CCommit : CWT/ICWT added
This commit is contained in:
Rafat Hussain
420
src/cwt.c
Executable file
420
src/cwt.c
Executable file
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/*
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Copyright (c) 2015, Rafat Hussain
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*/
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/*
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This code is a C translation ( with some modifications) of Wavelet Software provided by
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C. Torrence and G. Compo, and is available at URL: http://atoc.colorado.edu/research/wavelets/''.
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*/
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#include "cwt.h"
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static int factorial2(int N) {
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int factorial,i;
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factorial = 1;
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for (i = 1; i <= N;++i) {
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factorial *= i;
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}
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return factorial;
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}
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static double factorial3(int N) {
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int i;
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double factorial;
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factorial = 1;
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for (i = 1; i <= N; ++i) {
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factorial *= i;
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}
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return factorial;
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}
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double factorial(int N) {
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if (N > 40) {
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printf("This program is only valid for N <= 40 \n");
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return -1.0;
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}
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double fact[41] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000,
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20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000.0, 1124000727777607680000.0,
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25852016738884976640000.0, 620448401733239439360000.0, 15511210043330985984000000.0, 403291461126605635584000000.0, 10888869450418352160768000000.0,
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304888344611713860501504000000.0, 8841761993739701954543616000000.0, 265252859812191058636308480000000.0, 8222838654177922817725562880000000.0,
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263130836933693530167218012160000000.0, 8683317618811886495518194401280000000.0, 295232799039604140847618609643520000000.0, 10333147966386144929666651337523200000000.0,
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371993326789901217467999448150835200000000.0, 13763753091226345046315979581580902400000000.0, 523022617466601111760007224100074291200000000.0,
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20397882081197443358640281739902897356800000000.0, 815915283247897734345611269596115894272000000000.0 };
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return fact[N];
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}
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static void wave_function(int nk, double dt,int mother, double param,double scale1, double *kwave, double pi,double *period1,
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double *coi1, fft_data *daughter) {
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double norm, expnt, fourier_factor;
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int k, m;
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double temp;
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int sign,re;
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if (mother == 0) {
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//MORLET
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if (param < 0.0) {
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param = 6.0;
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}
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norm = sqrt(2.0*pi*scale1 / dt)*pow(pi,-0.25);
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for (k = 1; k <= nk / 2 + 1; ++k) {
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temp = (scale1*kwave[k-1] - param);
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expnt = -0.5 * temp * temp;
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daughter[k - 1].re = norm * exp(expnt);
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daughter[k - 1].im = 0.0;
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}
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for (k = nk / 2 + 2; k <= nk; ++k) {
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daughter[k - 1].re = daughter[k - 1].im = 0.0;
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}
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fourier_factor = (4.0*pi) / (param + sqrt(2.0 + param*param));
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*period1 = scale1*fourier_factor;
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*coi1 = fourier_factor / sqrt(2.0);
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}
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else if (mother == 1) {
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// PAUL
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if (param < 0.0) {
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param = 4.0;
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}
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m = (int)param;
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norm = sqrt(2.0*pi*scale1 / dt)*(pow(2.0,(double)m) / sqrt((double)(m*factorial(2 * m - 1))));
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for (k = 1; k <= nk / 2 + 1; ++k) {
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temp = scale1 * kwave[k - 1];
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expnt = - temp;
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daughter[k - 1].re = norm * pow(temp,(double)m) * exp(expnt);
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daughter[k - 1].im = 0.0;
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}
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for (k = nk / 2 + 2; k <= nk; ++k) {
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daughter[k - 1].re = daughter[k - 1].im = 0.0;
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}
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fourier_factor = (4.0*pi) / (2.0 * m + 1.0);
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*period1 = scale1*fourier_factor;
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*coi1 = fourier_factor * sqrt(2.0);
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}
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else if (mother == 2) {
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if (param < 0.0) {
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param = 2.0;
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}
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m = (int)param;
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if (m % 2 == 0) {
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re = 1;
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}
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else {
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re = 0;
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}
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if (m % 4 == 0 || m % 4 == 1) {
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sign = -1;
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}
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else {
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sign = 1;
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}
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norm = sqrt(2.0*pi*scale1 / dt)*sqrt(1.0 / gamma(m + 0.50));
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norm *= sign;
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if (re == 1) {
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for (k = 1; k <= nk; ++k) {
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temp = scale1 * kwave[k - 1];
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daughter[k - 1].re = norm*pow(temp,(double)m)*exp(-0.50*pow(temp,2.0));
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daughter[k - 1].im = 0.0;
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}
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}
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else if (re == 0) {
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for (k = 1; k <= nk; ++k) {
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temp = scale1 * kwave[k - 1];
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daughter[k - 1].re = 0.0;
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daughter[k - 1].im = norm*pow(temp, (double)m)*exp(-0.50*pow(temp, 2.0));
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}
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}
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fourier_factor = (2.0*pi) * sqrt(2.0 / (2.0 * m + 1.0));
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*period1 = scale1*fourier_factor;
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*coi1 = fourier_factor / sqrt(2.0);
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}
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}
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void cwavelet(double *y, int N, double dt, int mother, double param, double s0, double dj, int jtot, int npad,
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double *wave, double *scale, double *period, double *coi) {
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int i, j, k, iter;
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double ymean, freq1, pi, period1, coi1;
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double tmp1, tmp2;
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double scale1;
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double *kwave;
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fft_object obj, iobj;
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fft_data *ypad, *yfft,*daughter;
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pi = 4.0 * atan(1.0);
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if (npad < N) {
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printf("npad must be >= N \n");
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exit(-1);
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}
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obj = fft_init(npad, 1);
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iobj = fft_init(npad, -1);
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ypad = (fft_data*)malloc(sizeof(fft_data)* npad);
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yfft = (fft_data*)malloc(sizeof(fft_data)* npad);
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daughter = (fft_data*)malloc(sizeof(fft_data)* npad);
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kwave = (double*)malloc(sizeof(double)* npad);
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ymean = 0.0;
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for (i = 0; i < N; ++i) {
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ymean += y[i];
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}
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ymean /= N;
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for (i = 0; i < N; ++i) {
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ypad[i].re = y[i] - ymean;
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ypad[i].im = 0.0;
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}
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for (i = N; i < npad; ++i) {
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ypad[i].re = ypad[i].im = 0.0;
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}
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// Find FFT of the input y (ypad)
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fft_exec(obj, ypad, yfft);
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for (i = 0; i < npad; ++i) {
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yfft[i].re /= (double) npad;
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yfft[i].im /= (double) npad;
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}
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//Construct the wavenumber array
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freq1 = 2.0*pi / ((double)npad*dt);
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kwave[0] = 0.0;
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for (i = 1; i < npad / 2 + 1; ++i) {
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kwave[i] = i * freq1;
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}
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for (i = npad / 2 + 1; i < npad; ++i) {
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kwave[i] = -kwave[npad - i ];
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}
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// Main loop
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for (j = 1; j <= jtot; ++j) {
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scale1 = scale[j - 1];// = s0*pow(2.0, (double)(j - 1)*dj);
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wave_function(npad, dt, mother, param, scale1, kwave, pi,&period1,&coi1, daughter);
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period[j - 1] = period1;
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for (k = 0; k < npad; ++k) {
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tmp1 = daughter[k].re * yfft[k].re - daughter[k].im * yfft[k].im;
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tmp2 = daughter[k].re * yfft[k].im + daughter[k].im * yfft[k].re;
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daughter[k].re = tmp1;
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daughter[k].im = tmp2;
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}
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fft_exec(iobj, daughter, ypad);
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iter = 2 * (j - 1) * N;
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for (i = 0; i < N; ++i) {
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wave[iter + 2 * i] = ypad[i].re;
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wave[iter + 2 * i + 1] = ypad[i].im;
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}
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}
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for (i = 1; i <= (N + 1) / 2; ++i) {
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coi[i - 1] = coi1 * dt * ((double)i - 1.0);
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coi[N - i] = coi[i - 1];
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}
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free(kwave);
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free(ypad);
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free(yfft);
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free(daughter);
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free_fft(obj);
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free_fft(iobj);
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}
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void psi0(int mother, double param,double *val,int *real) {
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double pi,coeff;
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int m,sign;
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m = (int)param;
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pi = 4.0 * atan(1.0);
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if (mother == 0) {
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// Morlet
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*val = 1.0 / sqrt(sqrt(pi));
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*real = 1;
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}
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else if (mother == 1) {
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//Paul
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if (m % 2 == 0) {
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*real = 1;
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}
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else {
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*real = 0;
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}
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if (m % 4 == 0 || m % 4 == 1) {
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sign = 1;
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}
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else {
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sign = -1;
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}
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*val = sign * pow(2.0, (double)m) * factorial(m) / (sqrt(pi * factorial(2 * m)));
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}
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else if (mother == 2) {
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// D.O.G
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*real = 1;
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if (m % 2 == 0) {
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if (m % 4 == 0) {
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sign = -1;
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}
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else {
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sign = 1;
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}
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coeff = sign * pow(2.0, (double)m / 2) / gamma(0.5);
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*val = coeff * gamma(((double)m + 1.0) / 2.0) / sqrt(gamma(m + 0.50));
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}
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else {
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*val = 0;
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}
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}
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}
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static int maxabs(double *array,int N) {
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double maxval,temp;
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int i,index;
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maxval = 0.0;
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index = -1;
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for (i = 0; i < N; ++i) {
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temp = fabs(array[i]);
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if (temp >= maxval) {
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maxval = temp;
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index = i;
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}
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}
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return index;
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}
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double cdelta(int mother, double param, double psi0 ) {
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int N,i,j,iter;
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double *delta, *scale,*period,*wave,*coi,*mval;
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double den,cdel;
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double subscale,dt,dj,s0;
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int jtot;
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int maxarr;
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subscale = 8.0;
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dt = 0.25;
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if (mother == 0) {
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N = 16;
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s0 = dt/4;
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}
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else if (mother == 1) {
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N = 16;
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s0 = dt / 4.0;
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}
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else if (mother == 2)
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{
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s0 = dt/8.0;
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N = 256;
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if (param == 2.0) {
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subscale = 16.0;
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s0 = dt / 16.0;
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N = 2048;
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}
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}
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dj = 1.0 / subscale;
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jtot = 16 * (int) subscale;
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delta = (double*)malloc(sizeof(double)* N);
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wave = (double*)malloc(sizeof(double)* 2 * N * jtot);
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coi = (double*)malloc(sizeof(double)* N);
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scale = (double*)malloc(sizeof(double)* jtot);
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period = (double*)malloc(sizeof(double)* jtot);
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mval = (double*)malloc(sizeof(double)* N);
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delta[0] = 1;
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for (i = 1; i < N; ++i) {
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delta[i] = 0;
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}
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for (i = 0; i < jtot; ++i) {
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scale[i] = s0*pow(2.0, (double)(i)*dj);
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}
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cwavelet(delta, N, dt, mother, param, s0, dj, jtot, N, wave, scale, period, coi);
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for (i = 0; i < N; ++i) {
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mval[i] = 0;
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}
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for (j = 0; j < jtot; ++j) {
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iter = 2 * j * N;
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den = sqrt(scale[j]);
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for (i = 0; i < N; ++i) {
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mval[i] += wave[iter + 2 * i]/den;
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}
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}
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maxarr = maxabs(mval, N);
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cdel = sqrt(dt) * dj * mval[maxarr] / psi0;
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free(delta);
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free(wave);
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free(scale);
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free(period);
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free(coi);
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free(mval);
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return cdel;
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}
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void icwavelet(double *wave, int N, double *scale,int jtot,double dt,double dj,double cdelta,double psi0,double *oup) {
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int i, j,iter;
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double den, coeff;
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coeff = sqrt(dt) * dj / (cdelta *psi0);
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for (i = 0; i < N; ++i) {
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oup[i] = 0.0;
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}
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for (j = 0; j < jtot; ++j) {
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iter = 2 * j * N;
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den = sqrt(scale[j]);
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for (i = 0; i < N; ++i) {
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oup[i] += wave[iter + 2 * i] / den;
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}
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}
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for (i = 0; i < N; ++i) {
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oup[i] *= coeff;
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}
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}
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