 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ slqt02()

 subroutine slqt02 ( integer M, integer N, integer K, real, dimension( lda, * ) A, real, dimension( lda, * ) AF, real, dimension( lda, * ) Q, real, dimension( lda, * ) L, integer LDA, real, dimension( * ) TAU, real, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

SLQT02

Purpose:
``` SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with
orthonornmal rows that is defined as the product of k elementary
reflectors.

Given the LQ factorization of an m-by-n matrix A, SLQT02 generates
the orthogonal matrix Q defined by the factorization of the first k
rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
checks that the rows of Q are orthonormal.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q to be generated. N >= M >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SLQT01.``` [in] AF ``` AF is REAL array, dimension (LDA,N) Details of the LQ factorization of A, as returned by SGELQF. See SGELQF for further details.``` [out] Q ` Q is REAL array, dimension (LDA,N)` [out] L ` L is REAL array, dimension (LDA,M)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= N.``` [in] TAU ``` TAU is REAL array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.``` [out] WORK ` WORK is REAL 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 - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```

Definition at line 133 of file slqt02.f.

135*
136* -- LAPACK test routine --
137* -- LAPACK is a software package provided by Univ. of Tennessee, --
138* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*
140* .. Scalar Arguments ..
141 INTEGER K, LDA, LWORK, M, N
142* ..
143* .. Array Arguments ..
144 REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
145 \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
146 \$ WORK( LWORK )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 REAL ZERO, ONE
153 parameter( zero = 0.0e+0, one = 1.0e+0 )
154 REAL ROGUE
155 parameter( rogue = -1.0e+10 )
156* ..
157* .. Local Scalars ..
158 INTEGER INFO
159 REAL ANORM, EPS, RESID
160* ..
161* .. External Functions ..
162 REAL SLAMCH, SLANGE, SLANSY
163 EXTERNAL slamch, slange, slansy
164* ..
165* .. External Subroutines ..
166 EXTERNAL sgemm, slacpy, slaset, sorglq, ssyrk
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max, real
170* ..
171* .. Scalars in Common ..
172 CHARACTER*32 SRNAMT
173* ..
174* .. Common blocks ..
175 COMMON / srnamc / srnamt
176* ..
177* .. Executable Statements ..
178*
179 eps = slamch( 'Epsilon' )
180*
181* Copy the first k rows of the factorization to the array Q
182*
183 CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
184 CALL slacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
185*
186* Generate the first n columns of the matrix Q
187*
188 srnamt = 'SORGLQ'
189 CALL sorglq( m, n, k, q, lda, tau, work, lwork, info )
190*
191* Copy L(1:k,1:m)
192*
193 CALL slaset( 'Full', k, m, zero, zero, l, lda )
194 CALL slacpy( 'Lower', k, m, af, lda, l, lda )
195*
196* Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
197*
198 CALL sgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
199 \$ lda, one, l, lda )
200*
201* Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
202*
203 anorm = slange( '1', k, n, a, lda, rwork )
204 resid = slange( '1', k, m, l, lda, rwork )
205 IF( anorm.GT.zero ) THEN
206 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
207 ELSE
208 result( 1 ) = zero
209 END IF
210*
211* Compute I - Q*Q'
212*
213 CALL slaset( 'Full', m, m, zero, one, l, lda )
214 CALL ssyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
215 \$ lda )
216*
217* Compute norm( I - Q*Q' ) / ( N * EPS ) .
218*
219 resid = slansy( '1', 'Upper', m, l, lda, rwork )
220*
221 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
222*
223 RETURN
224*
225* End of SLQT02
226*
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGLQ
Definition: sorglq.f:127
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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