 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zget03()

 subroutine zget03 ( integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldainv, * ) AINV, integer LDAINV, complex*16, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision RCOND, double precision RESID )

ZGET03

Purpose:
``` ZGET03 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*16 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*16 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*16 array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV).``` [out] RESID ``` RESID is DOUBLE PRECISION norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 108 of file zget03.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  DOUBLE PRECISION RCOND, RESID
118 * ..
119 * .. Array Arguments ..
120  DOUBLE PRECISION RWORK( * )
121  COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
122  \$ WORK( LDWORK, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ZERO, ONE
129  parameter( zero = 0.0d+0, one = 1.0d+0 )
130  COMPLEX*16 CZERO, CONE
131  parameter( czero = ( 0.0d+0, 0.0d+0 ),
132  \$ cone = ( 1.0d+0, 0.0d+0 ) )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I
136  DOUBLE PRECISION AINVNM, ANORM, EPS
137 * ..
138 * .. External Functions ..
139  DOUBLE PRECISION DLAMCH, ZLANGE
140  EXTERNAL dlamch, zlange
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL zgemm
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC dble
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 = dlamch( 'Epsilon' )
161  anorm = zlange( '1', n, n, a, lda, rwork )
162  ainvnm = zlange( '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 zgemm( 'No transpose', 'No transpose', n, n, n, -cone, ainv,
173  \$ 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 = zlange( '1', n, n, work, ldwork, rwork )
181 *
182  resid = ( ( resid*rcond ) / eps ) / dble( n )
183 *
184  RETURN
185 *
186 * End of ZGET03
187 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
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