LAPACK  3.10.0
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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 125 of file zpot06.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, NEGCONE
148  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
149  parameter( negcone = ( -1.0d+0, 0.0d+0 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER IFAIL, J
153  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
154  COMPLEX*16 ZDUM
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  INTEGER IZAMAX
159  DOUBLE PRECISION DLAMCH, ZLANSY
160  EXTERNAL lsame, izamax, dlamch, zlansy
161 * ..
162 * .. External Subroutines ..
163  EXTERNAL zhemm
164 * ..
165 * .. Intrinsic Functions ..
166  INTRINSIC abs, dble, dimag, max
167 * ..
168 * .. Statement Functions ..
169  DOUBLE PRECISION CABS1
170 * ..
171 * .. Statement Function definitions ..
172  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
173 * ..
174 * ..
175 * .. Executable Statements ..
176 *
177 * Quick exit if N = 0 or NRHS = 0
178 *
179  IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
180  resid = zero
181  RETURN
182  END IF
183 *
184 * Exit with RESID = 1/EPS if ANORM = 0.
185 *
186  eps = dlamch( 'Epsilon' )
187  anorm = zlansy( 'I', uplo, n, a, lda, rwork )
188  IF( anorm.LE.zero ) THEN
189  resid = one / eps
190  RETURN
191  END IF
192 *
193 * Compute B - A*X and store in B.
194  ifail=0
195 *
196  CALL zhemm( 'Left', uplo, n, nrhs, negcone, a, lda, x,
197  $ ldx, cone, b, ldb )
198 *
199 * Compute the maximum over the number of right hand sides of
200 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
201 *
202  resid = zero
203  DO 10 j = 1, nrhs
204  bnorm = cabs1(b(izamax( n, b( 1, j ), 1 ),j))
205  xnorm = cabs1(x(izamax( n, x( 1, j ), 1 ),j))
206  IF( xnorm.LE.zero ) THEN
207  resid = one / eps
208  ELSE
209  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
210  END IF
211  10 CONTINUE
212 *
213  RETURN
214 *
215 * End of ZPOT06
216 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:191
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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