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alternative spline
This commit is contained in:
hrocho
parent
1e144980f3
commit
437b85ca37
3
catima.h
3
catima.h
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@ -27,11 +27,10 @@
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#include "catima/structures.h"
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#include "catima/calculations.h"
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#include "catima/material_database.h"
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#include "catima/storage.h"
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namespace catima{
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class Interpolator;
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/**
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* calculate dEdx for projectile-Material combination
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* @param p - Projectile
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258
spline.cpp
Normal file
258
spline.cpp
Normal file
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@ -0,0 +1,258 @@
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/*
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* This is modification of Tino Kluge tk spline
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* https://github.com/ttk592/spline/
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*
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* the modification is in LU caclulation,
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* optimized for tridiagonal matrices
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*/
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#include "spline.h"
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namespace catima{
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band_matrix::band_matrix(int dim)
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{
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resize(dim);
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}
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void band_matrix::resize(int dim)
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{
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assert(dim>0);
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a.resize(dim);
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d.resize(dim);
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c.resize(dim);
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}
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int band_matrix::dim() const
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{
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return d.size();
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}
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// defines the new operator (), so that we can access the elements
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// by A(i,j), index going from i=0,...,dim()-1
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double & band_matrix::operator () (int i, int j)
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{
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int k=j-i; // what band is the entry
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assert( (i>=0) && (i<dim()) && (j>=0) && (j<dim()) );
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assert(k<2 && k>-2);
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if(k>0)return c[i];
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else if(k==0) return d[i];
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else return a[i];
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}
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double band_matrix::operator () (int i, int j) const
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{
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int k=j-i; // what band is the entry
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assert( (i>=0) && (i<dim()) && (j>=0) && (j<dim()) );
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if(k>0)return c[i];
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else if(k==0) return d[i];
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else return a[i];
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}
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std::vector<double> band_matrix::trig_solve(const std::vector<double>& b) const
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{
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assert( this->dim()==(int)b.size() );
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std::vector<double> x(this->dim());
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std::vector<double> g(this->dim());
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int j_stop;
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double sum;
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assert(d[0]!=0.0);
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x[0] = b[0]/d[0];
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double bet = d[0];
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for(int j=1;j<this->dim();j++){
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g[j] = c[j-1]/bet;
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bet = d[j] - (a[j]*g[j]);
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assert(bet != 0.0);
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x[j] = (b[j]-a[j]*x[j-1])/bet;
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}
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for(int j=this->dim()-2;j>=0;j--){
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x[j] -= g[j+1]*x[j+1];
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}
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return x;
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}
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// spline implementation
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// -----------------------
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void spline::set_boundary(spline::bd_type left, double left_value,
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spline::bd_type right, double right_value,
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bool force_linear_extrapolation)
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{
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assert(n==0); // set_points() must not have happened yet
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m_left=left;
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m_right=right;
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m_left_value=left_value;
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m_right_value=right_value;
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m_force_linear_extrapolation=force_linear_extrapolation;
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}
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void spline::set_points(const double *x,
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const double *y,
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const size_t num
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)
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{
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assert(num>2);
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m_x=x;
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m_y=y;
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n=num;
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// TODO: maybe sort x and y, rather than returning an error
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for(int i=0; i<n-1; i++) {
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assert(m_x[i]<m_x[i+1]);
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}
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// setting up the matrix and right hand side of the equation system
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// for the parameters b[]
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band_matrix A(n);
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std::vector<double> rhs(n);
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for(int i=1; i<n-1; i++) {
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A(i,i-1)=1.0/3.0*(x[i]-x[i-1]);
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A(i,i)=2.0/3.0*(x[i+1]-x[i-1]);
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A(i,i+1)=1.0/3.0*(x[i+1]-x[i]);
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rhs[i]=(y[i+1]-y[i])/(x[i+1]-x[i]) - (y[i]-y[i-1])/(x[i]-x[i-1]);
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}
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// boundary conditions
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if(m_left == spline::bd_type::second_deriv) {
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// 2*b[0] = f''
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A(0,0)=2.0;
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A(0,1)=0.0;
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rhs[0]=m_left_value;
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} else{
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// c[0] = f', needs to be re-expressed in terms of b:
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// (2b[0]+b[1])(x[1]-x[0]) = 3 ((y[1]-y[0])/(x[1]-x[0]) - f')
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A(0,0)=2.0*(x[1]-x[0]);
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A(0,1)=1.0*(x[1]-x[0]);
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rhs[0]=3.0*((y[1]-y[0])/(x[1]-x[0])-m_left_value);
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}
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if(m_right == spline::bd_type::second_deriv) {
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// 2*b[n-1] = f''
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A(n-1,n-1)=2.0;
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A(n-1,n-2)=0.0;
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rhs[n-1]=m_right_value;
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} else{
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// c[n-1] = f', needs to be re-expressed in terms of b:
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// (b[n-2]+2b[n-1])(x[n-1]-x[n-2])
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// = 3 (f' - (y[n-1]-y[n-2])/(x[n-1]-x[n-2]))
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A(n-1,n-1)=2.0*(x[n-1]-x[n-2]);
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A(n-1,n-2)=1.0*(x[n-1]-x[n-2]);
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rhs[n-1]=3.0*(m_right_value-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));
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}
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// solve the equation system to obtain the parameters b[]
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//m_b=A.lu_solve(rhs);
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m_b=A.trig_solve(rhs);
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// calculate parameters a[] and c[] based on b[]
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m_a.resize(n);
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m_c.resize(n);
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for(int i=0; i<n-1; i++) {
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m_a[i]=1.0/3.0*(m_b[i+1]-m_b[i])/(x[i+1]-x[i]);
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m_c[i]=(y[i+1]-y[i])/(x[i+1]-x[i])
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- 1.0/3.0*(2.0*m_b[i]+m_b[i+1])*(x[i+1]-x[i]);
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}
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// for left extrapolation coefficients
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m_b0 = (m_force_linear_extrapolation==false) ? m_b[0] : 0.0;
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m_c0 = m_c[0];
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// for the right extrapolation coefficients
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// f_{n-1}(x) = b*(x-x_{n-1})^2 + c*(x-x_{n-1}) + y_{n-1}
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double h=x[n-1]-x[n-2];
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// m_b[n-1] is determined by the boundary condition
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m_a[n-1]=0.0;
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m_c[n-1]=3.0*m_a[n-2]*h*h+2.0*m_b[n-2]*h+m_c[n-2]; // = f'_{n-2}(x_{n-1})
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if(m_force_linear_extrapolation==true)
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m_b[n-1]=0.0;
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}
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double spline::operator() (double x) const
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{
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assert(n>2);
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// find the closest point m_x[idx] < x, idx=0 even if x<m_x[0]
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auto it=std::lower_bound(m_x,m_x+n,x);
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//int idx=std::max( int(it-m_x)-1, 0);
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if(it!=m_x)it--;
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int idx = std::distance(m_x,it);
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double mx = *it;
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double h=x-mx;
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double interpol;
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if(x<m_x[0]) {
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// extrapolation to the left
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interpol=(m_b0*h + m_c0)*h + m_y[0];
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} else if(x>m_x[n-1]) {
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// extrapolation to the right
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interpol=(m_b[n-1]*h + m_c[n-1])*h + m_y[n-1];
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} else {
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// interpolation
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interpol=((m_a[idx]*h + m_b[idx])*h + m_c[idx])*h + m_y[idx];
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}
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return interpol;
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}
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double spline::deriv(int order, double x) const
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{
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assert(order>0);
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// find the closest point m_x[idx] < x, idx=0 even if x<m_x[0]
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auto it=std::lower_bound(m_x,m_x+n,x);
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//int idx=std::max( int(it-m_x)-1, 0);
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if(it!=m_x)it--;
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int idx = std::distance(m_x,it);
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double mx = *it;
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double h=x-mx;
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double interpol;
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if(x<m_x[0]) {
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// extrapolation to the left
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switch(order) {
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case 1:
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interpol=2.0*m_b0*h + m_c0;
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break;
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case 2:
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interpol=2.0*m_b0*h;
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break;
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default:
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interpol=0.0;
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break;
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}
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} else if(x>m_x[n-1]) {
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// extrapolation to the right
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switch(order) {
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case 1:
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interpol=2.0*m_b[n-1]*h + m_c[n-1];
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break;
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case 2:
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interpol=2.0*m_b[n-1];
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break;
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default:
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interpol=0.0;
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break;
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}
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} else {
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// interpolation
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switch(order) {
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case 1:
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interpol=(3.0*m_a[idx]*h + 2.0*m_b[idx])*h + m_c[idx];
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break;
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case 2:
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interpol=6.0*m_a[idx]*h + 2.0*m_b[idx];
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break;
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case 3:
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interpol=6.0*m_a[idx];
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break;
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default:
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interpol=0.0;
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break;
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}
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}
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return interpol;
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}
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} // namespace tk
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93
spline.h
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93
spline.h
Normal file
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@ -0,0 +1,93 @@
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/*
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*
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* This is modification of Tino Kluge tk spline
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* calculation is optimized for tridiagonal matrices
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*
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* Copyright(C) 2017
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Affero General Public License for more details.
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* You should have received a copy of the GNU Affero General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef TK_SPLINE_H
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#define TK_SPLINE_H
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#include <cstdio>
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#include <cassert>
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#include <vector>
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#include <algorithm>
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namespace catima
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{
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// band matrix solver
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class band_matrix
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{
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private:
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std::vector<double> a;
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std::vector<double> d;
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std::vector<double> c;
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std::vector<double> save;
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public:
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band_matrix() {}; // constructor
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band_matrix(int dim); // constructor
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~band_matrix() {}; // destructor
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void resize(int dim); // init with dim,n_u,n_l
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int dim() const; // matrix dimension
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// access operator
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double & operator () (int i, int j); // write
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double operator () (int i, int j) const; // read
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// we can store an additional diogonal (in m_lower)
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std::vector<double> trig_solve(const std::vector<double>& b) const;
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};
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// spline interpolation
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class spline
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{
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public:
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enum class bd_type {
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first_deriv = 1,
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second_deriv = 2
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};
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private:
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const double *m_x, *m_y; // x,y coordinates of points
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size_t n=0;
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// interpolation parameters
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// f(x) = a*(x-x_i)^3 + b*(x-x_i)^2 + c*(x-x_i) + y_i
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std::vector<double> m_a,m_b,m_c; // spline coefficients
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double m_b0, m_c0; // for left extrapol
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bd_type m_left = bd_type::second_deriv;
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bd_type m_right = bd_type::second_deriv;
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double m_left_value = 0.0;
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double m_right_value = 0.0;
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bool m_force_linear_extrapolation = false;
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public:
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// set default boundary condition to be zero curvature at both ends
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spline(){}
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// optional, but if called it has to come be before set_points()
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void set_boundary(bd_type left, double left_value,
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bd_type right, double right_value,
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bool force_linear_extrapolation=false);
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void set_points(const double *x,
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const double *y,
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const size_t num);
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double operator() (double x) const;
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double deriv(int order, double x) const;
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};
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} // namespace tk
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#endif /* TK_SPLINE_H */
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49
storage.cpp
49
storage.cpp
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@ -1,6 +1,22 @@
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/*
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* Copyright(C) 2017
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
|
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* the Free Software Foundation, either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
* This program is distributed in the hope that it will be useful,
|
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
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* GNU Affero General Public License for more details.
|
||||
|
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* You should have received a copy of the GNU Affero General Public License
|
||||
* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include <math.h>
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#include <iostream>
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#include "storage.h"
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#include "catima/catima.h"
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namespace catima {
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Data _storage;
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EnergyTable<max_datapoints> energy_table(logEmin,logEmax);
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@ -58,7 +74,7 @@ DataPoint& Data::Get(const Projectile &p, const Material &t, const Config &c){
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}
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//////////// Interpolator ////////////////////////////////
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Interpolator::Interpolator(const double *x, const double *y, int num,interpolation_t type){
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InterpolatorGSL::InterpolatorGSL(const double *x, const double *y, int num,interpolation_t type){
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acc = gsl_interp_accel_alloc ();
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if(type==cspline)
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@ -71,7 +87,7 @@ Interpolator::Interpolator(const double *x, const double *y, int num,interpolati
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max= x[num-1];
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}
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Interpolator::Interpolator(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type){
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InterpolatorGSL::InterpolatorGSL(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type){
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//Interpolator(x.data(),y.data(),x.size());
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acc = gsl_interp_accel_alloc ();
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if(type==cspline)
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@ -84,21 +100,44 @@ Interpolator::Interpolator(const std::vector<double>& x, const std::vector<doubl
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max= x[x.size()-1];
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}
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Interpolator::~Interpolator(){
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InterpolatorGSL::~InterpolatorGSL(){
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gsl_interp_accel_free (acc);
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gsl_spline_free (spline);
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}
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double Interpolator::eval(double x){
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double InterpolatorGSL::eval(double x){
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if(x<min)x=min;
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if(x>max)x=max;
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return gsl_spline_eval(spline, x, acc);
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}
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double Interpolator::derivative(double x){
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double InterpolatorGSL::derivative(double x){
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if(x<min)x=min;
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if(x>max)x=max;
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return gsl_spline_eval_deriv (spline, x, acc);
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}
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//////////// Interpolator2 ////////////////////////////////
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#ifdef BUILTIN_SPLINE
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Interpolator2::Interpolator2(const double *x, const double *y, int num){
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ss.set_points(x,y,num);
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min= x[0];
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max= x[num-1];
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}
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double Interpolator2::eval(double x){
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if(x<min)x=min;
|
||||
if(x>max)x=max;
|
||||
return ss(x);
|
||||
}
|
||||
|
||||
double Interpolator2::derivative(double x){
|
||||
if(x<min)x=min;
|
||||
if(x>max)x=max;
|
||||
return ss.deriv(1,x);
|
||||
}
|
||||
#endif
|
||||
|
||||
}
|
||||
|
|
|
|||
43
storage.h
43
storage.h
|
|
@ -19,10 +19,16 @@
|
|||
|
||||
#include <vector>
|
||||
#include <iterator>
|
||||
#include <cmath>
|
||||
//#include <unordered_set>
|
||||
#include <gsl/gsl_spline.h>
|
||||
#include "catima/constants.h"
|
||||
#include "catima/catima.h"
|
||||
#include "catima/structures.h"
|
||||
#include "catima/config.h"
|
||||
|
||||
#ifdef BUILTIN_SPLINE
|
||||
#include "catima/spline.h"
|
||||
#endif
|
||||
|
||||
|
||||
namespace catima{
|
||||
|
|
@ -49,19 +55,19 @@ namespace catima{
|
|||
|
||||
template<int N>
|
||||
int EnergyTable_index(const EnergyTable<N> &table, double val){
|
||||
double lxval = log(val)/M_LN10;
|
||||
if(val<table.values[0] || val>table.values[table.num-1])return -1;
|
||||
int i = (int)lxval/table.step;
|
||||
double lxval = (log(val/table.values[0])/M_LN10);
|
||||
int i = (int)std::floor(lxval/table.step);
|
||||
return i;
|
||||
}
|
||||
|
||||
template<int N>
|
||||
double EnergyTable_interpolate(const EnergyTable<N> &table, double xval, double *y){
|
||||
double r;
|
||||
double lxval = log(xval)/M_LN10;
|
||||
if(xval<table.values[0] || xval>table.values[table.num-1])return 0.0;
|
||||
if(xval==table.values[table.num-1])return y[table.num-1];
|
||||
int i = (int)(lxval/table.step);
|
||||
double lxval = (log(xval/table.values[0])/M_LN10);
|
||||
int i = (int)std::floor(lxval/table.step);
|
||||
double linstep = table.values[i+1] - table.values[i];
|
||||
double x = 1.0 - ((xval - table.values[i])/linstep);
|
||||
r = (x*y[i]) + ((1-x)*y[i+1]);
|
||||
|
|
@ -113,11 +119,11 @@ namespace catima{
|
|||
};
|
||||
|
||||
/// Interpolation class, to store interpolated values
|
||||
class Interpolator{
|
||||
class InterpolatorGSL{
|
||||
public:
|
||||
Interpolator(const double *x, const double *y, int num,interpolation_t type=cspline);
|
||||
Interpolator(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type=cspline);
|
||||
~Interpolator();
|
||||
InterpolatorGSL(const double *x, const double *y, int num,interpolation_t type=cspline);
|
||||
InterpolatorGSL(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type=cspline);
|
||||
~InterpolatorGSL();
|
||||
double operator()(double x){return eval(x);};
|
||||
double eval(double x);
|
||||
double derivative(double x);
|
||||
|
|
@ -131,6 +137,22 @@ namespace catima{
|
|||
gsl_spline *spline;
|
||||
};
|
||||
|
||||
#ifdef BUILTIN_SPLINE
|
||||
class Interpolator2{
|
||||
public:
|
||||
Interpolator2(const double *x, const double *y, int num);
|
||||
double operator()(double x){return eval(x);};
|
||||
double eval(double x);
|
||||
double derivative(double x);
|
||||
double get_min(){return min;};
|
||||
double get_max(){return max;};
|
||||
|
||||
private:
|
||||
double min=0;
|
||||
double max=0;
|
||||
spline ss;
|
||||
};
|
||||
#endif
|
||||
extern Data _storage;
|
||||
|
||||
inline DataPoint& get_data(const Projectile &p, const Material &t, const Config &c=default_config){
|
||||
|
|
@ -138,6 +160,9 @@ namespace catima{
|
|||
}
|
||||
|
||||
bool operator==(const DataPoint &a, const DataPoint &b);
|
||||
|
||||
using InterpolatorLinear = InterpolatorGSL;
|
||||
using Interpolator = InterpolatorGSL;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -121,6 +121,19 @@ const lest::test specification[] =
|
|||
EXPECT(catima::energy_table.values[0]==exp(M_LN10*(catima::logEmin)));
|
||||
EXPECT(catima::energy_table.values[1]==exp(M_LN10*(catima::logEmin+step)));
|
||||
EXPECT(catima::energy_table.values[catima::max_datapoints-1]==approx(exp(M_LN10*(catima::logEmax))).epsilon(1e-6));
|
||||
},
|
||||
CASE("indexing"){
|
||||
double step = catima::energy_table.step;
|
||||
double val, dif;
|
||||
|
||||
EXPECT(EnergyTable_index(catima::energy_table, 0.0)==-1);
|
||||
|
||||
for(int i:{5,10,100,498}){
|
||||
val = catima::energy_table.values[i];
|
||||
dif = catima::energy_table.values[i+1] - val;
|
||||
EXPECT(EnergyTable_index(catima::energy_table, val)==i);
|
||||
EXPECT(EnergyTable_index(catima::energy_table, val+0.5*dif)==i);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user