 LAPACK  3.10.1 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 ).```

Definition at line 125 of file dpot02.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 A( LDA, * ), B( LDB, * ), RWORK( * ),
139  \$ X( LDX, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION ZERO, ONE
146  parameter( zero = 0.0d+0, one = 1.0d+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER J
150  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
151 * ..
152 * .. External Functions ..
153  DOUBLE PRECISION DASUM, DLAMCH, DLANSY
154  EXTERNAL dasum, dlamch, dlansy
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL dsymm
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC max
161 * ..
162 * .. Executable Statements ..
163 *
164 * Quick exit if N = 0 or NRHS = 0.
165 *
166  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
167  resid = zero
168  RETURN
169  END IF
170 *
171 * Exit with RESID = 1/EPS if ANORM = 0.
172 *
173  eps = dlamch( 'Epsilon' )
174  anorm = dlansy( '1', uplo, n, a, lda, rwork )
175  IF( anorm.LE.zero ) THEN
176  resid = one / eps
177  RETURN
178  END IF
179 *
180 * Compute B - A*X
181 *
182  CALL dsymm( 'Left', uplo, n, nrhs, -one, a, lda, x, ldx, one, b,
183  \$ ldb )
184 *
185 * Compute the maximum over the number of right hand sides of
186 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
187 *
188  resid = zero
189  DO 10 j = 1, nrhs
190  bnorm = dasum( n, b( 1, j ), 1 )
191  xnorm = dasum( n, x( 1, j ), 1 )
192  IF( xnorm.LE.zero ) THEN
193  resid = one / eps
194  ELSE
195  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
196  END IF
197  10 CONTINUE
198 *
199  RETURN
200 *
201 * End of DPOT02
202 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:189
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,...
Definition: dlansy.f:122
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