[37] | 1 | //#--------------------------------------------------------------------------- |
---|
| 2 | //# MathUtilities.cc: General math operations |
---|
| 3 | //#--------------------------------------------------------------------------- |
---|
| 4 | //# Copyright (C) 2004 |
---|
[125] | 5 | //# ATNF |
---|
[37] | 6 | //# |
---|
| 7 | //# This program is free software; you can redistribute it and/or modify it |
---|
| 8 | //# under the terms of the GNU General Public License as published by the Free |
---|
| 9 | //# Software Foundation; either version 2 of the License, or (at your option) |
---|
| 10 | //# any later version. |
---|
| 11 | //# |
---|
| 12 | //# This program is distributed in the hope that it will be useful, but |
---|
| 13 | //# WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
| 14 | //# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General |
---|
| 15 | //# Public License for more details. |
---|
| 16 | //# |
---|
| 17 | //# You should have received a copy of the GNU General Public License along |
---|
| 18 | //# with this program; if not, write to the Free Software Foundation, Inc., |
---|
| 19 | //# 675 Massachusetts Ave, Cambridge, MA 02139, USA. |
---|
| 20 | //# |
---|
| 21 | //# Correspondence concerning this software should be addressed as follows: |
---|
| 22 | //# Internet email: Malte.Marquarding@csiro.au |
---|
| 23 | //# Postal address: Malte Marquarding, |
---|
| 24 | //# Australia Telescope National Facility, |
---|
| 25 | //# P.O. Box 76, |
---|
| 26 | //# Epping, NSW, 2121, |
---|
| 27 | //# AUSTRALIA |
---|
| 28 | //# |
---|
| 29 | //# $Id: |
---|
| 30 | //#--------------------------------------------------------------------------- |
---|
| 31 | |
---|
[125] | 32 | #include <casa/aips.h> |
---|
[176] | 33 | #include <casa/Arrays/Vector.h> |
---|
[1373] | 34 | #include <casa/Arrays/Slice.h> |
---|
[137] | 35 | #include <casa/Arrays/MaskedArray.h> |
---|
[136] | 36 | #include <casa/Arrays/MaskArrMath.h> |
---|
[465] | 37 | #include <casa/Arrays/VectorSTLIterator.h> |
---|
[136] | 38 | #include <casa/BasicSL/String.h> |
---|
[1373] | 39 | #include <scimath/Mathematics/MedianSlider.h> |
---|
[1819] | 40 | #include <casa/Exceptions/Error.h> |
---|
[37] | 41 | |
---|
[1570] | 42 | #include <scimath/Fitting/LinearFit.h> |
---|
| 43 | #include <scimath/Functionals/Polynomial.h> |
---|
| 44 | #include <scimath/Mathematics/AutoDiff.h> |
---|
| 45 | |
---|
[2258] | 46 | #include <ctime> |
---|
| 47 | #include <sys/time.h> |
---|
[1570] | 48 | |
---|
[125] | 49 | #include "MathUtils.h" |
---|
| 50 | |
---|
| 51 | using namespace casa; |
---|
| 52 | |
---|
[829] | 53 | float mathutil::statistics(const String& which, |
---|
[996] | 54 | const MaskedArray<Float>& data) |
---|
[136] | 55 | { |
---|
| 56 | String str(which); |
---|
| 57 | str.upcase(); |
---|
[1819] | 58 | if (str.matches(String("MIN"))) { |
---|
[829] | 59 | return min(data); |
---|
[1819] | 60 | } else if (str.matches(String("MAX"))) { |
---|
[136] | 61 | return max(data); |
---|
[1819] | 62 | } else if (str.matches(String("SUMSQ"))) { |
---|
[136] | 63 | return sumsquares(data); |
---|
[1819] | 64 | } else if (str.matches(String("SUM"))) { |
---|
[136] | 65 | return sum(data); |
---|
[1819] | 66 | } else if (str.matches(String("MEAN"))) { |
---|
[136] | 67 | return mean(data); |
---|
[1819] | 68 | } else if (str.matches(String("VAR"))) { |
---|
[829] | 69 | return variance(data); |
---|
[1819] | 70 | } else if (str.matches(String("STDDEV"))) { |
---|
[136] | 71 | return stddev(data); |
---|
[1819] | 72 | } else if (str.matches(String("AVDEV"))) { |
---|
[136] | 73 | return avdev(data); |
---|
[1819] | 74 | } else if (str.matches(String("RMS"))) { |
---|
[136] | 75 | uInt n = data.nelementsValid(); |
---|
| 76 | return sqrt(sumsquares(data)/n); |
---|
[1819] | 77 | } else if (str.matches(String("MEDIAN"))) { |
---|
[136] | 78 | return median(data); |
---|
[1819] | 79 | } else { |
---|
| 80 | String msg = str + " is not a valid type of statistics"; |
---|
| 81 | throw(AipsError(msg)); |
---|
| 82 | } |
---|
[996] | 83 | return 0.0; |
---|
[136] | 84 | } |
---|
[176] | 85 | |
---|
[1819] | 86 | IPosition mathutil::minMaxPos(const String& which, |
---|
| 87 | const MaskedArray<Float>& data) |
---|
| 88 | { |
---|
| 89 | Float minVal, maxVal; |
---|
| 90 | IPosition minPos(data.ndim(), 0), maxPos(data.ndim(), 0); |
---|
| 91 | minMax(minVal, maxVal, minPos, maxPos, data); |
---|
| 92 | String str(which); |
---|
| 93 | str.upcase(); |
---|
| 94 | if (str.contains(String("MIN"))) { |
---|
| 95 | return minPos; |
---|
| 96 | } else if (str.contains(String("MAX"))) { |
---|
| 97 | return maxPos; |
---|
| 98 | } else { |
---|
| 99 | String msg = str + " is not a valid type of statistics"; |
---|
| 100 | throw(AipsError(msg)); |
---|
| 101 | } |
---|
| 102 | //return 0.0; |
---|
| 103 | } |
---|
[829] | 104 | |
---|
[209] | 105 | void mathutil::replaceMaskByZero(Vector<Float>& data, const Vector<Bool>& mask) |
---|
[176] | 106 | { |
---|
| 107 | for (uInt i=0; i<data.nelements(); i++) { |
---|
| 108 | if (!mask[i]) data[i] = 0.0; |
---|
| 109 | } |
---|
| 110 | } |
---|
[382] | 111 | |
---|
| 112 | |
---|
[829] | 113 | std::vector<std::string> mathutil::tovectorstring(const Vector<String>& in) |
---|
[382] | 114 | { |
---|
[465] | 115 | std::vector<std::string> out; |
---|
[1412] | 116 | out.reserve(in.nelements()); |
---|
| 117 | for (Array<String>::const_iterator it = in.begin(); it != in.end(); ++it) { |
---|
[465] | 118 | out.push_back(*it); |
---|
| 119 | } |
---|
| 120 | return out; |
---|
| 121 | } |
---|
| 122 | |
---|
[829] | 123 | Vector<String> mathutil::toVectorString(const std::vector<std::string>& in) |
---|
[465] | 124 | { |
---|
| 125 | Vector<String> out(in.size()); |
---|
[1412] | 126 | Array<String>::iterator oit = out.begin(); |
---|
| 127 | for (std::vector<std::string>::const_iterator it=in.begin() ; |
---|
| 128 | it != in.end(); ++it,++oit) { |
---|
| 129 | *oit = *it; |
---|
[465] | 130 | } |
---|
| 131 | return out; |
---|
| 132 | } |
---|
[1325] | 133 | |
---|
| 134 | void mathutil::hanning(Vector<Float>& out, Vector<Bool>& outmask, |
---|
| 135 | const Vector<Float>& in, const Vector<Bool>& mask, |
---|
| 136 | Bool relaxed, Bool ignoreOther) { |
---|
[2163] | 137 | (void) ignoreOther; //suppress unused warning |
---|
[1325] | 138 | Vector< Vector<Float> > weights(8); |
---|
| 139 | Vector<Float> vals(3); |
---|
| 140 | vals = 0.0;weights[0] = vals;// FFF |
---|
| 141 | vals[0] = 1.0; vals[1] = 0.0; vals[2] = 0.0; weights[1] = vals;// TFF |
---|
| 142 | vals[0] = 0.0; vals[1] = 1.0; vals[2] = 0.0; weights[2] = vals;// FTF |
---|
| 143 | vals[0] = 1.0/3.0; vals[1] = 2.0/3.0; vals[2] = 0.0; weights[3] = vals;// TTF |
---|
| 144 | vals[0] = 0.0; vals[1] = 0.0; vals[2] = 1.0;weights[4] = vals;// FFT |
---|
| 145 | vals[0] = 0.5; vals[1] = 0.0; vals[2] = 0.5; weights[5] = vals;// TFT |
---|
| 146 | vals[0] = 0.0; vals[1] = 2.0/3.0; vals[2] = 1.0/3.0; weights[6] = vals;// FTT |
---|
| 147 | vals[0] = 0.25; vals[1] = 0.5; vals[2] = 0.25; weights[7] = vals;// TTT |
---|
| 148 | // Chris' case |
---|
| 149 | Vector<Bool> weighted(8); |
---|
| 150 | if (relaxed) { |
---|
| 151 | weighted = False; |
---|
| 152 | weighted[7] = True; |
---|
| 153 | |
---|
| 154 | } else { |
---|
| 155 | weighted = True; |
---|
| 156 | weighted[0] = False; |
---|
| 157 | } |
---|
| 158 | |
---|
| 159 | out.resize(in.nelements()); |
---|
| 160 | outmask.resize(mask.nelements()); |
---|
| 161 | // make special case for first and last |
---|
| 162 | /// ...here |
---|
| 163 | // loop from 1..n-2 |
---|
| 164 | out.resize(in.nelements()); |
---|
| 165 | out[0] = in[0];out[out.nelements()-1] = in[in.nelements()-1]; |
---|
| 166 | outmask.resize(mask.nelements()); |
---|
[2125] | 167 | outmask[0] = mask[0]; outmask[outmask.nelements()-1] = mask[mask.nelements()-1]; |
---|
[1325] | 168 | uInt m;Vector<Float>* w; |
---|
| 169 | for (uInt i=1; i < out.nelements()-1;++i) { |
---|
| 170 | m = mask[i-1] + 2*mask[i] + 4*mask[i+1]; |
---|
| 171 | w = &(weights[m]); |
---|
| 172 | if (weighted[m]) { |
---|
| 173 | out[i] = (*w)[0]*in[i-1] + (*w)[1]*in[i] + (*w)[2]*in[i+1]; |
---|
| 174 | } else { // mask it |
---|
| 175 | out[i] = in[i];//use arbitrary value |
---|
| 176 | } |
---|
[2125] | 177 | outmask[i] = mask[i]; |
---|
[1325] | 178 | } |
---|
| 179 | } |
---|
[1373] | 180 | |
---|
| 181 | |
---|
| 182 | void mathutil::runningMedian(Vector<Float>& out, Vector<Bool>& outflag, |
---|
| 183 | const Vector<Float>& in, const Vector<Bool>& flag, |
---|
| 184 | float width) |
---|
| 185 | { |
---|
[2163] | 186 | uInt hwidth = Int(width+0.5); |
---|
| 187 | uInt fwidth = hwidth*2+1; |
---|
[1373] | 188 | out.resize(in.nelements()); |
---|
| 189 | outflag.resize(flag.nelements()); |
---|
| 190 | MedianSlider ms(hwidth); |
---|
| 191 | Slice sl(0, fwidth-1); |
---|
[1570] | 192 | Float medval = ms.add(const_cast<Vector<Float>& >(in)(sl), |
---|
[1373] | 193 | const_cast<Vector<Bool>& >(flag)(sl)); |
---|
[2163] | 194 | (void) medval;//suppress unused warning |
---|
[1373] | 195 | uInt n = in.nelements(); |
---|
| 196 | for (uInt i=hwidth; i<(n-hwidth); ++i) { |
---|
| 197 | // add data value |
---|
[1570] | 198 | out[i] = ms.add(in[i+hwidth], flag[i+hwidth]); |
---|
| 199 | outflag[i] = (ms.nval() == 0); |
---|
[1373] | 200 | } |
---|
[1570] | 201 | // replicate edge values from first value with full width of values |
---|
[1373] | 202 | for (uInt i=0;i<hwidth;++i) { |
---|
| 203 | out[i] = out[hwidth]; |
---|
[1570] | 204 | outflag[i] = outflag[hwidth]; |
---|
[1373] | 205 | out[n-1-i] = out[n-1-hwidth]; |
---|
[1570] | 206 | outflag[n-1-i] = outflag[n-1-hwidth]; |
---|
[1373] | 207 | } |
---|
| 208 | } |
---|
[1570] | 209 | |
---|
| 210 | void mathutil::polyfit(Vector<Float>& out, Vector<Bool>& outmask, |
---|
| 211 | const Vector<Float>& in, const Vector<Bool>& mask, |
---|
| 212 | float width, int order) |
---|
| 213 | { |
---|
[2163] | 214 | uInt hwidth = Int(width+0.5); |
---|
| 215 | uInt fwidth = hwidth*2+1; |
---|
[1570] | 216 | out.resize(in.nelements()); |
---|
| 217 | outmask.resize(mask.nelements()); |
---|
| 218 | LinearFit<Float> fitter; |
---|
| 219 | Polynomial<Float> poly(order); |
---|
| 220 | fitter.setFunction(poly); |
---|
| 221 | Vector<Float> sigma(fwidth); |
---|
| 222 | sigma = 1.0; |
---|
| 223 | Vector<Float> parms; |
---|
| 224 | Vector<Float> x(fwidth); |
---|
| 225 | indgen(x); |
---|
| 226 | |
---|
| 227 | uInt n = in.nelements(); |
---|
| 228 | |
---|
| 229 | for (uInt i=hwidth; i<(n-hwidth); ++i) { |
---|
| 230 | // add data value |
---|
| 231 | if (mask[i]) { |
---|
| 232 | Slice sl(i-hwidth, fwidth); |
---|
| 233 | const Vector<Float> &y = const_cast<Vector<Float>& >(in)(sl); |
---|
| 234 | const Vector<Bool> &m = const_cast<Vector<Bool>& >(mask)(sl); |
---|
| 235 | parms = fitter.fit(x, y, sigma, &m); |
---|
| 236 | |
---|
| 237 | poly.setCoefficients(parms); |
---|
| 238 | out[i] = poly(x[hwidth]);//cout << in[i] <<"->"<<out[i]<<endl; |
---|
| 239 | } else { |
---|
| 240 | out[i] = in[i]; |
---|
| 241 | } |
---|
| 242 | outmask[i] = mask[i]; |
---|
| 243 | } |
---|
| 244 | // replicate edge values from first value with full width of values |
---|
| 245 | for (uInt i=0;i<hwidth;++i) { |
---|
| 246 | out[i] = out[hwidth]; |
---|
| 247 | outmask[i] = outmask[hwidth]; |
---|
| 248 | out[n-1-i] = out[n-1-hwidth]; |
---|
| 249 | outmask[n-1-i] = outmask[n-1-hwidth]; |
---|
| 250 | } |
---|
| 251 | } |
---|
[2186] | 252 | |
---|
| 253 | void mathutil::doZeroOrderInterpolation(casa::Vector<casa::Float>& data, |
---|
| 254 | std::vector<bool>& mask) { |
---|
| 255 | int fstart = -1; |
---|
| 256 | int fend = -1; |
---|
| 257 | for (uInt i = 0; i < mask.size(); ++i) { |
---|
| 258 | if (!mask[i]) { |
---|
| 259 | fstart = i; |
---|
| 260 | while (!mask[i] && i < mask.size()) { |
---|
| 261 | fend = i; |
---|
| 262 | i++; |
---|
| 263 | } |
---|
| 264 | } |
---|
| 265 | |
---|
| 266 | // execute interpolation as the following criteria: |
---|
| 267 | // (1) for a masked region inside the spectrum, replace the spectral |
---|
| 268 | // values with the mean of those at the two channels just outside |
---|
| 269 | // the both edges of the masked region. |
---|
| 270 | // (2) for a masked region at the spectral edge, replace the values |
---|
| 271 | // with the one at the nearest non-masked channel. |
---|
| 272 | // (ZOH, but bilateral) |
---|
| 273 | Float interp = 0.0; |
---|
| 274 | if (fstart-1 > 0) { |
---|
| 275 | interp = data[fstart-1]; |
---|
| 276 | if (fend+1 < Int(data.nelements())) { |
---|
| 277 | interp = (interp + data[fend+1]) / 2.0; |
---|
| 278 | } |
---|
| 279 | } else { |
---|
| 280 | interp = data[fend+1]; |
---|
| 281 | } |
---|
| 282 | if (fstart > -1 && fend > -1) { |
---|
| 283 | for (int j = fstart; j <= fend; ++j) { |
---|
| 284 | data[j] = interp; |
---|
| 285 | } |
---|
| 286 | } |
---|
| 287 | |
---|
| 288 | fstart = -1; |
---|
| 289 | fend = -1; |
---|
| 290 | } |
---|
[2258] | 291 | |
---|
[2186] | 292 | } |
---|
[2258] | 293 | |
---|
| 294 | double mathutil::gettimeofday_sec() |
---|
| 295 | { |
---|
| 296 | struct timeval tv ; |
---|
| 297 | gettimeofday( &tv, NULL ) ; |
---|
| 298 | return tv.tv_sec + (double)tv.tv_usec*1.0e-6 ; |
---|
| 299 | } |
---|