LAPACK  3.10.0
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.

Definition at line 107 of file sget03.f.

109 *
110 * -- LAPACK test routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 *
114 * .. Scalar Arguments ..
115  INTEGER LDA, LDAINV, LDWORK, N
116  REAL RCOND, RESID
117 * ..
118 * .. Array Arguments ..
119  REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
120  $ WORK( LDWORK, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  REAL ZERO, ONE
127  parameter( zero = 0.0e+0, one = 1.0e+0 )
128 * ..
129 * .. Local Scalars ..
130  INTEGER I
131  REAL AINVNM, ANORM, EPS
132 * ..
133 * .. External Functions ..
134  REAL SLAMCH, SLANGE
135  EXTERNAL slamch, slange
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL sgemm
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC real
142 * ..
143 * .. Executable Statements ..
144 *
145 * Quick exit if N = 0.
146 *
147  IF( n.LE.0 ) THEN
148  rcond = one
149  resid = zero
150  RETURN
151  END IF
152 *
153 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
154 *
155  eps = slamch( 'Epsilon' )
156  anorm = slange( '1', n, n, a, lda, rwork )
157  ainvnm = slange( '1', n, n, ainv, ldainv, rwork )
158  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
159  rcond = zero
160  resid = one / eps
161  RETURN
162  END IF
163  rcond = ( one / anorm ) / ainvnm
164 *
165 * Compute I - A * AINV
166 *
167  CALL sgemm( 'No transpose', 'No transpose', n, n, n, -one,
168  $ ainv, ldainv, a, lda, zero, work, ldwork )
169  DO 10 i = 1, n
170  work( i, i ) = one + work( i, i )
171  10 CONTINUE
172 *
173 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
174 *
175  resid = slange( '1', n, n, work, ldwork, rwork )
176 *
177  resid = ( ( resid*rcond ) / eps ) / real( n )
178 *
179  RETURN
180 *
181 * End of SGET03
182 *
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:114
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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