LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cpot01.f
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1 *> \brief \b CPOT01
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 CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER LDA, LDAFAC, N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * REAL RWORK( * )
20 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CPOT01 reconstructs a Hermitian positive definite matrix A from
30 *> its L*L' or U'*U factorization and computes the residual
31 *> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
32 *> norm( U'*U - A ) / ( N * norm(A) * EPS ),
33 *> where EPS is the machine epsilon, L' is the conjugate transpose of L,
34 *> and U' is the conjugate transpose of U.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] UPLO
41 *> \verbatim
42 *> UPLO is CHARACTER*1
43 *> Specifies whether the upper or lower triangular part of the
44 *> Hermitian matrix A is stored:
45 *> = 'U': Upper triangular
46 *> = 'L': Lower triangular
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of rows and columns of the matrix A. N >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] A
56 *> \verbatim
57 *> A is COMPLEX array, dimension (LDA,N)
58 *> The original Hermitian matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] LDA
62 *> \verbatim
63 *> LDA is INTEGER
64 *> The leading dimension of the array A. LDA >= max(1,N)
65 *> \endverbatim
66 *>
67 *> \param[in,out] AFAC
68 *> \verbatim
69 *> AFAC is COMPLEX array, dimension (LDAFAC,N)
70 *> On entry, the factor L or U from the L * L**H or U**H * U
71 *> factorization of A.
72 *> Overwritten with the reconstructed matrix, and then with
73 *> the difference L * L**H - A (or U**H * U - A).
74 *> \endverbatim
75 *>
76 *> \param[in] LDAFAC
77 *> \verbatim
78 *> LDAFAC is INTEGER
79 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
80 *> \endverbatim
81 *>
82 *> \param[out] RWORK
83 *> \verbatim
84 *> RWORK is REAL array, dimension (N)
85 *> \endverbatim
86 *>
87 *> \param[out] RESID
88 *> \verbatim
89 *> RESID is REAL
90 *> If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS )
91 *> If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )
92 *> \endverbatim
93 *
94 * Authors:
95 * ========
96 *
97 *> \author Univ. of Tennessee
98 *> \author Univ. of California Berkeley
99 *> \author Univ. of Colorado Denver
100 *> \author NAG Ltd.
101 *
102 *> \ingroup complex_lin
103 *
104 * =====================================================================
105  SUBROUTINE cpot01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
106 *
107 * -- LAPACK test routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER UPLO
113  INTEGER LDA, LDAFAC, N
114  REAL RESID
115 * ..
116 * .. Array Arguments ..
117  REAL RWORK( * )
118  COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
119 * ..
120 *
121 * =====================================================================
122 *
123 * .. Parameters ..
124  REAL ZERO, ONE
125  parameter( zero = 0.0e+0, one = 1.0e+0 )
126 * ..
127 * .. Local Scalars ..
128  INTEGER I, J, K
129  REAL ANORM, EPS, TR
130  COMPLEX TC
131 * ..
132 * .. External Functions ..
133  LOGICAL LSAME
134  REAL CLANHE, SLAMCH
135  COMPLEX CDOTC
136  EXTERNAL lsame, clanhe, slamch, cdotc
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL cher, cscal, ctrmv
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC aimag, real
143 * ..
144 * .. Executable Statements ..
145 *
146 * Quick exit if N = 0.
147 *
148  IF( n.LE.0 ) THEN
149  resid = zero
150  RETURN
151  END IF
152 *
153 * Exit with RESID = 1/EPS if ANORM = 0.
154 *
155  eps = slamch( 'Epsilon' )
156  anorm = clanhe( '1', uplo, n, a, lda, rwork )
157  IF( anorm.LE.zero ) THEN
158  resid = one / eps
159  RETURN
160  END IF
161 *
162 * Check the imaginary parts of the diagonal elements and return with
163 * an error code if any are nonzero.
164 *
165  DO 10 j = 1, n
166  IF( aimag( afac( j, j ) ).NE.zero ) THEN
167  resid = one / eps
168  RETURN
169  END IF
170  10 CONTINUE
171 *
172 * Compute the product U**H * U, overwriting U.
173 *
174  IF( lsame( uplo, 'U' ) ) THEN
175  DO 20 k = n, 1, -1
176 *
177 * Compute the (K,K) element of the result.
178 *
179  tr = cdotc( k, afac( 1, k ), 1, afac( 1, k ), 1 )
180  afac( k, k ) = tr
181 *
182 * Compute the rest of column K.
183 *
184  CALL ctrmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
185  $ ldafac, afac( 1, k ), 1 )
186 *
187  20 CONTINUE
188 *
189 * Compute the product L * L**H, overwriting L.
190 *
191  ELSE
192  DO 30 k = n, 1, -1
193 *
194 * Add a multiple of column K of the factor L to each of
195 * columns K+1 through N.
196 *
197  IF( k+1.LE.n )
198  $ CALL cher( 'Lower', n-k, one, afac( k+1, k ), 1,
199  $ afac( k+1, k+1 ), ldafac )
200 *
201 * Scale column K by the diagonal element.
202 *
203  tc = afac( k, k )
204  CALL cscal( n-k+1, tc, afac( k, k ), 1 )
205 *
206  30 CONTINUE
207  END IF
208 *
209 * Compute the difference L * L**H - A (or U**H * U - A).
210 *
211  IF( lsame( uplo, 'U' ) ) THEN
212  DO 50 j = 1, n
213  DO 40 i = 1, j - 1
214  afac( i, j ) = afac( i, j ) - a( i, j )
215  40 CONTINUE
216  afac( j, j ) = afac( j, j ) - real( a( j, j ) )
217  50 CONTINUE
218  ELSE
219  DO 70 j = 1, n
220  afac( j, j ) = afac( j, j ) - real( a( j, j ) )
221  DO 60 i = j + 1, n
222  afac( i, j ) = afac( i, j ) - a( i, j )
223  60 CONTINUE
224  70 CONTINUE
225  END IF
226 *
227 * Compute norm(L*U - A) / ( N * norm(A) * EPS )
228 *
229  resid = clanhe( '1', uplo, n, afac, ldafac, rwork )
230 *
231  resid = ( ( resid / real( n ) ) / anorm ) / eps
232 *
233  RETURN
234 *
235 * End of CPOT01
236 *
237  END
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:147
subroutine cher(UPLO, N, ALPHA, X, INCX, A, LDA)
CHER
Definition: cher.f:135
subroutine cpot01(UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
CPOT01
Definition: cpot01.f:106