LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ spot02()

 subroutine spot02 ( character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid )

SPOT02

Purpose:
``` SPOT02 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)` [out] RESID ``` RESID is REAL 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 spot02.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 REAL RESID
136* ..
137* .. Array Arguments ..
138 REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
139 \$ X( LDX, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 REAL ZERO, ONE
146 parameter( zero = 0.0e+0, one = 1.0e+0 )
147* ..
148* .. Local Scalars ..
149 INTEGER J
150 REAL ANORM, BNORM, EPS, XNORM
151* ..
152* .. External Functions ..
153 REAL SASUM, SLAMCH, SLANSY
154 EXTERNAL sasum, slamch, slansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL ssymm
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 = slamch( 'Epsilon' )
174 anorm = slansy( '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 ssymm( '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 = sasum( n, b( 1, j ), 1 )
191 xnorm = sasum( 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 SPOT02
202*
real function sasum(n, sx, incx)
SASUM
Definition sasum.f:72
subroutine ssymm(side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
SSYMM
Definition ssymm.f:189
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slansy(norm, uplo, n, a, lda, work)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansy.f:122
Here is the call graph for this function:
Here is the caller graph for this function: