# dqrt03.f - Man Page

TESTING/LIN/dqrt03.f

## Synopsis

### Functions/Subroutines

subroutine **dqrt03** (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)**DQRT03**

## Function/Subroutine Documentation

### subroutine dqrt03 (integer m, integer n, integer k, double precision, dimension( lda, * ) af, double precision, dimension( lda, * ) c, double precision, dimension( lda, * ) cc, double precision, dimension( lda, * ) q, integer lda, double precision, dimension( * ) tau, double precision, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

**DQRT03**

**Purpose:**

DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'. DQRT03 compares the results of a call to DORMQR with the results of forming Q explicitly by a call to DORGQR and then performing matrix multiplication by a call to DGEMM.

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

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

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

*AF*AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of an m-by-n matrix, as returned by DGEQRF. See DGEQRF for further details.

*C*C is DOUBLE PRECISION array, dimension (LDA,N)

*CC*CC is DOUBLE PRECISION array, dimension (LDA,N)

*Q*Q is DOUBLE PRECISION array, dimension (LDA,M)

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

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

*WORK*WORK is DOUBLE PRECISION 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 m-by-m orthogonal matrix Q. RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **dqrt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dqrt03(3) is an alias of dqrt03.f(3).

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