LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cqrt02()

 subroutine cqrt02 ( integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

CQRT02

Purpose:
``` CQRT02 tests CUNGQR, 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, CQRT02 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 array, dimension (LDA,N) The m-by-n matrix A which was factorized by CQRT01.``` [in] AF ``` AF is COMPLEX array, dimension (LDA,N) Details of the QR factorization of A, as returned by CGEQRF. See CGEQRF for further details.``` [out] Q ` Q is COMPLEX array, dimension (LDA,N)` [out] R ` R is COMPLEX 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 array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.``` [out] WORK ` WORK is COMPLEX array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK.``` [out] RWORK ` RWORK is REAL array, dimension (M)` [out] RESULT ``` RESULT is REAL 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 cqrt02.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 REAL RESULT( * ), RWORK( * )
145 COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
146 \$ R( LDA, * ), TAU( * ), WORK( LWORK )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 REAL ZERO, ONE
153 parameter( zero = 0.0e+0, one = 1.0e+0 )
154 COMPLEX ROGUE
155 parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
156* ..
157* .. Local Scalars ..
158 INTEGER INFO
159 REAL ANORM, EPS, RESID
160* ..
161* .. External Functions ..
162 REAL CLANGE, CLANSY, SLAMCH
163 EXTERNAL clange, clansy, slamch
164* ..
165* .. External Subroutines ..
166 EXTERNAL cgemm, cherk, clacpy, claset, cungqr
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC cmplx, max, real
170* ..
171* .. Scalars in Common ..
172 CHARACTER*32 SRNAMT
173* ..
174* .. Common blocks ..
175 COMMON / srnamc / srnamt
176* ..
177* .. Executable Statements ..
178*
179 eps = slamch( 'Epsilon' )
180*
181* Copy the first k columns of the factorization to the array Q
182*
183 CALL claset( 'Full', m, n, rogue, rogue, q, lda )
184 CALL clacpy( '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 = 'CUNGQR'
189 CALL cungqr( m, n, k, q, lda, tau, work, lwork, info )
190*
191* Copy R(1:n,1:k)
192*
193 CALL claset( 'Full', n, k, cmplx( zero ), cmplx( zero ), r, lda )
194 CALL clacpy( 'Upper', n, k, af, lda, r, lda )
195*
196* Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
197*
198 CALL cgemm( 'Conjugate transpose', 'No transpose', n, k, m,
199 \$ cmplx( -one ), q, lda, a, lda, cmplx( one ), r, lda )
200*
201* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
202*
203 anorm = clange( '1', m, k, a, lda, rwork )
204 resid = clange( '1', n, k, r, lda, rwork )
205 IF( anorm.GT.zero ) THEN
206 result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
207 ELSE
208 result( 1 ) = zero
209 END IF
210*
211* Compute I - Q'*Q
212*
213 CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
214 CALL cherk( 'Upper', 'Conjugate transpose', n, m, -one, q, lda,
215 \$ one, r, lda )
216*
217* Compute norm( I - Q'*Q ) / ( M * EPS ) .
218*
219 resid = clansy( '1', 'Upper', n, r, lda, rwork )
220*
221 result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
222*
223 RETURN
224*
225* End of CQRT02
226*
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:128
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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