LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zpot02()

 subroutine zpot02 ( 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 )

ZPOT02

Purpose:
``` ZPOT02 computes the residual for the solution of a Hermitian 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 Hermitian 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 Hermitian 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 ).```
Date
December 2016

Definition at line 129 of file zpot02.f.

129 *
130 * -- LAPACK test routine (version 3.7.0) --
131 * -- LAPACK is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * December 2016
134 *
135 * .. Scalar Arguments ..
136  CHARACTER uplo
137  INTEGER lda, ldb, ldx, n, nrhs
138  DOUBLE PRECISION resid
139 * ..
140 * .. Array Arguments ..
141  DOUBLE PRECISION rwork( * )
142  COMPLEX*16 a( lda, * ), b( ldb, * ), x( ldx, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION zero, one
149  parameter( zero = 0.0d+0, one = 1.0d+0 )
150  COMPLEX*16 cone
151  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
152 * ..
153 * .. Local Scalars ..
154  INTEGER j
155  DOUBLE PRECISION anorm, bnorm, eps, xnorm
156 * ..
157 * .. External Functions ..
158  DOUBLE PRECISION dlamch, dzasum, zlanhe
159  EXTERNAL dlamch, dzasum, zlanhe
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zhemm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0 or NRHS = 0.
170 *
171  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
172  resid = zero
173  RETURN
174  END IF
175 *
176 * Exit with RESID = 1/EPS if ANORM = 0.
177 *
178  eps = dlamch( 'Epsilon' )
179  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
180  IF( anorm.LE.zero ) THEN
181  resid = one / eps
182  RETURN
183  END IF
184 *
185 * Compute B - A*X
186 *
187  CALL zhemm( 'Left', uplo, n, nrhs, -cone, a, lda, x, ldx, cone, b,
188  \$ ldb )
189 *
190 * Compute the maximum over the number of right hand sides of
191 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
192 *
193  resid = zero
194  DO 10 j = 1, nrhs
195  bnorm = dzasum( n, b( 1, j ), 1 )
196  xnorm = dzasum( n, x( 1, j ), 1 )
197  IF( xnorm.LE.zero ) THEN
198  resid = one / eps
199  ELSE
200  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
201  END IF
202  10 CONTINUE
203 *
204  RETURN
205 *
206 * End of ZPOT02
207 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: zlanhe.f:126
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
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