LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sget01()

subroutine sget01 ( integer  M,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
integer, dimension( * )  IPIV,
real, dimension( * )  RWORK,
real  RESID 
)

SGET01

Purpose:
 SGET01 reconstructs a matrix A from its L*U factorization and
 computes the residual
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The original M x N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in,out]AFAC
          AFAC is REAL array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the factors
          L and U from the L*U factorization as computed by SGETRF.
          Overwritten with the reconstructed matrix, and then with the
          difference L*U - A.
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from SGETRF.
[out]RWORK
          RWORK is REAL array, dimension (M)
[out]RESID
          RESID is REAL
          norm(L*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 109 of file sget01.f.

109 *
110 * -- LAPACK test routine (version 3.7.0) --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 * December 2016
114 *
115 * .. Scalar Arguments ..
116  INTEGER lda, ldafac, m, n
117  REAL resid
118 * ..
119 * .. Array Arguments ..
120  INTEGER ipiv( * )
121  REAL a( lda, * ), afac( ldafac, * ), rwork( * )
122 * ..
123 *
124 * =====================================================================
125 *
126 *
127 * .. Parameters ..
128  REAL zero, one
129  parameter( zero = 0.0e+0, one = 1.0e+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER i, j, k
133  REAL anorm, eps, t
134 * ..
135 * .. External Functions ..
136  REAL sdot, slamch, slange
137  EXTERNAL sdot, slamch, slange
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL sgemv, slaswp, sscal, strmv
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC min, real
144 * ..
145 * .. Executable Statements ..
146 *
147 * Quick exit if M = 0 or N = 0.
148 *
149  IF( m.LE.0 .OR. n.LE.0 ) THEN
150  resid = zero
151  RETURN
152  END IF
153 *
154 * Determine EPS and the norm of A.
155 *
156  eps = slamch( 'Epsilon' )
157  anorm = slange( '1', m, n, a, lda, rwork )
158 *
159 * Compute the product L*U and overwrite AFAC with the result.
160 * A column at a time of the product is obtained, starting with
161 * column N.
162 *
163  DO 10 k = n, 1, -1
164  IF( k.GT.m ) THEN
165  CALL strmv( 'Lower', 'No transpose', 'Unit', m, afac,
166  $ ldafac, afac( 1, k ), 1 )
167  ELSE
168 *
169 * Compute elements (K+1:M,K)
170 *
171  t = afac( k, k )
172  IF( k+1.LE.m ) THEN
173  CALL sscal( m-k, t, afac( k+1, k ), 1 )
174  CALL sgemv( 'No transpose', m-k, k-1, one,
175  $ afac( k+1, 1 ), ldafac, afac( 1, k ), 1, one,
176  $ afac( k+1, k ), 1 )
177  END IF
178 *
179 * Compute the (K,K) element
180 *
181  afac( k, k ) = t + sdot( k-1, afac( k, 1 ), ldafac,
182  $ afac( 1, k ), 1 )
183 *
184 * Compute elements (1:K-1,K)
185 *
186  CALL strmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
187  $ ldafac, afac( 1, k ), 1 )
188  END IF
189  10 CONTINUE
190  CALL slaswp( n, afac, ldafac, 1, min( m, n ), ipiv, -1 )
191 *
192 * Compute the difference L*U - A and store in AFAC.
193 *
194  DO 30 j = 1, n
195  DO 20 i = 1, m
196  afac( i, j ) = afac( i, j ) - a( i, j )
197  20 CONTINUE
198  30 CONTINUE
199 *
200 * Compute norm( L*U - A ) / ( N * norm(A) * EPS )
201 *
202  resid = slange( '1', m, n, afac, ldafac, rwork )
203 *
204  IF( anorm.LE.zero ) THEN
205  IF( resid.NE.zero )
206  $ resid = one / eps
207  ELSE
208  resid = ( ( resid / REAL( N ) ) / anorm ) / eps
209  END IF
210 *
211  RETURN
212 *
213 * End of SGET01
214 *
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:84
subroutine slaswp(N, A, LDA, K1, K2, IPIV, INCX)
SLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: slaswp.f:117
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:158
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
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
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