LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sget04()

 subroutine sget04 ( integer N, integer NRHS, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldxact, * ) XACT, integer LDXACT, real RCOND, real RESID )

SGET04

Purpose:
``` SGET04 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 REAL 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 REAL 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 REAL The reciprocal of the condition number of the coefficient matrix in the system of equations.``` [out] RESID ``` RESID is REAL The maximum over the NRHS solution vectors of ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )```

Definition at line 101 of file sget04.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  REAL RCOND, RESID
110 * ..
111 * .. Array Arguments ..
112  REAL X( LDX, * ), XACT( LDXACT, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  REAL ZERO
119  parameter( zero = 0.0e+0 )
120 * ..
121 * .. Local Scalars ..
122  INTEGER I, IX, J
123  REAL DIFFNM, EPS, XNORM
124 * ..
125 * .. External Functions ..
126  INTEGER ISAMAX
127  REAL SLAMCH
128  EXTERNAL isamax, slamch
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 = slamch( 'Epsilon' )
145  IF( rcond.LT.zero ) THEN
146  resid = 1.0 / 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 = isamax( 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 = 1.0 / eps
165  ELSE
166  resid = max( resid, ( diffnm / xnorm )*rcond )
167  END IF
168  20 CONTINUE
169  IF( resid*eps.LT.1.0 )
170  \$ resid = resid / eps
171 *
172  RETURN
173 *
174 * End of SGET04
175 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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