LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zsyt02.f
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1*> \brief \b ZSYT02
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 ZSYT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
12* RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER UPLO
16* INTEGER LDA, LDB, LDX, N, NRHS
17* DOUBLE PRECISION RESID
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION RWORK( * )
21* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> ZSYT02 computes the residual for a solution to a complex symmetric
31*> system of linear equations A*x = b:
32*>
33*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
34*>
35*> where EPS is the machine epsilon.
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 COMPLEX*16 array, dimension (LDA,N)
66*> The original complex symmetric matrix A.
67*> \endverbatim
68*>
69*> \param[in] LDA
70*> \verbatim
71*> LDA is INTEGER
72*> The leading dimension of the array A. LDA >= max(1,N)
73*> \endverbatim
74*>
75*> \param[in] X
76*> \verbatim
77*> X is COMPLEX*16 array, dimension (LDX,NRHS)
78*> The computed solution vectors for the system of linear
79*> equations.
80*> \endverbatim
81*>
82*> \param[in] LDX
83*> \verbatim
84*> LDX is INTEGER
85*> The leading dimension of the array X. LDX >= max(1,N).
86*> \endverbatim
87*>
88*> \param[in,out] B
89*> \verbatim
90*> B is COMPLEX*16 array, dimension (LDB,NRHS)
91*> On entry, the right hand side vectors for the system of
92*> linear equations.
93*> On exit, B is overwritten with the difference B - A*X.
94*> \endverbatim
95*>
96*> \param[in] LDB
97*> \verbatim
98*> LDB is INTEGER
99*> The leading dimension of the array B. LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] RWORK
103*> \verbatim
104*> RWORK is DOUBLE PRECISION array, dimension (N)
105*> \endverbatim
106*>
107*> \param[out] RESID
108*> \verbatim
109*> RESID is DOUBLE PRECISION
110*> The maximum over the number of right hand sides of
111*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
112*> \endverbatim
113*
114* Authors:
115* ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \ingroup complex16_lin
123*
124* =====================================================================
125 SUBROUTINE zsyt02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
126 \$ RESID )
127*
128* -- LAPACK test routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 CHARACTER UPLO
134 INTEGER LDA, LDB, LDX, N, NRHS
135 DOUBLE PRECISION RESID
136* ..
137* .. Array Arguments ..
138 DOUBLE PRECISION RWORK( * )
139 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE
146 parameter( zero = 0.0d+0, one = 1.0d+0 )
147 COMPLEX*16 CONE
148 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
149* ..
150* .. Local Scalars ..
151 INTEGER J
152 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
153* ..
154* .. External Functions ..
155 DOUBLE PRECISION DLAMCH, DZASUM, ZLANSY
156 EXTERNAL dlamch, dzasum, zlansy
157* ..
158* .. External Subroutines ..
159 EXTERNAL zsymm
160* ..
161* .. Intrinsic Functions ..
162 INTRINSIC max
163* ..
164* .. Executable Statements ..
165*
166* Quick exit if N = 0 or NRHS = 0
167*
168 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
169 resid = zero
170 RETURN
171 END IF
172*
173* Exit with RESID = 1/EPS if ANORM = 0.
174*
175 eps = dlamch( 'Epsilon' )
176 anorm = zlansy( '1', uplo, n, a, lda, rwork )
177 IF( anorm.LE.zero ) THEN
178 resid = one / eps
179 RETURN
180 END IF
181*
182* Compute B - A*X (or B - A'*X ) and store in B .
183*
184 CALL zsymm( 'Left', uplo, n, nrhs, -cone, a, lda, x, ldx, cone, b,
185 \$ ldb )
186*
187* Compute the maximum over the number of right hand sides of
188* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
189*
190 resid = zero
191 DO 10 j = 1, nrhs
192 bnorm = dzasum( n, b( 1, j ), 1 )
193 xnorm = dzasum( n, x( 1, j ), 1 )
194 IF( xnorm.LE.zero ) THEN
195 resid = one / eps
196 ELSE
197 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
198 END IF
199 10 CONTINUE
200*
201 RETURN
202*
203* End of ZSYT02
204*
205 END
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:189
subroutine zsyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZSYT02
Definition: zsyt02.f:127