1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin hes_lu_det.cpp}
Gradient of Determinant Using LU Factorization: Example and Test
################################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end hes_lu_det.cpp}
*/
// BEGIN C++
// Complex examples should supppress conversion warnings
# include <cppad/wno_conversion.hpp>
# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>
// The AD complex case is used by this example so must
// define a specializatgion of LeqZero,AbsGeq for the AD<Complex> case
namespace CppAD {
CPPAD_BOOL_BINARY( std::complex<double> , AbsGeq )
CPPAD_BOOL_UNARY( std::complex<double> , LeqZero )
}
bool HesLuDet(void)
{ bool ok = true;
using namespace CppAD;
typedef std::complex<double> Complex;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
size_t n = 2;
// object for computing determinants
det_by_lu< AD<Complex> > Det(n);
// independent and dependent variable vectors
CPPAD_TESTVECTOR(AD<Complex>) X(n * n);
CPPAD_TESTVECTOR(AD<Complex>) D(1);
// value of the independent variable
size_t i;
for(i = 0; i < n * n; i++)
X[i] = Complex( double(i), -double(i) );
// set the independent variables
Independent(X);
D[0] = Det(X);
// create the function object
ADFun<Complex> f(X, D);
// argument value
CPPAD_TESTVECTOR(Complex) x( n * n );
for(i = 0; i < n * n; i++)
x[i] = Complex( double(2 * i) , double(i) );
// first derivative of the determinant
CPPAD_TESTVECTOR(Complex) H( n * n * n * n );
H = f.Hessian(x, 0);
/*
f(x) = x[0] * x[3] - x[1] * x[2]
f'(x) = ( x[3], -x[2], -x[1], x[0] )
*/
Complex zero(0., 0.);
Complex one(1., 0.);
Complex Htrue[] = {
zero, zero, zero, one,
zero, zero, -one, zero,
zero, -one, zero, zero,
one, zero, zero, zero
};
for( i = 0; i < n*n*n*n; i++)
ok &= NearEqual( Htrue[i], H[i], eps99 , eps99 );
return ok;
}
// END C++
|
