LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zsyt02()

 subroutine zsyt02 ( character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) rwork, double precision resid )

ZSYT02

Purpose:
``` ZSYT02 computes the residual for a solution to a complex symmetric
system of linear equations  A*x = b:

RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),

where EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The original complex symmetric matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N)``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).```

Definition at line 125 of file zsyt02.f.

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*
double precision function dzasum(n, zx, incx)
DZASUM
Definition dzasum.f:72
subroutine zsymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZSYMM
Definition zsymm.f:189
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlansy(norm, uplo, n, a, lda, work)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlansy.f:123
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