1 | //#--------------------------------------------------------------------------- |
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2 | //# MathUtilities.cc: General math operations |
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3 | //#--------------------------------------------------------------------------- |
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4 | //# Copyright (C) 2004 |
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5 | //# ATNF |
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6 | //# |
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7 | //# This program is free software; you can redistribute it and/or modify it |
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8 | //# under the terms of the GNU General Public License as published by the Free |
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9 | //# Software Foundation; either version 2 of the License, or (at your option) |
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10 | //# any later version. |
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11 | //# |
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12 | //# This program is distributed in the hope that it will be useful, but |
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13 | //# WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | //# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General |
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15 | //# Public License for more details. |
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16 | //# |
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17 | //# You should have received a copy of the GNU General Public License along |
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18 | //# with this program; if not, write to the Free Software Foundation, Inc., |
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19 | //# 675 Massachusetts Ave, Cambridge, MA 02139, USA. |
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20 | //# |
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21 | //# Correspondence concerning this software should be addressed as follows: |
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22 | //# Internet email: Malte.Marquarding@csiro.au |
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23 | //# Postal address: Malte Marquarding, |
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24 | //# Australia Telescope National Facility, |
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25 | //# P.O. Box 76, |
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26 | //# Epping, NSW, 2121, |
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27 | //# AUSTRALIA |
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28 | //# |
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29 | //# $Id: |
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30 | //#--------------------------------------------------------------------------- |
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31 | |
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32 | #include <casa/aips.h> |
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33 | #include <casa/Arrays/Vector.h> |
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34 | #include <casa/Arrays/Slice.h> |
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35 | #include <casa/Arrays/MaskedArray.h> |
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36 | #include <casa/Arrays/MaskArrMath.h> |
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37 | #include <casa/Arrays/VectorSTLIterator.h> |
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38 | #include <casa/BasicSL/String.h> |
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39 | #include <scimath/Mathematics/MedianSlider.h> |
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40 | #include <casa/Exceptions/Error.h> |
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41 | |
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42 | #include <scimath/Fitting/LinearFit.h> |
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43 | #include <scimath/Functionals/Polynomial.h> |
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44 | #include <scimath/Mathematics/AutoDiff.h> |
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45 | |
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46 | |
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47 | #include "MathUtils.h" |
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48 | |
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49 | using namespace casa; |
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50 | |
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51 | float mathutil::statistics(const String& which, |
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52 | const MaskedArray<Float>& data) |
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53 | { |
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54 | String str(which); |
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55 | str.upcase(); |
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56 | if (str.matches(String("MIN"))) { |
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57 | return min(data); |
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58 | } else if (str.matches(String("MAX"))) { |
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59 | return max(data); |
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60 | } else if (str.matches(String("SUMSQ"))) { |
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61 | return sumsquares(data); |
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62 | } else if (str.matches(String("SUM"))) { |
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63 | return sum(data); |
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64 | } else if (str.matches(String("MEAN"))) { |
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65 | return mean(data); |
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66 | } else if (str.matches(String("VAR"))) { |
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67 | return variance(data); |
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68 | } else if (str.matches(String("STDDEV"))) { |
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69 | return stddev(data); |
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70 | } else if (str.matches(String("AVDEV"))) { |
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71 | return avdev(data); |
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72 | } else if (str.matches(String("RMS"))) { |
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73 | uInt n = data.nelementsValid(); |
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74 | return sqrt(sumsquares(data)/n); |
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75 | } else if (str.matches(String("MEDIAN"))) { |
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76 | return median(data); |
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77 | } else { |
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78 | String msg = str + " is not a valid type of statistics"; |
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79 | throw(AipsError(msg)); |
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80 | } |
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81 | return 0.0; |
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82 | } |
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83 | |
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84 | IPosition mathutil::minMaxPos(const String& which, |
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85 | const MaskedArray<Float>& data) |
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86 | { |
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87 | Float minVal, maxVal; |
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88 | IPosition minPos(data.ndim(), 0), maxPos(data.ndim(), 0); |
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89 | minMax(minVal, maxVal, minPos, maxPos, data); |
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90 | String str(which); |
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91 | str.upcase(); |
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92 | if (str.contains(String("MIN"))) { |
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93 | return minPos; |
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94 | } else if (str.contains(String("MAX"))) { |
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95 | return maxPos; |
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96 | } else { |
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97 | String msg = str + " is not a valid type of statistics"; |
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98 | throw(AipsError(msg)); |
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99 | } |
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100 | //return 0.0; |
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101 | } |
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102 | |
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103 | void mathutil::replaceMaskByZero(Vector<Float>& data, const Vector<Bool>& mask) |
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104 | { |
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105 | for (uInt i=0; i<data.nelements(); i++) { |
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106 | if (!mask[i]) data[i] = 0.0; |
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107 | } |
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108 | } |
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109 | |
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110 | |
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111 | std::vector<std::string> mathutil::tovectorstring(const Vector<String>& in) |
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112 | { |
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113 | std::vector<std::string> out; |
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114 | out.reserve(in.nelements()); |
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115 | for (Array<String>::const_iterator it = in.begin(); it != in.end(); ++it) { |
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116 | out.push_back(*it); |
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117 | } |
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118 | return out; |
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119 | } |
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120 | |
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121 | Vector<String> mathutil::toVectorString(const std::vector<std::string>& in) |
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122 | { |
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123 | Vector<String> out(in.size()); |
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124 | Array<String>::iterator oit = out.begin(); |
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125 | for (std::vector<std::string>::const_iterator it=in.begin() ; |
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126 | it != in.end(); ++it,++oit) { |
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127 | *oit = *it; |
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128 | } |
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129 | return out; |
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130 | } |
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131 | |
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132 | void mathutil::hanning(Vector<Float>& out, Vector<Bool>& outmask, |
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133 | const Vector<Float>& in, const Vector<Bool>& mask, |
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134 | Bool relaxed, Bool ignoreOther) { |
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135 | Vector< Vector<Float> > weights(8); |
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136 | Vector<Float> vals(3); |
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137 | vals = 0.0;weights[0] = vals;// FFF |
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138 | vals[0] = 1.0; vals[1] = 0.0; vals[2] = 0.0; weights[1] = vals;// TFF |
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139 | vals[0] = 0.0; vals[1] = 1.0; vals[2] = 0.0; weights[2] = vals;// FTF |
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140 | vals[0] = 1.0/3.0; vals[1] = 2.0/3.0; vals[2] = 0.0; weights[3] = vals;// TTF |
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141 | vals[0] = 0.0; vals[1] = 0.0; vals[2] = 1.0;weights[4] = vals;// FFT |
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142 | vals[0] = 0.5; vals[1] = 0.0; vals[2] = 0.5; weights[5] = vals;// TFT |
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143 | vals[0] = 0.0; vals[1] = 2.0/3.0; vals[2] = 1.0/3.0; weights[6] = vals;// FTT |
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144 | vals[0] = 0.25; vals[1] = 0.5; vals[2] = 0.25; weights[7] = vals;// TTT |
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145 | // Chris' case |
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146 | Vector<Bool> weighted(8); |
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147 | if (relaxed) { |
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148 | weighted = False; |
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149 | weighted[7] = True; |
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150 | |
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151 | } else { |
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152 | weighted = True; |
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153 | weighted[0] = False; |
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154 | } |
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155 | |
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156 | out.resize(in.nelements()); |
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157 | outmask.resize(mask.nelements()); |
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158 | // make special case for first and last |
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159 | /// ...here |
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160 | // loop from 1..n-2 |
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161 | out.resize(in.nelements()); |
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162 | out[0] = in[0];out[out.nelements()-1] = in[in.nelements()-1]; |
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163 | outmask.resize(mask.nelements()); |
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164 | outmask[0] = mask[0]; outmask[outmask.nelements()-1] = mask[mask.nelements()-1]; |
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165 | uInt m;Vector<Float>* w; |
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166 | for (uInt i=1; i < out.nelements()-1;++i) { |
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167 | m = mask[i-1] + 2*mask[i] + 4*mask[i+1]; |
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168 | w = &(weights[m]); |
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169 | if (weighted[m]) { |
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170 | out[i] = (*w)[0]*in[i-1] + (*w)[1]*in[i] + (*w)[2]*in[i+1]; |
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171 | } else { // mask it |
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172 | out[i] = in[i];//use arbitrary value |
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173 | } |
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174 | outmask[i] = mask[i]; |
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175 | } |
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176 | } |
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177 | |
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178 | |
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179 | void mathutil::runningMedian(Vector<Float>& out, Vector<Bool>& outflag, |
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180 | const Vector<Float>& in, const Vector<Bool>& flag, |
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181 | float width) |
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182 | { |
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183 | Int hwidth = Int(width+0.5); |
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184 | Int fwidth = hwidth*2+1; |
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185 | out.resize(in.nelements()); |
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186 | outflag.resize(flag.nelements()); |
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187 | MedianSlider ms(hwidth); |
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188 | Slice sl(0, fwidth-1); |
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189 | Float medval = ms.add(const_cast<Vector<Float>& >(in)(sl), |
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190 | const_cast<Vector<Bool>& >(flag)(sl)); |
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191 | uInt n = in.nelements(); |
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192 | for (uInt i=hwidth; i<(n-hwidth); ++i) { |
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193 | // add data value |
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194 | out[i] = ms.add(in[i+hwidth], flag[i+hwidth]); |
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195 | outflag[i] = (ms.nval() == 0); |
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196 | } |
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197 | // replicate edge values from first value with full width of values |
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198 | for (uInt i=0;i<hwidth;++i) { |
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199 | out[i] = out[hwidth]; |
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200 | outflag[i] = outflag[hwidth]; |
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201 | out[n-1-i] = out[n-1-hwidth]; |
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202 | outflag[n-1-i] = outflag[n-1-hwidth]; |
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203 | } |
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204 | } |
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205 | |
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206 | void mathutil::polyfit(Vector<Float>& out, Vector<Bool>& outmask, |
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207 | const Vector<Float>& in, const Vector<Bool>& mask, |
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208 | float width, int order) |
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209 | { |
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210 | Int hwidth = Int(width+0.5); |
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211 | Int fwidth = hwidth*2+1; |
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212 | out.resize(in.nelements()); |
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213 | outmask.resize(mask.nelements()); |
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214 | LinearFit<Float> fitter; |
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215 | Polynomial<Float> poly(order); |
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216 | fitter.setFunction(poly); |
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217 | Vector<Float> sigma(fwidth); |
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218 | sigma = 1.0; |
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219 | Vector<Float> parms; |
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220 | Vector<Float> x(fwidth); |
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221 | indgen(x); |
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222 | |
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223 | uInt n = in.nelements(); |
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224 | |
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225 | for (uInt i=hwidth; i<(n-hwidth); ++i) { |
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226 | // add data value |
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227 | if (mask[i]) { |
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228 | Slice sl(i-hwidth, fwidth); |
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229 | const Vector<Float> &y = const_cast<Vector<Float>& >(in)(sl); |
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230 | const Vector<Bool> &m = const_cast<Vector<Bool>& >(mask)(sl); |
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231 | parms = fitter.fit(x, y, sigma, &m); |
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232 | |
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233 | poly.setCoefficients(parms); |
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234 | out[i] = poly(x[hwidth]);//cout << in[i] <<"->"<<out[i]<<endl; |
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235 | } else { |
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236 | out[i] = in[i]; |
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237 | } |
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238 | outmask[i] = mask[i]; |
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239 | } |
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240 | // replicate edge values from first value with full width of values |
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241 | for (uInt i=0;i<hwidth;++i) { |
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242 | out[i] = out[hwidth]; |
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243 | outmask[i] = outmask[hwidth]; |
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244 | out[n-1-i] = out[n-1-hwidth]; |
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245 | outmask[n-1-i] = outmask[n-1-hwidth]; |
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246 | } |
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247 | } |
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