LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ 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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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