LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cppt02.f
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1 *> \brief \b CPPT02
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 CPPT02( 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 *> CPPT02 computes the residual in the solution of a Hermitian system
31 *> of linear equations A*x = b when packed storage is used for the
32 *> 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 *> Hermitian 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 Hermitian 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 *> \ingroup complex_lin
119 *
120 * =====================================================================
121  SUBROUTINE cppt02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
122  $ RESID )
123 *
124 * -- LAPACK test routine --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 *
128 * .. Scalar Arguments ..
129  CHARACTER UPLO
130  INTEGER LDB, LDX, N, NRHS
131  REAL RESID
132 * ..
133 * .. Array Arguments ..
134  REAL RWORK( * )
135  COMPLEX A( * ), B( LDB, * ), X( LDX, * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL ZERO, ONE
142  parameter( zero = 0.0e+0, one = 1.0e+0 )
143  COMPLEX CONE
144  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  REAL ANORM, BNORM, EPS, XNORM
149 * ..
150 * .. External Functions ..
151  REAL CLANHP, SCASUM, SLAMCH
152  EXTERNAL clanhp, scasum, slamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL chpmv
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if N = 0 or NRHS = 0.
163 *
164  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
165  resid = zero
166  RETURN
167  END IF
168 *
169 * Exit with RESID = 1/EPS if ANORM = 0.
170 *
171  eps = slamch( 'Epsilon' )
172  anorm = clanhp( '1', uplo, n, a, rwork )
173  IF( anorm.LE.zero ) THEN
174  resid = one / eps
175  RETURN
176  END IF
177 *
178 * Compute B - A*X for the matrix of right hand sides B.
179 *
180  DO 10 j = 1, nrhs
181  CALL chpmv( uplo, n, -cone, a, x( 1, j ), 1, cone, b( 1, j ),
182  $ 1 )
183  10 CONTINUE
184 *
185 * Compute the maximum over the number of right hand sides of
186 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
187 *
188  resid = zero
189  DO 20 j = 1, nrhs
190  bnorm = scasum( n, b( 1, j ), 1 )
191  xnorm = scasum( n, x( 1, j ), 1 )
192  IF( xnorm.LE.zero ) THEN
193  resid = one / eps
194  ELSE
195  resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
196  END IF
197  20 CONTINUE
198 *
199  RETURN
200 *
201 * End of CPPT02
202 *
203  END
subroutine chpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV
Definition: chpmv.f:149
subroutine cppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CPPT02
Definition: cppt02.f:123