[1230] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // |
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[807] | 27 | /** |
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| 28 | * \file |
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| 29 | * \brief Provides code for the general c2_function algebra which supports |
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| 30 | * fast, flexible operations on piecewise-twice-differentiable functions |
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| 31 | * |
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| 32 | * \author Created by R. A. Weller and Marcus H. Mendenhall on 7/9/05. |
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[1337] | 33 | * \author 2005 Vanderbilt University. |
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[807] | 34 | * |
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[1230] | 35 | * \version c2_function.cc,v 1.169 2008/05/22 12:45:19 marcus Exp |
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[807] | 36 | */ |
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| 37 | |
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| 38 | #include <iostream> |
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| 39 | #include <vector> |
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| 40 | #include <algorithm> |
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| 41 | #include <cstdlib> |
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| 42 | #include <numeric> |
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| 43 | #include <functional> |
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| 44 | #include <iterator> |
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| 45 | #include <cmath> |
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| 46 | #include <limits> |
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| 47 | #include <sstream> |
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| 48 | |
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| 49 | template <typename float_type> const std::string c2_function<float_type>::cvs_file_vers() const |
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[1230] | 50 | { return "c2_function.cc,v 1.169 2008/05/22 12:45:19 marcus Exp"; } |
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[807] | 51 | |
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| 52 | // find a pre-bracketed root of a c2_function, which is a MUCH easier job than general root finding |
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| 53 | // since the derivatives are known exactly, and smoothness is guaranteed. |
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| 54 | // this searches for f(x)=value, to make life a little easier than always searching for f(x)=0 |
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| 55 | template <typename float_type> float_type c2_function<float_type>::find_root(float_type lower_bracket, float_type upper_bracket, |
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| 56 | float_type start, float_type value, int *error, |
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| 57 | float_type *final_yprime, float_type *final_yprime2) const throw(c2_exception) |
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| 58 | { |
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| 59 | // find f(x)=value within the brackets, using the guarantees of smoothness associated with a c2_function |
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| 60 | // can use local f(x)=a*x**2 + b*x + c and solve quadratic to find root, then iterate |
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| 61 | |
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| 62 | float_type yp, yp2; // we will make unused pointers point here, to save null checks later |
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| 63 | if (!final_yprime) final_yprime=&yp; |
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| 64 | if (!final_yprime2) final_yprime2=&yp2; |
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| 65 | |
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| 66 | float_type ftol=5*(std::numeric_limits<float_type>::epsilon()*std::abs(value)+std::numeric_limits<float_type>::min()); |
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| 67 | float_type xtol=5*(std::numeric_limits<float_type>::epsilon()*(std::abs(upper_bracket)+std::abs(lower_bracket))+std::numeric_limits<float_type>::min()); |
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| 68 | |
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| 69 | float_type root=start; // start looking in the middle |
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| 70 | if(error) *error=0; // start out with error flag set to OK, if it is expected |
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| 71 | |
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| 72 | float_type c, b; |
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| 73 | |
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[1230] | 74 | if(!root_info) { |
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| 75 | root_info=new struct c2_root_info; |
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| 76 | root_info->inited=false; |
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| 77 | } |
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[807] | 78 | // this new logic is to keep track of where we were before, and lower the number of |
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| 79 | // function evaluations if we are searching inside the same bracket as before. |
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| 80 | // Since this root finder has, very often, the bracket of the entire domain of the function, |
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| 81 | // this makes a big difference, especially to c2_inverse_function |
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[1230] | 82 | if(!root_info->inited || upper_bracket != root_info->upper.x || lower_bracket != root_info->lower.x) { |
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| 83 | root_info->upper.x=upper_bracket; |
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| 84 | fill_fblock(root_info->upper); |
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| 85 | root_info->lower.x=lower_bracket; |
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| 86 | fill_fblock(root_info->lower); |
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| 87 | root_info->inited=true; |
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| 88 | } |
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[807] | 89 | |
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[1230] | 90 | float_type clower=root_info->lower.y-value; |
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| 91 | if(!clower) { |
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| 92 | *final_yprime=root_info->lower.yp; |
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| 93 | *final_yprime2=root_info->lower.ypp; |
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| 94 | return lower_bracket; |
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[807] | 95 | } |
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| 96 | |
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[1230] | 97 | float_type cupper=root_info->upper.y-value; |
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| 98 | if(!cupper) { |
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| 99 | *final_yprime=root_info->upper.yp; |
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| 100 | *final_yprime2=root_info->upper.ypp; |
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| 101 | return upper_bracket; |
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| 102 | } |
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| 103 | const float_type lower_sign = (clower < 0) ? -1 : 1; |
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| 104 | |
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| 105 | if(lower_sign*cupper >0) { |
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[807] | 106 | // argh, no sign change in here! |
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| 107 | if(error) { *error=1; return 0.0; } |
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| 108 | else { |
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| 109 | std::ostringstream outstr; |
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| 110 | outstr << "unbracketed root in find_root at xlower= " << lower_bracket << ", xupper= " << upper_bracket; |
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| 111 | outstr << ", value= " << value << ": bailing"; |
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| 112 | throw c2_exception(outstr.str().c_str()); |
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| 113 | } |
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| 114 | } |
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| 115 | |
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| 116 | float_type delta=upper_bracket-lower_bracket; // first error step |
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| 117 | c=value_with_derivatives(root, final_yprime, final_yprime2)-value; // compute initial values |
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| 118 | b=*final_yprime; // make a local copy for readability |
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| 119 | increment_evaluations(); |
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| 120 | |
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| 121 | while( |
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| 122 | std::abs(delta) > xtol && // absolute x step check |
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| 123 | std::abs(c) > ftol && // absolute y tolerance |
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| 124 | std::abs(c) > xtol*std::abs(b) // comparison to smallest possible Y step from derivative |
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| 125 | ) |
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| 126 | { |
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| 127 | float_type a=(*final_yprime2)/2; // second derivative is 2*a |
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| 128 | float_type disc=b*b-4*a*c; |
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| 129 | // std::cout << std::endl << "find_root_debug a,b,c,d " << a << " " << b << " " << c << " " << disc << std::endl; |
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| 130 | |
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| 131 | if(disc >= 0) { |
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| 132 | float_type q=-0.5*((b>=0)?(b+std::sqrt(disc)):(b-std::sqrt(disc))); |
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| 133 | if(q*q > std::abs(a*c)) delta=c/q; // since x1=q/a, x2=c/q, x1/x2=q^2/ac, this picks smaller step |
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| 134 | else delta=q/a; |
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| 135 | root+=delta; |
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| 136 | } |
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| 137 | |
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| 138 | if(disc < 0 || root<lower_bracket || root>upper_bracket || |
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| 139 | std::abs(delta) >= 0.5*(upper_bracket-lower_bracket)) { |
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| 140 | // if we jump out of the bracket, or aren't converging well, bisect |
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| 141 | root=0.5*(lower_bracket+upper_bracket); |
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| 142 | delta=upper_bracket-lower_bracket; |
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| 143 | } |
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| 144 | c=value_with_derivatives(root, final_yprime, final_yprime2)-value; // compute initial values |
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[1230] | 145 | if(c2_isnan(c)) { |
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| 146 | bad_x_point=root; |
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| 147 | return c; // return the nan if a computation failed |
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| 148 | } |
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[807] | 149 | b=*final_yprime; // make a local copy for readability |
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| 150 | increment_evaluations(); |
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| 151 | |
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| 152 | // now, close in bracket on whichever side this still brackets |
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[1230] | 153 | if(c*lower_sign < 0.0) { |
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[807] | 154 | cupper=c; |
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| 155 | upper_bracket=root; |
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| 156 | } else { |
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| 157 | clower=c; |
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| 158 | lower_bracket=root; |
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| 159 | } |
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| 160 | // std::cout << "find_root_debug x, y, dx " << root << " " << c << " " << delta << std::endl; |
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| 161 | } |
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| 162 | return root; |
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| 163 | } |
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| 164 | |
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| 165 | /* def partial_integrals(self, xgrid): |
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| 166 | Return the integrals of a function between the sampling points xgrid. The sum is the definite integral. |
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| 167 | This method uses an exact integration of the polynomial which matches the values and derivatives at the |
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| 168 | endpoints of a segment. Its error scales as h**6, if the input functions really are smooth. |
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| 169 | This could very well be used as a stepper for adaptive Romberg integration. |
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| 170 | For InterpolatingFunctions, it is likely that the Simpson's rule integrator is sufficient. |
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| 171 | #the weights come from an exact mathematica solution to the 5th order polynomial with the given values & derivatives |
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| 172 | #yint = (y0+y1)*dx/2 + dx^2*(yp0-yp1)/10 + dx^3 * (ypp0+ypp1)/120 ) |
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| 173 | */ |
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| 174 | |
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| 175 | // the recursive part of the integrator is agressively designed to minimize copying of data... lots of pointers |
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[1230] | 176 | template <typename float_type> float_type c2_function<float_type>::integrate_step(c2_integrate_recur &rb) const throw(c2_exception) |
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[807] | 177 | { |
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[1230] | 178 | std::vector< recur_item > &rb_stack=*rb.rb_stack; // heap-based stack of data for recursion |
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| 179 | rb_stack.clear(); |
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[807] | 180 | |
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[1230] | 181 | recur_item top; |
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| 182 | top.depth=0; top.done=false; top.f0index=0; top.f2index=0; top.step_sum=0; |
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[807] | 183 | |
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[1230] | 184 | // push storage for our initial elements |
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| 185 | rb_stack.push_back(top); |
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| 186 | rb_stack.back().f1=*rb.f0; |
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| 187 | rb_stack.back().done=true; // this element will never be evaluated further |
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[807] | 188 | |
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[1230] | 189 | rb_stack.push_back(top); |
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| 190 | rb_stack.back().f1=*rb.f1; |
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| 191 | rb_stack.back().done=true; // this element will never be evaluated further |
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| 192 | |
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| 193 | if(!rb.inited) { |
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[807] | 194 | switch(rb.derivs) { |
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| 195 | case 0: |
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| 196 | rb.eps_scale=0.1; rb.extrap_coef=16; break; |
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| 197 | case 1: |
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| 198 | rb.eps_scale=0.1; rb.extrap_coef=64; break; |
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| 199 | case 2: |
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| 200 | rb.eps_scale=0.02; rb.extrap_coef=1024; break; |
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| 201 | default: |
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| 202 | throw c2_exception("derivs must be 0, 1 or 2 in partial_integrals"); |
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| 203 | } |
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| 204 | |
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| 205 | rb.extrap2=1.0/(rb.extrap_coef-1.0); |
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[1230] | 206 | rb.dx_tolerance=10.0*std::numeric_limits<float_type>::epsilon(); |
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| 207 | rb.abs_tol_min=10.0*std::numeric_limits<float_type>::min(); |
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| 208 | rb.inited=true; |
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[807] | 209 | } |
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| 210 | |
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[1230] | 211 | // now, push our first real element |
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| 212 | top.f0index=0; // left element is stack[0] |
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| 213 | top.f2index=1; // right element is stack[1] |
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| 214 | top.abs_tol=rb.abs_tol; |
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| 215 | rb_stack.push_back(top); |
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[807] | 216 | |
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[1230] | 217 | while(rb_stack.size() > 2) { |
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| 218 | recur_item &back=rb_stack.back(); |
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| 219 | if(back.done) { |
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| 220 | float_type sum=back.step_sum; |
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| 221 | rb_stack.pop_back(); |
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| 222 | rb_stack.back().step_sum+=sum; // bump our sum up to the parent |
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| 223 | continue; |
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| 224 | } |
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| 225 | back.done=true; |
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[807] | 226 | |
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[1230] | 227 | c2_fblock<float_type> &f0=rb_stack[back.f0index].f1, &f2=rb_stack[back.f2index].f1; |
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| 228 | c2_fblock<float_type> &f1=back.f1; // will hold new middle values |
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| 229 | size_t f1index=rb_stack.size()-1; // our current offset |
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| 230 | float_type abs_tol=back.abs_tol; |
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| 231 | |
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| 232 | f1.x=0.5*(f0.x + f2.x); // center of interval |
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| 233 | float_type dx2=0.5*(f2.x - f0.x); |
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| 234 | |
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[807] | 235 | // check for underflow on step size, which prevents us from achieving specified accuracy. |
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[1230] | 236 | if(std::abs(dx2) < std::abs(f1.x)*rb.dx_tolerance || std::abs(dx2) < rb.abs_tol_min) { |
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[807] | 237 | std::ostringstream outstr; |
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[1230] | 238 | outstr << "Step size underflow in adaptive_partial_integrals at depth=" << back.depth << ", x= " << f1.x; |
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[807] | 239 | throw c2_exception(outstr.str().c_str()); |
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| 240 | } |
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| 241 | |
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[1230] | 242 | fill_fblock(f1); |
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| 243 | if(c2_isnan(f1.y)) { |
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| 244 | bad_x_point=f1.x; |
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| 245 | return f1.y; // can't go any further if a nan has appeared |
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| 246 | } |
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| 247 | |
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| 248 | bool yptrouble=f0.ypbad || f2.ypbad || f1.ypbad; |
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| 249 | bool ypptrouble=f0.yppbad || f2.yppbad || f1.yppbad; |
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| 250 | |
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| 251 | // select the real derivative count based on whether we are at a point where derivatives exist |
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| 252 | int derivs = std::min(rb.derivs, (yptrouble||ypptrouble)?(yptrouble?0:1):2); |
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| 253 | |
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| 254 | if(!back.depth) { // top level, total has not been initialized yet |
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| 255 | switch(derivs) { // create estimate of next lower order for first try |
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[807] | 256 | case 0: |
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[1230] | 257 | back.previous_estimate=(f0.y+f2.y)*dx2; break; |
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[807] | 258 | case 1: |
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[1230] | 259 | back.previous_estimate=(f0.y+4.0*f1.y+f2.y)*dx2/3.0; break; |
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[807] | 260 | case 2: |
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[1230] | 261 | back.previous_estimate=( (14*f0.y + 32*f1.y + 14*f2.y) + 2*dx2 * (f0.yp - f2.yp) ) * dx2 /30.; break; |
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[807] | 262 | default: |
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[1230] | 263 | back.previous_estimate=0.0; // just to suppress missing default warnings |
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[807] | 264 | } |
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[1230] | 265 | } |
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[807] | 266 | |
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| 267 | float_type left, right; |
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| 268 | |
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[1230] | 269 | // pre-compute constants so all multiplies use a small dynamic range |
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| 270 | // constants for 0 derivative integrator |
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| 271 | static const float_type c0c1=5./12., c0c2=8./12., c0c3=-1./12.; |
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| 272 | // constants for 1 derivative integrator |
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| 273 | static const float_type c1c1=101./240., c1c2=128./240., c1c3=11./240., |
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| 274 | c1c4=13./240., c1c5=-40./240., c1c6=-3./240.; |
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| 275 | // constants for 2 derivative integrator |
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| 276 | static const float_type c2c1=169./40320., c2c2=1024./ 40320., c2c3=-41./40320., |
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| 277 | c2c4=2727./40320., c2c5=-5040./40320., c2c6=423./40320., |
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| 278 | c2c7=17007./40320., c2c8=24576./40320., c2c9=-1263./40320.; |
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| 279 | |
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| 280 | switch(derivs) { |
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[807] | 281 | case 2: |
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| 282 | // use ninth-order estimates for each side, from full set of all values (!) (Thanks, Mathematica!) |
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[1230] | 283 | left= ( ( (c2c1*f0.ypp + c2c2*f1.ypp + c2c3*f2.ypp)*dx2 + |
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| 284 | (c2c4*f0.yp + c2c5*f1.yp + c2c6*f2.yp) )*dx2 + |
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| 285 | (c2c7*f0.y + c2c8*f1.y + c2c9*f2.y) )* dx2; |
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| 286 | right= ( ( (c2c1*f2.ypp + c2c2*f1.ypp + c2c3*f0.ypp)*dx2 - |
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| 287 | (c2c4*f2.yp + c2c5*f1.yp + c2c6*f0.yp) )*dx2 + |
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| 288 | (c2c7*f2.y + c2c8*f1.y + c2c9*f0.y) )* dx2; |
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| 289 | // std::cout << f0.x << " " << f1.x << " " << f2.x << std::endl ; |
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| 290 | // std::cout << f0.y << " " << f1.y << " " << f2.y << " " << left << " " << right << " " << total << std::endl ; |
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[807] | 291 | break; |
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| 292 | case 1: |
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[1230] | 293 | left= ( (c1c1*f0.y + c1c2*f1.y + c1c3*f2.y) + dx2*(c1c4*f0.yp + c1c5*f1.yp + c1c6*f2.yp) ) * dx2 ; |
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| 294 | right= ( (c1c1*f2.y + c1c2*f1.y + c1c3*f0.y) - dx2*(c1c4*f2.yp + c1c5*f1.yp + c1c6*f0.yp) ) * dx2 ; |
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[807] | 295 | break; |
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| 296 | case 0: |
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[1230] | 297 | left= (c0c1*f0.y + c0c2*f1.y + c0c3*f2.y)*dx2; |
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| 298 | right= (c0c1*f2.y + c0c2*f1.y + c0c3*f0.y)*dx2; |
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[807] | 299 | break; |
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| 300 | default: |
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| 301 | left=right=0.0; // suppress warnings about missing default |
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| 302 | break; |
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| 303 | } |
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| 304 | |
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| 305 | float_type lrsum=left+right; |
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| 306 | |
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[1230] | 307 | bool extrapolate=back.depth && rb.extrapolate && (derivs==rb.derivs); // only extrapolate if no trouble with derivs |
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| 308 | float_type eps=std::abs(back.previous_estimate-lrsum)*rb.eps_scale; |
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| 309 | if(extrapolate) eps*=rb.eps_scale; |
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[807] | 310 | |
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[1230] | 311 | if(rb.adapt && eps > abs_tol && eps > std::abs(lrsum)*rb.rel_tol) { |
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| 312 | // tolerance not met, subdivide & recur |
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| 313 | if(abs_tol > rb.abs_tol_min) abs_tol=abs_tol*0.5; // each half has half the error budget |
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| 314 | top.abs_tol=abs_tol; |
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| 315 | top.depth=back.depth+1; |
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| 316 | |
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| 317 | // save the last things we need from back before a push happens, in case |
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| 318 | // the push causes a reallocation and moves the whole stack. |
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| 319 | size_t f0index=back.f0index, f2index=back.f2index; |
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| 320 | |
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| 321 | top.f0index=f1index; top.f2index=f2index; // insert pointers to right side data into our recursion block |
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| 322 | top.previous_estimate=right; |
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| 323 | rb_stack.push_back(top); |
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| 324 | |
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| 325 | top.f0index=f0index; top.f2index=f1index; // insert pointers to left side data into our recursion block |
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| 326 | top.previous_estimate=left; |
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| 327 | rb_stack.push_back(top); |
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| 328 | |
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| 329 | } else if(extrapolate) { |
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| 330 | // extrapolation only happens on leaf nodes, where the tolerance was met. |
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| 331 | back.step_sum+=(rb.extrap_coef*lrsum - back.previous_estimate)*rb.extrap2; |
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[807] | 332 | } else { |
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[1230] | 333 | back.step_sum+=lrsum; |
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[807] | 334 | } |
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[1230] | 335 | } |
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| 336 | return rb_stack.back().step_sum; // last element on the stack holds the sum |
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[807] | 337 | } |
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| 338 | |
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| 339 | template <typename float_type> bool c2_function<float_type>::check_monotonicity( |
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[1230] | 340 | const std::vector<float_type> &data, const char message[]) const throw(c2_exception) |
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[807] | 341 | { |
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| 342 | size_t np=data.size(); |
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| 343 | if(np < 2) return false; // one point has no direction! |
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| 344 | |
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| 345 | bool rev=(data[1] < data[0]); // which way do data point? |
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| 346 | size_t i; |
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| 347 | |
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[1337] | 348 | if(!rev) for(i = 2; i < np && (data[i-1] < data[i]) ; i++) { } |
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| 349 | else for(i = 2; i < np &&(data[i-1] > data[i]) ; i++) { } |
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[807] | 350 | |
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| 351 | if(i != np) throw c2_exception(message); |
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| 352 | |
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| 353 | return rev; |
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| 354 | } |
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| 355 | |
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| 356 | template <typename float_type> void c2_function<float_type>::set_sampling_grid(const std::vector<float_type> &grid) throw(c2_exception) |
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| 357 | { |
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| 358 | bool rev=check_monotonicity(grid, "set_sampling_grid: sampling grid not monotonic"); |
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| 359 | |
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| 360 | if(!sampling_grid || no_overwrite_grid) sampling_grid=new std::vector<float_type>; |
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| 361 | (*sampling_grid)=grid; no_overwrite_grid=0; |
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| 362 | |
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| 363 | if(rev) std::reverse(sampling_grid->begin(), sampling_grid->end()); // make it increasing |
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| 364 | } |
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| 365 | |
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[1230] | 366 | template <typename float_type> void c2_function<float_type>:: |
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| 367 | get_sampling_grid(float_type xmin, float_type xmax, std::vector<float_type> &grid) const |
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[807] | 368 | { |
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[1230] | 369 | std::vector<float_type> *result=&grid; |
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| 370 | result->clear(); |
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[807] | 371 | |
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| 372 | if( !(sampling_grid) || !(sampling_grid->size()) || (xmax <= sampling_grid->front()) || (xmin >= sampling_grid->back()) ) { |
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| 373 | // nothing is known about the function in this region, return xmin and xmax |
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| 374 | result->push_back(xmin); |
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| 375 | result->push_back(xmax); |
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| 376 | } else { |
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| 377 | std::vector<float_type> &sg=*sampling_grid; // just a shortcut |
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| 378 | int np=sg.size(); |
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| 379 | int klo=0, khi=np-1, firstindex=0, lastindex=np-1; |
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| 380 | |
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| 381 | result->push_back(xmin); |
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| 382 | |
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| 383 | if(xmin > sg.front() ) { |
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| 384 | // hunt through table for position bracketing starting point |
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| 385 | while(khi-klo > 1) { |
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| 386 | int km=(khi+klo)/2; |
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| 387 | if(sg[km] > xmin) khi=km; |
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| 388 | else klo=km; |
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| 389 | } |
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| 390 | khi=klo+1; |
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| 391 | // khi now points to first point definitively beyond our first point, or last point of array |
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| 392 | firstindex=khi; |
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| 393 | khi=np-1; // restart upper end of search |
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| 394 | } |
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| 395 | |
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| 396 | if(xmax < sg.back()) { |
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| 397 | // hunt through table for position bracketing starting point |
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| 398 | while(khi-klo > 1) { |
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| 399 | int km=(khi+klo)/2; |
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| 400 | if(sg[km] > xmax) khi=km; |
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| 401 | else klo=km; |
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| 402 | } |
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| 403 | khi=klo+1; |
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| 404 | // khi now points to first point definitively beyond our last point, or last point of array |
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| 405 | lastindex=klo; |
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| 406 | } |
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| 407 | |
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| 408 | int initsize=result->size(); |
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| 409 | result->resize(initsize+(lastindex-firstindex+2)); |
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| 410 | std::copy(sg.begin()+firstindex, sg.begin()+lastindex+1, result->begin()+initsize); |
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| 411 | result->back()=xmax; |
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[1230] | 412 | |
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[807] | 413 | // this is the unrefined sampling grid... now check for very close points on front & back and fix if needed. |
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| 414 | preen_sampling_grid(result); |
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| 415 | } |
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| 416 | } |
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| 417 | |
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| 418 | template <typename float_type> void c2_function<float_type>::preen_sampling_grid(std::vector<float_type> *result) const |
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| 419 | { |
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| 420 | // this is the unrefined sampling grid... now check for very close points on front & back and fix if needed. |
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| 421 | if(result->size() > 2) { // may be able to prune dangerously close points near the ends if there are at least 3 points |
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| 422 | bool deleteit=false; |
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| 423 | float_type x0=(*result)[0], x1=(*result)[1]; |
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| 424 | float_type dx1=x1-x0; |
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| 425 | |
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| 426 | float_type ftol=10.0*(std::numeric_limits<float_type>::epsilon()*(std::abs(x0)+std::abs(x1))+std::numeric_limits<float_type>::min()); |
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| 427 | if(dx1 < ftol) deleteit=true; |
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| 428 | float_type dx2=(*result)[2]-x0; |
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| 429 | if(dx1/dx2 < 0.1) deleteit=true; // endpoint is very close to internal interesting point |
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| 430 | |
---|
| 431 | if(deleteit) result->erase(result->begin()+1); // delete redundant interesting point |
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| 432 | } |
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| 433 | |
---|
| 434 | if(result->size() > 2) { // may be able to prune dangerously close points near the ends if there are at least 3 points |
---|
| 435 | bool deleteit=false; |
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| 436 | int pos=result->size()-3; |
---|
| 437 | float_type x0=(*result)[pos+1], x1=(*result)[pos+2]; |
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| 438 | float_type dx1=x1-x0; |
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| 439 | |
---|
| 440 | float_type ftol=10.0*(std::numeric_limits<float_type>::epsilon()*(std::abs(x0)+std::abs(x1))+std::numeric_limits<float_type>::min()); |
---|
| 441 | if(dx1 < ftol) deleteit=true; |
---|
| 442 | float_type dx2=x1-(*result)[pos]; |
---|
| 443 | if(dx1/dx2 < 0.1) deleteit=true; // endpoint is very close to internal interesting point |
---|
| 444 | |
---|
| 445 | if(deleteit) result->erase(result->end()-2); // delete redundant interesting point |
---|
| 446 | } |
---|
| 447 | } |
---|
| 448 | |
---|
[1230] | 449 | template <typename float_type> void c2_function<float_type>:: |
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| 450 | refine_sampling_grid(std::vector<float_type> &grid, size_t refinement) const |
---|
[807] | 451 | { |
---|
| 452 | size_t np=grid.size(); |
---|
| 453 | size_t count=(np-1)*refinement + 1; |
---|
| 454 | float_type dxscale=1.0/refinement; |
---|
| 455 | |
---|
[1230] | 456 | std::vector<float_type> result(count); |
---|
[807] | 457 | |
---|
| 458 | for(size_t i=0; i<(np-1); i++) { |
---|
| 459 | float_type x=grid[i]; |
---|
| 460 | float_type dx=(grid[i+1]-x)*dxscale; |
---|
[1230] | 461 | for(size_t j=0; j<refinement; j++, x+=dx) result[i*refinement+j]=x; |
---|
[807] | 462 | } |
---|
[1230] | 463 | result.back()=grid.back(); |
---|
| 464 | grid=result; // copy the expanded grid back to the input |
---|
[807] | 465 | } |
---|
| 466 | |
---|
| 467 | template <typename float_type> float_type c2_function<float_type>::integral(float_type xmin, float_type xmax, std::vector<float_type> *partials, |
---|
[1230] | 468 | float_type abs_tol, float_type rel_tol, int derivs, bool adapt, bool extrapolate) const throw(c2_exception) |
---|
[807] | 469 | { |
---|
[1230] | 470 | if(xmin==xmax) { |
---|
| 471 | if(partials) partials->clear(); |
---|
| 472 | return 0.0; |
---|
| 473 | } |
---|
| 474 | std::vector<float_type> grid; |
---|
| 475 | get_sampling_grid(xmin, xmax, grid); |
---|
| 476 | float_type intg=partial_integrals(grid, partials, abs_tol, rel_tol, derivs, adapt, extrapolate); |
---|
[807] | 477 | return intg; |
---|
| 478 | } |
---|
| 479 | |
---|
| 480 | template <typename float_type> c2_function<float_type> &c2_function<float_type>::normalized_function(float_type xmin, float_type xmax, float_type norm) |
---|
[1230] | 481 | const throw(c2_exception) |
---|
[807] | 482 | { |
---|
| 483 | float_type intg=integral(xmin, xmax); |
---|
[1230] | 484 | return *new c2_scaled_function_p<float_type>(*this, norm/intg); |
---|
[807] | 485 | } |
---|
| 486 | |
---|
[1230] | 487 | template <typename float_type> c2_function<float_type> &c2_function<float_type>::square_normalized_function(float_type xmin, float_type xmax, float_type norm) |
---|
| 488 | const throw(c2_exception) |
---|
[807] | 489 | { |
---|
[1230] | 490 | c2_ptr<float_type> mesquared((*new c2_quadratic_p<float_type>(0., 0., 0., 1.))(*this)); |
---|
[807] | 491 | |
---|
[1230] | 492 | std::vector<float_type> grid; |
---|
| 493 | get_sampling_grid(xmin, xmax, grid); |
---|
| 494 | float_type intg=mesquared->partial_integrals(grid); |
---|
[807] | 495 | |
---|
[1230] | 496 | return *new c2_scaled_function_p<float_type>(*this, std::sqrt(norm/intg)); |
---|
[807] | 497 | } |
---|
| 498 | |
---|
| 499 | template <typename float_type> c2_function<float_type> &c2_function<float_type>::square_normalized_function( |
---|
| 500 | float_type xmin, float_type xmax, const c2_function<float_type> &weight, float_type norm) |
---|
[1230] | 501 | const throw(c2_exception) |
---|
[807] | 502 | { |
---|
[1230] | 503 | c2_ptr<float_type> weighted((*new c2_quadratic_p<float_type>(0., 0., 0., 1.))(*this) * weight); |
---|
[807] | 504 | |
---|
[1230] | 505 | std::vector<float_type> grid; |
---|
| 506 | get_sampling_grid(xmin, xmax, grid); |
---|
| 507 | float_type intg=weighted->partial_integrals(grid); |
---|
[807] | 508 | |
---|
[1230] | 509 | return *new c2_scaled_function_p<float_type>(*this, std::sqrt(norm/intg)); |
---|
[807] | 510 | } |
---|
| 511 | |
---|
| 512 | template <typename float_type> float_type c2_function<float_type>::partial_integrals( |
---|
| 513 | std::vector<float_type> xgrid, std::vector<float_type> *partials, |
---|
[1230] | 514 | float_type abs_tol, float_type rel_tol, int derivs, bool adapt, bool extrapolate) |
---|
| 515 | const throw(c2_exception) |
---|
[807] | 516 | { |
---|
| 517 | int np=xgrid.size(); |
---|
| 518 | |
---|
[1230] | 519 | c2_fblock<float_type> f0, f2; |
---|
[807] | 520 | struct c2_integrate_recur rb; |
---|
| 521 | rb.rel_tol=rel_tol; |
---|
| 522 | rb.extrapolate=extrapolate; |
---|
| 523 | rb.adapt=adapt; |
---|
| 524 | rb.derivs=derivs; |
---|
[1230] | 525 | std::vector< recur_item > rb_stack; |
---|
| 526 | rb_stack.reserve(20); // enough for most operations |
---|
| 527 | rb.rb_stack=&rb_stack; |
---|
| 528 | rb.inited=false; |
---|
| 529 | float_type dx_inv=1.0/std::abs(xgrid.back()-xgrid.front()); |
---|
[807] | 530 | |
---|
| 531 | if(partials) partials->resize(np-1); |
---|
| 532 | |
---|
| 533 | float_type sum=0.0; |
---|
| 534 | |
---|
| 535 | f2.x=xgrid[0]; |
---|
[1230] | 536 | fill_fblock(f2); |
---|
| 537 | if(c2_isnan(f2.y)) { |
---|
| 538 | bad_x_point=f2.x; |
---|
| 539 | return f2.y; // can't go any further if a nan has appeared |
---|
| 540 | } |
---|
[807] | 541 | |
---|
| 542 | for(int i=0; i<np-1; i++) { |
---|
| 543 | f0=f2; // copy upper bound to lower before computing new upper bound |
---|
| 544 | |
---|
| 545 | f2.x=xgrid[i+1]; |
---|
[1230] | 546 | fill_fblock(f2); |
---|
| 547 | if(c2_isnan(f2.y)) { |
---|
| 548 | bad_x_point=f2.x; |
---|
| 549 | return f2.y; // can't go any further if a nan has appeared |
---|
| 550 | } |
---|
[807] | 551 | |
---|
[1230] | 552 | rb.abs_tol=abs_tol*std::abs(f2.x-f0.x)*dx_inv; // distribute error tolerance over whole domain |
---|
| 553 | rb.f0=&f0; rb.f1=&f2; |
---|
[807] | 554 | float_type ps=integrate_step(rb); |
---|
| 555 | sum+=ps; |
---|
| 556 | if(partials) (*partials)[i]=ps; |
---|
[1230] | 557 | if(c2_isnan(ps)) break; // NaN stops integration |
---|
[807] | 558 | } |
---|
| 559 | return sum; |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | // generate a sampling grid at points separated by dx=5, which is intentionally |
---|
| 563 | // incommensurate with pi and 2*pi so grid errors are somewhat randomized |
---|
[1230] | 564 | template <typename float_type> void c2_sin_p<float_type>:: |
---|
| 565 | get_sampling_grid(float_type xmin, float_type xmax, std::vector<float_type> &grid) const |
---|
[807] | 566 | { |
---|
[1230] | 567 | grid.clear(); |
---|
| 568 | for(; xmin < xmax; xmin+=5.0) grid.push_back(xmin); |
---|
| 569 | grid.push_back(xmax); |
---|
| 570 | this->preen_sampling_grid(&grid); |
---|
[807] | 571 | } |
---|
| 572 | |
---|
[1230] | 573 | template <typename float_type> float_type c2_function_transformation<float_type>::evaluate( |
---|
| 574 | float_type xraw, |
---|
| 575 | float_type y, float_type yp0, float_type ypp0, |
---|
| 576 | float_type *yprime, float_type *yprime2) const |
---|
| 577 | { |
---|
| 578 | y=Y.fHasStaticTransforms ? Y.pOut(y) : Y.fOut(y); |
---|
| 579 | |
---|
| 580 | if(yprime || yprime2) { |
---|
[807] | 581 | |
---|
[1230] | 582 | float_type yp, yp2; |
---|
| 583 | if(X.fHasStaticTransforms && Y.fHasStaticTransforms) { |
---|
| 584 | float_type fpi=1.0/Y.pInPrime(y); |
---|
| 585 | float_type gp=X.pInPrime(xraw); |
---|
| 586 | // from Mathematica Dt[InverseFunction[f][y[g[x]]], x] |
---|
| 587 | yp=gp*yp0*fpi; // transformed derivative |
---|
| 588 | yp2=(gp*gp*ypp0 + X.pInDPrime(xraw)*yp0 - Y.pInDPrime(y)*yp*yp )*fpi; |
---|
| 589 | } else { |
---|
| 590 | float_type fpi=1.0/Y.fInPrime(y); |
---|
| 591 | float_type gp=X.fInPrime(xraw); |
---|
| 592 | // from Mathematica Dt[InverseFunction[f][y[g[x]]], x] |
---|
| 593 | yp=gp*yp0*fpi; // transformed derivative |
---|
| 594 | yp2=(gp*gp*ypp0 + X.fInDPrime(xraw)*yp0 - Y.fInDPrime(y)*yp*yp )*fpi; |
---|
| 595 | } |
---|
| 596 | if(yprime) *yprime=yp; |
---|
| 597 | if(yprime2) *yprime2=yp2; |
---|
| 598 | } |
---|
| 599 | return y; |
---|
| 600 | } |
---|
| 601 | |
---|
[807] | 602 | // The constructor |
---|
[1230] | 603 | template <typename float_type> interpolating_function_p<float_type> & interpolating_function_p<float_type>::load( |
---|
[807] | 604 | const std::vector<float_type> &x, const std::vector<float_type> &f, |
---|
| 605 | bool lowerSlopeNatural, float_type lowerSlope, |
---|
| 606 | bool upperSlopeNatural, float_type upperSlope, |
---|
[1230] | 607 | bool splined |
---|
| 608 | ) throw(c2_exception) |
---|
[807] | 609 | { |
---|
[1230] | 610 | c2_ptr<float_type> keepme(*this); |
---|
[807] | 611 | X= x; |
---|
| 612 | F= f; |
---|
| 613 | |
---|
| 614 | // Xraw is useful in some of the arithmetic operations between interpolating functions |
---|
| 615 | Xraw=x; |
---|
| 616 | |
---|
| 617 | set_domain(std::min(Xraw.front(), Xraw.back()),std::max(Xraw.front(), Xraw.back())); |
---|
[1230] | 618 | |
---|
[807] | 619 | if(x.size() != f.size()) { |
---|
| 620 | throw c2_exception("interpolating_function::init() -- x & y inputs are of different size"); |
---|
| 621 | } |
---|
| 622 | |
---|
| 623 | size_t np=X.size(); // they are the same now, so lets take a short cut |
---|
| 624 | |
---|
| 625 | if(np < 2) { |
---|
| 626 | throw c2_exception("interpolating_function::init() -- input < 2 elements "); |
---|
| 627 | } |
---|
| 628 | |
---|
| 629 | bool xraw_rev=check_monotonicity(Xraw, |
---|
| 630 | "interpolating_function::init() non-monotonic raw x input"); // which way does raw X point? sampling grid MUST be increasing |
---|
| 631 | |
---|
| 632 | if(!xraw_rev) { // we can use pointer to raw X values if they are in the right order |
---|
| 633 | set_sampling_grid_pointer(Xraw); // our intial grid of x values is certainly a good guess for 'interesting' points |
---|
| 634 | } else { |
---|
| 635 | set_sampling_grid(Xraw); // make a copy of it, and assure it is in right order |
---|
| 636 | } |
---|
| 637 | |
---|
[1230] | 638 | if(fTransform.X.fTransformed) { // check if X scale is nonlinear, and if so, do transform |
---|
| 639 | if(!lowerSlopeNatural) lowerSlope /= fTransform.X.fInPrime(X[0]); |
---|
| 640 | if(!upperSlopeNatural) upperSlope /= fTransform.X.fInPrime(X[np-1]); |
---|
| 641 | for(size_t i=0; i<np; i++) X[i]=fTransform.X.fIn(X[i]); |
---|
| 642 | } |
---|
| 643 | if(fTransform.Y.fTransformed) { // check if Y scale is nonlinear, and if so, do transform |
---|
| 644 | if(!lowerSlopeNatural) lowerSlope *= fTransform.Y.fInPrime(F[0]); |
---|
| 645 | if(!upperSlopeNatural) upperSlope *= fTransform.Y.fInPrime(F[np-1]); |
---|
| 646 | for(size_t i=0; i<np; i++) F[i]=fTransform.Y.fIn(F[i]); |
---|
[807] | 647 | } |
---|
| 648 | |
---|
| 649 | xInverted=check_monotonicity(X, |
---|
| 650 | "interpolating_function::init() non-monotonic transformed x input"); |
---|
| 651 | |
---|
[1230] | 652 | if(splined) spline(lowerSlopeNatural, lowerSlope, upperSlopeNatural, upperSlope); |
---|
| 653 | else y2.assign(np,0.0); |
---|
| 654 | |
---|
| 655 | lastKLow=0; |
---|
| 656 | keepme.release_for_return(); |
---|
| 657 | return *this; |
---|
| 658 | } |
---|
| 659 | |
---|
| 660 | /* |
---|
| 661 | // The constructor |
---|
| 662 | template <typename float_type> interpolating_function_p<float_type> & interpolating_function_p<float_type>::load_pairs( |
---|
| 663 | std::vector<std::pair<float_type, float_type> > &data, |
---|
| 664 | bool lowerSlopeNatural, float_type lowerSlope, |
---|
| 665 | bool upperSlopeNatural, float_type upperSlope, |
---|
| 666 | bool splined |
---|
| 667 | ) throw(c2_exception) |
---|
| 668 | { |
---|
| 669 | c2_ptr<float_type> keepme(*this); |
---|
| 670 | |
---|
| 671 | size_t np=data.size(); |
---|
| 672 | if(np < 2) { |
---|
| 673 | throw c2_exception("interpolating_function::init() -- input < 2 elements "); |
---|
| 674 | } |
---|
| 675 | |
---|
| 676 | // sort into ascending order |
---|
| 677 | std::sort(data.begin(), data.end(), comp_pair); |
---|
| 678 | |
---|
| 679 | std::vector<float_type> xtmp, ytmp; |
---|
| 680 | xtmp.reserve(np); |
---|
| 681 | ytmp.reserve(np); |
---|
| 682 | for (size_t i=0; i<np; i++) { |
---|
| 683 | xtmp.push_back(data[i].first); |
---|
| 684 | ytmp.push_back(data[i].second); |
---|
| 685 | } |
---|
| 686 | this->load(xtmp, ytmp, lowerSlopeNatural, lowerSlope, upperSlopeNatural, upperSlope, splined); |
---|
| 687 | |
---|
| 688 | keepme.release_for_return(); |
---|
| 689 | return *this; |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | template <typename float_type> interpolating_function_p<float_type> & |
---|
| 693 | interpolating_function_p<float_type>::load_random_generator_function( |
---|
| 694 | const std::vector<float_type> &bincenters, const c2_function<float_type> &binheights) |
---|
| 695 | throw(c2_exception) |
---|
| 696 | { |
---|
| 697 | c2_ptr<float_type> keepme(*this); |
---|
| 698 | |
---|
| 699 | std::vector<float_type> integral; |
---|
| 700 | c2_const_ptr<float_type> keepit(binheights); // manage function... not really needed here, but always safe. |
---|
| 701 | // integrate from first to last bin in original order, leaving results in integral |
---|
| 702 | // ask for relative error of 1e-6 on each bin, with absolute error set to 0 (since we don't know the data scale). |
---|
| 703 | float_type sum=binheights.partial_integrals(bincenters, &integral, 0.0, 1e-6); |
---|
| 704 | // the integral vector now has partial integrals... it must be accumulated by summing |
---|
| 705 | integral.insert(integral.begin(), 0.0); // integral from start to start is 0 |
---|
| 706 | float_type scale=1.0/sum; |
---|
| 707 | for(size_t i=1; i<integral.size(); i++) integral[i]=integral[i]*scale + integral[i-1]; |
---|
| 708 | integral.back()=1.0; // force exact value on boundary |
---|
| 709 | |
---|
| 710 | this->load(integral, bincenters, |
---|
| 711 | false, 1.0/(scale*binheights(bincenters.front() )), |
---|
| 712 | false, 1.0/(scale*binheights(bincenters.back() )) |
---|
| 713 | ); // use integral as x axis in inverse function |
---|
| 714 | keepme.release_for_return(); |
---|
| 715 | return *this; |
---|
| 716 | } |
---|
| 717 | |
---|
| 718 | template <typename float_type> interpolating_function_p<float_type> & |
---|
| 719 | interpolating_function_p<float_type>::load_random_generator_bins( |
---|
| 720 | const std::vector<float_type> &bins, const std::vector<float_type> &binheights) |
---|
| 721 | throw(c2_exception) |
---|
| 722 | { |
---|
| 723 | c2_ptr<float_type> keepme(*this); |
---|
| 724 | |
---|
| 725 | size_t np=binheights.size(); |
---|
| 726 | std::vector<float_type> integral(np+1), bin_edges(np+1); |
---|
| 727 | |
---|
| 728 | // compute the integral based on estimates of the bin edges from the given bin centers... |
---|
| 729 | // except for bin 0 & final bin, the edge of a bin is halfway between then center of the |
---|
| 730 | // bin and the center of the previous/next bin. |
---|
| 731 | // This gives width[n] = (center[n+1]+center[n])/2 - (center[n]+center[n-1])/2 = (center[n+1]-center[n-1])/2 |
---|
| 732 | // for the edges, assume a bin of width (center[1]-center[0]) or (center[np-1]-center[np-2]) |
---|
| 733 | // be careful that absolute values are used in case data are reversed. |
---|
| 734 | |
---|
| 735 | if(bins.size() == binheights.size()+1) { |
---|
| 736 | bin_edges=bins; // edges array was passed in |
---|
| 737 | } else if (bins.size() == binheights.size()) { |
---|
| 738 | bin_edges.front()=bins[0] - (bins[1]-bins[0])*0.5; // edge bin |
---|
| 739 | for(size_t i=1; i<np; i++) { |
---|
| 740 | bin_edges[i]=(bins[i]+bins[i-1])*0.5; |
---|
| 741 | } |
---|
| 742 | bin_edges.back()=bins[np-1] + (bins[np-1]-bins[np-2])*0.5; // edge bin |
---|
| 743 | } else { |
---|
| 744 | throw c2_exception("inconsistent bin vectors passed to load_random_generator_bins"); |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | float_type running_sum=0.0; |
---|
| 748 | for(size_t i=0; i<np; i++) { |
---|
| 749 | integral[i]=running_sum; |
---|
| 750 | if(!binheights[i]) throw c2_exception("empty bin passed to load_random_generator_bins"); |
---|
| 751 | running_sum+=binheights[i]*std::abs(bin_edges[i+1]-bin_edges[i]); |
---|
| 752 | } |
---|
| 753 | float_type scale=1.0/running_sum; |
---|
| 754 | for(size_t i=0; i<np; i++) integral[i]*=scale; |
---|
| 755 | integral.back()=1.0; // force exactly correct value on boundary |
---|
| 756 | this->load(integral, bin_edges, |
---|
| 757 | false, 1.0/(scale*binheights.front()), |
---|
| 758 | false, 1.0/(scale*binheights.back()) |
---|
| 759 | ); // use integral as x axis in inverse function |
---|
| 760 | keepme.release_for_return(); |
---|
| 761 | return *this; |
---|
| 762 | } |
---|
| 763 | */ |
---|
| 764 | |
---|
| 765 | // The spline table generator |
---|
| 766 | template <typename float_type> void interpolating_function_p<float_type>::spline( |
---|
| 767 | bool lowerSlopeNatural, float_type lowerSlope, |
---|
| 768 | bool upperSlopeNatural, float_type upperSlope |
---|
| 769 | ) throw(c2_exception) |
---|
| 770 | { |
---|
| 771 | // construct spline tables here. |
---|
[807] | 772 | // this code is a re-translation of the pythonlabtools spline algorithm from pythonlabtools.sourceforge.net |
---|
[1230] | 773 | size_t np=X.size(); |
---|
[807] | 774 | std::vector<float_type> u(np), dy(np-1), dx(np-1), dxi(np-1), dx2i(np-2), siga(np-2), dydx(np-1); |
---|
| 775 | |
---|
| 776 | std::transform(X.begin()+1, X.end(), X.begin(), dx.begin(), std::minus<float_type>() ); // dx=X[1:] - X [:-1] |
---|
| 777 | for(size_t i=0; i<dxi.size(); i++) dxi[i]=1.0/dx[i]; // dxi = 1/dx |
---|
| 778 | for(size_t i=0; i<dx2i.size(); i++) dx2i[i]=1.0/(X[i+2]-X[i]); |
---|
| 779 | |
---|
| 780 | std::transform(F.begin()+1, F.end(), F.begin(), dy.begin(), std::minus<float_type>() ); // dy = F[i+1]-F[i] |
---|
| 781 | std::transform(dx2i.begin(), dx2i.end(), dx.begin(), siga.begin(), std::multiplies<float_type>()); // siga = dx[:-1]*dx2i |
---|
| 782 | std::transform(dxi.begin(), dxi.end(), dy.begin(), dydx.begin(), std::multiplies<float_type>()); // dydx=dy/dx |
---|
| 783 | |
---|
| 784 | // u[i]=(y[i+1]-y[i])/float(x[i+1]-x[i]) - (y[i]-y[i-1])/float(x[i]-x[i-1]) |
---|
| 785 | std::transform(dydx.begin()+1, dydx.end(), dydx.begin(), u.begin()+1, std::minus<float_type>() ); // incomplete rendering of u = dydx[1:]-dydx[:-1] |
---|
| 786 | |
---|
| 787 | y2.resize(np,0.0); |
---|
| 788 | |
---|
| 789 | if(lowerSlopeNatural) { |
---|
| 790 | y2[0]=u[0]=0.0; |
---|
| 791 | } else { |
---|
| 792 | y2[0]= -0.5; |
---|
| 793 | u[0]=(3.0*dxi[0])*(dy[0]*dxi[0] -lowerSlope); |
---|
| 794 | } |
---|
| 795 | |
---|
| 796 | for(size_t i=1; i < np -1; i++) { // the inner loop |
---|
| 797 | float_type sig=siga[i-1]; |
---|
| 798 | float_type p=sig*y2[i-1]+2.0; |
---|
| 799 | y2[i]=(sig-1.0)/p; |
---|
| 800 | u[i]=(6.0*u[i]*dx2i[i-1] - sig*u[i-1])/p; |
---|
| 801 | } |
---|
| 802 | |
---|
| 803 | float_type qn, un; |
---|
| 804 | |
---|
| 805 | if(upperSlopeNatural) { |
---|
| 806 | qn=un=0.0; |
---|
| 807 | } else { |
---|
| 808 | qn= 0.5; |
---|
| 809 | un=(3.0*dxi[dxi.size()-1])*(upperSlope- dy[dy.size()-1]*dxi[dxi.size()-1] ); |
---|
| 810 | } |
---|
| 811 | |
---|
| 812 | y2[np-1]=(un-qn*u[np-2])/(qn*y2[np-2]+1.0); |
---|
| 813 | for (size_t k=np-1; k != 0; k--) y2[k-1]=y2[k-1]*y2[k]+u[k-1]; |
---|
[1230] | 814 | } |
---|
| 815 | |
---|
| 816 | template <typename float_type> interpolating_function_p<float_type> &interpolating_function_p<float_type>::sample_function( |
---|
| 817 | const c2_function<float_type> &func, |
---|
| 818 | float_type xmin, float_type xmax, float_type abs_tol, float_type rel_tol, |
---|
| 819 | bool lowerSlopeNatural, float_type lowerSlope, |
---|
| 820 | bool upperSlopeNatural, float_type upperSlope |
---|
| 821 | ) throw(c2_exception) |
---|
| 822 | { |
---|
| 823 | c2_ptr<float_type> keepme(*this); |
---|
[807] | 824 | |
---|
[1230] | 825 | const c2_transformation<float_type> &XX=fTransform.X, &YY=fTransform.Y; // shortcuts |
---|
| 826 | |
---|
| 827 | // set up our params to look like the samplng function for now |
---|
| 828 | sampler_function=func; |
---|
| 829 | std::vector<float_type> grid; |
---|
| 830 | func.get_sampling_grid(xmin, xmax, grid); |
---|
| 831 | size_t gsize=grid.size(); |
---|
| 832 | if(XX.fTransformed) for(size_t i=0; i<gsize; i++) grid[i]=XX.fIn(grid[i]); |
---|
| 833 | set_sampling_grid_pointer(grid); |
---|
| 834 | |
---|
| 835 | // float_type xmin1=fXin(xmin), xmax1=fXin(xmax); // bounds in transformed space |
---|
| 836 | // get a list of points needed in transformed space, directly into our tables |
---|
| 837 | this->adaptively_sample(grid.front(), grid.back(), 8*abs_tol, 8*rel_tol, 0, &X, &F); |
---|
| 838 | // clear the sampler function now, since otherwise our value_with_derivatives is broken |
---|
| 839 | sampler_function.unset_function(); |
---|
| 840 | |
---|
| 841 | xInverted=check_monotonicity(X, |
---|
| 842 | "interpolating_function::init() non-monotonic transformed x input"); |
---|
| 843 | |
---|
| 844 | size_t np=X.size(); |
---|
| 845 | |
---|
| 846 | // Xraw is useful in some of the arithmetic operations between interpolating functions |
---|
| 847 | if(!XX.fTransformed) Xraw=X; |
---|
| 848 | else { |
---|
| 849 | Xraw.resize(np); |
---|
| 850 | for (size_t i=1; i<np-1; i++) Xraw[i]=XX.fOut(X[i]); |
---|
| 851 | Xraw.front()=xmin; |
---|
| 852 | Xraw.back()=xmax; |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | bool xraw_rev=check_monotonicity(Xraw, |
---|
| 856 | "interpolating_function::init() non-monotonic raw x input"); |
---|
| 857 | // which way does raw X point? sampling grid MUST be increasing |
---|
| 858 | |
---|
| 859 | if(!xraw_rev) { // we can use pointer to raw X values if they are in the right order |
---|
| 860 | set_sampling_grid_pointer(Xraw); |
---|
| 861 | // our intial grid of x values is certainly a good guess for 'interesting' points |
---|
| 862 | } else { |
---|
| 863 | set_sampling_grid(Xraw); // make a copy of it, and assure it is in right order |
---|
| 864 | } |
---|
| 865 | |
---|
| 866 | if(XX.fTransformed) { // check if X scale is nonlinear, and if so, do transform |
---|
| 867 | if(!lowerSlopeNatural) lowerSlope /= XX.fInPrime(xmin); |
---|
| 868 | if(!upperSlopeNatural) upperSlope /= XX.fInPrime(xmax); |
---|
| 869 | } |
---|
| 870 | if(YY.fTransformed) { // check if Y scale is nonlinear, and if so, do transform |
---|
| 871 | if(!lowerSlopeNatural) lowerSlope *= YY.fInPrime(func(xmin)); |
---|
| 872 | if(!upperSlopeNatural) upperSlope *= YY.fInPrime(func(xmax)); |
---|
| 873 | } |
---|
| 874 | // note that each of ends has 3 points with two equal gaps, since they were obtained by bisection |
---|
| 875 | // so the step sizes are easy to get |
---|
| 876 | // the 'natural slope' option for sampled functions has a different meaning than |
---|
| 877 | // for normal splines. In this case, the derivative is adjusted to make the |
---|
| 878 | // second derivative constant on the last two points at each end |
---|
| 879 | // which is consistent with the error sampling technique we used to get here |
---|
| 880 | if(lowerSlopeNatural) { |
---|
| 881 | float_type hlower=X[1]-X[0]; |
---|
| 882 | lowerSlope=0.5*(-F[2]-3*F[0]+4*F[1])/hlower; |
---|
| 883 | lowerSlopeNatural=false; // it's not the usual meaning of natural any more |
---|
| 884 | } |
---|
| 885 | if(upperSlopeNatural) { |
---|
| 886 | float_type hupper=X[np-1]-X[np-2]; |
---|
| 887 | upperSlope=0.5*(F[np-3]+3*F[np-1]-4*F[np-2])/hupper; |
---|
| 888 | upperSlopeNatural=false; // it's not the usual meaning of natural any more |
---|
| 889 | } |
---|
| 890 | this->set_domain(xmin, xmax); |
---|
| 891 | |
---|
| 892 | spline(lowerSlopeNatural, lowerSlope, upperSlopeNatural, upperSlope); |
---|
| 893 | lastKLow=0; |
---|
| 894 | keepme.release_for_return(); |
---|
| 895 | return *this; |
---|
[807] | 896 | } |
---|
| 897 | |
---|
| 898 | // This function is the reason for this class to exist |
---|
| 899 | // it computes the interpolated function, and (if requested) its proper first and second derivatives including all coordinate transforms |
---|
[1230] | 900 | template <typename float_type> float_type interpolating_function_p<float_type>::value_with_derivatives( |
---|
[807] | 901 | float_type x, float_type *yprime, float_type *yprime2) const throw(c2_exception) |
---|
| 902 | { |
---|
[1230] | 903 | if(sampler_function.valid()) { |
---|
| 904 | // if this is non-null, we are sampling data for later, so just return raw function |
---|
| 905 | // however, transform it into our sampling space, first. |
---|
| 906 | if(yprime) *yprime=0; |
---|
| 907 | if(yprime2) *yprime2=0; |
---|
| 908 | sampler_function->increment_evaluations(); |
---|
| 909 | return fTransform.Y.fIn(sampler_function(fTransform.X.fOut(x))); // derivatives are completely undefined |
---|
| 910 | } |
---|
| 911 | |
---|
[807] | 912 | if(x < this->xmin() || x > this->xmax()) { |
---|
| 913 | std::ostringstream outstr; |
---|
| 914 | outstr << "Interpolating function argument " << x << " out of range " << this->xmin() << " -- " << this ->xmax() << ": bailing"; |
---|
| 915 | throw c2_exception(outstr.str().c_str()); |
---|
| 916 | } |
---|
| 917 | |
---|
| 918 | float_type xraw=x; |
---|
| 919 | |
---|
[1230] | 920 | if(fTransform.X.fTransformed) x=fTransform.X.fHasStaticTransforms? |
---|
| 921 | fTransform.X.pIn(x) : fTransform.X.fIn(x); // save time by explicitly testing for identity function here |
---|
[807] | 922 | |
---|
| 923 | int klo=0, khi=X.size()-1; |
---|
[1230] | 924 | |
---|
| 925 | if(khi < 0) throw c2_exception("Uninitialized interpolating function being evaluated"); |
---|
[807] | 926 | |
---|
[1230] | 927 | const float_type *XX=&X[lastKLow]; // make all fast checks short offsets from here |
---|
| 928 | |
---|
[807] | 929 | if(!xInverted) { // select search depending on whether transformed X is increasing or decreasing |
---|
[1230] | 930 | if((XX[0] <= x) && (XX[1] >= x) ) { // already bracketed |
---|
[807] | 931 | klo=lastKLow; |
---|
[1230] | 932 | } else if((XX[1] <= x) && (XX[2] >= x)) { // in next bracket to the right |
---|
[807] | 933 | klo=lastKLow+1; |
---|
[1230] | 934 | } else if(lastKLow > 0 && (XX[-1] <= x) && (XX[0] >= x)) { // in next bracket to the left |
---|
[807] | 935 | klo=lastKLow-1; |
---|
| 936 | } else { // not bracketed, not close, start over |
---|
| 937 | // search for new KLow |
---|
| 938 | while(khi-klo > 1) { |
---|
| 939 | int km=(khi+klo)/2; |
---|
| 940 | if(X[km] > x) khi=km; |
---|
| 941 | else klo=km; |
---|
| 942 | } |
---|
| 943 | } |
---|
| 944 | } else { |
---|
[1230] | 945 | if((XX[0] >= x) && (XX[1] <= x) ) { // already bracketed |
---|
[807] | 946 | klo=lastKLow; |
---|
[1230] | 947 | } else if((XX[1] >= x) && (XX[2] <= x)) { // in next bracket to the right |
---|
[807] | 948 | klo=lastKLow+1; |
---|
[1230] | 949 | } else if(lastKLow > 0 && (XX[-1] >= x) && (XX[0] <= x)) { // in next bracket to the left |
---|
[807] | 950 | klo=lastKLow-1; |
---|
| 951 | } else { // not bracketed, not close, start over |
---|
| 952 | // search for new KLow |
---|
| 953 | while(khi-klo > 1) { |
---|
| 954 | int km=(khi+klo)/2; |
---|
| 955 | if(X[km] < x) khi=km; |
---|
| 956 | else klo=km; |
---|
| 957 | } |
---|
| 958 | } |
---|
| 959 | } |
---|
| 960 | |
---|
| 961 | khi=klo+1; |
---|
| 962 | lastKLow=klo; |
---|
| 963 | |
---|
| 964 | float_type h=X[khi]-X[klo]; |
---|
| 965 | |
---|
| 966 | float_type a=(X[khi]-x)/h; |
---|
| 967 | float_type b=1.0-a; |
---|
| 968 | float_type ylo=F[klo], yhi=F[khi], y2lo=y2[klo], y2hi=y2[khi]; |
---|
| 969 | float_type y=a*ylo+b*yhi+((a*a*a-a)*y2lo+(b*b*b-b)*y2hi)*(h*h)/6.0; |
---|
[1230] | 970 | |
---|
| 971 | float_type yp0=0; // the derivative in interpolating table coordinates |
---|
| 972 | float_type ypp0=0; // second derivative |
---|
[807] | 973 | |
---|
| 974 | if(yprime || yprime2) { |
---|
[1230] | 975 | yp0=(yhi-ylo)/h+((3*b*b-1)*y2hi-(3*a*a-1)*y2lo)*h/6.0; // the derivative in interpolating table coordinates |
---|
| 976 | ypp0=b*y2hi+a*y2lo; // second derivative |
---|
[807] | 977 | } |
---|
| 978 | |
---|
[1230] | 979 | if(fTransform.isIdentity) { |
---|
| 980 | if(yprime) *yprime=yp0; |
---|
| 981 | if(yprime2) *yprime2=ypp0; |
---|
| 982 | return y; |
---|
| 983 | } else return fTransform.evaluate(xraw, y, yp0, ypp0, yprime, yprime2); |
---|
[807] | 984 | } |
---|
| 985 | |
---|
[1230] | 986 | template <typename float_type> void interpolating_function_p<float_type>::set_lower_extrapolation(float_type bound) |
---|
[807] | 987 | { |
---|
| 988 | int kl = 0 ; |
---|
| 989 | int kh=kl+1; |
---|
[1230] | 990 | float_type xx=fTransform.X.fIn(bound); |
---|
[807] | 991 | float_type h0=X[kh]-X[kl]; |
---|
| 992 | float_type h1=xx-X[kl]; |
---|
| 993 | float_type yextrap=F[kl]+((F[kh]-F[kl])/h0 - h0*(y2[kl]+2.0*y2[kh])/6.0)*h1+y2[kl]*h1*h1/2.0; |
---|
| 994 | |
---|
| 995 | X.insert(X.begin(), xx); |
---|
| 996 | F.insert(F.begin(), yextrap); |
---|
| 997 | y2.insert(y2.begin(), y2.front()); // duplicate first or last element |
---|
| 998 | Xraw.insert(Xraw.begin(), bound); |
---|
| 999 | if (bound < this->fXMin) this->fXMin=bound; // check for reversed data |
---|
| 1000 | else this->fXMax=bound; |
---|
| 1001 | |
---|
| 1002 | //printf("%10.4f %10.4f %10.4f %10.4f %10.4f\n", bound, xx, h0, h1, yextrap); |
---|
| 1003 | //for(int i=0; i<X.size(); i++) printf("%4d %10.4f %10.4f %10.4f %10.4f \n", i, Xraw[i], X[i], F[i], y2[i]); |
---|
| 1004 | } |
---|
| 1005 | |
---|
[1230] | 1006 | template <typename float_type> void interpolating_function_p<float_type>::set_upper_extrapolation(float_type bound) |
---|
[807] | 1007 | { |
---|
| 1008 | int kl = X.size()-2 ; |
---|
| 1009 | int kh=kl+1; |
---|
[1230] | 1010 | float_type xx=fTransform.X.fIn(bound); |
---|
[807] | 1011 | float_type h0=X[kh]-X[kl]; |
---|
| 1012 | float_type h1=xx-X[kl]; |
---|
| 1013 | float_type yextrap=F[kl]+((F[kh]-F[kl])/h0 - h0*(y2[kl]+2.0*y2[kh])/6.0)*h1+y2[kl]*h1*h1/2.0; |
---|
| 1014 | |
---|
| 1015 | X.insert(X.end(), xx); |
---|
| 1016 | F.insert(F.end(), yextrap); |
---|
| 1017 | y2.insert(y2.end(), y2.back()); // duplicate first or last element |
---|
| 1018 | Xraw.insert(Xraw.end(), bound); |
---|
| 1019 | if (bound < this->fXMin) this->fXMin=bound; // check for reversed data |
---|
| 1020 | else this->fXMax=bound; |
---|
| 1021 | //printf("%10.4f %10.4f %10.4f %10.4f %10.4f\n", bound, xx, h0, h1, yextrap); |
---|
| 1022 | //for(int i=0; i<X.size(); i++) printf("%4d %10.4f %10.4f %10.4f %10.4f \n", i, Xraw[i], X[i], F[i], y2[i]); |
---|
| 1023 | } |
---|
| 1024 | |
---|
| 1025 | // return a new interpolating_function which is the unary function of an existing interpolating_function |
---|
| 1026 | // can also be used to generate a resampling of another c2_function on a different grid |
---|
| 1027 | // by creating a=interpolating_function(x,x) |
---|
| 1028 | // and doing b=a.unary_operator(c) where c is a c2_function (probably another interpolating_function) |
---|
| 1029 | |
---|
[1230] | 1030 | template <typename float_type> interpolating_function_p<float_type>& |
---|
| 1031 | interpolating_function_p<float_type>::unary_operator(const c2_function<float_type> &source) const |
---|
[807] | 1032 | { |
---|
| 1033 | size_t np=X.size(); |
---|
| 1034 | std::vector<float_type>yv(np); |
---|
[1230] | 1035 | c2_ptr<float_type> comp(source(*this)); |
---|
[807] | 1036 | float_type yp0, yp1, ypp; |
---|
| 1037 | |
---|
[1230] | 1038 | for(size_t i=1; i<np-1; i++) { |
---|
| 1039 | yv[i]=source(fTransform.Y.fOut(F[i])); // copy pointwise the function of our data values |
---|
[807] | 1040 | } |
---|
| 1041 | |
---|
[1230] | 1042 | yv.front()=comp(Xraw.front(), &yp0, &ypp); // get derivative at front |
---|
| 1043 | yv.back()= comp(Xraw.back(), &yp1, &ypp); // get derivative at back |
---|
[807] | 1044 | |
---|
[1230] | 1045 | interpolating_function_p ©=clone(); |
---|
| 1046 | copy.load(this->Xraw, yv, false, yp0, false, yp1); |
---|
| 1047 | |
---|
| 1048 | return copy; |
---|
[807] | 1049 | } |
---|
| 1050 | |
---|
| 1051 | template <typename float_type> void |
---|
[1230] | 1052 | interpolating_function_p<float_type>::get_data(std::vector<float_type> &xvals, std::vector<float_type> &yvals) const throw() |
---|
[807] | 1053 | { |
---|
| 1054 | |
---|
| 1055 | xvals=Xraw; |
---|
| 1056 | yvals.resize(F.size()); |
---|
| 1057 | |
---|
[1230] | 1058 | for(size_t i=0; i<F.size(); i++) yvals[i]=fTransform.Y.fOut(F[i]); |
---|
[807] | 1059 | } |
---|
| 1060 | |
---|
[1230] | 1061 | template <typename float_type> interpolating_function_p<float_type> & |
---|
| 1062 | interpolating_function_p<float_type>::binary_operator(const c2_function<float_type> &rhs, |
---|
| 1063 | const c2_binary_function<float_type> *combining_stub) const |
---|
[807] | 1064 | { |
---|
| 1065 | size_t np=X.size(); |
---|
| 1066 | std::vector<float_type> yv(np); |
---|
[1230] | 1067 | c2_constant_p<float_type> fval(0); |
---|
[807] | 1068 | float_type yp0, yp1, ypp; |
---|
| 1069 | |
---|
[1230] | 1070 | c2_const_ptr<float_type> stub(*combining_stub); // manage ownership |
---|
| 1071 | |
---|
| 1072 | for(size_t i=1; i<np-1; i++) { |
---|
| 1073 | fval.reset(fTransform.Y.fOut(F[i])); // update the constant function pointwise |
---|
| 1074 | yv[i]=combining_stub->combine(fval, rhs, Xraw[i], (float_type *)0, (float_type *)0); // compute rhs & combine without derivatives |
---|
[807] | 1075 | } |
---|
| 1076 | |
---|
[1230] | 1077 | yv.front()=combining_stub->combine(*this, rhs, Xraw.front(), &yp0, &ypp); // get derivative at front |
---|
| 1078 | yv.back()= combining_stub->combine(*this, rhs, Xraw.back(), &yp1, &ypp); // get derivative at back |
---|
[807] | 1079 | |
---|
[1230] | 1080 | interpolating_function_p ©=clone(); |
---|
| 1081 | copy.load(this->Xraw, yv, false, yp0, false, yp1); |
---|
| 1082 | |
---|
| 1083 | return copy; |
---|
[807] | 1084 | } |
---|
| 1085 | |
---|
[1230] | 1086 | template <typename float_type> c2_inverse_function_p<float_type>::c2_inverse_function_p(const c2_function<float_type> &source) |
---|
| 1087 | : c2_function<float_type>(), func(source) |
---|
[807] | 1088 | { |
---|
| 1089 | float_type l=source.xmin(); |
---|
| 1090 | float_type r=source.xmax(); |
---|
| 1091 | start_hint=(l+r)*0.5; // guess that we start in the middle |
---|
| 1092 | // compute our domain assuming the function is monotonic so its values on its domain boundaries are our domain |
---|
| 1093 | float_type ly=source(l); |
---|
| 1094 | float_type ry=source(r); |
---|
| 1095 | if (ly > ry) { |
---|
| 1096 | float_type t=ly; ly=ry; ry=t; |
---|
| 1097 | } |
---|
| 1098 | set_domain(ly, ry); |
---|
| 1099 | } |
---|
| 1100 | |
---|
[1230] | 1101 | template <typename float_type> float_type c2_inverse_function_p<float_type>::value_with_derivatives( |
---|
[807] | 1102 | float_type x, float_type *yprime, float_type *yprime2 |
---|
| 1103 | ) const throw(c2_exception) |
---|
| 1104 | { |
---|
| 1105 | float_type l=this->func->xmin(); |
---|
| 1106 | float_type r=this->func->xmax(); |
---|
| 1107 | float_type yp, ypp; |
---|
| 1108 | float_type y=this->func->find_root(l, r, get_start_hint(x), x, 0, &yp, &ypp); |
---|
| 1109 | start_hint=y; |
---|
| 1110 | if(yprime) *yprime=1.0/yp; |
---|
| 1111 | if(yprime2) *yprime2=-ypp/(yp*yp*yp); |
---|
| 1112 | return y; |
---|
| 1113 | } |
---|
| 1114 | |
---|
| 1115 | //accumulated_histogram starts with binned data, generates the integral, and generates a piecewise linear interpolating_function |
---|
| 1116 | //If drop_zeros is true, it merges empty bins together before integration |
---|
| 1117 | //Note that the resulting interpolating_function is guaranteed to be increasing (if drop_zeros is false) |
---|
| 1118 | // or stricly increasing (if drop_zeros is true) |
---|
| 1119 | //If inverse_function is true, it drop zeros, integrates, and returns the inverse function which is useful |
---|
| 1120 | // for random number generation based on the input distribution. |
---|
| 1121 | //If normalize is true, the big end of the integral is scaled to 1. |
---|
| 1122 | //If the data are passed in reverse order (large X first), the integral is carried out from the big end, |
---|
| 1123 | // and then the data are reversed to the result in in increasing X order. |
---|
| 1124 | template <typename float_type> accumulated_histogram<float_type>::accumulated_histogram( |
---|
| 1125 | const std::vector<float_type>binedges, const std::vector<float_type> binheights, |
---|
| 1126 | bool normalize, bool inverse_function, bool drop_zeros) |
---|
| 1127 | { |
---|
| 1128 | |
---|
| 1129 | int np=binheights.size(); |
---|
| 1130 | |
---|
| 1131 | std::vector<float_type> be, bh; |
---|
| 1132 | if(drop_zeros || inverse_function) { //inverse functions cannot have any zero bins or they have vertical sections |
---|
| 1133 | if(binheights[0] || !inverse_function) { // conserve lower x bound if not an inverse function |
---|
| 1134 | be.push_back(binedges[0]); |
---|
| 1135 | bh.push_back(binheights[0]); |
---|
| 1136 | } |
---|
| 1137 | for(int i=1; i<np-1; i++) { |
---|
| 1138 | if(binheights[i]) { |
---|
| 1139 | be.push_back(binedges[i]); |
---|
| 1140 | bh.push_back(binheights[i]); |
---|
| 1141 | } |
---|
| 1142 | } |
---|
| 1143 | if(binheights[np-1] || !inverse_function) { |
---|
| 1144 | bh.push_back(binheights[np-1]); |
---|
| 1145 | be.push_back(binedges[np-1]); |
---|
| 1146 | be.push_back(binedges[np]); // push both sides of the last bin if needed |
---|
| 1147 | } |
---|
| 1148 | np=bh.size(); // set np to compressed size of bin array |
---|
| 1149 | } else { |
---|
| 1150 | be=binedges; |
---|
| 1151 | bh=binheights; |
---|
| 1152 | } |
---|
| 1153 | std::vector<float_type> cum(np+1, 0.0); |
---|
| 1154 | for(int i=1; i<=np; i++) cum[i]=bh[i]*(be[i]-be[i-1])+cum[i-1]; // accumulate bins, leaving bin 0 as 0 |
---|
| 1155 | if(be[1] < be[0]) { // if bins passed in backwards, reverse them |
---|
| 1156 | std::reverse(be.begin(), be.end()); |
---|
| 1157 | std::reverse(cum.begin(), cum.end()); |
---|
| 1158 | for(unsigned int i=0; i<cum.size(); i++) cum[i]*=-1; // flip sign on reversed data |
---|
| 1159 | } |
---|
| 1160 | if(normalize) { |
---|
| 1161 | float_type m=1.0/std::max(cum[0], cum[np]); |
---|
| 1162 | for(int i=0; i<=np; i++) cum[i]*=m; |
---|
| 1163 | } |
---|
[1230] | 1164 | if(inverse_function) interpolating_function_p<float_type>(cum, be); // use cum as x axis in inverse function |
---|
| 1165 | else interpolating_function_p<float_type>(be, cum); // else use lower bin edge as x axis |
---|
[807] | 1166 | std::fill(this->y2.begin(), this->y2.end(), 0.0); // clear second derivatives, to we are piecewise linear |
---|
| 1167 | } |
---|
| 1168 | |
---|
[1230] | 1169 | template <typename float_type> c2_piecewise_function_p<float_type>::c2_piecewise_function_p() |
---|
[807] | 1170 | : c2_function<float_type>(), lastKLow(-1) |
---|
| 1171 | { |
---|
| 1172 | this->sampling_grid=new std::vector<float_type>; // this always has a smapling grid |
---|
| 1173 | } |
---|
| 1174 | |
---|
[1230] | 1175 | template <typename float_type> c2_piecewise_function_p<float_type>::~c2_piecewise_function_p() |
---|
[807] | 1176 | { |
---|
| 1177 | } |
---|
| 1178 | |
---|
[1230] | 1179 | template <typename float_type> float_type c2_piecewise_function_p<float_type>::value_with_derivatives( |
---|
[807] | 1180 | float_type x, float_type *yprime, float_type *yprime2 |
---|
| 1181 | ) const throw(c2_exception) |
---|
| 1182 | { |
---|
| 1183 | |
---|
| 1184 | size_t np=functions.size(); |
---|
| 1185 | if(!np) throw c2_exception("attempting to evaluate an empty piecewise function"); |
---|
| 1186 | |
---|
| 1187 | if(x < this->xmin() || x > this->xmax()) { |
---|
| 1188 | std::ostringstream outstr; |
---|
| 1189 | outstr << "piecewise function argument " << x << " out of range " << this->xmin() << " -- " << this->xmax(); |
---|
| 1190 | throw c2_exception(outstr.str().c_str()); |
---|
| 1191 | } |
---|
| 1192 | |
---|
| 1193 | int klo=0; |
---|
| 1194 | |
---|
| 1195 | if(lastKLow >= 0 && functions[lastKLow]->xmin() <= x && functions[lastKLow]->xmax() > x) { |
---|
| 1196 | klo=lastKLow; |
---|
| 1197 | } else { |
---|
| 1198 | int khi=np; |
---|
| 1199 | while(khi-klo > 1) { |
---|
| 1200 | int km=(khi+klo)/2; |
---|
| 1201 | if(functions[km]->xmin() > x) khi=km; |
---|
| 1202 | else klo=km; |
---|
| 1203 | } |
---|
| 1204 | } |
---|
| 1205 | lastKLow=klo; |
---|
| 1206 | return functions[klo]->value_with_derivatives(x, yprime, yprime2); |
---|
| 1207 | } |
---|
| 1208 | |
---|
[1230] | 1209 | template <typename float_type> void c2_piecewise_function_p<float_type>::append_function( |
---|
| 1210 | const c2_function<float_type> &func) throw(c2_exception) |
---|
[807] | 1211 | { |
---|
[1230] | 1212 | c2_const_ptr<float_type> keepfunc(func); // manage function before we can throw any exceptions |
---|
[807] | 1213 | if(functions.size()) { // check whether there are any gaps to fill, etc. |
---|
[1230] | 1214 | const c2_function<float_type> &tail=functions.back(); |
---|
[807] | 1215 | float_type x0=tail.xmax(); |
---|
| 1216 | float_type x1=func.xmin(); |
---|
| 1217 | if(x0 < x1) { |
---|
| 1218 | // must insert a connector if x0 < x1 |
---|
| 1219 | float_type y0=tail(x0); |
---|
| 1220 | float_type y1=func(x1); |
---|
[1230] | 1221 | c2_function<float_type> &connector=*new c2_linear_p<float_type>(x0, y0, (y1-y0)/(x1-x0)); |
---|
| 1222 | connector.set_domain(x0,x1); |
---|
| 1223 | functions.push_back(c2_const_ptr<float_type>(connector)); |
---|
[807] | 1224 | this->sampling_grid->push_back(x1); |
---|
| 1225 | } else if(x0>x1) throw c2_exception("function domains not increasing in c2_piecewise_function"); |
---|
| 1226 | } |
---|
[1230] | 1227 | functions.push_back(keepfunc); |
---|
[807] | 1228 | // extend our domain to include all known functions |
---|
| 1229 | this->set_domain(functions.front()->xmin(), functions.back()->xmax()); |
---|
| 1230 | // extend our sampling grid with the new function's grid, with the first point dropped to avoid duplicates |
---|
[1230] | 1231 | std::vector<float_type> newgrid; |
---|
| 1232 | func.get_sampling_grid(func.xmin(), func.xmax(), newgrid); |
---|
[807] | 1233 | this->sampling_grid->insert(this->sampling_grid->end(), newgrid.begin()+1, newgrid.end()); |
---|
| 1234 | } |
---|
| 1235 | |
---|
[1230] | 1236 | template <typename float_type> c2_connector_function_p<float_type>::c2_connector_function_p( |
---|
| 1237 | float_type x0, const c2_function<float_type> &f0, float_type x2, const c2_function<float_type> &f2, |
---|
[807] | 1238 | bool auto_center, float_type y1) |
---|
[1230] | 1239 | : c2_function<float_type>() |
---|
| 1240 | { |
---|
| 1241 | c2_const_ptr<float_type> left(f0), right(f2); // make sure if these are unowned, they get deleted |
---|
| 1242 | c2_fblock<float_type> fb0, fb2; |
---|
| 1243 | fb0.x=x0; |
---|
| 1244 | f0.fill_fblock(fb0); |
---|
| 1245 | fb2.x=x2; |
---|
| 1246 | f2.fill_fblock(fb2); |
---|
| 1247 | init(fb0, fb2, auto_center, y1); |
---|
| 1248 | } |
---|
[807] | 1249 | |
---|
[1230] | 1250 | template <typename float_type> c2_connector_function_p<float_type>::c2_connector_function_p( |
---|
| 1251 | float_type x0, float_type y0, float_type yp0, float_type ypp0, |
---|
| 1252 | float_type x2, float_type y2, float_type yp2, float_type ypp2, |
---|
| 1253 | bool auto_center, float_type y1) |
---|
| 1254 | : c2_function<float_type>() |
---|
[807] | 1255 | { |
---|
[1230] | 1256 | c2_fblock<float_type> fb0, fb2; |
---|
| 1257 | fb0.x=x0; fb0.y=y0; fb0.yp=yp0; fb0.ypp=ypp0; |
---|
| 1258 | fb2.x=x2; fb2.y=y2; fb2.yp=yp2; fb2.ypp=ypp2; |
---|
| 1259 | init(fb0, fb2, auto_center, y1); |
---|
| 1260 | } |
---|
[807] | 1261 | |
---|
[1230] | 1262 | template <typename float_type> c2_connector_function_p<float_type>::c2_connector_function_p( |
---|
| 1263 | const c2_fblock<float_type> &fb0, |
---|
| 1264 | const c2_fblock<float_type> &fb2, |
---|
| 1265 | bool auto_center, float_type y1) |
---|
| 1266 | : c2_function<float_type>() |
---|
| 1267 | { |
---|
| 1268 | init(fb0, fb2, auto_center, y1); |
---|
| 1269 | } |
---|
| 1270 | |
---|
| 1271 | template <typename float_type> void c2_connector_function_p<float_type>::init( |
---|
| 1272 | const c2_fblock<float_type> &fb0, |
---|
| 1273 | const c2_fblock<float_type> &fb2, |
---|
| 1274 | bool auto_center, float_type y1) |
---|
| 1275 | { |
---|
| 1276 | float_type dx=(fb2.x-fb0.x)/2.0; |
---|
| 1277 | fhinv=1.0/dx; |
---|
| 1278 | |
---|
[807] | 1279 | // scale derivs to put function on [-1,1] since mma solution is done this way |
---|
[1230] | 1280 | float_type yp0=fb0.yp*dx; |
---|
| 1281 | float_type yp2=fb2.yp*dx; |
---|
| 1282 | float_type ypp0=fb0.ypp*dx*dx; |
---|
| 1283 | float_type ypp2=fb2.ypp*dx*dx; |
---|
[807] | 1284 | |
---|
[1230] | 1285 | float_type ff0=(8*(fb0.y + fb2.y) + 5*(yp0 - yp2) + ypp0 + ypp2)*0.0625; |
---|
[807] | 1286 | if(auto_center) y1=ff0; // forces ff to be 0 if we are auto-centering |
---|
| 1287 | |
---|
[1230] | 1288 | // y[x_] = y1 + x (a + b x) + x [(x-1) (x+1)] (c + d x) + x (x-1)^2 (x+1)^2 (e + f x) |
---|
| 1289 | // y' = a + 2 b x + d x [(x+1)(x-1)] + (c + d x)(3x^2-1) + f x [(x+1)(x-1)]^2 + (e + f x)[(x+1)(x-1)](5x^2-1) |
---|
| 1290 | // y'' = 2 b + 6x(c + d x) + 2d(3x^2-1) + 4x(e + f x)(5x^2-3) + 2f(x^2-1)(5x^2-1) |
---|
[807] | 1291 | fy1=y1; |
---|
[1230] | 1292 | fa=(fb2.y - fb0.y)*0.5; |
---|
| 1293 | fb=(fb0.y + fb2.y)*0.5 - y1; |
---|
| 1294 | fc=(yp2+yp0-2.*fa)*0.25; |
---|
| 1295 | fd=(yp2-yp0-4.*fb)*0.25; |
---|
| 1296 | fe=(ypp2-ypp0-12.*fc)*0.0625; |
---|
[807] | 1297 | ff=(ff0 - y1); |
---|
[1230] | 1298 | this->set_domain(fb0.x, fb2.x); // this is where the function is valid |
---|
[807] | 1299 | } |
---|
| 1300 | |
---|
[1230] | 1301 | template <typename float_type> c2_connector_function_p<float_type>::~c2_connector_function_p() |
---|
[807] | 1302 | { |
---|
| 1303 | } |
---|
| 1304 | |
---|
[1230] | 1305 | template <typename float_type> float_type c2_connector_function_p<float_type>::value_with_derivatives( |
---|
[807] | 1306 | float_type x, float_type *yprime, float_type *yprime2 |
---|
| 1307 | ) const throw(c2_exception) |
---|
| 1308 | { |
---|
[1230] | 1309 | float_type x0=this->xmin(), x2=this->xmax(); |
---|
| 1310 | float_type dx=(x-(x0+x2)*0.5)*fhinv; |
---|
| 1311 | float_type q1=(x-x0)*(x-x2)*fhinv*fhinv; // exactly vanish all bits at both ends |
---|
| 1312 | float_type q2=dx*q1; |
---|
[807] | 1313 | |
---|
[1230] | 1314 | float_type r1=fa+fb*dx; |
---|
| 1315 | float_type r2=fc+fd*dx; |
---|
| 1316 | float_type r3=fe+ff*dx; |
---|
| 1317 | |
---|
| 1318 | float_type y=fy1+dx*r1+q2*r2+q1*q2*r3; |
---|
| 1319 | |
---|
[807] | 1320 | if(yprime || yprime2) { |
---|
[1230] | 1321 | float_type q3=3*q1+2; |
---|
| 1322 | float_type q4=5*q1+4; |
---|
| 1323 | if(yprime) *yprime=(fa+2*fb*dx+fd*q2+r2*q3+ff*q1*q2+q1*q4*r3)*fhinv; |
---|
| 1324 | if(yprime2) *yprime2=2*(fb+fd*q3+3*dx*r2+ff*q1*q4+r3*(2*dx*(5*q1+2)))*fhinv*fhinv; |
---|
[807] | 1325 | } |
---|
| 1326 | return y; |
---|
| 1327 | } |
---|
[1230] | 1328 | |
---|
| 1329 | // the recursive part of the sampler is agressively designed to minimize copying of data... lots of pointers |
---|
| 1330 | template <typename float_type> void c2_function<float_type>::sample_step(c2_sample_recur &rb) const throw(c2_exception) |
---|
| 1331 | { |
---|
| 1332 | std::vector< recur_item > &rb_stack=*rb.rb_stack; // heap-based stack of data for recursion |
---|
| 1333 | rb_stack.clear(); |
---|
| 1334 | |
---|
| 1335 | recur_item top; |
---|
| 1336 | top.depth=0; top.done=false; top.f0index=0; top.f2index=0; |
---|
| 1337 | |
---|
| 1338 | // push storage for our initial elements |
---|
| 1339 | rb_stack.push_back(top); |
---|
| 1340 | rb_stack.back().f1=*rb.f0; |
---|
| 1341 | rb_stack.back().done=true; |
---|
| 1342 | |
---|
| 1343 | rb_stack.push_back(top); |
---|
| 1344 | rb_stack.back().f1=*rb.f1; |
---|
| 1345 | rb_stack.back().done=true; |
---|
| 1346 | |
---|
| 1347 | if(!rb.inited) { |
---|
| 1348 | rb.dx_tolerance=10.0*std::numeric_limits<float_type>::epsilon(); |
---|
| 1349 | rb.abs_tol_min=10.0*std::numeric_limits<float_type>::min(); |
---|
| 1350 | rb.inited=true; |
---|
| 1351 | } |
---|
| 1352 | |
---|
| 1353 | // now, push our first real element |
---|
| 1354 | top.f0index=0; // left element is stack[0] |
---|
| 1355 | top.f2index=1; // right element is stack[1] |
---|
| 1356 | rb_stack.push_back(top); |
---|
| 1357 | |
---|
| 1358 | while(rb_stack.size() > 2) { |
---|
| 1359 | recur_item &back=rb_stack.back(); |
---|
| 1360 | if(back.done) { |
---|
| 1361 | rb_stack.pop_back(); |
---|
| 1362 | continue; |
---|
| 1363 | } |
---|
| 1364 | back.done=true; |
---|
| 1365 | |
---|
| 1366 | c2_fblock<float_type> &f0=rb_stack[back.f0index].f1, &f2=rb_stack[back.f2index].f1; |
---|
| 1367 | c2_fblock<float_type> &f1=back.f1; // will hold new middle values |
---|
| 1368 | size_t f1index=rb_stack.size()-1; // our current offset |
---|
| 1369 | |
---|
| 1370 | // std::cout << "processing: " << rb_stack.size() << " " << |
---|
| 1371 | // (&back-&rb_stack.front()) << " " << back.depth << " " << f0.x << " " << f2.x << std::endl; |
---|
| 1372 | |
---|
| 1373 | f1.x=0.5*(f0.x + f2.x); // center of interval |
---|
| 1374 | float_type dx2=0.5*(f2.x - f0.x); |
---|
| 1375 | |
---|
| 1376 | // check for underflow on step size, which prevents us from achieving specified accuracy. |
---|
| 1377 | if(std::abs(dx2) < std::abs(f1.x)*rb.dx_tolerance || std::abs(dx2) < rb.abs_tol_min) { |
---|
| 1378 | std::ostringstream outstr; |
---|
| 1379 | outstr << "Step size underflow in adaptive_sampling at depth=" << back.depth << ", x= " << f1.x; |
---|
| 1380 | throw c2_exception(outstr.str().c_str()); |
---|
| 1381 | } |
---|
| 1382 | |
---|
| 1383 | fill_fblock(f1); |
---|
| 1384 | |
---|
| 1385 | if(c2_isnan(f1.y) || f1.ypbad || f1.yppbad) { |
---|
| 1386 | // can't go any further if a nan has appeared |
---|
| 1387 | bad_x_point=f1.x; |
---|
| 1388 | throw c2_exception("NaN encountered while sampling function"); |
---|
| 1389 | } |
---|
| 1390 | |
---|
| 1391 | float_type eps; |
---|
| 1392 | if(rb.derivs==2) { |
---|
| 1393 | // this is code from connector_function to compute the value at the midpoint |
---|
| 1394 | // it is re-included here to avoid constructing a complete c2connector |
---|
| 1395 | // just to find out if we are close enough |
---|
| 1396 | float_type ff0=(8*(f0.y + f2.y) + 5*(f0.yp - f2.yp)*dx2 + (f0.ypp+f2.ypp)*dx2*dx2)*0.0625; |
---|
| 1397 | // we are converging as at least x**5 and bisecting, so real error on final step is smaller |
---|
| 1398 | eps=std::abs(ff0-f1.y)/32.0; |
---|
| 1399 | } else { |
---|
| 1400 | // there are two tolerances to meet... the shift in the estimate of the actual point, |
---|
| 1401 | // and the difference between the current points and the extremum |
---|
| 1402 | // build all the coefficients needed to construct the local parabola |
---|
| 1403 | float_type ypcenter, ypp; |
---|
| 1404 | if (rb.derivs==1) { |
---|
| 1405 | // linear extrapolation error using exact derivs |
---|
| 1406 | eps = (std::abs(f0.y+f0.yp*dx2-f1.y)+std::abs(f2.y-f2.yp*dx2-f1.y))*0.125; |
---|
| 1407 | ypcenter=2*f1.yp*dx2; // first deriv scaled so this interval is on [-1,1] |
---|
| 1408 | ypp=2*(f2.yp-f0.yp)*dx2*dx2; // second deriv estimate scaled so this interval is on [-1,1] |
---|
| 1409 | } else { |
---|
| 1410 | // linear interpolation error without derivs if we are at top level |
---|
| 1411 | // or 3-point parabolic interpolation estimates from previous level, if available |
---|
| 1412 | ypcenter=(f2.y-f0.y)*0.5; // derivative estimate at center |
---|
| 1413 | ypp=(f2.y+f0.y-2*f1.y); // second deriv estimate |
---|
| 1414 | if(back.depth==0) eps=std::abs((f0.y+f2.y)*0.5 - f1.y)*2; // penalize first step |
---|
| 1415 | else eps=std::abs(f1.y-back.previous_estimate)*0.25; |
---|
| 1416 | } |
---|
| 1417 | float_type ypleft=ypcenter-ypp; // derivative at left edge |
---|
| 1418 | float_type ypright=ypcenter+ypp; // derivative at right edge |
---|
| 1419 | float_type extremum_eps=0; |
---|
| 1420 | if((ypleft*ypright) <=0) // y' changes sign if we have an extremum |
---|
| 1421 | { |
---|
| 1422 | // compute position and value of the extremum this way |
---|
| 1423 | float_type xext=-ypcenter/ypp; |
---|
| 1424 | float_type yext=f1.y + xext*ypcenter + 0.5*xext*xext*ypp; |
---|
| 1425 | // and then find the the smallest offset of it from a point, looking in the left or right side |
---|
| 1426 | if(xext <=0) extremum_eps=std::min(std::abs(f0.y-yext), std::abs(f1.y-yext)); |
---|
| 1427 | else extremum_eps=std::min(std::abs(f2.y-yext), std::abs(f1.y-yext)); |
---|
| 1428 | } |
---|
| 1429 | eps=std::max(eps, extremum_eps); // if previous shot was really bad, keep trying |
---|
| 1430 | } |
---|
| 1431 | |
---|
| 1432 | if(eps < rb.abs_tol || eps < std::abs(f1.y)*rb.rel_tol) { |
---|
| 1433 | if(rb.out) { |
---|
| 1434 | // we've met the tolerance, and are building a function, append two connectors |
---|
| 1435 | rb.out->append_function( |
---|
| 1436 | *new c2_connector_function_p<float_type>(f0, f1, true, 0.0) |
---|
| 1437 | ); |
---|
| 1438 | rb.out->append_function( |
---|
| 1439 | *new c2_connector_function_p<float_type>(f1, f2, true, 0.0) |
---|
| 1440 | ); |
---|
| 1441 | } |
---|
| 1442 | if(rb.xvals && rb.yvals) { |
---|
| 1443 | rb.xvals->push_back(f0.x); |
---|
| 1444 | rb.xvals->push_back(f1.x); |
---|
| 1445 | rb.yvals->push_back(f0.y); |
---|
| 1446 | rb.yvals->push_back(f1.y); |
---|
| 1447 | // the value at f2 will get pushed in the next segment... it is not forgotten |
---|
| 1448 | } |
---|
| 1449 | } else { |
---|
| 1450 | top.depth=back.depth+1; // increment depth counter |
---|
| 1451 | |
---|
| 1452 | // save the last things we need from back before a push happens, in case |
---|
| 1453 | // the push causes a reallocation and moves the whole stack. |
---|
| 1454 | size_t f0index=back.f0index, f2index=back.f2index; |
---|
| 1455 | float_type left=0, right=0; |
---|
| 1456 | if(rb.derivs==0) { |
---|
| 1457 | // compute three-point parabolic interpolation estimate of right-hand and left-hand midpoint |
---|
| 1458 | left=(6*f1.y + 3*f0.y - f2.y) * 0.125; |
---|
| 1459 | right=(6*f1.y + 3*f2.y - f0.y) * 0.125; |
---|
| 1460 | } |
---|
| 1461 | |
---|
| 1462 | top.f0index=f1index; top.f2index=f2index; // insert pointers to right side data into our recursion block |
---|
| 1463 | top.previous_estimate=right; |
---|
| 1464 | rb_stack.push_back(top); |
---|
| 1465 | |
---|
| 1466 | top.f0index=f0index; top.f2index=f1index; // insert pointers to left side data into our recursion block |
---|
| 1467 | top.previous_estimate=left; |
---|
| 1468 | rb_stack.push_back(top); |
---|
| 1469 | } |
---|
| 1470 | } |
---|
| 1471 | } |
---|
| 1472 | |
---|
| 1473 | template <typename float_type> c2_piecewise_function_p<float_type> * |
---|
| 1474 | c2_function<float_type>::adaptively_sample( |
---|
| 1475 | float_type xmin, float_type xmax, |
---|
| 1476 | float_type abs_tol, float_type rel_tol, |
---|
| 1477 | int derivs, std::vector<float_type> *xvals, std::vector<float_type> *yvals) const throw(c2_exception) |
---|
| 1478 | { |
---|
| 1479 | c2_fblock<float_type> f0, f2; |
---|
| 1480 | c2_sample_recur rb; |
---|
| 1481 | std::vector< recur_item > rb_stack; |
---|
| 1482 | rb_stack.reserve(20); // enough for most operations |
---|
| 1483 | rb.rb_stack=&rb_stack; |
---|
| 1484 | rb.out=0; |
---|
| 1485 | if(derivs==2) rb.out=new c2_piecewise_function_p<float_type>(); |
---|
| 1486 | c2_ptr<float_type> pieces(*rb.out); // manage this function, if any, so it deletes on an exception |
---|
| 1487 | rb.rel_tol=rel_tol; |
---|
| 1488 | rb.abs_tol=abs_tol; |
---|
| 1489 | rb.xvals=xvals; |
---|
| 1490 | rb.yvals=yvals; |
---|
| 1491 | rb.derivs=derivs; |
---|
| 1492 | rb.inited=false; |
---|
| 1493 | |
---|
| 1494 | if(xvals && yvals) { |
---|
| 1495 | xvals->clear(); |
---|
| 1496 | yvals->clear(); |
---|
| 1497 | } |
---|
| 1498 | |
---|
| 1499 | // create xgrid as a automatic-variable copy of the sampling grid so the exception handler correctly |
---|
| 1500 | // disposes of it. |
---|
| 1501 | std::vector<float_type> xgrid; |
---|
| 1502 | get_sampling_grid(xmin, xmax, xgrid); |
---|
| 1503 | int np=xgrid.size(); |
---|
| 1504 | |
---|
| 1505 | f2.x=xgrid[0]; |
---|
| 1506 | fill_fblock(f2); |
---|
| 1507 | if(c2_isnan(f2.y) || f2.ypbad || f2.yppbad) { |
---|
| 1508 | // can't go any further if a nan has appeared |
---|
| 1509 | bad_x_point=f2.x; |
---|
| 1510 | throw c2_exception("NaN encountered while sampling function"); |
---|
| 1511 | } |
---|
| 1512 | |
---|
| 1513 | for(int i=0; i<np-1; i++) { |
---|
| 1514 | f0=f2; // copy upper bound to lower before computing new upper bound |
---|
| 1515 | |
---|
| 1516 | f2.x=xgrid[i+1]; |
---|
| 1517 | fill_fblock(f2); |
---|
| 1518 | if(c2_isnan(f2.y) || f2.ypbad || f2.yppbad) { |
---|
| 1519 | // can't go any further if a nan has appeared |
---|
| 1520 | bad_x_point=f2.x; |
---|
| 1521 | throw c2_exception("NaN encountered while sampling function"); |
---|
| 1522 | } |
---|
| 1523 | |
---|
| 1524 | rb.f0=&f0; rb.f1=&f2; |
---|
| 1525 | sample_step(rb); |
---|
| 1526 | } |
---|
| 1527 | if(xvals && yvals) { // push final point in vector |
---|
| 1528 | xvals->push_back(f2.x); |
---|
| 1529 | yvals->push_back(f2.y); |
---|
| 1530 | } |
---|
| 1531 | |
---|
| 1532 | if(rb.out) rb.out->set_sampling_grid(xgrid); // reflect old sampling grid, which still should be right |
---|
| 1533 | pieces.release_for_return(); // unmanage the piecewise_function so we can return it |
---|
| 1534 | return rb.out; |
---|
| 1535 | } |
---|
| 1536 | |
---|
| 1537 | template <typename float_type, typename Final> |
---|
| 1538 | interpolating_function_p<float_type> & inverse_integrated_density_function( |
---|
| 1539 | const std::vector<float_type> &bincenters, const c2_function<float_type> &binheights) |
---|
| 1540 | throw(c2_exception) |
---|
| 1541 | { |
---|
| 1542 | return (new Final())->load_random_generator_function(bincenters, binheights); |
---|
| 1543 | } |
---|
| 1544 | |
---|
| 1545 | template <typename float_type, typename Final> |
---|
| 1546 | interpolating_function_p<float_type> & inverse_integrated_density_bins( |
---|
| 1547 | const std::vector<float_type> &bins, const std::vector<float_type> &binheights) |
---|
| 1548 | throw(c2_exception) |
---|
| 1549 | { |
---|
| 1550 | return (new Final())->load_random_generator_bins(bins, binheights); |
---|
| 1551 | } |
---|