 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cqlt02()

 subroutine cqlt02 ( integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

CQLT02

Purpose:
``` CQLT02 tests CUNGQL, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.

Given the QL factorization of an m-by-n matrix A, CQLT02 generates
the orthogonal matrix Q defined by the factorization of the last k
columns of A; it compares L(m-n+1:m,n-k+1:n) with
Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), 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 CQLT01.``` [in] AF ``` AF is COMPLEX array, dimension (LDA,N) Details of the QL factorization of A, as returned by CGEQLF. See CGEQLF for further details.``` [out] Q ` Q is COMPLEX array, dimension (LDA,N)` [out] L ` L is COMPLEX array, dimension (LDA,N)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= M.``` [in] TAU ``` TAU is COMPLEX array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL 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( L - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```

Definition at line 134 of file cqlt02.f.

136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  INTEGER K, LDA, LWORK, M, N
143 * ..
144 * .. Array Arguments ..
145  REAL RESULT( * ), RWORK( * )
146  COMPLEX A( LDA, * ), AF( LDA, * ), L( LDA, * ),
147  \$ Q( LDA, * ), TAU( * ), WORK( LWORK )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL ZERO, ONE
154  parameter( zero = 0.0e+0, one = 1.0e+0 )
155  COMPLEX ROGUE
156  parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
157 * ..
158 * .. Local Scalars ..
159  INTEGER INFO
160  REAL ANORM, EPS, RESID
161 * ..
162 * .. External Functions ..
163  REAL CLANGE, CLANSY, SLAMCH
164  EXTERNAL clange, clansy, slamch
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL cgemm, cherk, clacpy, claset, cungql
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC cmplx, max, real
171 * ..
172 * .. Scalars in Common ..
173  CHARACTER*32 SRNAMT
174 * ..
175 * .. Common blocks ..
176  COMMON / srnamc / srnamt
177 * ..
178 * .. Executable Statements ..
179 *
180 * Quick return if possible
181 *
182  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
183  result( 1 ) = zero
184  result( 2 ) = zero
185  RETURN
186  END IF
187 *
188  eps = slamch( 'Epsilon' )
189 *
190 * Copy the last k columns of the factorization to the array Q
191 *
192  CALL claset( 'Full', m, n, rogue, rogue, q, lda )
193  IF( k.LT.m )
194  \$ CALL clacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
195  \$ q( 1, n-k+1 ), lda )
196  IF( k.GT.1 )
197  \$ CALL clacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
198  \$ q( m-k+1, n-k+2 ), lda )
199 *
200 * Generate the last n columns of the matrix Q
201 *
202  srnamt = 'CUNGQL'
203  CALL cungql( m, n, k, q, lda, tau( n-k+1 ), work, lwork, info )
204 *
205 * Copy L(m-n+1:m,n-k+1:n)
206 *
207  CALL claset( 'Full', n, k, cmplx( zero ), cmplx( zero ),
208  \$ l( m-n+1, n-k+1 ), lda )
209  CALL clacpy( 'Lower', k, k, af( m-k+1, n-k+1 ), lda,
210  \$ l( m-k+1, n-k+1 ), lda )
211 *
212 * Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
213 *
214  CALL cgemm( 'Conjugate transpose', 'No transpose', n, k, m,
215  \$ cmplx( -one ), q, lda, a( 1, n-k+1 ), lda,
216  \$ cmplx( one ), l( m-n+1, n-k+1 ), lda )
217 *
218 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
219 *
220  anorm = clange( '1', m, k, a( 1, n-k+1 ), lda, rwork )
221  resid = clange( '1', n, k, l( m-n+1, n-k+1 ), lda, rwork )
222  IF( anorm.GT.zero ) THEN
223  result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
224  ELSE
225  result( 1 ) = zero
226  END IF
227 *
228 * Compute I - Q'*Q
229 *
230  CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), l, lda )
231  CALL cherk( 'Upper', 'Conjugate transpose', n, m, -one, q, lda,
232  \$ one, l, lda )
233 *
234 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
235 *
236  resid = clansy( '1', 'Upper', n, l, lda, rwork )
237 *
238  result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
239 *
240  RETURN
241 *
242 * End of CQLT02
243 *
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 cungql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQL
Definition: cungql.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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