 LAPACK  3.10.1 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 )```

Definition at line 124 of file zlqt01.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 zgelqf, zgemm, zherk, zlacpy, zlaset, zunglq
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 = 'ZGELQF'
180  CALL zgelqf( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
185  IF( n.GT.1 )
186  \$ CALL zlacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187 *
188 * Generate the n-by-n matrix Q
189 *
190  srnamt = 'ZUNGLQ'
191  CALL zunglq( n, n, minmn, q, lda, tau, work, lwork, info )
192 *
193 * Copy L
194 *
195  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), l,
196  \$ lda )
197  CALL zlacpy( 'Lower', m, n, af, lda, l, lda )
198 *
199 * Compute L - A*Q'
200 *
201  CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
202  \$ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), l,
203  \$ lda )
204 *
205 * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
206 *
207  anorm = zlange( '1', m, n, a, lda, rwork )
208  resid = zlange( '1', m, n, l, lda, rwork )
209  IF( anorm.GT.zero ) THEN
210  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
211  ELSE
212  result( 1 ) = zero
213  END IF
214 *
215 * Compute I - Q*Q'
216 *
217  CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), l, lda )
218  CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
219  \$ lda )
220 *
221 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
222 *
223  resid = zlansy( '1', 'Upper', n, l, lda, rwork )
224 *
225  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
226 *
227  RETURN
228 *
229 * End of ZLQT01
230 *
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 zgelqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGELQF
Definition: zgelqf.f:143
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 zunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ
Definition: zunglq.f:127
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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