LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
sppt03.f
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1 *> \brief \b SPPT03
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 SPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDWORK, N
17 * REAL RCOND, RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL A( * ), AINV( * ), RWORK( * ),
21 * \$ WORK( LDWORK, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> SPPT03 computes the residual for a symmetric packed matrix times its
31 *> inverse:
32 *> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
33 *> where EPS is the machine epsilon.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] UPLO
40 *> \verbatim
41 *> UPLO is CHARACTER*1
42 *> Specifies whether the upper or lower triangular part of the
43 *> symmetric matrix A is stored:
44 *> = 'U': Upper triangular
45 *> = 'L': Lower triangular
46 *> \endverbatim
47 *>
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGER
51 *> The number of rows and columns of the matrix A. N >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] A
55 *> \verbatim
56 *> A is REAL array, dimension (N*(N+1)/2)
57 *> The original symmetric matrix A, stored as a packed
58 *> triangular matrix.
59 *> \endverbatim
60 *>
61 *> \param[in] AINV
62 *> \verbatim
63 *> AINV is REAL array, dimension (N*(N+1)/2)
64 *> The (symmetric) inverse of the matrix A, stored as a packed
65 *> triangular matrix.
66 *> \endverbatim
67 *>
68 *> \param[out] WORK
69 *> \verbatim
70 *> WORK is REAL array, dimension (LDWORK,N)
71 *> \endverbatim
72 *>
73 *> \param[in] LDWORK
74 *> \verbatim
75 *> LDWORK is INTEGER
76 *> The leading dimension of the array WORK. LDWORK >= max(1,N).
77 *> \endverbatim
78 *>
79 *> \param[out] RWORK
80 *> \verbatim
81 *> RWORK is REAL array, dimension (N)
82 *> \endverbatim
83 *>
84 *> \param[out] RCOND
85 *> \verbatim
86 *> RCOND is REAL
87 *> The reciprocal of the condition number of A, computed as
88 *> ( 1/norm(A) ) / norm(AINV).
89 *> \endverbatim
90 *>
91 *> \param[out] RESID
92 *> \verbatim
93 *> RESID is REAL
94 *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
95 *> \endverbatim
96 *
97 * Authors:
98 * ========
99 *
100 *> \author Univ. of Tennessee
101 *> \author Univ. of California Berkeley
102 *> \author Univ. of Colorado Denver
103 *> \author NAG Ltd.
104 *
105 *> \date November 2011
106 *
107 *> \ingroup single_lin
108 *
109 * =====================================================================
110  SUBROUTINE sppt03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
111  \$ resid )
112 *
113 * -- LAPACK test routine (version 3.4.0) --
114 * -- LAPACK is a software package provided by Univ. of Tennessee, --
115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116 * November 2011
117 *
118 * .. Scalar Arguments ..
119  CHARACTER uplo
120  INTEGER ldwork, n
121  REAL rcond, resid
122 * ..
123 * .. Array Arguments ..
124  REAL a( * ), ainv( * ), rwork( * ),
125  \$ work( ldwork, * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  REAL zero, one
132  parameter( zero = 0.0e+0, one = 1.0e+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER i, j, jj
136  REAL ainvnm, anorm, eps
137 * ..
138 * .. External Functions ..
139  LOGICAL lsame
140  REAL slamch, slange, slansp
141  EXTERNAL lsame, slamch, slange, slansp
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC real
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL scopy, sspmv
148 * ..
149 * .. Executable Statements ..
150 *
151 * Quick exit if N = 0.
152 *
153  IF( n.LE.0 ) THEN
154  rcond = one
155  resid = zero
156  return
157  END IF
158 *
159 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
160 *
161  eps = slamch( 'Epsilon' )
162  anorm = slansp( '1', uplo, n, a, rwork )
163  ainvnm = slansp( '1', uplo, n, ainv, rwork )
164  IF( anorm.LE.zero .OR. ainvnm.EQ.zero ) THEN
165  rcond = zero
166  resid = one / eps
167  return
168  END IF
169  rcond = ( one / anorm ) / ainvnm
170 *
171 * UPLO = 'U':
172 * Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
173 * expand it to a full matrix, then multiply by A one column at a
174 * time, moving the result one column to the left.
175 *
176  IF( lsame( uplo, 'U' ) ) THEN
177 *
178 * Copy AINV
179 *
180  jj = 1
181  DO 10 j = 1, n - 1
182  CALL scopy( j, ainv( jj ), 1, work( 1, j+1 ), 1 )
183  CALL scopy( j-1, ainv( jj ), 1, work( j, 2 ), ldwork )
184  jj = jj + j
185  10 continue
186  jj = ( ( n-1 )*n ) / 2 + 1
187  CALL scopy( n-1, ainv( jj ), 1, work( n, 2 ), ldwork )
188 *
189 * Multiply by A
190 *
191  DO 20 j = 1, n - 1
192  CALL sspmv( 'Upper', n, -one, a, work( 1, j+1 ), 1, zero,
193  \$ work( 1, j ), 1 )
194  20 continue
195  CALL sspmv( 'Upper', n, -one, a, ainv( jj ), 1, zero,
196  \$ work( 1, n ), 1 )
197 *
198 * UPLO = 'L':
199 * Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
200 * and multiply by A, moving each column to the right.
201 *
202  ELSE
203 *
204 * Copy AINV
205 *
206  CALL scopy( n-1, ainv( 2 ), 1, work( 1, 1 ), ldwork )
207  jj = n + 1
208  DO 30 j = 2, n
209  CALL scopy( n-j+1, ainv( jj ), 1, work( j, j-1 ), 1 )
210  CALL scopy( n-j, ainv( jj+1 ), 1, work( j, j ), ldwork )
211  jj = jj + n - j + 1
212  30 continue
213 *
214 * Multiply by A
215 *
216  DO 40 j = n, 2, -1
217  CALL sspmv( 'Lower', n, -one, a, work( 1, j-1 ), 1, zero,
218  \$ work( 1, j ), 1 )
219  40 continue
220  CALL sspmv( 'Lower', n, -one, a, ainv( 1 ), 1, zero,
221  \$ work( 1, 1 ), 1 )
222 *
223  END IF
224 *
225 * Add the identity matrix to WORK .
226 *
227  DO 50 i = 1, n
228  work( i, i ) = work( i, i ) + one
229  50 continue
230 *
231 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
232 *
233  resid = slange( '1', n, n, work, ldwork, rwork )
234 *
235  resid = ( ( resid*rcond ) / eps ) / REAL( n )
236 *
237  return
238 *
239 * End of SPPT03
240 *
241  END