LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zspt02 ( 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 )

ZSPT02

Purpose:
``` ZSPT02 computes the residual in the solution of a complex 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 complex 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 COMPLEX*16 array, dimension (N*(N+1)/2) The original complex symmetric 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 ).```
Date
November 2011

Definition at line 125 of file zspt02.f.

125 *
126 * -- LAPACK test routine (version 3.4.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * November 2011
130 *
131 * .. Scalar Arguments ..
132  CHARACTER uplo
133  INTEGER ldb, ldx, n, nrhs
134  DOUBLE PRECISION resid
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION rwork( * )
138  COMPLEX*16 a( * ), b( ldb, * ), x( ldx, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION zero, one
145  parameter ( zero = 0.0d+0, one = 1.0d+0 )
146  COMPLEX*16 cone
147  parameter ( cone = ( 1.0d+0, 0.0d+0 ) )
148 * ..
149 * .. Local Scalars ..
150  INTEGER j
151  DOUBLE PRECISION anorm, bnorm, eps, xnorm
152 * ..
153 * .. External Functions ..
154  DOUBLE PRECISION dlamch, dzasum, zlansp
155  EXTERNAL dlamch, dzasum, zlansp
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL zspmv
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 = dlamch( 'Epsilon' )
175  anorm = zlansp( '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 zspmv( 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 = dzasum( n, b( 1, j ), 1 )
194  xnorm = dzasum( 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 ZSPT02
205 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix ...
Definition: zspmv.f:153
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:54
double precision function zlansp(NORM, UPLO, N, AP, WORK)
ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Definition: zlansp.f:117

Here is the call graph for this function:

Here is the caller graph for this function: