LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zppt02()

 subroutine zppt02 ( character UPLO, integer N, integer NRHS, complex*16, dimension( * ) A, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

ZPPT02

Purpose:
``` ZPPT02 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*16 array, dimension (N*(N+1)/2) The original Hermitian matrix A, stored as a packed triangular matrix.``` [in] X ``` X is COMPLEX*16 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*16 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 121 of file zppt02.f.

123 *
124 * -- LAPACK test routine --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 *
128 * .. Scalar Arguments ..
129  CHARACTER UPLO
130  INTEGER LDB, LDX, N, NRHS
131  DOUBLE PRECISION RESID
132 * ..
133 * .. Array Arguments ..
134  DOUBLE PRECISION RWORK( * )
135  COMPLEX*16 A( * ), B( LDB, * ), X( LDX, * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  DOUBLE PRECISION ZERO, ONE
142  parameter( zero = 0.0d+0, one = 1.0d+0 )
143  COMPLEX*16 CONE
144  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
149 * ..
150 * .. External Functions ..
151  DOUBLE PRECISION DLAMCH, DZASUM, ZLANHP
152  EXTERNAL dlamch, dzasum, zlanhp
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL zhpmv
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if N = 0 or NRHS = 0.
163 *
164  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
165  resid = zero
166  RETURN
167  END IF
168 *
169 * Exit with RESID = 1/EPS if ANORM = 0.
170 *
171  eps = dlamch( 'Epsilon' )
172  anorm = zlanhp( '1', uplo, n, a, rwork )
173  IF( anorm.LE.zero ) THEN
174  resid = one / eps
175  RETURN
176  END IF
177 *
178 * Compute B - A*X for the matrix of right hand sides B.
179 *
180  DO 10 j = 1, nrhs
181  CALL zhpmv( uplo, n, -cone, a, x( 1, j ), 1, cone, b( 1, j ),
182  \$ 1 )
183  10 CONTINUE
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 20 j = 1, nrhs
190  bnorm = dzasum( n, b( 1, j ), 1 )
191  xnorm = dzasum( 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  20 CONTINUE
198 *
199  RETURN
200 *
201 * End of ZPPT02
202 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zhpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZHPMV
Definition: zhpmv.f:149
double precision function zlanhp(NORM, UPLO, N, AP, WORK)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhp.f:117
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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