LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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 dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:189
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
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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