LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cpbt01.f
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1 *> \brief \b CPBT01
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 CPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER KD, LDA, LDAFAC, N
17 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL RWORK( * )
21 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CPBT01 reconstructs a Hermitian positive definite band matrix A from
31 *> its L*L' or U'*U factorization and computes the residual
32 *> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
33 *> norm( U'*U - A ) / ( N * norm(A) * EPS ),
34 *> where EPS is the machine epsilon, L' is the conjugate transpose of
35 *> L, and U' is the conjugate transpose of U.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] UPLO
42 *> \verbatim
43 *> UPLO is CHARACTER*1
44 *> Specifies whether the upper or lower triangular part of the
45 *> Hermitian matrix A is stored:
46 *> = 'U': Upper triangular
47 *> = 'L': Lower triangular
48 *> \endverbatim
49 *>
50 *> \param[in] N
51 *> \verbatim
52 *> N is INTEGER
53 *> The number of rows and columns of the matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] KD
57 *> \verbatim
58 *> KD is INTEGER
59 *> The number of super-diagonals of the matrix A if UPLO = 'U',
60 *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] A
64 *> \verbatim
65 *> A is COMPLEX array, dimension (LDA,N)
66 *> The original Hermitian band matrix A. If UPLO = 'U', the
67 *> upper triangular part of A is stored as a band matrix; if
68 *> UPLO = 'L', the lower triangular part of A is stored. The
69 *> columns of the appropriate triangle are stored in the columns
70 *> of A and the diagonals of the triangle are stored in the rows
71 *> of A. See CPBTRF for further details.
72 *> \endverbatim
73 *>
74 *> \param[in] LDA
75 *> \verbatim
76 *> LDA is INTEGER.
77 *> The leading dimension of the array A. LDA >= max(1,KD+1).
78 *> \endverbatim
79 *>
80 *> \param[in] AFAC
81 *> \verbatim
82 *> AFAC is COMPLEX array, dimension (LDAFAC,N)
83 *> The factored form of the matrix A. AFAC contains the factor
84 *> L or U from the L*L' or U'*U factorization in band storage
85 *> format, as computed by CPBTRF.
86 *> \endverbatim
87 *>
88 *> \param[in] LDAFAC
89 *> \verbatim
90 *> LDAFAC is INTEGER
91 *> The leading dimension of the array AFAC.
92 *> LDAFAC >= max(1,KD+1).
93 *> \endverbatim
94 *>
95 *> \param[out] RWORK
96 *> \verbatim
97 *> RWORK is REAL array, dimension (N)
98 *> \endverbatim
99 *>
100 *> \param[out] RESID
101 *> \verbatim
102 *> RESID is REAL
103 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
104 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
105 *> \endverbatim
106 *
107 * Authors:
108 * ========
109 *
110 *> \author Univ. of Tennessee
111 *> \author Univ. of California Berkeley
112 *> \author Univ. of Colorado Denver
113 *> \author NAG Ltd.
114 *
115 *> \ingroup complex_lin
116 *
117 * =====================================================================
118  SUBROUTINE cpbt01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
119  $ RESID )
120 *
121 * -- LAPACK test routine --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 *
125 * .. Scalar Arguments ..
126  CHARACTER UPLO
127  INTEGER KD, LDA, LDAFAC, N
128  REAL RESID
129 * ..
130 * .. Array Arguments ..
131  REAL RWORK( * )
132  COMPLEX A( LDA, * ), AFAC( LDAFAC, * )
133 * ..
134 *
135 * =====================================================================
136 *
137 *
138 * .. Parameters ..
139  REAL ZERO, ONE
140  parameter( zero = 0.0e+0, one = 1.0e+0 )
141 * ..
142 * .. Local Scalars ..
143  INTEGER I, J, K, KC, KLEN, ML, MU
144  REAL AKK, ANORM, EPS
145 * ..
146 * .. External Functions ..
147  LOGICAL LSAME
148  REAL CLANHB, SLAMCH
149  COMPLEX CDOTC
150  EXTERNAL lsame, clanhb, slamch, cdotc
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL cher, csscal, ctrmv
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC aimag, max, min, real
157 * ..
158 * .. Executable Statements ..
159 *
160 * Quick exit if N = 0.
161 *
162  IF( n.LE.0 ) THEN
163  resid = zero
164  RETURN
165  END IF
166 *
167 * Exit with RESID = 1/EPS if ANORM = 0.
168 *
169  eps = slamch( 'Epsilon' )
170  anorm = clanhb( '1', uplo, n, kd, a, lda, rwork )
171  IF( anorm.LE.zero ) THEN
172  resid = one / eps
173  RETURN
174  END IF
175 *
176 * Check the imaginary parts of the diagonal elements and return with
177 * an error code if any are nonzero.
178 *
179  IF( lsame( uplo, 'U' ) ) THEN
180  DO 10 j = 1, n
181  IF( aimag( afac( kd+1, j ) ).NE.zero ) THEN
182  resid = one / eps
183  RETURN
184  END IF
185  10 CONTINUE
186  ELSE
187  DO 20 j = 1, n
188  IF( aimag( afac( 1, j ) ).NE.zero ) THEN
189  resid = one / eps
190  RETURN
191  END IF
192  20 CONTINUE
193  END IF
194 *
195 * Compute the product U'*U, overwriting U.
196 *
197  IF( lsame( uplo, 'U' ) ) THEN
198  DO 30 k = n, 1, -1
199  kc = max( 1, kd+2-k )
200  klen = kd + 1 - kc
201 *
202 * Compute the (K,K) element of the result.
203 *
204  akk = cdotc( klen+1, afac( kc, k ), 1, afac( kc, k ), 1 )
205  afac( kd+1, k ) = akk
206 *
207 * Compute the rest of column K.
208 *
209  IF( klen.GT.0 )
210  $ CALL ctrmv( 'Upper', 'Conjugate', 'Non-unit', klen,
211  $ afac( kd+1, k-klen ), ldafac-1,
212  $ afac( kc, k ), 1 )
213 *
214  30 CONTINUE
215 *
216 * UPLO = 'L': Compute the product L*L', overwriting L.
217 *
218  ELSE
219  DO 40 k = n, 1, -1
220  klen = min( kd, n-k )
221 *
222 * Add a multiple of column K of the factor L to each of
223 * columns K+1 through N.
224 *
225  IF( klen.GT.0 )
226  $ CALL cher( 'Lower', klen, one, afac( 2, k ), 1,
227  $ afac( 1, k+1 ), ldafac-1 )
228 *
229 * Scale column K by the diagonal element.
230 *
231  akk = afac( 1, k )
232  CALL csscal( klen+1, akk, afac( 1, k ), 1 )
233 *
234  40 CONTINUE
235  END IF
236 *
237 * Compute the difference L*L' - A or U'*U - A.
238 *
239  IF( lsame( uplo, 'U' ) ) THEN
240  DO 60 j = 1, n
241  mu = max( 1, kd+2-j )
242  DO 50 i = mu, kd + 1
243  afac( i, j ) = afac( i, j ) - a( i, j )
244  50 CONTINUE
245  60 CONTINUE
246  ELSE
247  DO 80 j = 1, n
248  ml = min( kd+1, n-j+1 )
249  DO 70 i = 1, ml
250  afac( i, j ) = afac( i, j ) - a( i, j )
251  70 CONTINUE
252  80 CONTINUE
253  END IF
254 *
255 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
256 *
257  resid = clanhb( '1', uplo, n, kd, afac, ldafac, rwork )
258 *
259  resid = ( ( resid / real( n ) ) / anorm ) / eps
260 *
261  RETURN
262 *
263 * End of CPBT01
264 *
265  END
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.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 cpbt01(UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
CPBT01
Definition: cpbt01.f:120