 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dpot02()

 subroutine dpot02 ( 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 )

DPOT02

Purpose:
``` DPOT02 computes the residual for the solution of a 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 DOUBLE PRECISION array, dimension (LDA,N) The original symmetric 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. 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. 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 dpot02.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 a( lda, * ), b( ldb, * ), rwork( * ),
142  \$ x( ldx, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION zero, one
149  parameter( zero = 0.0d+0, one = 1.0d+0 )
150 * ..
151 * .. Local Scalars ..
152  INTEGER j
153  DOUBLE PRECISION anorm, bnorm, eps, xnorm
154 * ..
155 * .. External Functions ..
156  DOUBLE PRECISION dasum, dlamch, dlansy
157  EXTERNAL dasum, dlamch, dlansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL dsymm
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC max
164 * ..
165 * .. Executable Statements ..
166 *
167 * Quick exit if N = 0 or NRHS = 0.
168 *
169  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
170  resid = zero
171  RETURN
172  END IF
173 *
174 * Exit with RESID = 1/EPS if ANORM = 0.
175 *
176  eps = dlamch( 'Epsilon' )
177  anorm = dlansy( '1', uplo, n, a, lda, rwork )
178  IF( anorm.LE.zero ) THEN
179  resid = one / eps
180  RETURN
181  END IF
182 *
183 * Compute B - A*X
184 *
185  CALL dsymm( 'Left', uplo, n, nrhs, -one, a, lda, x, ldx, one, b,
186  \$ ldb )
187 *
188 * Compute the maximum over the number of right hand sides of
189 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
190 *
191  resid = zero
192  DO 10 j = 1, nrhs
193  bnorm = dasum( n, b( 1, j ), 1 )
194  xnorm = dasum( n, x( 1, j ), 1 )
195  IF( xnorm.LE.zero ) THEN
196  resid = one / eps
197  ELSE
198  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
199  END IF
200  10 CONTINUE
201 *
202  RETURN
203 *
204 * End of DPOT02
205 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:191
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
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