LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zpst01.f
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1 *> \brief \b ZPST01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
12 * PIV, RWORK, RESID, RANK )
13 *
14 * .. Scalar Arguments ..
15 * DOUBLE PRECISION RESID
16 * INTEGER LDA, LDAFAC, LDPERM, N, RANK
17 * CHARACTER UPLO
18 * ..
19 * .. Array Arguments ..
20 * COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ),
21 * \$ PERM( LDPERM, * )
22 * DOUBLE PRECISION RWORK( * )
23 * INTEGER PIV( * )
24 * ..
25 *
26 *
27 *> \par Purpose:
28 * =============
29 *>
30 *> \verbatim
31 *>
32 *> ZPST01 reconstructs an Hermitian positive semidefinite matrix A
33 *> from its L or U factors and the permutation matrix P and computes
34 *> the residual
35 *> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
36 *> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
37 *> where EPS is the machine epsilon, L' is the conjugate transpose of L,
38 *> and U' is the conjugate transpose of U.
39 *> \endverbatim
40 *
41 * Arguments:
42 * ==========
43 *
44 *> \param[in] UPLO
45 *> \verbatim
46 *> UPLO is CHARACTER*1
47 *> Specifies whether the upper or lower triangular part of the
48 *> Hermitian matrix A is stored:
49 *> = 'U': Upper triangular
50 *> = 'L': Lower triangular
51 *> \endverbatim
52 *>
53 *> \param[in] N
54 *> \verbatim
55 *> N is INTEGER
56 *> The number of rows and columns of the matrix A. N >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in] A
60 *> \verbatim
61 *> A is COMPLEX*16 array, dimension (LDA,N)
62 *> The original Hermitian matrix A.
63 *> \endverbatim
64 *>
65 *> \param[in] LDA
66 *> \verbatim
67 *> LDA is INTEGER
68 *> The leading dimension of the array A. LDA >= max(1,N)
69 *> \endverbatim
70 *>
71 *> \param[in] AFAC
72 *> \verbatim
73 *> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
74 *> The factor L or U from the L*L' or U'*U
75 *> factorization of A.
76 *> \endverbatim
77 *>
78 *> \param[in] LDAFAC
79 *> \verbatim
80 *> LDAFAC is INTEGER
81 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
82 *> \endverbatim
83 *>
84 *> \param[out] PERM
85 *> \verbatim
86 *> PERM is COMPLEX*16 array, dimension (LDPERM,N)
87 *> Overwritten with the reconstructed matrix, and then with the
88 *> difference P*L*L'*P' - A (or P*U'*U*P' - A)
89 *> \endverbatim
90 *>
91 *> \param[in] LDPERM
92 *> \verbatim
93 *> LDPERM is INTEGER
94 *> The leading dimension of the array PERM.
95 *> LDAPERM >= max(1,N).
96 *> \endverbatim
97 *>
98 *> \param[in] PIV
99 *> \verbatim
100 *> PIV is INTEGER array, dimension (N)
101 *> PIV is such that the nonzero entries are
102 *> P( PIV( K ), K ) = 1.
103 *> \endverbatim
104 *>
105 *> \param[out] RWORK
106 *> \verbatim
107 *> RWORK is DOUBLE PRECISION array, dimension (N)
108 *> \endverbatim
109 *>
110 *> \param[out] RESID
111 *> \verbatim
112 *> RESID is DOUBLE PRECISION
113 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
114 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
115 *> \endverbatim
116 *>
117 *> \param[in] RANK
118 *> \verbatim
119 *> RANK is INTEGER
120 *> number of nonzero singular values of A.
121 *> \endverbatim
122 *
123 * Authors:
124 * ========
125 *
126 *> \author Univ. of Tennessee
127 *> \author Univ. of California Berkeley
128 *> \author Univ. of Colorado Denver
129 *> \author NAG Ltd.
130 *
131 *> \ingroup complex16_lin
132 *
133 * =====================================================================
134  SUBROUTINE zpst01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
135  \$ PIV, RWORK, RESID, RANK )
136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  DOUBLE PRECISION RESID
143  INTEGER LDA, LDAFAC, LDPERM, N, RANK
144  CHARACTER UPLO
145 * ..
146 * .. Array Arguments ..
147  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ),
148  \$ perm( ldperm, * )
149  DOUBLE PRECISION RWORK( * )
150  INTEGER PIV( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION ZERO, ONE
157  parameter( zero = 0.0d+0, one = 1.0d+0 )
158  COMPLEX*16 CZERO
159  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
160 * ..
161 * .. Local Scalars ..
162  COMPLEX*16 TC
163  DOUBLE PRECISION ANORM, EPS, TR
164  INTEGER I, J, K
165 * ..
166 * .. External Functions ..
167  COMPLEX*16 ZDOTC
168  DOUBLE PRECISION DLAMCH, ZLANHE
169  LOGICAL LSAME
170  EXTERNAL zdotc, dlamch, zlanhe, lsame
171 * ..
172 * .. External Subroutines ..
173  EXTERNAL zher, zscal, ztrmv
174 * ..
175 * .. Intrinsic Functions ..
176  INTRINSIC dble, dconjg, dimag
177 * ..
178 * .. Executable Statements ..
179 *
180 * Quick exit if N = 0.
181 *
182  IF( n.LE.0 ) THEN
183  resid = zero
184  RETURN
185  END IF
186 *
187 * Exit with RESID = 1/EPS if ANORM = 0.
188 *
189  eps = dlamch( 'Epsilon' )
190  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
191  IF( anorm.LE.zero ) THEN
192  resid = one / eps
193  RETURN
194  END IF
195 *
196 * Check the imaginary parts of the diagonal elements and return with
197 * an error code if any are nonzero.
198 *
199  DO 100 j = 1, n
200  IF( dimag( afac( j, j ) ).NE.zero ) THEN
201  resid = one / eps
202  RETURN
203  END IF
204  100 CONTINUE
205 *
206 * Compute the product U'*U, overwriting U.
207 *
208  IF( lsame( uplo, 'U' ) ) THEN
209 *
210  IF( rank.LT.n ) THEN
211  DO 120 j = rank + 1, n
212  DO 110 i = rank + 1, j
213  afac( i, j ) = czero
214  110 CONTINUE
215  120 CONTINUE
216  END IF
217 *
218  DO 130 k = n, 1, -1
219 *
220 * Compute the (K,K) element of the result.
221 *
222  tr = zdotc( k, afac( 1, k ), 1, afac( 1, k ), 1 )
223  afac( k, k ) = tr
224 *
225 * Compute the rest of column K.
226 *
227  CALL ztrmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
228  \$ ldafac, afac( 1, k ), 1 )
229 *
230  130 CONTINUE
231 *
232 * Compute the product L*L', overwriting L.
233 *
234  ELSE
235 *
236  IF( rank.LT.n ) THEN
237  DO 150 j = rank + 1, n
238  DO 140 i = j, n
239  afac( i, j ) = czero
240  140 CONTINUE
241  150 CONTINUE
242  END IF
243 *
244  DO 160 k = n, 1, -1
245 * Add a multiple of column K of the factor L to each of
246 * columns K+1 through N.
247 *
248  IF( k+1.LE.n )
249  \$ CALL zher( 'Lower', n-k, one, afac( k+1, k ), 1,
250  \$ afac( k+1, k+1 ), ldafac )
251 *
252 * Scale column K by the diagonal element.
253 *
254  tc = afac( k, k )
255  CALL zscal( n-k+1, tc, afac( k, k ), 1 )
256  160 CONTINUE
257 *
258  END IF
259 *
260 * Form P*L*L'*P' or P*U'*U*P'
261 *
262  IF( lsame( uplo, 'U' ) ) THEN
263 *
264  DO 180 j = 1, n
265  DO 170 i = 1, n
266  IF( piv( i ).LE.piv( j ) ) THEN
267  IF( i.LE.j ) THEN
268  perm( piv( i ), piv( j ) ) = afac( i, j )
269  ELSE
270  perm( piv( i ), piv( j ) ) = dconjg( afac( j, i ) )
271  END IF
272  END IF
273  170 CONTINUE
274  180 CONTINUE
275 *
276 *
277  ELSE
278 *
279  DO 200 j = 1, n
280  DO 190 i = 1, n
281  IF( piv( i ).GE.piv( j ) ) THEN
282  IF( i.GE.j ) THEN
283  perm( piv( i ), piv( j ) ) = afac( i, j )
284  ELSE
285  perm( piv( i ), piv( j ) ) = dconjg( afac( j, i ) )
286  END IF
287  END IF
288  190 CONTINUE
289  200 CONTINUE
290 *
291  END IF
292 *
293 * Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
294 *
295  IF( lsame( uplo, 'U' ) ) THEN
296  DO 220 j = 1, n
297  DO 210 i = 1, j - 1
298  perm( i, j ) = perm( i, j ) - a( i, j )
299  210 CONTINUE
300  perm( j, j ) = perm( j, j ) - dble( a( j, j ) )
301  220 CONTINUE
302  ELSE
303  DO 240 j = 1, n
304  perm( j, j ) = perm( j, j ) - dble( a( j, j ) )
305  DO 230 i = j + 1, n
306  perm( i, j ) = perm( i, j ) - a( i, j )
307  230 CONTINUE
308  240 CONTINUE
309  END IF
310 *
311 * Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
312 * ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
313 *
314  resid = zlanhe( '1', uplo, n, perm, ldafac, rwork )
315 *
316  resid = ( ( resid / dble( n ) ) / anorm ) / eps
317 *
318  RETURN
319 *
320 * End of ZPST01
321 *
322  END
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
subroutine zher(UPLO, N, ALPHA, X, INCX, A, LDA)
ZHER
Definition: zher.f:135
subroutine zpst01(UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
ZPST01
Definition: zpst01.f:136