LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zlqt01()

 subroutine zlqt01 ( 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 )

ZLQT01

Purpose:
``` ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests ZUNGLQ which forms the n-by-n
orthogonal matrix Q.

ZLQT01 compares L with A*Q', 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 LQ factorization of A, as returned by ZGELQF. See ZGELQF for further details.``` [out] Q ``` Q is COMPLEX*16 array, dimension (LDA,N) The n-by-n 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 L. 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 ZGELQF.``` [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 (max(M,N))` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```
Date
December 2016

Definition at line 128 of file zlqt01.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 zgelqf, zgemm, zherk, zlacpy, zlaset, zunglq
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 = 'ZGELQF'
183  CALL zgelqf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
188  IF( n.GT.1 )
189  \$ CALL zlacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
190 *
191 * Generate the n-by-n matrix Q
192 *
193  srnamt = 'ZUNGLQ'
194  CALL zunglq( n, n, minmn, q, lda, tau, work, lwork, info )
195 *
196 * Copy L
197 *
198  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), l,
199  \$ lda )
200  CALL zlacpy( 'Lower', m, n, af, lda, l, lda )
201 *
202 * Compute L - A*Q'
203 *
204  CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
205  \$ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), l,
206  \$ lda )
207 *
208 * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
209 *
210  anorm = zlange( '1', m, n, a, lda, rwork )
211  resid = zlange( '1', m, n, l, lda, rwork )
212  IF( anorm.GT.zero ) THEN
213  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
214  ELSE
215  result( 1 ) = zero
216  END IF
217 *
218 * Compute I - Q*Q'
219 *
220  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), l, lda )
221  CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
222  \$ lda )
223 *
224 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
225 *
226  resid = zlansy( '1', 'Upper', n, l, lda, rwork )
227 *
228  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
229 *
230  RETURN
231 *
232 * End of ZLQT01
233 *
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 zgelqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGELQF
Definition: zgelqf.f:137
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 zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:175
subroutine zunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ
Definition: zunglq.f:129
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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