LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ zqlt01()

subroutine zqlt01 ( integer  M,
integer  N,
complex*16, dimension( lda, * )  A,
complex*16, dimension( lda, * )  AF,
complex*16, dimension( lda, * )  Q,
complex*16, dimension( lda, * )  L,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

ZQLT01

Purpose:
 ZQLT01 tests ZGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests ZUNGQL which forms the m-by-m
 orthogonal matrix Q.

 ZQLT01 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*16 array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          Details of the QL factorization of A, as returned by ZGEQLF.
          See ZGEQLF for further details.
[out]Q
          Q is COMPLEX*16 array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.
[out]L
          L 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 ZGEQLF.
[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( 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 zqlt01.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, * ), L( LDA, * ),
137 $ Q( 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, zgeqlf, zherk, zlacpy, zlaset, zungql
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 = 'ZGEQLF'
180 CALL zgeqlf( 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 IF( m.GE.n ) THEN
186 IF( n.LT.m .AND. n.GT.0 )
187 $ CALL zlacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
188 IF( n.GT.1 )
189 $ CALL zlacpy( '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 zlacpy( '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 = 'ZUNGQL'
200 CALL zungql( m, m, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy L
203*
204 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), l,
205 $ lda )
206 IF( m.GE.n ) THEN
207 IF( n.GT.0 )
208 $ CALL zlacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
209 $ l( m-n+1, 1 ), lda )
210 ELSE
211 IF( n.GT.m .AND. m.GT.0 )
212 $ CALL zlacpy( 'Full', m, n-m, af, lda, l, lda )
213 IF( m.GT.0 )
214 $ CALL zlacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
215 $ l( 1, n-m+1 ), lda )
216 END IF
217*
218* Compute L - Q'*A
219*
220 CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
221 $ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), l,
222 $ lda )
223*
224* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
225*
226 anorm = zlange( '1', m, n, a, lda, rwork )
227 resid = zlange( '1', m, n, l, lda, rwork )
228 IF( anorm.GT.zero ) THEN
229 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
230 ELSE
231 result( 1 ) = zero
232 END IF
233*
234* Compute I - Q'*Q
235*
236 CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), l, lda )
237 CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
238 $ one, l, lda )
239*
240* Compute norm( I - Q'*Q ) / ( M * EPS ) .
241*
242 resid = zlansy( '1', 'Upper', m, l, lda, rwork )
243*
244 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
245*
246 RETURN
247*
248* End of ZQLT01
249*
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 zgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQLF
Definition: zgeqlf.f:138
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 zungql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQL
Definition: zungql.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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