 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dget04()

 subroutine dget04 ( integer N, integer NRHS, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact, * ) XACT, integer LDXACT, double precision RCOND, double precision RESID )

DGET04

Purpose:
``` DGET04 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dget04.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 DOUBLE PRECISION 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* ..
125* .. External Functions ..
126 INTEGER IDAMAX
127 DOUBLE PRECISION DLAMCH
128 EXTERNAL idamax, dlamch
129* ..
130* .. Intrinsic Functions ..
131 INTRINSIC abs, max
132* ..
133* .. Executable Statements ..
134*
135* Quick exit if N = 0 or NRHS = 0.
136*
137 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
138 resid = zero
139 RETURN
140 END IF
141*
142* Exit with RESID = 1/EPS if RCOND is invalid.
143*
144 eps = dlamch( 'Epsilon' )
145 IF( rcond.LT.zero ) THEN
146 resid = 1.0d0 / eps
147 RETURN
148 END IF
149*
150* Compute the maximum of
151* norm(X - XACT) / ( norm(XACT) * EPS )
152* over all the vectors X and XACT .
153*
154 resid = zero
155 DO 20 j = 1, nrhs
156 ix = idamax( n, xact( 1, j ), 1 )
157 xnorm = abs( xact( ix, j ) )
158 diffnm = zero
159 DO 10 i = 1, n
160 diffnm = max( diffnm, abs( x( i, j )-xact( i, j ) ) )
161 10 CONTINUE
162 IF( xnorm.LE.zero ) THEN
163 IF( diffnm.GT.zero )
164 \$ resid = 1.0d0 / eps
165 ELSE
166 resid = max( resid, ( diffnm / xnorm )*rcond )
167 END IF
168 20 CONTINUE
169 IF( resid*eps.LT.1.0d0 )
170 \$ resid = resid / eps
171*
172 RETURN
173*
174* End of DGET04
175*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
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