 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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 )```

Definition at line 105 of file dget01.f.

107*
108* -- LAPACK test routine --
109* -- LAPACK is a software package provided by Univ. of Tennessee, --
110* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111*
112* .. Scalar Arguments ..
113 INTEGER LDA, LDAFAC, M, N
114 DOUBLE PRECISION RESID
115* ..
116* .. Array Arguments ..
117 INTEGER IPIV( * )
118 DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
119* ..
120*
121* =====================================================================
122*
123*
124* .. Parameters ..
125 DOUBLE PRECISION ZERO, ONE
126 parameter( zero = 0.0d+0, one = 1.0d+0 )
127* ..
128* .. Local Scalars ..
129 INTEGER I, J, K
130 DOUBLE PRECISION ANORM, EPS, T
131* ..
132* .. External Functions ..
133 DOUBLE PRECISION DDOT, DLAMCH, DLANGE
134 EXTERNAL ddot, dlamch, dlange
135* ..
136* .. External Subroutines ..
137 EXTERNAL dgemv, dlaswp, dscal, dtrmv
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC dble, min
141* ..
142* .. Executable Statements ..
143*
144* Quick exit if M = 0 or N = 0.
145*
146 IF( m.LE.0 .OR. n.LE.0 ) THEN
147 resid = zero
148 RETURN
149 END IF
150*
151* Determine EPS and the norm of A.
152*
153 eps = dlamch( 'Epsilon' )
154 anorm = dlange( '1', m, n, a, lda, rwork )
155*
156* Compute the product L*U and overwrite AFAC with the result.
157* A column at a time of the product is obtained, starting with
158* column N.
159*
160 DO 10 k = n, 1, -1
161 IF( k.GT.m ) THEN
162 CALL dtrmv( 'Lower', 'No transpose', 'Unit', m, afac,
163 \$ ldafac, afac( 1, k ), 1 )
164 ELSE
165*
166* Compute elements (K+1:M,K)
167*
168 t = afac( k, k )
169 IF( k+1.LE.m ) THEN
170 CALL dscal( m-k, t, afac( k+1, k ), 1 )
171 CALL dgemv( 'No transpose', m-k, k-1, one,
172 \$ afac( k+1, 1 ), ldafac, afac( 1, k ), 1, one,
173 \$ afac( k+1, k ), 1 )
174 END IF
175*
176* Compute the (K,K) element
177*
178 afac( k, k ) = t + ddot( k-1, afac( k, 1 ), ldafac,
179 \$ afac( 1, k ), 1 )
180*
181* Compute elements (1:K-1,K)
182*
183 CALL dtrmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
184 \$ ldafac, afac( 1, k ), 1 )
185 END IF
186 10 CONTINUE
187 CALL dlaswp( n, afac, ldafac, 1, min( m, n ), ipiv, -1 )
188*
189* Compute the difference L*U - A and store in AFAC.
190*
191 DO 30 j = 1, n
192 DO 20 i = 1, m
193 afac( i, j ) = afac( i, j ) - a( i, j )
194 20 CONTINUE
195 30 CONTINUE
196*
197* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
198*
199 resid = dlange( '1', m, n, afac, ldafac, rwork )
200*
201 IF( anorm.LE.zero ) THEN
202 IF( resid.NE.zero )
203 \$ resid = one / eps
204 ELSE
205 resid = ( ( resid / dble( n ) ) / anorm ) / eps
206 END IF
207*
208 RETURN
209*
210* End of DGET01
211*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:82
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:147
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
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:114
subroutine dlaswp(N, A, LDA, K1, K2, IPIV, INCX)
DLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: dlaswp.f:115
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