LAPACK  3.10.0
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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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