/usr/include/qm-dsp/maths/Polyfit.h is in libqm-dsp-dev 1.7.1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 | /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
//---------------------------------------------------------------------------
#ifndef PolyfitHPP
#define PolyfitHPP
//---------------------------------------------------------------------------
// Least-squares curve fitting class for arbitrary data types
/*
{ ******************************************
**** Scientific Subroutine Library ****
**** for C++ Builder ****
******************************************
The following programs were written by Allen Miller and appear in the
book entitled "Pascal Programs For Scientists And Engineers" which is
published by Sybex, 1981.
They were originally typed and submitted to MTPUG in Oct. 1982
Juergen Loewner
Hoher Heckenweg 3
D-4400 Muenster
They have had minor corrections and adaptations for Turbo Pascal by
Jeff Weiss
1572 Peacock Ave.
Sunnyvale, CA 94087.
2000 Oct 28 Updated for Delphi 4, open array parameters.
This allows the routine to be generalised so that it is no longer
hard-coded to make a specific order of best fit or work with a
specific number of points.
2001 Jan 07 Update Web site address
Copyright © David J Taylor, Edinburgh and others listed above
Web site: www.satsignal.net
E-mail: davidtaylor@writeme.com
}*/
///////////////////////////////////////////////////////////////////////////////
// Modified by CLandone for VC6 Aug 2004
///////////////////////////////////////////////////////////////////////////////
#include <iostream>
using std::vector;
class TPolyFit
{
typedef vector<vector<double> > Matrix;
public:
static double PolyFit2 (const vector<double> &x, // does the work
const vector<double> &y,
vector<double> &coef);
private:
TPolyFit &operator = (const TPolyFit &); // disable assignment
TPolyFit(); // and instantiation
TPolyFit(const TPolyFit&); // and copying
static void Square (const Matrix &x, // Matrix multiplication routine
const vector<double> &y,
Matrix &a, // A = transpose X times X
vector<double> &g, // G = Y times X
const int nrow, const int ncol);
// Forms square coefficient matrix
static bool GaussJordan (Matrix &b, // square matrix of coefficients
const vector<double> &y, // constant vector
vector<double> &coef); // solution vector
// returns false if matrix singular
static bool GaussJordan2(Matrix &b,
const vector<double> &y,
Matrix &w,
vector<vector<int> > &index);
};
// some utility functions
namespace NSUtility
{
inline void swap(double &a, double &b) {double t = a; a = b; b = t;}
void zeroise(vector<double> &array, int n);
void zeroise(vector<int> &array, int n);
void zeroise(vector<vector<double> > &matrix, int m, int n);
void zeroise(vector<vector<int> > &matrix, int m, int n);
inline double sqr(const double &x) {return x * x;}
};
//---------------------------------------------------------------------------
// Implementation
//---------------------------------------------------------------------------
using namespace NSUtility;
//------------------------------------------------------------------------------------------
// main PolyFit routine
double TPolyFit::PolyFit2 (const vector<double> &x,
const vector<double> &y,
vector<double> &coefs)
// nterms = coefs.size()
// npoints = x.size()
{
int i, j;
double xi, yi, yc, srs, sum_y, sum_y2;
Matrix xmatr; // Data matrix
Matrix a;
vector<double> g; // Constant vector
const int npoints(x.size());
const int nterms(coefs.size());
double correl_coef;
zeroise(g, nterms);
zeroise(a, nterms, nterms);
zeroise(xmatr, npoints, nterms);
if (nterms < 1) {
std::cerr << "ERROR: PolyFit called with less than one term" << std::endl;
return 0;
}
if(npoints < 2) {
std::cerr << "ERROR: PolyFit called with less than two points" << std::endl;
return 0;
}
if(npoints != (int)y.size()) {
std::cerr << "ERROR: PolyFit called with x and y of unequal size" << std::endl;
return 0;
}
for(i = 0; i < npoints; ++i)
{
// { setup x matrix }
xi = x[i];
xmatr[i][0] = 1.0; // { first column }
for(j = 1; j < nterms; ++j)
xmatr[i][j] = xmatr [i][j - 1] * xi;
}
Square (xmatr, y, a, g, npoints, nterms);
if(!GaussJordan (a, g, coefs))
return -1;
sum_y = 0.0;
sum_y2 = 0.0;
srs = 0.0;
for(i = 0; i < npoints; ++i)
{
yi = y[i];
yc = 0.0;
for(j = 0; j < nterms; ++j)
yc += coefs [j] * xmatr [i][j];
srs += sqr (yc - yi);
sum_y += yi;
sum_y2 += yi * yi;
}
// If all Y values are the same, avoid dividing by zero
correl_coef = sum_y2 - sqr (sum_y) / npoints;
// Either return 0 or the correct value of correlation coefficient
if (correl_coef != 0)
correl_coef = srs / correl_coef;
if (correl_coef >= 1)
correl_coef = 0.0;
else
correl_coef = sqrt (1.0 - correl_coef);
return correl_coef;
}
//------------------------------------------------------------------------
// Matrix multiplication routine
// A = transpose X times X
// G = Y times X
// Form square coefficient matrix
void TPolyFit::Square (const Matrix &x,
const vector<double> &y,
Matrix &a,
vector<double> &g,
const int nrow,
const int ncol)
{
int i, k, l;
for(k = 0; k < ncol; ++k)
{
for(l = 0; l < k + 1; ++l)
{
a [k][l] = 0.0;
for(i = 0; i < nrow; ++i)
{
a[k][l] += x[i][l] * x [i][k];
if(k != l)
a[l][k] = a[k][l];
}
}
g[k] = 0.0;
for(i = 0; i < nrow; ++i)
g[k] += y[i] * x[i][k];
}
}
//---------------------------------------------------------------------------------
bool TPolyFit::GaussJordan (Matrix &b,
const vector<double> &y,
vector<double> &coef)
//b square matrix of coefficients
//y constant vector
//coef solution vector
//ncol order of matrix got from b.size()
{
/*
{ Gauss Jordan matrix inversion and solution }
{ B (n, n) coefficient matrix becomes inverse }
{ Y (n) original constant vector }
{ W (n, m) constant vector(s) become solution vector }
{ DETERM is the determinant }
{ ERROR = 1 if singular }
{ INDEX (n, 3) }
{ NV is number of constant vectors }
*/
int ncol(b.size());
int irow, icol;
vector<vector<int> >index;
Matrix w;
zeroise(w, ncol, ncol);
zeroise(index, ncol, 3);
if(!GaussJordan2(b, y, w, index))
return false;
// Interchange columns
int m;
for (int i = 0; i < ncol; ++i)
{
m = ncol - i - 1;
if(index [m][0] != index [m][1])
{
irow = index [m][0];
icol = index [m][1];
for(int k = 0; k < ncol; ++k)
swap (b[k][irow], b[k][icol]);
}
}
for(int k = 0; k < ncol; ++k)
{
if(index [k][2] != 0)
{
std::cerr << "ERROR: Error in PolyFit::GaussJordan: matrix is singular" << std::endl;
return false;
}
}
for( int i = 0; i < ncol; ++i)
coef[i] = w[i][0];
return true;
} // end; { procedure GaussJordan }
//----------------------------------------------------------------------------------------------
bool TPolyFit::GaussJordan2(Matrix &b,
const vector<double> &y,
Matrix &w,
vector<vector<int> > &index)
{
//GaussJordan2; // first half of GaussJordan
// actual start of gaussj
double big, t;
double pivot;
double determ;
int irow, icol;
int ncol(b.size());
int nv = 1; // single constant vector
for(int i = 0; i < ncol; ++i)
{
w[i][0] = y[i]; // copy constant vector
index[i][2] = -1;
}
determ = 1.0;
for(int i = 0; i < ncol; ++i)
{
// Search for largest element
big = 0.0;
for(int j = 0; j < ncol; ++j)
{
if(index[j][2] != 0)
{
for(int k = 0; k < ncol; ++k)
{
if(index[k][2] > 0) {
std::cerr << "ERROR: Error in PolyFit::GaussJordan2: matrix is singular" << std::endl;
return false;
}
if(index[k][2] < 0 && fabs(b[j][k]) > big)
{
irow = j;
icol = k;
big = fabs(b[j][k]);
}
} // { k-loop }
}
} // { j-loop }
index [icol][2] = index [icol][2] + 1;
index [i][0] = irow;
index [i][1] = icol;
// Interchange rows to put pivot on diagonal
// GJ3
if(irow != icol)
{
determ = -determ;
for(int m = 0; m < ncol; ++m)
swap (b [irow][m], b[icol][m]);
if (nv > 0)
for (int m = 0; m < nv; ++m)
swap (w[irow][m], w[icol][m]);
} // end GJ3
// divide pivot row by pivot column
pivot = b[icol][icol];
determ *= pivot;
b[icol][icol] = 1.0;
for(int m = 0; m < ncol; ++m)
b[icol][m] /= pivot;
if(nv > 0)
for(int m = 0; m < nv; ++m)
w[icol][m] /= pivot;
// Reduce nonpivot rows
for(int n = 0; n < ncol; ++n)
{
if(n != icol)
{
t = b[n][icol];
b[n][icol] = 0.0;
for(int m = 0; m < ncol; ++m)
b[n][m] -= b[icol][m] * t;
if(nv > 0)
for(int m = 0; m < nv; ++m)
w[n][m] -= w[icol][m] * t;
}
}
} // { i-loop }
return true;
}
//----------------------------------------------------------------------------------------------
//------------------------------------------------------------------------------------
// Utility functions
//--------------------------------------------------------------------------
// fills a vector with zeros.
void NSUtility::zeroise(vector<double> &array, int n)
{
array.clear();
for(int j = 0; j < n; ++j)
array.push_back(0);
}
//--------------------------------------------------------------------------
// fills a vector with zeros.
void NSUtility::zeroise(vector<int> &array, int n)
{
array.clear();
for(int j = 0; j < n; ++j)
array.push_back(0);
}
//--------------------------------------------------------------------------
// fills a (m by n) matrix with zeros.
void NSUtility::zeroise(vector<vector<double> > &matrix, int m, int n)
{
vector<double> zero;
zeroise(zero, n);
matrix.clear();
for(int j = 0; j < m; ++j)
matrix.push_back(zero);
}
//--------------------------------------------------------------------------
// fills a (m by n) matrix with zeros.
void NSUtility::zeroise(vector<vector<int> > &matrix, int m, int n)
{
vector<int> zero;
zeroise(zero, n);
matrix.clear();
for(int j = 0; j < m; ++j)
matrix.push_back(zero);
}
//--------------------------------------------------------------------------
#endif
|