 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sppt02()

 subroutine sppt02 ( character UPLO, integer N, integer NRHS, real, dimension( * ) A, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID )

SPPT02

Purpose:
``` SPPT02 computes the residual in the solution of a symmetric system
of linear equations  A*x = b  when packed storage is used for the
coefficient matrix.  The ratio computed is

RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),

where EPS is the machine precision.```
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 (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.``` [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 120 of file sppt02.f.

122 *
123 * -- LAPACK test routine --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 *
127 * .. Scalar Arguments ..
128  CHARACTER UPLO
129  INTEGER LDB, LDX, N, NRHS
130  REAL RESID
131 * ..
132 * .. Array Arguments ..
133  REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  REAL ZERO, ONE
140  parameter( zero = 0.0e+0, one = 1.0e+0 )
141 * ..
142 * .. Local Scalars ..
143  INTEGER J
144  REAL ANORM, BNORM, EPS, XNORM
145 * ..
146 * .. External Functions ..
147  REAL SASUM, SLAMCH, SLANSP
148  EXTERNAL sasum, slamch, slansp
149 * ..
150 * .. External Subroutines ..
151  EXTERNAL sspmv
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC max
155 * ..
156 * .. Executable Statements ..
157 *
158 * Quick exit if N = 0 or NRHS = 0.
159 *
160  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
161  resid = zero
162  RETURN
163  END IF
164 *
165 * Exit with RESID = 1/EPS if ANORM = 0.
166 *
167  eps = slamch( 'Epsilon' )
168  anorm = slansp( '1', uplo, n, a, rwork )
169  IF( anorm.LE.zero ) THEN
170  resid = one / eps
171  RETURN
172  END IF
173 *
174 * Compute B - A*X for the matrix of right hand sides B.
175 *
176  DO 10 j = 1, nrhs
177  CALL sspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
178  10 CONTINUE
179 *
180 * Compute the maximum over the number of right hand sides of
181 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
182 *
183  resid = zero
184  DO 20 j = 1, nrhs
185  bnorm = sasum( n, b( 1, j ), 1 )
186  xnorm = sasum( n, x( 1, j ), 1 )
187  IF( xnorm.LE.zero ) THEN
188  resid = one / eps
189  ELSE
190  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
191  END IF
192  20 CONTINUE
193 *
194  RETURN
195 *
196 * End of SPPT02
197 *
real function slansp(NORM, UPLO, N, AP, WORK)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansp.f:114
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
Definition: sspmv.f:147
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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