LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sppt02.f
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1*> \brief \b SPPT02
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 SPPT02( 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 A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> SPPT02 computes the residual in the solution of a symmetric system
30*> of linear equations A*x = b when packed storage is used for the
31*> coefficient matrix. The ratio computed is
32*>
33*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
34*>
35*> where EPS is the machine precision.
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*> symmetric 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] NRHS
57*> \verbatim
58*> NRHS is INTEGER
59*> The number of columns of B, the matrix of right hand sides.
60*> NRHS >= 0.
61*> \endverbatim
62*>
63*> \param[in] A
64*> \verbatim
65*> A is REAL array, dimension (N*(N+1)/2)
66*> The original symmetric matrix A, stored as a packed
67*> triangular matrix.
68*> \endverbatim
69*>
70*> \param[in] X
71*> \verbatim
72*> X is REAL array, dimension (LDX,NRHS)
73*> The computed solution vectors for the system of linear
74*> equations.
75*> \endverbatim
76*>
77*> \param[in] LDX
78*> \verbatim
79*> LDX is INTEGER
80*> The leading dimension of the array X. LDX >= max(1,N).
81*> \endverbatim
82*>
83*> \param[in,out] B
84*> \verbatim
85*> B is REAL array, dimension (LDB,NRHS)
86*> On entry, the right hand side vectors for the system of
87*> linear equations.
88*> On exit, B is overwritten with the difference B - A*X.
89*> \endverbatim
90*>
91*> \param[in] LDB
92*> \verbatim
93*> LDB is INTEGER
94*> The leading dimension of the array B. LDB >= max(1,N).
95*> \endverbatim
96*>
97*> \param[out] RWORK
98*> \verbatim
99*> RWORK is REAL array, dimension (N)
100*> \endverbatim
101*>
102*> \param[out] RESID
103*> \verbatim
104*> RESID is REAL
105*> The maximum over the number of right hand sides of
106*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
107*> \endverbatim
108*
109* Authors:
110* ========
111*
112*> \author Univ. of Tennessee
113*> \author Univ. of California Berkeley
114*> \author Univ. of Colorado Denver
115*> \author NAG Ltd.
116*
117*> \ingroup single_lin
118*
119* =====================================================================
120 SUBROUTINE sppt02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
121 \$ RESID )
122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER UPLO
129 INTEGER LDB, LDX, N, NRHS
130 REAL RESID
131* ..
132* .. Array Arguments ..
133 REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
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 J
144 REAL ANORM, BNORM, EPS, XNORM
145* ..
146* .. External Functions ..
147 REAL SASUM, SLAMCH, SLANSP
148 EXTERNAL sasum, slamch, slansp
149* ..
150* .. External Subroutines ..
151 EXTERNAL sspmv
152* ..
153* .. Intrinsic Functions ..
154 INTRINSIC max
155* ..
156* .. Executable Statements ..
157*
158* Quick exit if N = 0 or NRHS = 0.
159*
160 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
161 resid = zero
162 RETURN
163 END IF
164*
165* Exit with RESID = 1/EPS if ANORM = 0.
166*
167 eps = slamch( 'Epsilon' )
168 anorm = slansp( '1', uplo, n, a, rwork )
169 IF( anorm.LE.zero ) THEN
170 resid = one / eps
171 RETURN
172 END IF
173*
174* Compute B - A*X for the matrix of right hand sides B.
175*
176 DO 10 j = 1, nrhs
177 CALL sspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
178 10 CONTINUE
179*
180* Compute the maximum over the number of right hand sides of
181* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
182*
183 resid = zero
184 DO 20 j = 1, nrhs
185 bnorm = sasum( n, b( 1, j ), 1 )
186 xnorm = sasum( n, x( 1, j ), 1 )
187 IF( xnorm.LE.zero ) THEN
188 resid = one / eps
189 ELSE
190 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
191 END IF
192 20 CONTINUE
193*
194 RETURN
195*
196* End of SPPT02
197*
198 END
subroutine sspmv(uplo, n, alpha, ap, x, incx, beta, y, incy)
SSPMV
Definition sspmv.f:147
subroutine sppt02(uplo, n, nrhs, a, x, ldx, b, ldb, rwork, resid)
SPPT02
Definition sppt02.f:122