LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sget03()

subroutine sget03 ( integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldainv, * )  AINV,
integer  LDAINV,
real, dimension( ldwork, * )  WORK,
integer  LDWORK,
real, dimension( * )  RWORK,
real  RCOND,
real  RESID 
)

SGET03

Purpose:
 SGET03 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 REAL 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 REAL 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 REAL 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.
Date
December 2016

Definition at line 111 of file sget03.f.

111 *
112 * -- LAPACK test routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117 * .. Scalar Arguments ..
118  INTEGER lda, ldainv, ldwork, n
119  REAL rcond, resid
120 * ..
121 * .. Array Arguments ..
122  REAL a( lda, * ), ainv( ldainv, * ), rwork( * ),
123  $ work( ldwork, * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  REAL zero, one
130  parameter( zero = 0.0e+0, one = 1.0e+0 )
131 * ..
132 * .. Local Scalars ..
133  INTEGER i
134  REAL ainvnm, anorm, eps
135 * ..
136 * .. External Functions ..
137  REAL slamch, slange
138  EXTERNAL slamch, slange
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL sgemm
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC real
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick exit if N = 0.
149 *
150  IF( n.LE.0 ) THEN
151  rcond = one
152  resid = zero
153  RETURN
154  END IF
155 *
156 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157 *
158  eps = slamch( 'Epsilon' )
159  anorm = slange( '1', n, n, a, lda, rwork )
160  ainvnm = slange( '1', n, n, ainv, ldainv, rwork )
161  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
162  rcond = zero
163  resid = one / eps
164  RETURN
165  END IF
166  rcond = ( one / anorm ) / ainvnm
167 *
168 * Compute I - A * AINV
169 *
170  CALL sgemm( 'No transpose', 'No transpose', n, n, n, -one,
171  $ ainv, ldainv, a, lda, zero, work, ldwork )
172  DO 10 i = 1, n
173  work( i, i ) = one + work( i, i )
174  10 CONTINUE
175 *
176 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
177 *
178  resid = slange( '1', n, n, work, ldwork, rwork )
179 *
180  resid = ( ( resid*rcond ) / eps ) / REAL( n )
181 *
182  RETURN
183 *
184 * End of SGET03
185 *
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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