LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
cspt02.f
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1 *> \brief \b CSPT02
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 CSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDB, LDX, N, NRHS
17 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL RWORK( * )
21 * COMPLEX A( * ), B( LDB, * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CSPT02 computes the residual in the solution of a complex symmetric
31 *> system of linear equations A*x = b when packed storage is used for
32 *> the coefficient matrix. The ratio computed is
33 *>
34 *> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
35 *>
36 *> where EPS is the machine precision.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] UPLO
43 *> \verbatim
44 *> UPLO is CHARACTER*1
45 *> Specifies whether the upper or lower triangular part of the
46 *> complex symmetric matrix A is stored:
47 *> = 'U': Upper triangular
48 *> = 'L': Lower triangular
49 *> \endverbatim
50 *>
51 *> \param[in] N
52 *> \verbatim
53 *> N is INTEGER
54 *> The number of rows and columns of the matrix A. N >= 0.
55 *> \endverbatim
56 *>
57 *> \param[in] NRHS
58 *> \verbatim
59 *> NRHS is INTEGER
60 *> The number of columns of B, the matrix of right hand sides.
61 *> NRHS >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] A
65 *> \verbatim
66 *> A is COMPLEX array, dimension (N*(N+1)/2)
67 *> The original complex symmetric matrix A, stored as a packed
68 *> triangular matrix.
69 *> \endverbatim
70 *>
71 *> \param[in] X
72 *> \verbatim
73 *> X is COMPLEX array, dimension (LDX,NRHS)
74 *> The computed solution vectors for the system of linear
75 *> equations.
76 *> \endverbatim
77 *>
78 *> \param[in] LDX
79 *> \verbatim
80 *> LDX is INTEGER
81 *> The leading dimension of the array X. LDX >= max(1,N).
82 *> \endverbatim
83 *>
84 *> \param[in,out] B
85 *> \verbatim
86 *> B is COMPLEX array, dimension (LDB,NRHS)
87 *> On entry, the right hand side vectors for the system of
88 *> linear equations.
89 *> On exit, B is overwritten with the difference B - A*X.
90 *> \endverbatim
91 *>
92 *> \param[in] LDB
93 *> \verbatim
94 *> LDB is INTEGER
95 *> The leading dimension of the array B. LDB >= max(1,N).
96 *> \endverbatim
97 *>
98 *> \param[out] RWORK
99 *> \verbatim
100 *> RWORK is REAL array, dimension (N)
101 *> \endverbatim
102 *>
103 *> \param[out] RESID
104 *> \verbatim
105 *> RESID is REAL
106 *> The maximum over the number of right hand sides of
107 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
108 *> \endverbatim
109 *
110 * Authors:
111 * ========
112 *
113 *> \author Univ. of Tennessee
114 *> \author Univ. of California Berkeley
115 *> \author Univ. of Colorado Denver
116 *> \author NAG Ltd.
117 *
118 *> \date December 2016
119 *
120 *> \ingroup complex_lin
121 *
122 * =====================================================================
123  SUBROUTINE cspt02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
124  \$ RESID )
125 *
126 * -- LAPACK test routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER UPLO
133  INTEGER LDB, LDX, N, NRHS
134  REAL RESID
135 * ..
136 * .. Array Arguments ..
137  REAL RWORK( * )
138  COMPLEX A( * ), B( ldb, * ), X( ldx, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL ZERO, ONE
145  parameter( zero = 0.0e+0, one = 1.0e+0 )
146  COMPLEX CONE
147  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
148 * ..
149 * .. Local Scalars ..
150  INTEGER J
151  REAL ANORM, BNORM, EPS, XNORM
152 * ..
153 * .. External Functions ..
154  REAL CLANSP, SCASUM, SLAMCH
155  EXTERNAL clansp, scasum, slamch
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL cspmv
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC max
162 * ..
163 * .. Executable Statements ..
164 *
165 * Quick exit if N = 0 or NRHS = 0
166 *
167  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
168  resid = zero
169  RETURN
170  END IF
171 *
172 * Exit with RESID = 1/EPS if ANORM = 0.
173 *
174  eps = slamch( 'Epsilon' )
175  anorm = clansp( '1', uplo, n, a, rwork )
176  IF( anorm.LE.zero ) THEN
177  resid = one / eps
178  RETURN
179  END IF
180 *
181 * Compute B - A*X for the matrix of right hand sides B.
182 *
183  DO 10 j = 1, nrhs
184  CALL cspmv( uplo, n, -cone, a, x( 1, j ), 1, cone, b( 1, j ),
185  \$ 1 )
186  10 CONTINUE
187 *
188 * Compute the maximum over the number of right hand sides of
189 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
190 *
191  resid = zero
192  DO 20 j = 1, nrhs
193  bnorm = scasum( n, b( 1, j ), 1 )
194  xnorm = scasum( n, x( 1, j ), 1 )
195  IF( xnorm.LE.zero ) THEN
196  resid = one / eps
197  ELSE
198  resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
199  END IF
200  20 CONTINUE
201 *
202  RETURN
203 *
204 * End of CSPT02
205 *
206  END
subroutine cspt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CSPT02
Definition: cspt02.f:125
subroutine cspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix ...
Definition: cspmv.f:153