LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ spst01()

 subroutine spst01 ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( ldperm, * ) PERM, integer LDPERM, integer, dimension( * ) PIV, real, dimension( * ) RWORK, real RESID, integer RANK )

SPST01

Purpose:
``` SPST01 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)` [out] RESID ``` RESID is REAL 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.```

Definition at line 132 of file spst01.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 REAL RESID
141 INTEGER LDA, LDAFAC, LDPERM, N, RANK
142 CHARACTER UPLO
143* ..
144* .. Array Arguments ..
145 REAL A( LDA, * ), AFAC( LDAFAC, * ),
146 \$ PERM( LDPERM, * ), RWORK( * )
147 INTEGER PIV( * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 REAL ZERO, ONE
154 parameter( zero = 0.0e+0, one = 1.0e+0 )
155* ..
156* .. Local Scalars ..
157 REAL ANORM, EPS, T
158 INTEGER I, J, K
159* ..
160* .. External Functions ..
161 REAL SDOT, SLAMCH, SLANSY
162 LOGICAL LSAME
163 EXTERNAL sdot, slamch, slansy, lsame
164* ..
165* .. External Subroutines ..
166 EXTERNAL sscal, ssyr, strmv
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC real
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 = slamch( 'Epsilon' )
183 anorm = slansy( '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 = sdot( 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 strmv( '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 ssyr( '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 sscal( 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 = slansy( '1', uplo, n, perm, ldafac, rwork )
296*
297 resid = ( ( resid / real( n ) ) / anorm ) / eps
298*
299 RETURN
300*
301* End of SPST01
302*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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 sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:132
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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