LAPACK  3.10.0 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 )```

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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