 LAPACK  3.10.1 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 )```

Definition at line 124 of file sqlt01.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 sgemm, sgeqlf, slacpy, slaset, sorgql, 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 = 'SGEQLF'
180  CALL sgeqlf( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL slaset( 'Full', m, m, rogue, rogue, q, lda )
185  IF( m.GE.n ) THEN
186  IF( n.LT.m .AND. n.GT.0 )
187  \$ CALL slacpy( 'Full', m-n, n, af, lda, q( 1, m-n+1 ), lda )
188  IF( n.GT.1 )
189  \$ CALL slacpy( 'Upper', n-1, n-1, af( m-n+1, 2 ), lda,
190  \$ q( m-n+1, m-n+2 ), lda )
191  ELSE
192  IF( m.GT.1 )
193  \$ CALL slacpy( 'Upper', m-1, m-1, af( 1, n-m+2 ), lda,
194  \$ q( 1, 2 ), lda )
195  END IF
196 *
197 * Generate the m-by-m matrix Q
198 *
199  srnamt = 'SORGQL'
200  CALL sorgql( m, m, minmn, q, lda, tau, work, lwork, info )
201 *
202 * Copy L
203 *
204  CALL slaset( 'Full', m, n, zero, zero, l, lda )
205  IF( m.GE.n ) THEN
206  IF( n.GT.0 )
207  \$ CALL slacpy( 'Lower', n, n, af( m-n+1, 1 ), lda,
208  \$ l( m-n+1, 1 ), lda )
209  ELSE
210  IF( n.GT.m .AND. m.GT.0 )
211  \$ CALL slacpy( 'Full', m, n-m, af, lda, l, lda )
212  IF( m.GT.0 )
213  \$ CALL slacpy( 'Lower', m, m, af( 1, n-m+1 ), lda,
214  \$ l( 1, n-m+1 ), lda )
215  END IF
216 *
217 * Compute L - Q'*A
218 *
219  CALL sgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
220  \$ lda, one, l, lda )
221 *
222 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
223 *
224  anorm = slange( '1', m, n, a, lda, rwork )
225  resid = slange( '1', m, n, l, lda, rwork )
226  IF( anorm.GT.zero ) THEN
227  result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
228  ELSE
229  result( 1 ) = zero
230  END IF
231 *
232 * Compute I - Q'*Q
233 *
234  CALL slaset( 'Full', m, m, zero, one, l, lda )
235  CALL ssyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, l,
236  \$ lda )
237 *
238 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
239 *
240  resid = slansy( '1', 'Upper', m, l, lda, rwork )
241 *
242  result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
243 *
244  RETURN
245 *
246 * End of SQLT01
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 sgeqlf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQLF
Definition: sgeqlf.f:138
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.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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