LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cget03()

subroutine cget03 ( integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldainv, * )  AINV,
integer  LDAINV,
complex, dimension( ldwork, * )  WORK,
integer  LDWORK,
real, dimension( * )  RWORK,
real  RCOND,
real  RESID 
)

CGET03

Purpose:
 CGET03 computes the residual for a general matrix times its inverse:
    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is COMPLEX array, dimension (LDA,N)
          The original N x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]AINV
          AINV is COMPLEX array, dimension (LDAINV,N)
          The inverse of the matrix A.
[in]LDAINV
          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).
[out]WORK
          WORK is COMPLEX array, dimension (LDWORK,N)
[in]LDWORK
          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RCOND
          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).
[out]RESID
          RESID is REAL
          norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 108 of file cget03.f.

110 *
111 * -- LAPACK test routine --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 *
115 * .. Scalar Arguments ..
116  INTEGER LDA, LDAINV, LDWORK, N
117  REAL RCOND, RESID
118 * ..
119 * .. Array Arguments ..
120  REAL RWORK( * )
121  COMPLEX A( LDA, * ), AINV( LDAINV, * ),
122  $ WORK( LDWORK, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  REAL ZERO, ONE
129  parameter( zero = 0.0e+0, one = 1.0e+0 )
130  COMPLEX CZERO, CONE
131  parameter( czero = ( 0.0e+0, 0.0e+0 ),
132  $ cone = ( 1.0e+0, 0.0e+0 ) )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I
136  REAL AINVNM, ANORM, EPS
137 * ..
138 * .. External Functions ..
139  REAL CLANGE, SLAMCH
140  EXTERNAL clange, slamch
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL cgemm
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC real
147 * ..
148 * .. Executable Statements ..
149 *
150 * Quick exit if N = 0.
151 *
152  IF( n.LE.0 ) THEN
153  rcond = one
154  resid = zero
155  RETURN
156  END IF
157 *
158 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
159 *
160  eps = slamch( 'Epsilon' )
161  anorm = clange( '1', n, n, a, lda, rwork )
162  ainvnm = clange( '1', n, n, ainv, ldainv, rwork )
163  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
164  rcond = zero
165  resid = one / eps
166  RETURN
167  END IF
168  rcond = ( one/anorm ) / ainvnm
169 *
170 * Compute I - A * AINV
171 *
172  CALL cgemm( 'No transpose', 'No transpose', n, n, n, -cone,
173  $ ainv, ldainv, a, lda, czero, work, ldwork )
174  DO 10 i = 1, n
175  work( i, i ) = cone + work( i, i )
176  10 CONTINUE
177 *
178 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
179 *
180  resid = clange( '1', n, n, work, ldwork, rwork )
181 *
182  resid = ( ( resid*rcond )/eps ) / real( n )
183 *
184  RETURN
185 *
186 * End of CGET03
187 *
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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