LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
cppt01.f
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1 *> \brief \b CPPT01
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 CPPT01( UPLO, N, A, AFAC, RWORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * REAL RWORK( * )
20 * COMPLEX A( * ), AFAC( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CPPT01 reconstructs a Hermitian positive definite packed matrix A
30 *> from 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
34 *> L, 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 (N*(N+1)/2)
58 *> The original Hermitian matrix A, stored as a packed
59 *> triangular matrix.
60 *> \endverbatim
61 *>
62 *> \param[in,out] AFAC
63 *> \verbatim
64 *> AFAC is COMPLEX array, dimension (N*(N+1)/2)
65 *> On entry, the factor L or U from the L*L' or U'*U
66 *> factorization of A, stored as a packed triangular matrix.
67 *> Overwritten with the reconstructed matrix, and then with the
68 *> difference L*L' - A (or U'*U - A).
69 *> \endverbatim
70 *>
71 *> \param[out] RWORK
72 *> \verbatim
73 *> RWORK is REAL array, dimension (N)
74 *> \endverbatim
75 *>
76 *> \param[out] RESID
77 *> \verbatim
78 *> RESID is REAL
79 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
80 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
81 *> \endverbatim
82 *
83 * Authors:
84 * ========
85 *
86 *> \author Univ. of Tennessee
87 *> \author Univ. of California Berkeley
88 *> \author Univ. of Colorado Denver
89 *> \author NAG Ltd.
90 *
91 *> \ingroup complex_lin
92 *
93 * =====================================================================
94  SUBROUTINE cppt01( UPLO, N, A, AFAC, RWORK, RESID )
95 *
96 * -- LAPACK test routine --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 *
100 * .. Scalar Arguments ..
101  CHARACTER UPLO
102  INTEGER N
103  REAL RESID
104 * ..
105 * .. Array Arguments ..
106  REAL RWORK( * )
107  COMPLEX A( * ), AFAC( * )
108 * ..
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113  REAL ZERO, ONE
114  parameter( zero = 0.0e+0, one = 1.0e+0 )
115 * ..
116 * .. Local Scalars ..
117  INTEGER I, K, KC
118  REAL ANORM, EPS, TR
119  COMPLEX TC
120 * ..
121 * .. External Functions ..
122  LOGICAL LSAME
123  REAL CLANHP, SLAMCH
124  COMPLEX CDOTC
125  EXTERNAL lsame, clanhp, slamch, cdotc
126 * ..
127 * .. External Subroutines ..
128  EXTERNAL chpr, cscal, ctpmv
129 * ..
130 * .. Intrinsic Functions ..
131  INTRINSIC aimag, real
132 * ..
133 * .. Executable Statements ..
134 *
135 * Quick exit if N = 0
136 *
137  IF( n.LE.0 ) THEN
138  resid = zero
139  RETURN
140  END IF
141 *
142 * Exit with RESID = 1/EPS if ANORM = 0.
143 *
144  eps = slamch( 'Epsilon' )
145  anorm = clanhp( '1', uplo, n, a, rwork )
146  IF( anorm.LE.zero ) THEN
147  resid = one / eps
148  RETURN
149  END IF
150 *
151 * Check the imaginary parts of the diagonal elements and return with
152 * an error code if any are nonzero.
153 *
154  kc = 1
155  IF( lsame( uplo, 'U' ) ) THEN
156  DO 10 k = 1, n
157  IF( aimag( afac( kc ) ).NE.zero ) THEN
158  resid = one / eps
159  RETURN
160  END IF
161  kc = kc + k + 1
162  10 CONTINUE
163  ELSE
164  DO 20 k = 1, n
165  IF( aimag( afac( kc ) ).NE.zero ) THEN
166  resid = one / eps
167  RETURN
168  END IF
169  kc = kc + n - k + 1
170  20 CONTINUE
171  END IF
172 *
173 * Compute the product U'*U, overwriting U.
174 *
175  IF( lsame( uplo, 'U' ) ) THEN
176  kc = ( n*( n-1 ) ) / 2 + 1
177  DO 30 k = n, 1, -1
178 *
179 * Compute the (K,K) element of the result.
180 *
181  tr = cdotc( k, afac( kc ), 1, afac( kc ), 1 )
182  afac( kc+k-1 ) = tr
183 *
184 * Compute the rest of column K.
185 *
186  IF( k.GT.1 ) THEN
187  CALL ctpmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
188  \$ afac( kc ), 1 )
189  kc = kc - ( k-1 )
190  END IF
191  30 CONTINUE
192 *
193 * Compute the difference L*L' - A
194 *
195  kc = 1
196  DO 50 k = 1, n
197  DO 40 i = 1, k - 1
198  afac( kc+i-1 ) = afac( kc+i-1 ) - a( kc+i-1 )
199  40 CONTINUE
200  afac( kc+k-1 ) = afac( kc+k-1 ) - real( a( kc+k-1 ) )
201  kc = kc + k
202  50 CONTINUE
203 *
204 * Compute the product L*L', overwriting L.
205 *
206  ELSE
207  kc = ( n*( n+1 ) ) / 2
208  DO 60 k = n, 1, -1
209 *
210 * Add a multiple of column K of the factor L to each of
211 * columns K+1 through N.
212 *
213  IF( k.LT.n )
214  \$ CALL chpr( 'Lower', n-k, one, afac( kc+1 ), 1,
215  \$ afac( kc+n-k+1 ) )
216 *
217 * Scale column K by the diagonal element.
218 *
219  tc = afac( kc )
220  CALL cscal( n-k+1, tc, afac( kc ), 1 )
221 *
222  kc = kc - ( n-k+2 )
223  60 CONTINUE
224 *
225 * Compute the difference U'*U - A
226 *
227  kc = 1
228  DO 80 k = 1, n
229  afac( kc ) = afac( kc ) - real( a( kc ) )
230  DO 70 i = k + 1, n
231  afac( kc+i-k ) = afac( kc+i-k ) - a( kc+i-k )
232  70 CONTINUE
233  kc = kc + n - k + 1
234  80 CONTINUE
235  END IF
236 *
237 * Compute norm( L*U - A ) / ( N * norm(A) * EPS )
238 *
239  resid = clanhp( '1', uplo, n, afac, rwork )
240 *
241  resid = ( ( resid / real( n ) ) / anorm ) / eps
242 *
243  RETURN
244 *
245 * End of CPPT01
246 *
247  END
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine chpr(UPLO, N, ALPHA, X, INCX, AP)
CHPR
Definition: chpr.f:130
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine cppt01(UPLO, N, A, AFAC, RWORK, RESID)
CPPT01
Definition: cppt01.f:95