LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 124 of file zqrt01p.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, zgeqrfp, 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 = 'ZGEQRFP'
180 CALL zgeqrfp( 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 ZQRT01P
229*
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
zgeqrfp
subroutine zgeqrfp(m, n, a, lda, tau, work, lwork, info)
ZGEQRFP
Definition zgeqrfp.f:149
zherk
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
zlacpy
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
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
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
zlansy
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
zlaset
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
zungqr
subroutine zungqr(m, n, k, a, lda, tau, work, lwork, info)
ZUNGQR
Definition zungqr.f:128
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