 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zqrt01p()

 subroutine zqrt01p ( 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 )

ZQRT01P

Purpose:
``` ZQRT01P tests ZGEQRFP, 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.

ZQRT01P 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 ZGEQRFP. See ZGEQRFP 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 ZGEQRFP.``` [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 )```
Date
December 2016

Definition at line 128 of file zqrt01p.f.

128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  DOUBLE PRECISION result( * ), rwork( * )
139  COMPLEX*16 a( lda, * ), af( lda, * ), q( lda, * ),
140  \$ r( lda, * ), tau( * ), work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION zero, one
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  COMPLEX*16 rogue
149  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  DOUBLE PRECISION anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  DOUBLE PRECISION dlamch, zlange, zlansy
157  EXTERNAL dlamch, zlange, zlansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL zgemm, zgeqrfp, zherk, zlacpy, zlaset, zungqr
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC dble, dcmplx, max, min
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 srnamt
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = dlamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL zlacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'ZGEQRFP'
183  CALL zgeqrfp( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
188  CALL zlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
189 *
190 * Generate the m-by-m matrix Q
191 *
192  srnamt = 'ZUNGQR'
193  CALL zungqr( m, m, minmn, q, lda, tau, work, lwork, info )
194 *
195 * Copy R
196 *
197  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
198  \$ lda )
199  CALL zlacpy( 'Upper', m, n, af, lda, r, lda )
200 *
201 * Compute R - Q'*A
202 *
203  CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
204  \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
205  \$ lda )
206 *
207 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
208 *
209  anorm = zlange( '1', m, n, a, lda, rwork )
210  resid = zlange( '1', m, n, r, lda, rwork )
211  IF( anorm.GT.zero ) THEN
212  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
213  ELSE
214  result( 1 ) = zero
215  END IF
216 *
217 * Compute I - Q'*Q
218 *
219  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), r, lda )
220  CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
221  \$ one, r, lda )
222 *
223 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
224 *
225  resid = zlansy( '1', 'Upper', m, r, lda, rwork )
226 *
227  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
228 *
229  RETURN
230 *
231 * End of ZQRT01P
232 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQRFP
Definition: zgeqrfp.f:141
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:130
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:117
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: zlansy.f:125
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:108
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175
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