LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ srqt01()

 subroutine srqt01 ( integer M, integer N, real, dimension( lda, * ) A, real, dimension( lda, * ) AF, real, dimension( lda, * ) Q, real, dimension( lda, * ) R, integer LDA, real, dimension( * ) TAU, real, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

SRQT01

Purpose:
``` SRQT01 tests SGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests SORGRQ which forms the n-by-n
orthogonal matrix Q.

SRQT01 compares R 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 REAL array, dimension (LDA,N) The m-by-n matrix A.``` [out] AF ``` AF is REAL array, dimension (LDA,N) Details of the RQ factorization of A, as returned by SGERQF. See SGERQF for further details.``` [out] Q ``` Q is REAL array, dimension (LDA,N) The n-by-n orthogonal matrix Q.``` [out] R ` R is REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGERQF.``` [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 (max(M,N))` [out] RESULT ``` RESULT is REAL array, dimension (2) The test ratios: RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```

Definition at line 124 of file srqt01.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 REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
136 \$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
137 \$ WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145 REAL ROGUE
146 parameter( rogue = -1.0e+10 )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 REAL ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 REAL SLAMCH, SLANGE, SLANSY
154 EXTERNAL slamch, slange, slansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL sgemm, sgerqf, slacpy, slaset, sorgrq, ssyrk
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC max, min, real
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 = slamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL slacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'SGERQF'
180 CALL sgerqf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
185 IF( m.LE.n ) THEN
186 IF( m.GT.0 .AND. m.LT.n )
187 \$ CALL slacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188 IF( m.GT.1 )
189 \$ CALL slacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
190 \$ q( n-m+2, n-m+1 ), lda )
191 ELSE
192 IF( n.GT.1 )
193 \$ CALL slacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
194 \$ q( 2, 1 ), lda )
195 END IF
196*
197* Generate the n-by-n matrix Q
198*
199 srnamt = 'SORGRQ'
200 CALL sorgrq( n, n, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy R
203*
204 CALL slaset( 'Full', m, n, zero, zero, r, lda )
205 IF( m.LE.n ) THEN
206 IF( m.GT.0 )
207 \$ CALL slacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
208 \$ r( 1, n-m+1 ), lda )
209 ELSE
210 IF( m.GT.n .AND. n.GT.0 )
211 \$ CALL slacpy( 'Full', m-n, n, af, lda, r, lda )
212 IF( n.GT.0 )
213 \$ CALL slacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
214 \$ r( m-n+1, 1 ), lda )
215 END IF
216*
217* Compute R - A*Q'
218*
219 CALL sgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
220 \$ lda, one, r, lda )
221*
222* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
223*
224 anorm = slange( '1', m, n, a, lda, rwork )
225 resid = slange( '1', m, n, r, lda, rwork )
226 IF( anorm.GT.zero ) THEN
227 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
228 ELSE
229 result( 1 ) = zero
230 END IF
231*
232* Compute I - Q*Q'
233*
234 CALL slaset( 'Full', n, n, zero, one, r, lda )
235 CALL ssyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
236 \$ lda )
237*
238* Compute norm( I - Q*Q' ) / ( N * EPS ) .
239*
240 resid = slansy( '1', 'Upper', n, r, lda, rwork )
241*
242 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
243*
244 RETURN
245*
246* End of SRQT01
247*
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 sgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF
Definition: sgerqf.f:139
subroutine sorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGRQ
Definition: sorgrq.f:128
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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