LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sqrt01()

subroutine sqrt01 ( 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 
)

SQRT01

Purpose:
 SQRT01 tests SGEQRF, 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.

 SQRT01 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 SGEQRF.
          See SGEQRF 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 SGEQRF.
[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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 124 of file sqrt01.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, sgeqrf, slacpy, slaset, sorgqr, 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 = 'SGEQRF'
180 CALL sgeqrf( 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 CALL slacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186*
187* Generate the m-by-m matrix Q
188*
189 srnamt = 'SORGQR'
190 CALL sorgqr( m, m, minmn, q, lda, tau, work, lwork, info )
191*
192* Copy R
193*
194 CALL slaset( 'Full', m, n, zero, zero, r, lda )
195 CALL slacpy( 'Upper', m, n, af, lda, r, lda )
196*
197* Compute R - Q'*A
198*
199 CALL sgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
200 $ lda, one, r, lda )
201*
202* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
203*
204 anorm = slange( '1', m, n, a, lda, rwork )
205 resid = slange( '1', m, n, r, lda, rwork )
206 IF( anorm.GT.zero ) THEN
207 result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
208 ELSE
209 result( 1 ) = zero
210 END IF
211*
212* Compute I - Q'*Q
213*
214 CALL slaset( 'Full', m, m, zero, one, r, lda )
215 CALL ssyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, r,
216 $ lda )
217*
218* Compute norm( I - Q'*Q ) / ( M * EPS ) .
219*
220 resid = slansy( '1', 'Upper', m, r, lda, rwork )
221*
222 result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
223*
224 RETURN
225*
226* End of SQRT01
227*
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
subroutine sgeqrf(m, n, a, lda, tau, work, lwork, info)
SGEQRF
Definition sgeqrf.f:146
subroutine ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK
Definition ssyrk.f:169
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 slamch(cmach)
SLAMCH
Definition slamch.f:68
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
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 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 sorgqr(m, n, k, a, lda, tau, work, lwork, info)
SORGQR
Definition sorgqr.f:128
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