 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dget01()

 subroutine dget01 ( integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, double precision, dimension( * ) RWORK, double precision RESID )

DGET01

Purpose:
``` DGET01 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DGETRF. 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 DGETRF.``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (M)` [out] RESID ``` RESID is DOUBLE PRECISION norm(L*U - A) / ( N * norm(A) * EPS )```
Date
December 2016

Definition at line 109 of file dget01.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  DOUBLE PRECISION resid
118 * ..
119 * .. Array Arguments ..
120  INTEGER ipiv( * )
121  DOUBLE PRECISION a( lda, * ), afac( ldafac, * ), rwork( * )
122 * ..
123 *
124 * =====================================================================
125 *
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION zero, one
129  parameter( zero = 0.0d+0, one = 1.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER i, j, k
133  DOUBLE PRECISION anorm, eps, t
134 * ..
135 * .. External Functions ..
136  DOUBLE PRECISION ddot, dlamch, dlange
137  EXTERNAL ddot, dlamch, dlange
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL dgemv, dlaswp, dscal, dtrmv
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC dble, min
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 = dlamch( 'Epsilon' )
157  anorm = dlange( '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 dtrmv( '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 dscal( m-k, t, afac( k+1, k ), 1 )
174  CALL dgemv( '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 + ddot( k-1, afac( k, 1 ), ldafac,
182  \$ afac( 1, k ), 1 )
183 *
184 * Compute elements (1:K-1,K)
185 *
186  CALL dtrmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
187  \$ ldafac, afac( 1, k ), 1 )
188  END IF
189  10 CONTINUE
190  CALL dlaswp( 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 = dlange( '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 / dble( n ) ) / anorm ) / eps
209  END IF
210 *
211  RETURN
212 *
213 * End of DGET01
214 *
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:84
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:149
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:158
subroutine dlaswp(N, A, LDA, K1, K2, IPIV, INCX)
DLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: dlaswp.f:117
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