LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zqrt01()

 subroutine zqrt01 ( integer M, integer N, 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 )

ZQRT01

Purpose:
``` ZQRT01 tests ZGEQRF, which computes the QR factorization of an m-by-n
matrix A, and partially tests ZUNGQR which forms the m-by-m
orthogonal matrix Q.

ZQRT01 compares R with Q'*A, and checks that Q is orthogonal.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A.``` [out] 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,M) The m-by-m orthogonal matrix Q.``` [out] R ` R is COMPLEX*16 array, dimension (LDA,max(M,N))` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).``` [out] TAU ``` TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by ZGEQRF.``` [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 124 of file zqrt01.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 INTEGER LDA, LWORK, M, N
133* ..
134* .. Array Arguments ..
135 DOUBLE PRECISION RESULT( * ), RWORK( * )
136 COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
137 \$ R( LDA, * ), TAU( * ), WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145 COMPLEX*16 ROGUE
146 parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 DOUBLE PRECISION ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
154 EXTERNAL dlamch, zlange, zlansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL zgemm, zgeqrf, zherk, zlacpy, zlaset, zungqr
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC dble, dcmplx, max, min
161* ..
162* .. Scalars in Common ..
163 CHARACTER*32 SRNAMT
164* ..
165* .. Common blocks ..
166 COMMON / srnamc / srnamt
167* ..
168* .. Executable Statements ..
169*
170 minmn = min( m, n )
171 eps = dlamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL zlacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'ZGEQRF'
180 CALL zgeqrf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
185 CALL zlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186*
187* Generate the m-by-m matrix Q
188*
189 srnamt = 'ZUNGQR'
190 CALL zungqr( m, m, minmn, q, lda, tau, work, lwork, info )
191*
192* Copy R
193*
194 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
195 \$ lda )
196 CALL zlacpy( 'Upper', m, n, af, lda, r, lda )
197*
198* Compute R - Q'*A
199*
200 CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
201 \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
202 \$ lda )
203*
204* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
205*
206 anorm = zlange( '1', m, n, a, lda, rwork )
207 resid = zlange( '1', m, n, r, lda, rwork )
208 IF( anorm.GT.zero ) THEN
209 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
210 ELSE
211 result( 1 ) = zero
212 END IF
213*
214* Compute I - Q'*Q
215*
216 CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), r, lda )
217 CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
218 \$ one, r, lda )
219*
220* Compute norm( I - Q'*Q ) / ( M * EPS ) .
221*
222 resid = zlansy( '1', 'Upper', m, r, lda, rwork )
223*
224 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
225*
226 RETURN
227*
228* End of ZQRT01
229*
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
subroutine zgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.
Definition: zgeqrf.f:152
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