LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dpot06 ( character UPLO, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

DPOT06

Purpose:
``` DPOT06 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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
November 2011

Definition at line 129 of file dpot06.f.

129 *
130 * -- LAPACK test routine (version 3.4.0) --
131 * -- LAPACK is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * November 2011
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 a( lda, * ), b( ldb, * ), rwork( * ),
142  \$ x( ldx, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION zero, one, negone
149  parameter ( zero = 0.0d+0, one = 1.0d+0 )
150  parameter ( negone = -1.0d+0 )
151 * ..
152 * .. Local Scalars ..
153  INTEGER ifail, j
154  DOUBLE PRECISION anorm, bnorm, eps, xnorm
155 * ..
156 * .. External Functions ..
157  INTEGER idamax
158  DOUBLE PRECISION dlamch, dlansy
159  EXTERNAL idamax, dlamch, dlansy
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL dsymm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max, abs
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0 or NRHS = 0
170 *
171  IF( n.LE.0 .OR. nrhs.EQ.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 = dlansy( 'I', 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 and store in B.
186  ifail=0
187 *
188  CALL dsymm( 'Left', uplo, n, nrhs, negone, a, lda, x,
189  \$ ldx, one, b, ldb )
190 *
191 * Compute the maximum over the number of right hand sides of
192 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
193 *
194  resid = zero
195  DO 10 j = 1, nrhs
196  bnorm = abs(b(idamax( n, b( 1, j ), 1 ),j))
197  xnorm = abs(x(idamax( n, x( 1, j ), 1 ),j))
198  IF( xnorm.LE.zero ) THEN
199  resid = one / eps
200  ELSE
201  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
202  END IF
203  10 CONTINUE
204 *
205  RETURN
206 *
207 * End of DPOT06
208 *
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:191

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