LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

◆ zqrt02()

 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
orthonornmal 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
 [in] M ``` M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A which was factorized by ZQRT01.``` [in] 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.``` [out] Q ` Q is COMPLEX*16 array, dimension (LDA,N)` [out] R ` R is COMPLEX*16 array, dimension (LDA,N)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M.``` [in] TAU ``` TAU is COMPLEX*16 array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK.``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (M)` [out] 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 )```

Definition at line 133 of file zqrt02.f.

135 *
136 * -- LAPACK test routine --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  INTEGER K, LDA, LWORK, M, N
142 * ..
143 * .. Array Arguments ..
144  DOUBLE PRECISION RESULT( * ), RWORK( * )
145  COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
146  \$ R( LDA, * ), TAU( * ), WORK( LWORK )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ZERO, ONE
153  parameter( zero = 0.0d+0, one = 1.0d+0 )
154  COMPLEX*16 ROGUE
155  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
156 * ..
157 * .. Local Scalars ..
158  INTEGER INFO
159  DOUBLE PRECISION ANORM, EPS, RESID
160 * ..
161 * .. External Functions ..
162  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
163  EXTERNAL dlamch, zlange, zlansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zgemm, zherk, zlacpy, zlaset, zungqr
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC dble, dcmplx, max
170 * ..
171 * .. Scalars in Common ..
172  CHARACTER*32 SRNAMT
173 * ..
174 * .. Common blocks ..
175  COMMON / srnamc / srnamt
176 * ..
177 * .. Executable Statements ..
178 *
179  eps = dlamch( 'Epsilon' )
180 *
181 * Copy the first k columns of the factorization to the array Q
182 *
183  CALL zlaset( 'Full', m, n, rogue, rogue, q, lda )
184  CALL zlacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
185 *
186 * Generate the first n columns of the matrix Q
187 *
188  srnamt = 'ZUNGQR'
189  CALL zungqr( m, n, k, q, lda, tau, work, lwork, info )
190 *
191 * Copy R(1:n,1:k)
192 *
193  CALL zlaset( 'Full', n, k, dcmplx( zero ), dcmplx( zero ), r,
194  \$ lda )
195  CALL zlacpy( 'Upper', n, k, af, lda, r, lda )
196 *
197 * Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
198 *
199  CALL zgemm( 'Conjugate transpose', 'No transpose', n, k, m,
200  \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
201  \$ lda )
202 *
203 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
204 *
205  anorm = zlange( '1', m, k, a, lda, rwork )
206  resid = zlange( '1', n, k, r, lda, rwork )
207  IF( anorm.GT.zero ) THEN
208  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
209  ELSE
210  result( 1 ) = zero
211  END IF
212 *
213 * Compute I - Q'*Q
214 *
215  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), r, lda )
216  CALL zherk( 'Upper', 'Conjugate transpose', n, m, -one, q, lda,
217  \$ one, r, lda )
218 *
219 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
220 *
221  resid = zlansy( '1', 'Upper', n, r, lda, rwork )
222 *
223  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
224 *
225  RETURN
226 *
227 * End of ZQRT02
228 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:128
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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