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GaussianIntegralGradHessian.cpp
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1 #include "GaussianIntegralGradHessian.h"
2 
3 #include <cmath>
4 #include <vector>
5 
6 using namespace std;
7 using namespace Eigen;
8 
9 namespace FitNewton
10 {
11  GaussianIntegralGradHessian::GaussianIntegralGradHessian() : FunctionGradHessian(3, 2)
12  {
13 
14  }
15 
16 
17  GaussianIntegralGradHessian::~GaussianIntegralGradHessian()
18  {
19 
20  }
21 
22 
23  FunctionGradHessian* GaussianIntegralGradHessian::Clone() const
24  {
25  GaussianIntegralGradHessian* clone = new GaussianIntegralGradHessian();
26  clone->setFixedPar(0, fixedpars[0]);
27  clone->setFixedPar(1, fixedpars[1]);
28  return clone;
29  }
30 
31 
32  bool GaussianIntegralGradHessian::calcValGradHessian(const VectorXd& x, double& val, VectorXd& grad, MatrixXd& hessian)
33  {
34  double temp0 = (fixedpars[0] - x(1));
35  double temp0_2 = temp0*temp0;
36  double temp1 = (fixedpars[1] - x(1));
37  double temp1_2 = temp1*temp1;
38  double temp2 = 1./x(2);
39  double sqrt_pi_o_2 = 0x1.40d931ff627059657ca41fae722cep0;
40  double sqrt_1_o_2 = 0xb.504f333f9de6484597d89b3754abep-4;
41 
42  val = sqrt_pi_o_2*x(0)*x(2)*( erf(sqrt_1_o_2*temp1*temp2) - erf(sqrt_1_o_2*temp0*temp2) );
43 
44  double temp2_2 = temp2*temp2;
45  double etemp1 = exp(-temp1_2*0.5*temp2_2);
46  double etemp0 = exp(-temp0_2*0.5*temp2_2);
47 
48  double temp4 = 1./x(0);
49  double temp5 = ( -etemp1*temp1 + etemp0*temp0 );
50 
51  grad(0) = val*temp4;
52  grad(1) = x(0)*(-etemp1 + etemp0);
53  grad(2) = temp2*( val + x(0)*temp5 );
54 
55  hessian(0,0) = 0.;
56  hessian(0,1) = temp4*grad(1);
57  hessian(0,2) = temp4*grad(2);
58  hessian(1,1) = x(0)*temp2_2*temp5;
59  hessian(1,2) = x(0)*temp2*temp2_2*( -etemp1*temp1_2 + etemp0*temp0_2 );
60  hessian(2,2) = x(0)*temp2_2*temp2_2*( -etemp1*temp1_2*temp1 + -etemp0*temp0_2*temp0 );
61  return true;
62  }
63 }
64 
65 
66 // f = sqrt(pi/2.)*x0*x2*(erf((1/sqrt(2))*(t1-x1)/x2) - erf((1/sqrt(2))*(t0-x1)/x2))
67 //
68 // df/dx0 = f/x0
69 // df/dx1 = x0*[ -exp(-(t1-x1)^2/(2*x2^2)) + exp(-(t0-x1)^2/(2*x2^2)) ]
70 // df/dx2 = (1/x2)*(f + x0*[ -exp(-(t1-x1)^2/(2*x2^2))*(t1-x1) + exp(-(t0-x1)^2/(2*x2^2))*(t0-x1) ])
71 //
72 // d^2f/dx0^2 = 0
73 // d^2f/dx0dx1 = (df/dx1)/x0
74 // d^2f/dx0dx2 = (df/dx2)/x0
75 // d^2f/dx1^2 = (x0/x2^2)*[ -exp(-(t1-x1)^2/(2*x2^2))*(t1-x1) + exp(-(t0-x1)^2/(2*x2^2))*(t0-x1) ]
76 // d^2f/dx1dx2 = (x0/x2^3)*[ -exp(-(t1-x1)^2/(2*x2^2))*(t1-x1)^2 + exp(-(t0-x1)^2/(2*x2^2))*(t0-x1)^2 ]
77 // d^2f/dx2^2 = (x0/x2^4)*[ -exp(-(t1-x1)^2/(2*x2^2))*(t1-x1)^3 + exp(-(t0-x1)^2/(2*x2^2))*(t0-x1)^3 ]
78