LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cqlt01()

subroutine cqlt01 ( integer  M,
integer  N,
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 
)

CQLT01

Purpose:
 CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests CUNGQL which forms the m-by-m
 orthogonal matrix Q.

 CQLT01 compares L 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 array, dimension (LDA,N)
          The m-by-n matrix A.
[out]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,M)
          The m-by-m orthogonal matrix Q.
[out]L
          L is COMPLEX 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 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGEQLF.
[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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 124 of file cqlt01.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 REAL RESULT( * ), RWORK( * )
136 COMPLEX A( LDA, * ), AF( LDA, * ), L( LDA, * ),
137 $ Q( LDA, * ), TAU( * ), WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145 COMPLEX ROGUE
146 parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 REAL ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 REAL CLANGE, CLANSY, SLAMCH
154 EXTERNAL clange, clansy, slamch
155* ..
156* .. External Subroutines ..
157 EXTERNAL cgemm, cgeqlf, cherk, clacpy, claset, cungql
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC cmplx, max, min, real
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 = slamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL clacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'CGEQLF'
180 CALL cgeqlf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL claset( 'Full', m, m, rogue, rogue, q, lda )
185 IF( m.GE.n ) THEN
186 IF( n.LT.m .AND. n.GT.0 )
187 $ CALL clacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
188 IF( n.GT.1 )
189 $ CALL clacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
190 $ q( m-n+1, m-n+2 ), lda )
191 ELSE
192 IF( m.GT.1 )
193 $ CALL clacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
194 $ q( 1, 2 ), lda )
195 END IF
196*
197* Generate the m-by-m matrix Q
198*
199 srnamt = 'CUNGQL'
200 CALL cungql( m, m, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy L
203*
204 CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), l, lda )
205 IF( m.GE.n ) THEN
206 IF( n.GT.0 )
207 $ CALL clacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
208 $ l( m-n+1, 1 ), lda )
209 ELSE
210 IF( n.GT.m .AND. m.GT.0 )
211 $ CALL clacpy( 'Full', m, n-m, af, lda, l, lda )
212 IF( m.GT.0 )
213 $ CALL clacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
214 $ l( 1, n-m+1 ), lda )
215 END IF
216*
217* Compute L - Q'*A
218*
219 CALL cgemm( 'Conjugate transpose', 'No transpose', m, n, m,
220 $ cmplx( -one ), q, lda, a, lda, cmplx( one ), l, lda )
221*
222* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
223*
224 anorm = clange( '1', m, n, a, lda, rwork )
225 resid = clange( '1', m, n, l, lda, rwork )
226 IF( anorm.GT.zero ) THEN
227 result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
228 ELSE
229 result( 1 ) = zero
230 END IF
231*
232* Compute I - Q'*Q
233*
234 CALL claset( 'Full', m, m, cmplx( zero ), cmplx( one ), l, lda )
235 CALL cherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
236 $ one, l, lda )
237*
238* Compute norm( I - Q'*Q ) / ( M * EPS ) .
239*
240 resid = clansy( '1', 'Upper', m, l, lda, rwork )
241*
242 result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
243*
244 RETURN
245*
246* End of CQLT01
247*
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 cgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQLF
Definition: cgeqlf.f:138
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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