Purpose:

SQLT02 tests SORGQL, which generates an m-by-n matrix Q with
orthonormal columns that is defined as the product of k elementary
reflectors.

Given the QL factorization of an m-by-n matrix A, SQLT02 generates
the orthogonal matrix Q defined by the factorization of the last k
columns of A; it compares L(m-n+1:m,n-k+1:n) with
Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
orthonormal.
Parameters

M

M is INTEGER
The number of rows of the matrix Q to be generated.  M >= 0.

N

N is INTEGER
The number of columns of the matrix Q to be generated.
M >= N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.

A

A is REAL array, dimension (LDA,N)
The m-by-n matrix A which was factorized by SQLT01.

AF

AF is REAL array, dimension (LDA,N)
Details of the QL factorization of A, as returned by SGEQLF.
See SGEQLF for further details.

Q

Q is REAL array, dimension (LDA,N)

L

L is REAL array, dimension (LDA,N)

LDA

LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= M.

TAU

TAU is REAL array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QL factorization in AF.

WORK

WORK is REAL array, dimension (LWORK)

LWORK

LWORK is INTEGER
The dimension of the array WORK.

RWORK

RWORK is REAL array, dimension (M)

RESULT

RESULT is REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file sqlt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqlt02(3) is an alias of sqlt02.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK