 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 )```
Date
December 2016

Definition at line 128 of file zqlt01.f.

128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  DOUBLE PRECISION result( * ), rwork( * )
139  COMPLEX*16 a( lda, * ), af( lda, * ), l( lda, * ),
140  \$ q( lda, * ), tau( * ), work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION zero, one
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  COMPLEX*16 rogue
149  parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  DOUBLE PRECISION anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  DOUBLE PRECISION dlamch, zlange, zlansy
157  EXTERNAL dlamch, zlange, zlansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL zgemm, zgeqlf, zherk, zlacpy, zlaset, zungql
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC dble, dcmplx, max, min
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 srnamt
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = dlamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL zlacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'ZGEQLF'
183  CALL zgeqlf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
188  IF( m.GE.n ) THEN
189  IF( n.LT.m .AND. n.GT.0 )
190  \$ CALL zlacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
191  IF( n.GT.1 )
192  \$ CALL zlacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
193  \$ q( m-n+1, m-n+2 ), lda )
194  ELSE
195  IF( m.GT.1 )
196  \$ CALL zlacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
197  \$ q( 1, 2 ), lda )
198  END IF
199 *
200 * Generate the m-by-m matrix Q
201 *
202  srnamt = 'ZUNGQL'
203  CALL zungql( m, m, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy L
206 *
207  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), l,
208  \$ lda )
209  IF( m.GE.n ) THEN
210  IF( n.GT.0 )
211  \$ CALL zlacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
212  \$ l( m-n+1, 1 ), lda )
213  ELSE
214  IF( n.GT.m .AND. m.GT.0 )
215  \$ CALL zlacpy( 'Full', m, n-m, af, lda, l, lda )
216  IF( m.GT.0 )
217  \$ CALL zlacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
218  \$ l( 1, n-m+1 ), lda )
219  END IF
220 *
221 * Compute L - Q'*A
222 *
223  CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
224  \$ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), l,
225  \$ lda )
226 *
227 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
228 *
229  anorm = zlange( '1', m, n, a, lda, rwork )
230  resid = zlange( '1', m, n, l, lda, rwork )
231  IF( anorm.GT.zero ) THEN
232  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
233  ELSE
234  result( 1 ) = zero
235  END IF
236 *
237 * Compute I - Q'*Q
238 *
239  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), l, lda )
240  CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
241  \$ one, l, lda )
242 *
243 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
244 *
245  resid = zlansy( '1', 'Upper', m, l, lda, rwork )
246 *
247  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
248 *
249  RETURN
250 *
251 * End of ZQLT01
252 *
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:117
subroutine zgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQLF
Definition: zgeqlf.f:140
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:108
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: zlansy.f:125
subroutine zungql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQL
Definition: zungql.f:130
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
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