LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sqrt01p ( 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 )

SQRT01P

Purpose:
``` SQRT01P tests SGEQRFP, which computes the QR factorization of an m-by-n
matrix A, and partially tests SORGQR which forms the m-by-m
orthogonal matrix Q.

SQRT01P compares R 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 QR factorization of A, as returned by SGEQRFP. See SGEQRFP for further details.``` [out] Q ``` Q is REAL array, dimension (LDA,M) The m-by-m 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 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 SGEQRFP.``` [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( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```
Date
November 2011

Definition at line 128 of file sqrt01p.f.

128 *
129 * -- LAPACK test routine (version 3.4.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2011
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  REAL a( lda, * ), af( lda, * ), q( lda, * ),
139  \$ r( 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, sgeqrfp, slacpy, slaset, sorgqr, 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 = 'SGEQRFP'
183  CALL sgeqrfp( 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  CALL slacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
189 *
190 * Generate the m-by-m matrix Q
191 *
192  srnamt = 'SORGQR'
193  CALL sorgqr( m, m, minmn, q, lda, tau, work, lwork, info )
194 *
195 * Copy R
196 *
197  CALL slaset( 'Full', m, n, zero, zero, r, lda )
198  CALL slacpy( 'Upper', m, n, af, lda, r, lda )
199 *
200 * Compute R - Q'*A
201 *
202  CALL sgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
203  \$ lda, one, r, lda )
204 *
205 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
206 *
207  anorm = slange( '1', m, n, a, lda, rwork )
208  resid = slange( '1', m, n, r, lda, rwork )
209  IF( anorm.GT.zero ) THEN
210  result( 1 ) = ( ( resid / REAL( MAX( 1, M ) ) ) / anorm ) / eps
211  ELSE
212  result( 1 ) = zero
213  END IF
214 *
215 * Compute I - Q'*Q
216 *
217  CALL slaset( 'Full', m, m, zero, one, r, lda )
218  CALL ssyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, r,
219  \$ lda )
220 *
221 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
222 *
223  resid = slansy( '1', 'Upper', m, r, lda, rwork )
224 *
225  result( 2 ) = ( resid / REAL( MAX( 1, M ) ) ) / eps
226 *
227  RETURN
228 *
229 * End of SQRT01P
230 *
subroutine sgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQRFP
Definition: sgeqrfp.f:141
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
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
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 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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:130
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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