 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cppt02()

 subroutine cppt02 ( character UPLO, integer N, integer NRHS, complex, dimension( * ) A, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID )

CPPT02

Purpose:
``` CPPT02 computes the residual in the solution of a Hermitian 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 Hermitian 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 COMPLEX array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.``` [in] X ``` X is COMPLEX 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 COMPLEX 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 ).```
Date
December 2016

Definition at line 125 of file cppt02.f.

125 *
126 * -- LAPACK test routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER uplo
133  INTEGER ldb, ldx, n, nrhs
134  REAL resid
135 * ..
136 * .. Array Arguments ..
137  REAL rwork( * )
138  COMPLEX a( * ), b( ldb, * ), x( ldx, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL zero, one
145  parameter( zero = 0.0e+0, one = 1.0e+0 )
146  COMPLEX cone
147  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
148 * ..
149 * .. Local Scalars ..
150  INTEGER j
151  REAL anorm, bnorm, eps, xnorm
152 * ..
153 * .. External Functions ..
154  REAL clanhp, scasum, slamch
155  EXTERNAL clanhp, scasum, slamch
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL chpmv
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC max
162 * ..
163 * .. Executable Statements ..
164 *
165 * Quick exit if N = 0 or NRHS = 0.
166 *
167  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
168  resid = zero
169  RETURN
170  END IF
171 *
172 * Exit with RESID = 1/EPS if ANORM = 0.
173 *
174  eps = slamch( 'Epsilon' )
175  anorm = clanhp( '1', uplo, n, a, rwork )
176  IF( anorm.LE.zero ) THEN
177  resid = one / eps
178  RETURN
179  END IF
180 *
181 * Compute B - A*X for the matrix of right hand sides B.
182 *
183  DO 10 j = 1, nrhs
184  CALL chpmv( uplo, n, -cone, a, x( 1, j ), 1, cone, b( 1, j ),
185  \$ 1 )
186  10 CONTINUE
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 20 j = 1, nrhs
193  bnorm = scasum( n, b( 1, j ), 1 )
194  xnorm = scasum( 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  20 CONTINUE
201 *
202  RETURN
203 *
204 * End of CPPT02
205 *
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:74
subroutine chpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV
Definition: chpmv.f:151
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
real function clanhp(NORM, UPLO, N, AP, WORK)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
Definition: clanhp.f:119
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