sqrt02.f - Man Page

TESTING/LIN/sqrt02.f

Synopsis

Functions/Subroutines

subroutine sqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
SQRT02

Function/Subroutine Documentation

subroutine sqrt02 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SQRT02

Purpose:

 SQRT02 tests SORGQR, which generates an m-by-n matrix Q with
 orthonormal columns that is defined as the product of k elementary
 reflectors.

 Given the QR factorization of an m-by-n matrix A, SQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 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 SQRT01.

AF

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

Q

          Q is REAL array, dimension (LDA,N)

R

          R is REAL array, dimension (LDA,N)

LDA

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

TAU

          TAU is REAL array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR 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( R - 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 133 of file sqrt02.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page sqrt02(3) is an alias of sqrt02.f(3).

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