LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slqt01()

subroutine slqt01 ( integer  m,
integer  n,
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 
)

SLQT01

Purpose:
 SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n
 matrix A, and partially tests SORGLQ which forms the n-by-n
 orthogonal matrix Q.

 SLQT01 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 REAL array, dimension (LDA,N)
          The m-by-n matrix A.
[out]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)
          The n-by-n orthogonal matrix Q.
[out]L
          L 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 SGELQF.
[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( L - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 124 of file slqt01.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, * ), L( LDA, * ),
136 $ Q( 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 sgelqf, sgemm, slacpy, slaset, sorglq, 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 = 'SGELQF'
180 CALL sgelqf( 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( n.GT.1 )
186 $ CALL slacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187*
188* Generate the n-by-n matrix Q
189*
190 srnamt = 'SORGLQ'
191 CALL sorglq( n, n, minmn, q, lda, tau, work, lwork, info )
192*
193* Copy L
194*
195 CALL slaset( 'Full', m, n, zero, zero, l, lda )
196 CALL slacpy( 'Lower', m, n, af, lda, l, lda )
197*
198* Compute L - A*Q'
199*
200 CALL sgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
201 $ lda, one, l, lda )
202*
203* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
204*
205 anorm = slange( '1', m, n, a, lda, rwork )
206 resid = slange( '1', m, n, l, lda, rwork )
207 IF( anorm.GT.zero ) THEN
208 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
209 ELSE
210 result( 1 ) = zero
211 END IF
212*
213* Compute I - Q*Q'
214*
215 CALL slaset( 'Full', n, n, zero, one, l, lda )
216 CALL ssyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
217 $ lda )
218*
219* Compute norm( I - Q*Q' ) / ( N * EPS ) .
220*
221 resid = slansy( '1', 'Upper', n, l, lda, rwork )
222*
223 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
224*
225 RETURN
226*
227* End of SLQT01
228*
sgelqf
subroutine sgelqf(m, n, a, lda, tau, work, lwork, info)
SGELQF
Definition sgelqf.f:143
sgemm
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
ssyrk
subroutine ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK
Definition ssyrk.f:169
slacpy
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
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
slange
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
slansy
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
slaset
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
sorglq
subroutine sorglq(m, n, k, a, lda, tau, work, lwork, info)
SORGLQ
Definition sorglq.f:127
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