LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
spbt01.f
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1 *> \brief \b SPBT01
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 SPBT01( 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 A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SPBT01 reconstructs a symmetric positive definite band 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
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 *> symmetric 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] KD
56 *> \verbatim
57 *> KD is INTEGER
58 *> The number of super-diagonals of the matrix A if UPLO = 'U',
59 *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is REAL array, dimension (LDA,N)
65 *> The original symmetric band matrix A. If UPLO = 'U', the
66 *> upper triangular part of A is stored as a band matrix; if
67 *> UPLO = 'L', the lower triangular part of A is stored. The
68 *> columns of the appropriate triangle are stored in the columns
69 *> of A and the diagonals of the triangle are stored in the rows
70 *> of A. See SPBTRF for further details.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER.
76 *> The leading dimension of the array A. LDA >= max(1,KD+1).
77 *> \endverbatim
78 *>
79 *> \param[in] AFAC
80 *> \verbatim
81 *> AFAC is REAL array, dimension (LDAFAC,N)
82 *> The factored form of the matrix A. AFAC contains the factor
83 *> L or U from the L*L' or U'*U factorization in band storage
84 *> format, as computed by SPBTRF.
85 *> \endverbatim
86 *>
87 *> \param[in] LDAFAC
88 *> \verbatim
89 *> LDAFAC is INTEGER
90 *> The leading dimension of the array AFAC.
91 *> LDAFAC >= max(1,KD+1).
92 *> \endverbatim
93 *>
94 *> \param[out] RWORK
95 *> \verbatim
96 *> RWORK is REAL array, dimension (N)
97 *> \endverbatim
98 *>
99 *> \param[out] RESID
100 *> \verbatim
101 *> RESID is REAL
102 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
103 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
104 *> \endverbatim
105 *
106 * Authors:
107 * ========
108 *
109 *> \author Univ. of Tennessee
110 *> \author Univ. of California Berkeley
111 *> \author Univ. of Colorado Denver
112 *> \author NAG Ltd.
113 *
114 *> \ingroup single_lin
115 *
116 * =====================================================================
117  SUBROUTINE spbt01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
118  $ RESID )
119 *
120 * -- LAPACK test routine --
121 * -- LAPACK is a software package provided by Univ. of Tennessee, --
122 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123 *
124 * .. Scalar Arguments ..
125  CHARACTER UPLO
126  INTEGER KD, LDA, LDAFAC, N
127  REAL RESID
128 * ..
129 * .. Array Arguments ..
130  REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 *
136 * .. Parameters ..
137  REAL ZERO, ONE
138  parameter( zero = 0.0e+0, one = 1.0e+0 )
139 * ..
140 * .. Local Scalars ..
141  INTEGER I, J, K, KC, KLEN, ML, MU
142  REAL ANORM, EPS, T
143 * ..
144 * .. External Functions ..
145  LOGICAL LSAME
146  REAL SDOT, SLAMCH, SLANSB
147  EXTERNAL lsame, sdot, slamch, slansb
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL sscal, ssyr, strmv
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC max, min, real
154 * ..
155 * .. Executable Statements ..
156 *
157 * Quick exit if N = 0.
158 *
159  IF( n.LE.0 ) THEN
160  resid = zero
161  RETURN
162  END IF
163 *
164 * Exit with RESID = 1/EPS if ANORM = 0.
165 *
166  eps = slamch( 'Epsilon' )
167  anorm = slansb( '1', uplo, n, kd, a, lda, rwork )
168  IF( anorm.LE.zero ) THEN
169  resid = one / eps
170  RETURN
171  END IF
172 *
173 * Compute the product U'*U, overwriting U.
174 *
175  IF( lsame( uplo, 'U' ) ) THEN
176  DO 10 k = n, 1, -1
177  kc = max( 1, kd+2-k )
178  klen = kd + 1 - kc
179 *
180 * Compute the (K,K) element of the result.
181 *
182  t = sdot( klen+1, afac( kc, k ), 1, afac( kc, k ), 1 )
183  afac( kd+1, k ) = t
184 *
185 * Compute the rest of column K.
186 *
187  IF( klen.GT.0 )
188  $ CALL strmv( 'Upper', 'Transpose', 'Non-unit', klen,
189  $ afac( kd+1, k-klen ), ldafac-1,
190  $ afac( kc, k ), 1 )
191 *
192  10 CONTINUE
193 *
194 * UPLO = 'L': Compute the product L*L', overwriting L.
195 *
196  ELSE
197  DO 20 k = n, 1, -1
198  klen = min( kd, n-k )
199 *
200 * Add a multiple of column K of the factor L to each of
201 * columns K+1 through N.
202 *
203  IF( klen.GT.0 )
204  $ CALL ssyr( 'Lower', klen, one, afac( 2, k ), 1,
205  $ afac( 1, k+1 ), ldafac-1 )
206 *
207 * Scale column K by the diagonal element.
208 *
209  t = afac( 1, k )
210  CALL sscal( klen+1, t, afac( 1, k ), 1 )
211 *
212  20 CONTINUE
213  END IF
214 *
215 * Compute the difference L*L' - A or U'*U - A.
216 *
217  IF( lsame( uplo, 'U' ) ) THEN
218  DO 40 j = 1, n
219  mu = max( 1, kd+2-j )
220  DO 30 i = mu, kd + 1
221  afac( i, j ) = afac( i, j ) - a( i, j )
222  30 CONTINUE
223  40 CONTINUE
224  ELSE
225  DO 60 j = 1, n
226  ml = min( kd+1, n-j+1 )
227  DO 50 i = 1, ml
228  afac( i, j ) = afac( i, j ) - a( i, j )
229  50 CONTINUE
230  60 CONTINUE
231  END IF
232 *
233 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
234 *
235  resid = slansb( 'I', uplo, n, kd, afac, ldafac, rwork )
236 *
237  resid = ( ( resid / real( n ) ) / anorm ) / eps
238 *
239  RETURN
240 *
241 * End of SPBT01
242 *
243  END
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
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
subroutine spbt01(UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
SPBT01
Definition: spbt01.f:119