LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sqlt01()

subroutine sqlt01 ( 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 
)

SQLT01

Purpose:
 SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests SORGQL which forms the m-by-m
 orthogonal matrix Q.

 SQLT01 compares L with Q'*A, 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 QL factorization of A, as returned by SGEQLF.
          See SGEQLF for further details.
[out]Q
          Q is REAL array, dimension (LDA,M)
          The m-by-m 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 R.
          LDA >= max(M,N).
[out]TAU
          TAU is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGEQLF.
[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 - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 128 of file sqlt01.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  REAL a( lda, * ), af( lda, * ), l( lda, * ),
139  $ q( lda, * ), result( * ), rwork( * ), tau( * ),
140  $ work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL zero, one
147  parameter( zero = 0.0e+0, one = 1.0e+0 )
148  REAL rogue
149  parameter( rogue = -1.0e+10 )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  REAL anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  REAL slamch, slange, slansy
157  EXTERNAL slamch, slange, slansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL sgemm, sgeqlf, slacpy, slaset, sorgql, ssyrk
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC max, min, real
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 = slamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL slacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'SGEQLF'
183  CALL sgeqlf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
188  IF( m.GE.n ) THEN
189  IF( n.LT.m .AND. n.GT.0 )
190  $ CALL slacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
191  IF( n.GT.1 )
192  $ CALL slacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
193  $ q( m-n+1, m-n+2 ), lda )
194  ELSE
195  IF( m.GT.1 )
196  $ CALL slacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
197  $ q( 1, 2 ), lda )
198  END IF
199 *
200 * Generate the m-by-m matrix Q
201 *
202  srnamt = 'SORGQL'
203  CALL sorgql( m, m, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy L
206 *
207  CALL slaset( 'Full', m, n, zero, zero, l, lda )
208  IF( m.GE.n ) THEN
209  IF( n.GT.0 )
210  $ CALL slacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
211  $ l( m-n+1, 1 ), lda )
212  ELSE
213  IF( n.GT.m .AND. m.GT.0 )
214  $ CALL slacpy( 'Full', m, n-m, af, lda, l, lda )
215  IF( m.GT.0 )
216  $ CALL slacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
217  $ l( 1, n-m+1 ), lda )
218  END IF
219 *
220 * Compute L - Q'*A
221 *
222  CALL sgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
223  $ lda, one, l, lda )
224 *
225 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
226 *
227  anorm = slange( '1', m, n, a, lda, rwork )
228  resid = slange( '1', m, n, l, lda, rwork )
229  IF( anorm.GT.zero ) THEN
230  result( 1 ) = ( ( resid / REAL( MAX( 1, M ) ) ) / anorm ) / eps
231  ELSE
232  result( 1 ) = zero
233  END IF
234 *
235 * Compute I - Q'*Q
236 *
237  CALL slaset( 'Full', m, m, zero, one, l, lda )
238  CALL ssyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, l,
239  $ lda )
240 *
241 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
242 *
243  resid = slansy( '1', 'Upper', m, l, lda, rwork )
244 *
245  result( 2 ) = ( resid / REAL( MAX( 1, M ) ) ) / eps
246 *
247  RETURN
248 *
249 * End of SQLT01
250 *
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine sgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQLF
Definition: sgeqlf.f:140
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.f:130
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:116
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:112
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
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, or the element of largest absolute value of a real symmetric matrix.
Definition: slansy.f:124
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