LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dget01.f
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1 *> \brief \b DGET01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LDAFAC, M, N
16 * DOUBLE PRECISION RESID
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DGET01 reconstructs a matrix A from its L*U factorization and
30 *> computes the residual
31 *> norm(L*U - A) / ( N * norm(A) * EPS ),
32 *> where EPS is the machine epsilon.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] M
39 *> \verbatim
40 *> M is INTEGER
41 *> The number of rows of the matrix A. M >= 0.
42 *> \endverbatim
43 *>
44 *> \param[in] N
45 *> \verbatim
46 *> N is INTEGER
47 *> The number of columns of the matrix A. N >= 0.
48 *> \endverbatim
49 *>
50 *> \param[in] A
51 *> \verbatim
52 *> A is DOUBLE PRECISION array, dimension (LDA,N)
53 *> The original M x N matrix A.
54 *> \endverbatim
55 *>
56 *> \param[in] LDA
57 *> \verbatim
58 *> LDA is INTEGER
59 *> The leading dimension of the array A. LDA >= max(1,M).
60 *> \endverbatim
61 *>
62 *> \param[in,out] AFAC
63 *> \verbatim
64 *> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
65 *> The factored form of the matrix A. AFAC contains the factors
66 *> L and U from the L*U factorization as computed by DGETRF.
67 *> Overwritten with the reconstructed matrix, and then with the
68 *> difference L*U - A.
69 *> \endverbatim
70 *>
71 *> \param[in] LDAFAC
72 *> \verbatim
73 *> LDAFAC is INTEGER
74 *> The leading dimension of the array AFAC. LDAFAC >= max(1,M).
75 *> \endverbatim
76 *>
77 *> \param[in] IPIV
78 *> \verbatim
79 *> IPIV is INTEGER array, dimension (N)
80 *> The pivot indices from DGETRF.
81 *> \endverbatim
82 *>
83 *> \param[out] RWORK
84 *> \verbatim
85 *> RWORK is DOUBLE PRECISION array, dimension (M)
86 *> \endverbatim
87 *>
88 *> \param[out] RESID
89 *> \verbatim
90 *> RESID is DOUBLE PRECISION
91 *> norm(L*U - A) / ( N * norm(A) * EPS )
92 *> \endverbatim
93 *
94 * Authors:
95 * ========
96 *
97 *> \author Univ. of Tennessee
98 *> \author Univ. of California Berkeley
99 *> \author Univ. of Colorado Denver
100 *> \author NAG Ltd.
101 *
102 *> \ingroup double_lin
103 *
104 * =====================================================================
105  SUBROUTINE dget01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
106  $ RESID )
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 *
212  END
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
subroutine dget01(M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
DGET01
Definition: dget01.f:107
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