LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 )```
Date
November 2011

Definition at line 104 of file dget04.f.

104 *
105 * -- LAPACK test routine (version 3.4.0) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * November 2011
109 *
110 * .. Scalar Arguments ..
111  INTEGER ldx, ldxact, n, nrhs
112  DOUBLE PRECISION rcond, resid
113 * ..
114 * .. Array Arguments ..
115  DOUBLE PRECISION x( ldx, * ), xact( ldxact, * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  DOUBLE PRECISION zero
122  parameter ( zero = 0.0d+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER i, ix, j
126  DOUBLE PRECISION diffnm, eps, xnorm
127 * ..
128 * .. External Functions ..
129  INTEGER idamax
130  DOUBLE PRECISION dlamch
131  EXTERNAL idamax, dlamch
132 * ..
133 * .. Intrinsic Functions ..
134  INTRINSIC abs, max
135 * ..
136 * .. Executable Statements ..
137 *
138 * Quick exit if N = 0 or NRHS = 0.
139 *
140  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
141  resid = zero
142  RETURN
143  END IF
144 *
145 * Exit with RESID = 1/EPS if RCOND is invalid.
146 *
147  eps = dlamch( 'Epsilon' )
148  IF( rcond.LT.zero ) THEN
149  resid = 1.0d0 / eps
150  RETURN
151  END IF
152 *
153 * Compute the maximum of
154 * norm(X - XACT) / ( norm(XACT) * EPS )
155 * over all the vectors X and XACT .
156 *
157  resid = zero
158  DO 20 j = 1, nrhs
159  ix = idamax( n, xact( 1, j ), 1 )
160  xnorm = abs( xact( ix, j ) )
161  diffnm = zero
162  DO 10 i = 1, n
163  diffnm = max( diffnm, abs( x( i, j )-xact( i, j ) ) )
164  10 CONTINUE
165  IF( xnorm.LE.zero ) THEN
166  IF( diffnm.GT.zero )
167  \$ resid = 1.0d0 / eps
168  ELSE
169  resid = max( resid, ( diffnm / xnorm )*rcond )
170  END IF
171  20 CONTINUE
172  IF( resid*eps.LT.1.0d0 )
173  \$ resid = resid / eps
174 *
175  RETURN
176 *
177 * End of DGET04
178 *
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65

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