# zqrt02.f - Man Page

TESTING/LIN/zqrt02.f

## Synopsis

### Functions/Subroutines

subroutine **zqrt02** (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)**ZQRT02**

## Function/Subroutine Documentation

### subroutine zqrt02 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

**ZQRT02**

**Purpose:**

ZQRT02 tests ZUNGQR, 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, ZQRT02 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 COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A which was factorized by ZQRT01.

*AF*AF is COMPLEX*16 array, dimension (LDA,N) Details of the QR factorization of A, as returned by ZGEQRF. See ZGEQRF for further details.

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

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

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

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

*WORK*WORK is COMPLEX*16 array, dimension (LWORK)

*LWORK*LWORK is INTEGER The dimension of the array WORK.

*RWORK*RWORK is DOUBLE PRECISION array, dimension (M)

*RESULT*RESULT is DOUBLE PRECISION 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 **zqrt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zqrt02(3) is an alias of zqrt02.f(3).

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