LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zget04()

 subroutine zget04 ( integer n, integer nrhs, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision rcond, double precision resid )

ZGET04

Purpose:
``` ZGET04 computes the difference between a computed solution and the
true solution to a system of linear equations.

RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
where RCOND is the reciprocal of the condition number and EPS is the
machine epsilon.```
Parameters
 [in] N ``` N is INTEGER The number of rows of the matrices X and XACT. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of the matrices X and XACT. NRHS >= 0.``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in] XACT ``` XACT is COMPLEX*16 array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.``` [in] LDXACT ``` LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).``` [in] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of the coefficient matrix in the system of equations.``` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the NRHS solution vectors of ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )```

Definition at line 101 of file zget04.f.

102*
103* -- LAPACK test routine --
104* -- LAPACK is a software package provided by Univ. of Tennessee, --
105* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106*
107* .. Scalar Arguments ..
108 INTEGER LDX, LDXACT, N, NRHS
109 DOUBLE PRECISION RCOND, RESID
110* ..
111* .. Array Arguments ..
112 COMPLEX*16 X( LDX, * ), XACT( LDXACT, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 DOUBLE PRECISION ZERO
119 parameter( zero = 0.0d+0 )
120* ..
121* .. Local Scalars ..
122 INTEGER I, IX, J
123 DOUBLE PRECISION DIFFNM, EPS, XNORM
124 COMPLEX*16 ZDUM
125* ..
126* .. External Functions ..
127 INTEGER IZAMAX
128 DOUBLE PRECISION DLAMCH
129 EXTERNAL izamax, dlamch
130* ..
131* .. Intrinsic Functions ..
132 INTRINSIC abs, dble, dimag, max
133* ..
134* .. Statement Functions ..
135 DOUBLE PRECISION CABS1
136* ..
137* .. Statement Function definitions ..
138 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
139* ..
140* .. Executable Statements ..
141*
142* Quick exit if N = 0 or NRHS = 0.
143*
144 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
145 resid = zero
146 RETURN
147 END IF
148*
149* Exit with RESID = 1/EPS if RCOND is invalid.
150*
151 eps = dlamch( 'Epsilon' )
152 IF( rcond.LT.zero ) THEN
153 resid = 1.0d0 / eps
154 RETURN
155 END IF
156*
157* Compute the maximum of
158* norm(X - XACT) / ( norm(XACT) * EPS )
159* over all the vectors X and XACT .
160*
161 resid = zero
162 DO 20 j = 1, nrhs
163 ix = izamax( n, xact( 1, j ), 1 )
164 xnorm = cabs1( xact( ix, j ) )
165 diffnm = zero
166 DO 10 i = 1, n
167 diffnm = max( diffnm, cabs1( x( i, j )-xact( i, j ) ) )
168 10 CONTINUE
169 IF( xnorm.LE.zero ) THEN
170 IF( diffnm.GT.zero )
171 \$ resid = 1.0d0 / eps
172 ELSE
173 resid = max( resid, ( diffnm / xnorm )*rcond )
174 END IF
175 20 CONTINUE
176 IF( resid*eps.LT.1.0d0 )
177 \$ resid = resid / eps
178*
179 RETURN
180*
181* End of ZGET04
182*
integer function izamax(n, zx, incx)
IZAMAX
Definition izamax.f:71
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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