LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cget04()

subroutine cget04 ( integer  N,
integer  NRHS,
complex, dimension( ldx, * )  X,
integer  LDX,
complex, dimension( ldxact, * )  XACT,
integer  LDXACT,
real  RCOND,
real  RESID 
)

CGET04

Purpose:
 CGET04 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 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 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 cget04.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  COMPLEX 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  COMPLEX ZDUM
125 * ..
126 * .. External Functions ..
127  INTEGER ICAMAX
128  REAL SLAMCH
129  EXTERNAL icamax, slamch
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC abs, aimag, max, real
133 * ..
134 * .. Statement Functions ..
135  REAL CABS1
136 * ..
137 * .. Statement Function definitions ..
138  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( 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 = slamch( 'Epsilon' )
152  IF( rcond.LT.zero ) THEN
153  resid = 1.0 / 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 = icamax( 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 = 1.0 / eps
172  ELSE
173  resid = max( resid, ( diffnm / xnorm )*rcond )
174  END IF
175  20 CONTINUE
176  IF( resid*eps.LT.1.0 )
177  $ resid = resid / eps
178 *
179  RETURN
180 *
181 * End of CGET04
182 *
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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