LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dpst01()

subroutine dpst01 ( character uplo,
integer n,
double precision, dimension( lda, * ) a,
integer lda,
double precision, dimension( ldafac, * ) afac,
integer ldafac,
double precision, dimension( ldperm, * ) perm,
integer ldperm,
integer, dimension( * ) piv,
double precision, dimension( * ) rwork,
double precision resid,
integer rank )

DPST01

Purpose:
!>
!> DPST01 reconstructs a symmetric positive semidefinite matrix A
!> from its L or U factors and the permutation matrix P and computes
!> the residual
!>    norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
!>    norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
!> where EPS is the machine epsilon.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
[in]N
!>          N is INTEGER
!>          The number of rows and columns of the matrix A.  N >= 0.
!>
[in]A
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The original symmetric matrix A.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N)
!>
[in]AFAC
!>          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
!>          The factor L or U from the L*L' or U'*U
!>          factorization of A.
!>
[in]LDAFAC
!>          LDAFAC is INTEGER
!>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
!>
[out]PERM
!>          PERM is DOUBLE PRECISION array, dimension (LDPERM,N)
!>          Overwritten with the reconstructed matrix, and then with the
!>          difference P*L*L'*P' - A (or P*U'*U*P' - A)
!>
[in]LDPERM
!>          LDPERM is INTEGER
!>          The leading dimension of the array PERM.
!>          LDAPERM >= max(1,N).
!>
[in]PIV
!>          PIV is INTEGER array, dimension (N)
!>          PIV is such that the nonzero entries are
!>          P( PIV( K ), K ) = 1.
!>
[out]RWORK
!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>
[out]RESID
!>          RESID is DOUBLE PRECISION
!>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
!>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
!>
[in]RANK
!>          RANK is INTEGER
!>          number of nonzero singular values of A.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 132 of file dpst01.f.

134*
135* -- LAPACK test routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 DOUBLE PRECISION RESID
141 INTEGER LDA, LDAFAC, LDPERM, N, RANK
142 CHARACTER UPLO
143* ..
144* .. Array Arguments ..
145 DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ),
146 $ PERM( LDPERM, * ), RWORK( * )
147 INTEGER PIV( * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 DOUBLE PRECISION ZERO, ONE
154 parameter( zero = 0.0d+0, one = 1.0d+0 )
155* ..
156* .. Local Scalars ..
157 DOUBLE PRECISION ANORM, EPS, T
158 INTEGER I, J, K
159* ..
160* .. External Functions ..
161 DOUBLE PRECISION DDOT, DLAMCH, DLANSY
162 LOGICAL LSAME
163 EXTERNAL ddot, dlamch, dlansy, lsame
164* ..
165* .. External Subroutines ..
166 EXTERNAL dscal, dsyr, dtrmv
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC dble
170* ..
171* .. Executable Statements ..
172*
173* Quick exit if N = 0.
174*
175 IF( n.LE.0 ) THEN
176 resid = zero
177 RETURN
178 END IF
179*
180* Exit with RESID = 1/EPS if ANORM = 0.
181*
182 eps = dlamch( 'Epsilon' )
183 anorm = dlansy( '1', uplo, n, a, lda, rwork )
184 IF( anorm.LE.zero ) THEN
185 resid = one / eps
186 RETURN
187 END IF
188*
189* Compute the product U'*U, overwriting U.
190*
191 IF( lsame( uplo, 'U' ) ) THEN
192*
193 IF( rank.LT.n ) THEN
194 DO 110 j = rank + 1, n
195 DO 100 i = rank + 1, j
196 afac( i, j ) = zero
197 100 CONTINUE
198 110 CONTINUE
199 END IF
200*
201 DO 120 k = n, 1, -1
202*
203* Compute the (K,K) element of the result.
204*
205 t = ddot( k, afac( 1, k ), 1, afac( 1, k ), 1 )
206 afac( k, k ) = t
207*
208* Compute the rest of column K.
209*
210 CALL dtrmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
211 $ ldafac, afac( 1, k ), 1 )
212*
213 120 CONTINUE
214*
215* Compute the product L*L', overwriting L.
216*
217 ELSE
218*
219 IF( rank.LT.n ) THEN
220 DO 140 j = rank + 1, n
221 DO 130 i = j, n
222 afac( i, j ) = zero
223 130 CONTINUE
224 140 CONTINUE
225 END IF
226*
227 DO 150 k = n, 1, -1
228* Add a multiple of column K of the factor L to each of
229* columns K+1 through N.
230*
231 IF( k+1.LE.n )
232 $ CALL dsyr( 'Lower', n-k, one, afac( k+1, k ), 1,
233 $ afac( k+1, k+1 ), ldafac )
234*
235* Scale column K by the diagonal element.
236*
237 t = afac( k, k )
238 CALL dscal( n-k+1, t, afac( k, k ), 1 )
239 150 CONTINUE
240*
241 END IF
242*
243* Form P*L*L'*P' or P*U'*U*P'
244*
245 IF( lsame( uplo, 'U' ) ) THEN
246*
247 DO 170 j = 1, n
248 DO 160 i = 1, n
249 IF( piv( i ).LE.piv( j ) ) THEN
250 IF( i.LE.j ) THEN
251 perm( piv( i ), piv( j ) ) = afac( i, j )
252 ELSE
253 perm( piv( i ), piv( j ) ) = afac( j, i )
254 END IF
255 END IF
256 160 CONTINUE
257 170 CONTINUE
258*
259*
260 ELSE
261*
262 DO 190 j = 1, n
263 DO 180 i = 1, n
264 IF( piv( i ).GE.piv( j ) ) THEN
265 IF( i.GE.j ) THEN
266 perm( piv( i ), piv( j ) ) = afac( i, j )
267 ELSE
268 perm( piv( i ), piv( j ) ) = afac( j, i )
269 END IF
270 END IF
271 180 CONTINUE
272 190 CONTINUE
273*
274 END IF
275*
276* Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
277*
278 IF( lsame( uplo, 'U' ) ) THEN
279 DO 210 j = 1, n
280 DO 200 i = 1, j
281 perm( i, j ) = perm( i, j ) - a( i, j )
282 200 CONTINUE
283 210 CONTINUE
284 ELSE
285 DO 230 j = 1, n
286 DO 220 i = j, n
287 perm( i, j ) = perm( i, j ) - a( i, j )
288 220 CONTINUE
289 230 CONTINUE
290 END IF
291*
292* Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
293* ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
294*
295 resid = dlansy( '1', uplo, n, perm, ldafac, rwork )
296*
297 resid = ( ( resid / dble( n ) ) / anorm ) / eps
298*
299 RETURN
300*
301* End of DPST01
302*
ddot
double precision function ddot(n, dx, incx, dy, incy)
DDOT
Definition ddot.f:82
dsyr
subroutine dsyr(uplo, n, alpha, x, incx, a, lda)
DSYR
Definition dsyr.f:132
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlansy
double precision function dlansy(norm, uplo, n, a, lda, work)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlansy.f:120
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
dtrmv
subroutine dtrmv(uplo, trans, diag, n, a, lda, x, incx)
DTRMV
Definition dtrmv.f:147
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