# zrqt03.f - Man Page

TESTING/LIN/zrqt03.f

## Synopsis

### Functions/Subroutines

subroutine **zrqt03** (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)**ZRQT03**

## Function/Subroutine Documentation

### subroutine zrqt03 (integer m, integer n, integer k, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) c, complex*16, dimension( lda, * ) cc, complex*16, dimension( lda, * ) q, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

**ZRQT03**

**Purpose:**

ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. ZRQT03 compares the results of a call to ZUNMRQ with the results of forming Q explicitly by a call to ZUNGRQ and then performing matrix multiplication by a call to ZGEMM.

**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 COMPLEX*16 array, dimension (LDA,N) Details of the RQ factorization of an m-by-n matrix, as returned by ZGERQF. See CGERQF for further details.

*C*C is COMPLEX*16 array, dimension (LDA,N)

*CC*CC is COMPLEX*16 array, dimension (LDA,N)

*Q*Q is COMPLEX*16 array, dimension (LDA,N)

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

*TAU*TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.

*WORK*WORK is COMPLEX*16 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 DOUBLE PRECISION array, dimension (M)

*RESULT*RESULT is DOUBLE PRECISION 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 **zrqt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zrqt03(3) is an alias of zrqt03.f(3).

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