LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zpot06()

 subroutine zpot06 ( 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 )

ZPOT06

Purpose:
``` ZPOT06 computes the residual for a solution of a system of linear
equations  A*x = b :
RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * 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 M x N 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. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', 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. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', 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 zpot06.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, negcone
151  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
152  parameter( negcone = ( -1.0d+0, 0.0d+0 ) )
153 * ..
154 * .. Local Scalars ..
155  INTEGER ifail, j
156  DOUBLE PRECISION anorm, bnorm, eps, xnorm
157  COMPLEX*16 zdum
158 * ..
159 * .. External Functions ..
160  LOGICAL lsame
161  INTEGER izamax
162  DOUBLE PRECISION dlamch, zlansy
163  EXTERNAL lsame, izamax, dlamch, zlansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zhemm
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC abs, dble, dimag, max
170 * ..
171 * .. Statement Functions ..
172  DOUBLE PRECISION cabs1
173 * ..
174 * .. Statement Function definitions ..
175  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
176 * ..
177 * ..
178 * .. Executable Statements ..
179 *
180 * Quick exit if N = 0 or NRHS = 0
181 *
182  IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
183  resid = zero
184  RETURN
185  END IF
186 *
187 * Exit with RESID = 1/EPS if ANORM = 0.
188 *
189  eps = dlamch( 'Epsilon' )
190  anorm = zlansy( 'I', uplo, n, a, lda, rwork )
191  IF( anorm.LE.zero ) THEN
192  resid = one / eps
193  RETURN
194  END IF
195 *
196 * Compute B - A*X and store in B.
197  ifail=0
198 *
199  CALL zhemm( 'Left', uplo, n, nrhs, negcone, a, lda, x,
200  \$ ldx, cone, b, ldb )
201 *
202 * Compute the maximum over the number of right hand sides of
203 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
204 *
205  resid = zero
206  DO 10 j = 1, nrhs
207  bnorm = cabs1(b(izamax( n, b( 1, j ), 1 ),j))
208  xnorm = cabs1(x(izamax( n, x( 1, j ), 1 ),j))
209  IF( xnorm.LE.zero ) THEN
210  resid = one / eps
211  ELSE
212  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
213  END IF
214  10 CONTINUE
215 *
216  RETURN
217 *
218 * End of ZPOT06
219 *
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: zlansy.f:125
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:73
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