# srqt03.f - Man Page

TESTING/LIN/srqt03.f

## Synopsis

### Functions/Subroutines

subroutine **srqt03** (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)**SRQT03**

## Function/Subroutine Documentation

### subroutine srqt03 (integer m, integer n, integer k, real, dimension( lda, * ) af, real, dimension( lda, * ) c, real, dimension( lda, * ) cc, real, dimension( lda, * ) q, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

**SRQT03**

**Purpose:**

SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. SRQT03 compares the results of a call to SORMRQ with the results of forming Q explicitly by a call to SORGRQ and then performing matrix multiplication by a call to SGEMM.

**Parameters***M*M is INTEGER The number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0.

*N*N is INTEGER The order of the orthogonal matrix Q. N >= 0.

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

*AF*AF is REAL array, dimension (LDA,N) Details of the RQ factorization of an m-by-n matrix, as returned by SGERQF. See SGERQF for further details.

*C*C is REAL array, dimension (LDA,N)

*CC*CC is REAL array, dimension (LDA,N)

*Q*Q is REAL array, dimension (LDA,N)

*LDA*LDA is INTEGER The leading dimension of the arrays AF, C, CC, and Q.

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

*WORK*WORK is REAL array, dimension (LWORK)

*LWORK*LWORK is INTEGER The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.

*RWORK*RWORK is REAL array, dimension (M)

*RESULT*RESULT is REAL array, dimension (4) The test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **srqt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page srqt03(3) is an alias of srqt03.f(3).

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