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CCommit : CWT/ICWT added
This commit is contained in:
Rafat Hussain
parent
dc38e9f39b
commit
69bf4dc0b0
@ -1,7 +1,7 @@
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wavelib
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=======
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C Implementation of Wavelet Transform (DWT,SWT and MODWT) and Packet Transform ( Full Tree Decomposition and Best Basis DPWT).
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C Implementation of Wavelet Transform (DWT,SWT and MODWT) and Packet Transform ( Full Tree Decomposition and Best Basis DWPT).
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Discrete Wavelet Transform Methods Implemented
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@ -14,6 +14,16 @@ extern "C" {
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#define fft_type double
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#endif
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#ifndef cplx_type
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#define cplx_type double
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#endif
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typedef struct cplx_t {
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cplx_type re;
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cplx_type im;
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} cplx_data;
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typedef struct wave_set* wave_object;
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wave_object wave_init(char* wname);
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@ -153,6 +163,34 @@ struct wpt_set{
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};
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typedef struct cwt_set* cwt_object;
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cwt_object cwt_init(char* wave, double param, int siglength,double dt, int J);
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struct cwt_set{
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char wave[10];// Wavelet - morl/morlet,paul,dog/dgauss
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int siglength;// Length of Input Data
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int J;// Total Number of Scales
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double s0;// Smallest scale. It depends on the sampling rate. s0 <= 2 * dt for most wavelets
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double dt;// Sampling Rate
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double dj;// Separation between scales. eg., scale = s0 * 2 ^ ( [0:N-1] *dj ) or scale = s0 *[0:N-1] * dj
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char type[10];// Scale Type - Power or Linear
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int pow;// Base of Power in case type = pow. Typical value is pow = 2
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int sflag;
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int pflag;
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int npad;
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int mother;
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double m;// Wavelet parameter param
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double smean;// Input Signal mean
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cplx_data *output;
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double *scale;
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double *period;
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double *coi;
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double params[0];
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};
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void dwt(wt_object wt, double *inp);
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void idwt(wt_object wt, double *dwtop);
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@ -189,6 +227,18 @@ int getDWPTNodelength(wpt_object wt, int X);
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void getDWPTCoeffs(wpt_object wt, int X, int Y, double *coeffs, int N);
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void setCWTScales(cwt_object wt, double s0, double dj, char *type, int power);
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void setCWTScaleVector(cwt_object wt, double *scale, int J, double s0, double dj);
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void setCWTPadding(cwt_object wt, int pad);
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void cwt(cwt_object wt, double *inp);
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void icwt(cwt_object wt, double *cwtop);
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int getCWTScaleLength(int N);
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void wave_summary(wave_object obj);
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void wt_summary(wt_object wt);
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@ -197,6 +247,8 @@ void wtree_summary(wtree_object wt);
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void wpt_summary(wpt_object wt);
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void cwt_summary(cwt_object wt);;
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void wave_free(wave_object object);
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void wt_free(wt_object object);
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@ -205,6 +257,8 @@ void wtree_free(wtree_object object);
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void wpt_free(wpt_object object);
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void cwt_free(cwt_object object);
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#ifdef __cplusplus
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}
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@ -3,17 +3,23 @@
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include_directories(${CMAKE_CURRENT_SOURCE_DIR})
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set(SOURCE_FILES conv.c
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cwt.c
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cwtmath.c
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hsfft.c
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real.c
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wavefilt.c
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wavefunc.c
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wavelib.c
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wtmath.c
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)
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set(HEADER_FILES conv.h
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cwt.h
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cwtmath.h
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hsfft.h
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real.h
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wavefilt.h
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wavefunc.h
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wavelib.h
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wtmath.h
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)
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420
src/cwt.c
Executable file
420
src/cwt.c
Executable file
@ -0,0 +1,420 @@
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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);
|
||||
mval = (double*)malloc(sizeof(double)* N);
|
||||
|
||||
|
||||
delta[0] = 1;
|
||||
|
||||
for (i = 1; i < N; ++i) {
|
||||
delta[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < jtot; ++i) {
|
||||
scale[i] = s0*pow(2.0, (double)(i)*dj);
|
||||
}
|
||||
|
||||
cwavelet(delta, N, dt, mother, param, s0, dj, jtot, N, wave, scale, period, coi);
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
mval[i] = 0;
|
||||
}
|
||||
|
||||
for (j = 0; j < jtot; ++j) {
|
||||
iter = 2 * j * N;
|
||||
den = sqrt(scale[j]);
|
||||
for (i = 0; i < N; ++i) {
|
||||
mval[i] += wave[iter + 2 * i]/den;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
maxarr = maxabs(mval, N);
|
||||
|
||||
cdel = sqrt(dt) * dj * mval[maxarr] / psi0;
|
||||
|
||||
free(delta);
|
||||
free(wave);
|
||||
|
||||
free(scale);
|
||||
free(period);
|
||||
free(coi);
|
||||
free(mval);
|
||||
|
||||
return cdel;
|
||||
}
|
||||
|
||||
void icwavelet(double *wave, int N, double *scale,int jtot,double dt,double dj,double cdelta,double psi0,double *oup) {
|
||||
int i, j,iter;
|
||||
double den, coeff;
|
||||
|
||||
coeff = sqrt(dt) * dj / (cdelta *psi0);
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
oup[i] = 0.0;
|
||||
}
|
||||
|
||||
for (j = 0; j < jtot; ++j) {
|
||||
iter = 2 * j * N;
|
||||
den = sqrt(scale[j]);
|
||||
for (i = 0; i < N; ++i) {
|
||||
oup[i] += wave[iter + 2 * i] / den;
|
||||
}
|
||||
}
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
oup[i] *= coeff;
|
||||
}
|
||||
}
|
||||
29
src/cwt.h
Executable file
29
src/cwt.h
Executable file
@ -0,0 +1,29 @@
|
||||
#ifndef CWT_H_
|
||||
#define CWT_H_
|
||||
|
||||
#include "wavefunc.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
void cwavelet(double *y, int N, double dt, int mother, double param, double s0, double dj, int jtot, int npad,
|
||||
double *wave, double *scale, double *period, double *coi);
|
||||
|
||||
void psi0(int mother, double param, double *val, int *real);
|
||||
|
||||
double factorial(int N);
|
||||
|
||||
double cdelta(int mother, double param, double psi0);
|
||||
|
||||
void icwavelet(double *wave, int N, double *scale, int jtot, double dt, double dj, double cdelta, double psi0, double *oup);
|
||||
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
#endif /* WAVELIB_H_ */
|
||||
|
||||
|
||||
296
src/cwtmath.c
Executable file
296
src/cwtmath.c
Executable file
@ -0,0 +1,296 @@
|
||||
#include "cwtmath.h"
|
||||
|
||||
static void nsfft_fd(fft_object obj, fft_data *inp, fft_data *oup,double lb,double ub,double *w) {
|
||||
int M,N,i,j,L;
|
||||
double delta,den,theta,tempr,tempi,plb;
|
||||
double *temp1,*temp2;
|
||||
|
||||
N = obj->N;
|
||||
L = N/2;
|
||||
//w = (double*)malloc(sizeof(double)*N);
|
||||
|
||||
M = divideby(N, 2);
|
||||
|
||||
if (M == 0) {
|
||||
printf("The Non-Standard FFT Length must be a power of 2");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
temp1 = (double*)malloc(sizeof(double)*L);
|
||||
temp2 = (double*)malloc(sizeof(double)*L);
|
||||
|
||||
delta = (ub - lb)/ N;
|
||||
j = -N;
|
||||
den = 2 * (ub-lb);
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
w[i] = (double)j/den;
|
||||
j += 2;
|
||||
}
|
||||
|
||||
fft_exec(obj,inp,oup);
|
||||
|
||||
|
||||
for (i = 0; i < L; ++i) {
|
||||
temp1[i] = oup[i].re;
|
||||
temp2[i] = oup[i].im;
|
||||
}
|
||||
|
||||
for (i = 0; i < N - L; ++i) {
|
||||
oup[i].re = oup[i + L].re;
|
||||
oup[i].im = oup[i + L].im;
|
||||
}
|
||||
|
||||
for (i = 0; i < L; ++i) {
|
||||
oup[N - L + i].re = temp1[i];
|
||||
oup[N - L + i].im = temp2[i];
|
||||
}
|
||||
|
||||
plb = PI2 * lb;
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
tempr = oup[i].re;
|
||||
tempi = oup[i].im;
|
||||
theta = w[i] * plb;
|
||||
|
||||
oup[i].re = delta * (tempr*cos(theta) + tempi*sin(theta));
|
||||
oup[i].im = delta * (tempi*cos(theta) - tempr*sin(theta));
|
||||
}
|
||||
|
||||
|
||||
//free(w);
|
||||
free(temp1);
|
||||
free(temp2);
|
||||
}
|
||||
|
||||
static void nsfft_bk(fft_object obj, fft_data *inp, fft_data *oup,double lb,double ub,double *t) {
|
||||
int M,N,i,j,L;
|
||||
double *w;
|
||||
double delta,den,plb,theta;
|
||||
double *temp1,*temp2;
|
||||
fft_data *inpt;
|
||||
|
||||
N = obj->N;
|
||||
L = N/2;
|
||||
|
||||
M = divideby(N, 2);
|
||||
|
||||
if (M == 0) {
|
||||
printf("The Non-Standard FFT Length must be a power of 2");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
temp1 = (double*)malloc(sizeof(double)*L);
|
||||
temp2 = (double*)malloc(sizeof(double)*L);
|
||||
w = (double*)malloc(sizeof(double)*N);
|
||||
inpt = (fft_data*) malloc (sizeof(fft_data) * N);
|
||||
|
||||
delta = (ub - lb)/ N;
|
||||
j = -N;
|
||||
den = 2 * (ub-lb);
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
w[i] = (double)j/den;
|
||||
j += 2;
|
||||
}
|
||||
|
||||
plb = PI2 * lb;
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
theta = w[i] * plb;
|
||||
|
||||
inpt[i].re = (inp[i].re*cos(theta) - inp[i].im*sin(theta))/delta;
|
||||
inpt[i].im = (inp[i].im*cos(theta) + inp[i].re*sin(theta))/delta;
|
||||
}
|
||||
|
||||
for (i = 0; i < L; ++i) {
|
||||
temp1[i] = inpt[i].re;
|
||||
temp2[i] = inpt[i].im;
|
||||
}
|
||||
|
||||
for (i = 0; i < N - L; ++i) {
|
||||
inpt[i].re = inpt[i + L].re;
|
||||
inpt[i].im = inpt[i + L].im;
|
||||
}
|
||||
|
||||
for (i = 0; i < L; ++i) {
|
||||
inpt[N - L + i].re = temp1[i];
|
||||
inpt[N - L + i].im = temp2[i];
|
||||
}
|
||||
|
||||
fft_exec(obj,inpt,oup);
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
t[i] = lb + i*delta;
|
||||
}
|
||||
|
||||
free(w);
|
||||
free(temp1);
|
||||
free(temp2);
|
||||
free(inpt);
|
||||
}
|
||||
|
||||
void nsfft_exec(fft_object obj, fft_data *inp, fft_data *oup,double lb,double ub,double *w) {
|
||||
if (obj->sgn == 1) {
|
||||
nsfft_fd(obj,inp,oup,lb,ub,w);
|
||||
} else if (obj->sgn == -1) {
|
||||
nsfft_bk(obj,inp,oup,lb,ub,w);
|
||||
}
|
||||
}
|
||||
|
||||
static double fix(double x) {
|
||||
// Rounds to the integer nearest to zero
|
||||
if (x >= 0.) {
|
||||
return floor(x);
|
||||
} else {
|
||||
return ceil(x);
|
||||
}
|
||||
}
|
||||
|
||||
int nint(double N) {
|
||||
int i;
|
||||
|
||||
i = (int)(N + 0.49999);
|
||||
|
||||
return i;
|
||||
}
|
||||
|
||||
double gamma(double x) {
|
||||
/*
|
||||
* This C program code is based on W J Cody's fortran code.
|
||||
* http://www.netlib.org/specfun/gamma
|
||||
*
|
||||
* References:
|
||||
"An Overview of Software Development for Special Functions",
|
||||
W. J. Cody, Lecture Notes in Mathematics, 506,
|
||||
Numerical Analysis Dundee, 1975, G. A. Watson (ed.),
|
||||
Springer Verlag, Berlin, 1976.
|
||||
|
||||
Computer Approximations, Hart, Et. Al., Wiley and sons, New York, 1968.
|
||||
*/
|
||||
|
||||
// numerator and denominator coefficients for 1 <= x <= 2
|
||||
|
||||
double y,oup,fact,sum,y2,yi,z,nsum,dsum;
|
||||
int swi,n,i;
|
||||
|
||||
double spi = 0.9189385332046727417803297;
|
||||
double pi = 3.1415926535897932384626434;
|
||||
double xmax = 171.624e+0;
|
||||
double xinf = 1.79e308;
|
||||
double eps = 2.22e-16;
|
||||
double xninf = 1.79e-308;
|
||||
|
||||
double num[8] = { -1.71618513886549492533811e+0,
|
||||
2.47656508055759199108314e+1,
|
||||
-3.79804256470945635097577e+2,
|
||||
6.29331155312818442661052e+2,
|
||||
8.66966202790413211295064e+2,
|
||||
-3.14512729688483675254357e+4,
|
||||
-3.61444134186911729807069e+4,
|
||||
6.64561438202405440627855e+4 };
|
||||
|
||||
double den[8] = { -3.08402300119738975254353e+1,
|
||||
3.15350626979604161529144e+2,
|
||||
-1.01515636749021914166146e+3,
|
||||
-3.10777167157231109440444e+3,
|
||||
2.25381184209801510330112e+4,
|
||||
4.75584627752788110767815e+3,
|
||||
-1.34659959864969306392456e+5,
|
||||
-1.15132259675553483497211e+5 };
|
||||
|
||||
// Coefficients for Hart's Minimax approximation x >= 12
|
||||
|
||||
|
||||
double c[7] = { -1.910444077728e-03,
|
||||
8.4171387781295e-04,
|
||||
-5.952379913043012e-04,
|
||||
7.93650793500350248e-04,
|
||||
-2.777777777777681622553e-03,
|
||||
8.333333333333333331554247e-02,
|
||||
5.7083835261e-03 };
|
||||
|
||||
y = x;
|
||||
swi = 0;
|
||||
fact = 1.0;
|
||||
n = 0;
|
||||
|
||||
|
||||
if ( y < 0.) {
|
||||
// Negative x
|
||||
y = -x;
|
||||
yi = fix(y);
|
||||
oup = y - yi;
|
||||
|
||||
if (oup != 0.0) {
|
||||
if (yi != fix(yi * .5) * 2.) {
|
||||
swi = 1;
|
||||
}
|
||||
fact = -pi / sin(pi * oup);
|
||||
y += 1.;
|
||||
} else {
|
||||
return xinf;
|
||||
}
|
||||
}
|
||||
|
||||
if (y < eps) {
|
||||
if (y >= xninf) {
|
||||
oup = 1.0/y;
|
||||
} else {
|
||||
return xinf;
|
||||
}
|
||||
|
||||
} else if (y < 12.) {
|
||||
yi = y;
|
||||
if ( y < 1.) {
|
||||
z = y;
|
||||
y += 1.;
|
||||
} else {
|
||||
n = ( int ) y - 1;
|
||||
y -= ( double ) n;
|
||||
z = y - 1.0;
|
||||
}
|
||||
nsum = 0.;
|
||||
dsum = 1.;
|
||||
for (i = 0; i < 8; ++i) {
|
||||
nsum = (nsum + num[i]) * z;
|
||||
dsum = dsum * z + den[i];
|
||||
}
|
||||
oup = nsum / dsum + 1.;
|
||||
|
||||
if (yi < y) {
|
||||
|
||||
oup /= yi;
|
||||
} else if (yi > y) {
|
||||
|
||||
for (i = 0; i < n; ++i) {
|
||||
oup *= y;
|
||||
y += 1.;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
} else {
|
||||
if (y <= xmax) {
|
||||
y2 = y * y;
|
||||
sum = c[6];
|
||||
for (i = 0; i < 6; ++i) {
|
||||
sum = sum / y2 + c[i];
|
||||
}
|
||||
sum = sum / y - y + spi;
|
||||
sum += (y - .5) * log(y);
|
||||
oup = exp(sum);
|
||||
} else {
|
||||
return(xinf);
|
||||
}
|
||||
}
|
||||
|
||||
if (swi) {
|
||||
oup = -oup;
|
||||
}
|
||||
if (fact != 1.) {
|
||||
oup = fact / oup;
|
||||
}
|
||||
|
||||
return oup;
|
||||
}
|
||||
22
src/cwtmath.h
Executable file
22
src/cwtmath.h
Executable file
@ -0,0 +1,22 @@
|
||||
#ifndef CWTMATH_H_
|
||||
#define CWTMATH_H_
|
||||
|
||||
#include "wtmath.h"
|
||||
#include "hsfft.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
void nsfft_exec(fft_object obj, fft_data *inp, fft_data *oup,double lb,double ub,double *w);// lb -lower bound, ub - upper bound, w - time or frequency grid (Size N)
|
||||
|
||||
double gamma(double x);
|
||||
|
||||
int nint(double N);
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
#endif /* WAVELIB_H_ */
|
||||
210
src/wavefunc.c
Executable file
210
src/wavefunc.c
Executable file
@ -0,0 +1,210 @@
|
||||
#include "wavefunc.h"
|
||||
|
||||
void meyer(int N,double lb,double ub,double *phi,double *psi,double *tgrid) {
|
||||
int M,i;
|
||||
double *w;
|
||||
double delta,j;
|
||||
double theta,x,x2,x3,x4,v,cs,sn;
|
||||
double wf;
|
||||
fft_data *phiw,*psiw,*oup;
|
||||
fft_object obj;
|
||||
|
||||
M = divideby(N, 2);
|
||||
|
||||
if (M == 0) {
|
||||
printf("Size of Wavelet must be a power of 2");
|
||||
exit(1);
|
||||
}
|
||||
if (lb >= ub) {
|
||||
printf("upper bound must be greater than lower bound");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
obj = fft_init(N,-1);
|
||||
w = (double*)malloc(sizeof(double)*N);
|
||||
phiw = (fft_data*) malloc (sizeof(fft_data) * N);
|
||||
psiw = (fft_data*) malloc (sizeof(fft_data) * N);
|
||||
oup = (fft_data*) malloc (sizeof(fft_data) * N);
|
||||
|
||||
delta = 2 * (ub-lb) / PI2;
|
||||
|
||||
j = (double) N;
|
||||
j *= -1.0;
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
w[i] = j / delta;
|
||||
j += 2.0;
|
||||
psiw[i].re = psiw[i].im = 0.0;
|
||||
phiw[i].re = phiw[i].im = 0.0;
|
||||
}
|
||||
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
wf = fabs(w[i]);
|
||||
if (wf <= PI2/3.0) {
|
||||
phiw[i].re = 1.0;
|
||||
}
|
||||
if (wf > PI2/3.0 && wf <= 2 * PI2 / 3.0) {
|
||||
x = (3 * wf / PI2) - 1.0;
|
||||
x2 = x*x;
|
||||
x3 = x2 * x;
|
||||
x4 = x3 *x;
|
||||
v = x4 *(35 - 84*x + 70*x2 - 20*x3);
|
||||
theta = v * PI2 / 4.0;
|
||||
cs = cos(theta);
|
||||
sn = sin(theta);
|
||||
|
||||
phiw[i].re = cs;
|
||||
psiw[i].re = cos(w[i]/2.0) * sn;
|
||||
psiw[i].im = sin(w[i]/2.0) * sn;
|
||||
}
|
||||
if (wf > 2.0 * PI2/3.0 && wf <= 4 * PI2 / 3.0) {
|
||||
x = (1.5 * wf / PI2) - 1.0;
|
||||
x2 = x*x;
|
||||
x3 = x2 * x;
|
||||
x4 = x3 *x;
|
||||
v = x4 *(35 - 84*x + 70*x2 - 20*x3);
|
||||
theta = v * PI2 / 4.0;
|
||||
cs = cos(theta);
|
||||
|
||||
psiw[i].re = cos(w[i]/2.0) * cs;
|
||||
psiw[i].im = sin(w[i]/2.0) * cs;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
nsfft_exec(obj,phiw,oup,lb,ub,tgrid);
|
||||
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
phi[i] = oup[i].re/N;
|
||||
}
|
||||
|
||||
nsfft_exec(obj,psiw,oup,lb,ub,tgrid);
|
||||
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
psi[i] = oup[i].re/N;
|
||||
}
|
||||
|
||||
|
||||
|
||||
free(oup);
|
||||
free(phiw);
|
||||
free(psiw);
|
||||
free(w);
|
||||
}
|
||||
|
||||
void gauss(int N,int p,double lb,double ub,double *psi,double *t) {
|
||||
double delta,num,den,t2,t4;
|
||||
int i;
|
||||
|
||||
if (lb >= ub) {
|
||||
printf("upper bound must be greater than lower bound");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
t[0] = lb;
|
||||
t[N-1] = ub;
|
||||
delta = (ub - lb) / (N-1);
|
||||
for(i = 1; i < N-1;++i) {
|
||||
t[i] = lb + delta * i;
|
||||
}
|
||||
|
||||
den = sqrt(gamma(p+0.5));
|
||||
|
||||
if ((p+1)%2 == 0) {
|
||||
num = 1.0;
|
||||
} else {
|
||||
num = -1.0;
|
||||
}
|
||||
|
||||
num /= den;
|
||||
|
||||
//printf("\n%g\n",num);
|
||||
|
||||
if (p == 1) {
|
||||
for(i = 0; i < N;++i) {
|
||||
psi[i] = -t[i] * exp(- t[i] * t[i]/2.0) * num;
|
||||
}
|
||||
} else if (p == 2) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = (-1.0 + t2) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 3) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = t[i] * (3.0 - t2) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 4) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = (t2 * t2 - 6.0 * t2 + 3.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 5) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = t[i] * (-t2 * t2 + 10.0 * t2 - 15.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 6) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = (t2 * t2 * t2 - 15.0 * t2 * t2 + 45.0 * t2 - 15.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 7) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
psi[i] = t[i] * (-t2 * t2 * t2 + 21.0 * t2 * t2 - 105.0 * t2 + 105.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 8) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
t4 = t2 * t2;
|
||||
psi[i] = (t4 * t4 - 28.0 * t4 * t2 + 210.0 * t4 - 420.0 * t2 + 105.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 9) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
t4 = t2 * t2;
|
||||
psi[i] = t[i] * (- t4 * t4 + 36.0 * t4 * t2 - 378.0 * t4 + 1260.0 * t2 - 945.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else if (p == 10) {
|
||||
for(i = 0; i < N;++i) {
|
||||
t2 = t[i] * t[i];
|
||||
t4 = t2 * t2;
|
||||
psi[i] = (t4 * t4 * t2 - 45.0 * t4 * t4 + 630.0 * t4 * t2 - 3150.0 * t4 + 4725.0 * t2 - 945.0) * exp(- t2/2.0) * num;
|
||||
}
|
||||
} else {
|
||||
printf("\n The Gaussian Derivative Wavelet is only available for Derivatives 1 to 10");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
|
||||
|
||||
}
|
||||
|
||||
void mexhat(int N,double lb,double ub,double *psi,double *t) {
|
||||
gauss(N,2,lb,ub,psi,t);
|
||||
}
|
||||
|
||||
void morlet(int N,double lb,double ub,double *psi,double *t) {
|
||||
int i;
|
||||
double delta;
|
||||
|
||||
if (lb >= ub) {
|
||||
printf("upper bound must be greater than lower bound");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
t[0] = lb;
|
||||
t[N-1] = ub;
|
||||
delta = (ub - lb) / (N-1);
|
||||
for(i = 1; i < N-1;++i) {
|
||||
t[i] = lb + delta * i;
|
||||
}
|
||||
|
||||
for(i = 0; i < N;++i) {
|
||||
psi[i] = exp(- t[i] * t[i] / 2.0) * cos(5 * t[i]);
|
||||
}
|
||||
}
|
||||
24
src/wavefunc.h
Executable file
24
src/wavefunc.h
Executable file
@ -0,0 +1,24 @@
|
||||
#ifndef WAVEFUNC_H_
|
||||
#define WAVEFUNC_H_
|
||||
|
||||
#include "cwtmath.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
void meyer(int N,double lb,double ub,double *phi,double *psi,double *tgrid);
|
||||
|
||||
void gauss(int N,int p,double lb,double ub,double *psi,double *t);
|
||||
|
||||
void mexhat(int N,double lb,double ub,double *psi,double *t);
|
||||
|
||||
void morlet(int N,double lb,double ub,double *psi,double *t);
|
||||
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
#endif /* WAVEFUNC_H_ */
|
||||
4913
src/wavelib.c
4913
src/wavelib.c
File diff suppressed because it is too large
Load Diff
402
src/wavelib.h
402
src/wavelib.h
@ -1,176 +1,230 @@
|
||||
/*
|
||||
Copyright (c) 2014, Rafat Hussain
|
||||
*/
|
||||
#ifndef WAVELIB_H_
|
||||
#define WAVELIB_H_
|
||||
|
||||
#include "wtmath.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
#if defined(_MSC_VER)
|
||||
#pragma warning(disable : 4200)
|
||||
#pragma warning(disable : 4996)
|
||||
#endif
|
||||
|
||||
typedef struct wave_set* wave_object;
|
||||
|
||||
wave_object wave_init(char* wname);
|
||||
|
||||
struct wave_set{
|
||||
char wname[50];
|
||||
int filtlength;// When all filters are of the same length. [Matlab uses zero-padding to make all filters of the same length]
|
||||
int lpd_len;// Default filtlength = lpd_len = lpr_len = hpd_len = hpr_len
|
||||
int hpd_len;
|
||||
int lpr_len;
|
||||
int hpr_len;
|
||||
double *lpd;
|
||||
double *hpd;
|
||||
double *lpr;
|
||||
double *hpr;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wt_set* wt_object;
|
||||
|
||||
wt_object wt_init(wave_object wave,char* method, int siglength, int J);
|
||||
|
||||
struct wt_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
char method[10];
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
char cmethod[10]; // Convolution Method - "direct" or "FFT"
|
||||
|
||||
int N; //
|
||||
int cfftset;
|
||||
int zpad;
|
||||
int length[102];
|
||||
double *output;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wtree_set* wtree_object;
|
||||
|
||||
wtree_object wtree_init(wave_object wave, int siglength, int J);
|
||||
|
||||
struct wtree_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
char method[10];
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
|
||||
int N; //
|
||||
int nodes;
|
||||
int cfftset;
|
||||
int zpad;
|
||||
int length[102];
|
||||
double *output;
|
||||
int *nodelength;
|
||||
int *coeflength;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wpt_set* wpt_object;
|
||||
|
||||
wpt_object wpt_init(wave_object wave, int siglength, int J);
|
||||
|
||||
struct wpt_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
char entropy[20];
|
||||
double eparam;
|
||||
|
||||
int N; //
|
||||
int nodes;
|
||||
int length[102];
|
||||
double *output;
|
||||
double *costvalues;
|
||||
double *basisvector;
|
||||
int *nodeindex;
|
||||
int *numnodeslevel;
|
||||
int *coeflength;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
|
||||
void dwt(wt_object wt, double *inp);
|
||||
|
||||
void idwt(wt_object wt, double *dwtop);
|
||||
|
||||
void wtree(wtree_object wt, double *inp);
|
||||
|
||||
void dwpt(wpt_object wt, double *inp);
|
||||
|
||||
void idwpt(wpt_object wt, double *dwtop);
|
||||
|
||||
void swt(wt_object wt, double *inp);
|
||||
|
||||
void iswt(wt_object wt, double *swtop);
|
||||
|
||||
void modwt(wt_object wt, double *inp);
|
||||
|
||||
void imodwt(wt_object wt, double *dwtop);
|
||||
|
||||
void setDWTExtension(wt_object wt, char *extension);
|
||||
|
||||
void setWTREEExtension(wtree_object wt, char *extension);
|
||||
|
||||
void setDWPTExtension(wpt_object wt, char *extension);
|
||||
|
||||
void setDWPTEntropy(wpt_object wt, char *entropy, double eparam);
|
||||
|
||||
void setWTConv(wt_object wt, char *cmethod);
|
||||
|
||||
int getWTREENodelength(wtree_object wt, int X);
|
||||
|
||||
void getWTREECoeffs(wtree_object wt, int X, int Y, double *coeffs, int N);
|
||||
|
||||
int getDWPTNodelength(wpt_object wt, int X);
|
||||
|
||||
void getDWPTCoeffs(wpt_object wt, int X, int Y, double *coeffs, int N);
|
||||
|
||||
void wave_summary(wave_object obj);
|
||||
|
||||
void wt_summary(wt_object wt);
|
||||
|
||||
void wtree_summary(wtree_object wt);
|
||||
|
||||
void wpt_summary(wpt_object wt);
|
||||
|
||||
void wave_free(wave_object object);
|
||||
|
||||
void wt_free(wt_object object);
|
||||
|
||||
void wtree_free(wtree_object object);
|
||||
|
||||
void wpt_free(wpt_object object);
|
||||
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
#endif /* WAVELIB_H_ */
|
||||
*/
|
||||
#ifndef WAVELIB_H_
|
||||
#define WAVELIB_H_
|
||||
|
||||
#include "wtmath.h"
|
||||
#include "cwt.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
#if defined(_MSC_VER)
|
||||
#pragma warning(disable : 4200)
|
||||
#pragma warning(disable : 4996)
|
||||
#endif
|
||||
|
||||
#ifndef cplx_type
|
||||
#define cplx_type double
|
||||
#endif
|
||||
|
||||
|
||||
typedef struct cplx_t {
|
||||
cplx_type re;
|
||||
cplx_type im;
|
||||
} cplx_data;
|
||||
|
||||
typedef struct wave_set* wave_object;
|
||||
|
||||
wave_object wave_init(char* wname);
|
||||
|
||||
struct wave_set{
|
||||
char wname[50];
|
||||
int filtlength;// When all filters are of the same length. [Matlab uses zero-padding to make all filters of the same length]
|
||||
int lpd_len;// Default filtlength = lpd_len = lpr_len = hpd_len = hpr_len
|
||||
int hpd_len;
|
||||
int lpr_len;
|
||||
int hpr_len;
|
||||
double *lpd;
|
||||
double *hpd;
|
||||
double *lpr;
|
||||
double *hpr;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wt_set* wt_object;
|
||||
|
||||
wt_object wt_init(wave_object wave,char* method, int siglength, int J);
|
||||
|
||||
struct wt_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
char method[10];
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
char cmethod[10]; // Convolution Method - "direct" or "FFT"
|
||||
|
||||
int N; //
|
||||
int cfftset;
|
||||
int zpad;
|
||||
int length[102];
|
||||
double *output;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wtree_set* wtree_object;
|
||||
|
||||
wtree_object wtree_init(wave_object wave, int siglength, int J);
|
||||
|
||||
struct wtree_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
char method[10];
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
|
||||
int N; //
|
||||
int nodes;
|
||||
int cfftset;
|
||||
int zpad;
|
||||
int length[102];
|
||||
double *output;
|
||||
int *nodelength;
|
||||
int *coeflength;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct wpt_set* wpt_object;
|
||||
|
||||
wpt_object wpt_init(wave_object wave, int siglength, int J);
|
||||
|
||||
struct wpt_set{
|
||||
wave_object wave;
|
||||
conv_object cobj;
|
||||
int siglength;// Length of the original signal.
|
||||
int outlength;// Length of the output DWT vector
|
||||
int lenlength;// Length of the Output Dimension Vector "length"
|
||||
int J; // Number of decomposition Levels
|
||||
int MaxIter;// Maximum Iterations J <= MaxIter
|
||||
int even;// even = 1 if signal is of even length. even = 0 otherwise
|
||||
char ext[10];// Type of Extension used - "per" or "sym"
|
||||
char entropy[20];
|
||||
double eparam;
|
||||
|
||||
int N; //
|
||||
int nodes;
|
||||
int length[102];
|
||||
double *output;
|
||||
double *costvalues;
|
||||
double *basisvector;
|
||||
int *nodeindex;
|
||||
int *numnodeslevel;
|
||||
int *coeflength;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
typedef struct cwt_set* cwt_object;
|
||||
|
||||
cwt_object cwt_init(char* wave, double param, int siglength,double dt, int J);
|
||||
|
||||
struct cwt_set{
|
||||
char wave[10];// Wavelet - morl/morlet,paul,dog/dgauss
|
||||
int siglength;// Length of Input Data
|
||||
int J;// Total Number of Scales
|
||||
double s0;// Smallest scale. It depends on the sampling rate. s0 <= 2 * dt for most wavelets
|
||||
double dt;// Sampling Rate
|
||||
double dj;// Separation between scales. eg., scale = s0 * 2 ^ ( [0:N-1] *dj ) or scale = s0 *[0:N-1] * dj
|
||||
char type[10];// Scale Type - Power or Linear
|
||||
int pow;// Base of Power in case type = pow. Typical value is pow = 2
|
||||
int sflag;
|
||||
int pflag;
|
||||
int npad;
|
||||
int mother;
|
||||
double m;// Wavelet parameter param
|
||||
double smean;// Input Signal mean
|
||||
|
||||
cplx_data *output;
|
||||
double *scale;
|
||||
double *period;
|
||||
double *coi;
|
||||
double params[0];
|
||||
};
|
||||
|
||||
|
||||
void dwt(wt_object wt, double *inp);
|
||||
|
||||
void idwt(wt_object wt, double *dwtop);
|
||||
|
||||
void wtree(wtree_object wt, double *inp);
|
||||
|
||||
void dwpt(wpt_object wt, double *inp);
|
||||
|
||||
void idwpt(wpt_object wt, double *dwtop);
|
||||
|
||||
void swt(wt_object wt, double *inp);
|
||||
|
||||
void iswt(wt_object wt, double *swtop);
|
||||
|
||||
void modwt(wt_object wt, double *inp);
|
||||
|
||||
void imodwt(wt_object wt, double *dwtop);
|
||||
|
||||
void setDWTExtension(wt_object wt, char *extension);
|
||||
|
||||
void setWTREEExtension(wtree_object wt, char *extension);
|
||||
|
||||
void setDWPTExtension(wpt_object wt, char *extension);
|
||||
|
||||
void setDWPTEntropy(wpt_object wt, char *entropy, double eparam);
|
||||
|
||||
void setWTConv(wt_object wt, char *cmethod);
|
||||
|
||||
int getWTREENodelength(wtree_object wt, int X);
|
||||
|
||||
void getWTREECoeffs(wtree_object wt, int X, int Y, double *coeffs, int N);
|
||||
|
||||
int getDWPTNodelength(wpt_object wt, int X);
|
||||
|
||||
void getDWPTCoeffs(wpt_object wt, int X, int Y, double *coeffs, int N);
|
||||
|
||||
void setCWTScales(cwt_object wt, double s0, double dj, char *type, int power);
|
||||
|
||||
void setCWTScaleVector(cwt_object wt, double *scale, int J, double s0, double dj);
|
||||
|
||||
void setCWTPadding(cwt_object wt, int pad);
|
||||
|
||||
void cwt(cwt_object wt, double *inp);
|
||||
|
||||
void icwt(cwt_object wt, double *cwtop);
|
||||
|
||||
int getCWTScaleLength(int N);
|
||||
|
||||
void wave_summary(wave_object obj);
|
||||
|
||||
void wt_summary(wt_object wt);
|
||||
|
||||
void wtree_summary(wtree_object wt);
|
||||
|
||||
void wpt_summary(wpt_object wt);
|
||||
|
||||
void cwt_summary(cwt_object wt);
|
||||
|
||||
void wave_free(wave_object object);
|
||||
|
||||
void wt_free(wt_object object);
|
||||
|
||||
void wtree_free(wtree_object object);
|
||||
|
||||
void wpt_free(wpt_object object);
|
||||
|
||||
void cwt_free(cwt_object object);
|
||||
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
#endif /* WAVELIB_H_ */
|
||||
|
||||
109
test/cwttest.c
Normal file
109
test/cwttest.c
Normal file
@ -0,0 +1,109 @@
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <string.h>
|
||||
#include <math.h>
|
||||
#include "../header/wavelib.h"
|
||||
|
||||
int main() {
|
||||
int i, N, J,subscale,a0,iter,nd,k;
|
||||
double *inp,*oup;
|
||||
double dt, dj,s0, param,mn;
|
||||
double td,tn,den, num, recon_mean, recon_var;
|
||||
cwt_object wt;
|
||||
|
||||
FILE *ifp;
|
||||
double temp[1200];
|
||||
|
||||
char *wave = "morlet";// Set Morlet wavelet. Other options "paul" and "dog"
|
||||
char *type = "pow";
|
||||
|
||||
N = 504;
|
||||
param = 6.0;
|
||||
subscale = 4;
|
||||
dt = 0.25;
|
||||
s0 = dt;
|
||||
dj = 1.0 / (double)subscale;
|
||||
J = 11 * subscale; // Total Number of scales
|
||||
a0 = 2;//power
|
||||
|
||||
ifp = fopen("sst_nino3.dat", "r");
|
||||
i = 0;
|
||||
if (!ifp) {
|
||||
printf("Cannot Open File");
|
||||
exit(100);
|
||||
}
|
||||
while (!feof(ifp)) {
|
||||
fscanf(ifp, "%lf \n", &temp[i]);
|
||||
i++;
|
||||
}
|
||||
|
||||
fclose(ifp);
|
||||
|
||||
wt = cwt_init(wave, param, N,dt, J);
|
||||
|
||||
inp = (double*)malloc(sizeof(double)* N);
|
||||
oup = (double*)malloc(sizeof(double)* N);
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
inp[i] = temp[i] ;
|
||||
}
|
||||
|
||||
setCWTScales(wt, s0, dj, type, a0);
|
||||
|
||||
cwt(wt, inp);
|
||||
|
||||
printf("\n MEAN %g \n", wt->smean);
|
||||
|
||||
mn = 0.0;
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
mn += sqrt(wt->output[i].re * wt->output[i].re + wt->output[i].im * wt->output[i].im);
|
||||
}
|
||||
|
||||
cwt_summary(wt);
|
||||
|
||||
printf("\n abs mean %g \n", mn / N);
|
||||
|
||||
printf("\n\n");
|
||||
printf("Let CWT w = w(j, n/2 - 1) where n = %d\n\n", N);
|
||||
nd = N/2 - 1;
|
||||
|
||||
printf("%-15s%-15s%-15s%-15s \n","j","Scale","Period","ABS(w)^2");
|
||||
for(k = 0; k < wt->J;++k) {
|
||||
iter = nd + k * N;
|
||||
printf("%-15d%-15lf%-15lf%-15lf \n",k,wt->scale[k],wt->period[k],
|
||||
wt->output[iter].re * wt->output[iter].re + wt->output[iter].im * wt->output[iter].im);
|
||||
}
|
||||
|
||||
icwt(wt, oup);
|
||||
|
||||
num = den = recon_var = recon_mean = 0.0;
|
||||
printf("\n\n");
|
||||
printf("Signal Reconstruction\n");
|
||||
printf("%-15s%-15s%-15s \n","i","Input(i)","Output(i)");
|
||||
|
||||
for (i = N - 10; i < N; ++i) {
|
||||
printf("%-15d%-15lf%-15lf \n", i,inp[i] , oup[i]);
|
||||
}
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
//printf("%g %g \n", oup[i] ,inp[i] - wt->smean);
|
||||
td = inp[i] ;
|
||||
tn = oup[i] - td;
|
||||
num += (tn * tn);
|
||||
den += (td * td);
|
||||
recon_mean += oup[i];
|
||||
}
|
||||
|
||||
recon_var = sqrt(num / N);
|
||||
recon_mean /= N;
|
||||
|
||||
printf("\nRMS Error %g \n", sqrt(num) / sqrt(den));
|
||||
printf("\nVariance %g \n", recon_var);
|
||||
printf("\nMean %g \n", recon_mean);
|
||||
|
||||
free(inp);
|
||||
free(oup);
|
||||
cwt_free(wt);
|
||||
return 0;
|
||||
}
|
||||
504
test/sst_nino3.dat
Executable file
504
test/sst_nino3.dat
Executable file
@ -0,0 +1,504 @@
|
||||
-0.15
|
||||
-0.30
|
||||
-0.14
|
||||
-0.41
|
||||
-0.46
|
||||
-0.66
|
||||
-0.50
|
||||
-0.80
|
||||
-0.95
|
||||
-0.72
|
||||
-0.31
|
||||
-0.71
|
||||
-1.04
|
||||
-0.77
|
||||
-0.86
|
||||
-0.84
|
||||
-0.41
|
||||
-0.49
|
||||
-0.48
|
||||
-0.72
|
||||
-1.21
|
||||
-0.80
|
||||
0.16
|
||||
0.46
|
||||
0.40
|
||||
1.00
|
||||
2.17
|
||||
2.50
|
||||
2.34
|
||||
0.80
|
||||
0.14
|
||||
-0.06
|
||||
-0.34
|
||||
-0.71
|
||||
-0.34
|
||||
-0.73
|
||||
-0.48
|
||||
-0.11
|
||||
0.22
|
||||
0.51
|
||||
0.51
|
||||
0.25
|
||||
-0.10
|
||||
-0.33
|
||||
-0.42
|
||||
-0.23
|
||||
-0.53
|
||||
-0.44
|
||||
-0.30
|
||||
0.15
|
||||
0.09
|
||||
0.19
|
||||
-0.06
|
||||
0.25
|
||||
0.30
|
||||
0.81
|
||||
0.26
|
||||
0.10
|
||||
0.34
|
||||
1.01
|
||||
-0.31
|
||||
-0.90
|
||||
-0.73
|
||||
-0.92
|
||||
-0.73
|
||||
-0.31
|
||||
-0.03
|
||||
0.12
|
||||
0.37
|
||||
0.82
|
||||
1.22
|
||||
1.83
|
||||
1.60
|
||||
0.34
|
||||
-0.72
|
||||
-0.87
|
||||
-0.85
|
||||
-0.40
|
||||
-0.39
|
||||
-0.65
|
||||
0.07
|
||||
0.67
|
||||
0.39
|
||||
0.03
|
||||
-0.17
|
||||
-0.76
|
||||
-0.87
|
||||
-1.36
|
||||
-1.10
|
||||
-0.99
|
||||
-0.78
|
||||
-0.93
|
||||
-0.87
|
||||
-0.44
|
||||
-0.34
|
||||
-0.50
|
||||
-0.39
|
||||
-0.04
|
||||
0.42
|
||||
0.62
|
||||
0.17
|
||||
0.23
|
||||
1.03
|
||||
1.54
|
||||
1.09
|
||||
0.01
|
||||
0.12
|
||||
-0.27
|
||||
-0.47
|
||||
-0.41
|
||||
-0.37
|
||||
-0.36
|
||||
-0.39
|
||||
0.43
|
||||
1.05
|
||||
1.58
|
||||
1.25
|
||||
0.86
|
||||
0.60
|
||||
0.21
|
||||
0.19
|
||||
-0.23
|
||||
-0.29
|
||||
0.18
|
||||
0.12
|
||||
0.71
|
||||
1.42
|
||||
1.59
|
||||
0.93
|
||||
-0.25
|
||||
-0.66
|
||||
-0.95
|
||||
-0.47
|
||||
0.06
|
||||
0.70
|
||||
0.81
|
||||
0.78
|
||||
1.43
|
||||
1.22
|
||||
1.05
|
||||
0.44
|
||||
-0.35
|
||||
-0.67
|
||||
-0.84
|
||||
-0.66
|
||||
-0.45
|
||||
-0.12
|
||||
-0.20
|
||||
-0.16
|
||||
-0.47
|
||||
-0.52
|
||||
-0.79
|
||||
-0.80
|
||||
-0.62
|
||||
-0.86
|
||||
-1.29
|
||||
-1.04
|
||||
-1.05
|
||||
-0.75
|
||||
-0.81
|
||||
-0.90
|
||||
-0.25
|
||||
0.62
|
||||
1.22
|
||||
0.96
|
||||
0.21
|
||||
-0.11
|
||||
-0.25
|
||||
-0.24
|
||||
-0.43
|
||||
0.23
|
||||
0.67
|
||||
0.78
|
||||
0.41
|
||||
0.98
|
||||
1.28
|
||||
1.45
|
||||
1.02
|
||||
0.03
|
||||
-0.59
|
||||
-1.34
|
||||
-0.99
|
||||
-1.49
|
||||
-1.74
|
||||
-1.33
|
||||
-0.55
|
||||
-0.51
|
||||
-0.36
|
||||
-0.99
|
||||
0.32
|
||||
1.04
|
||||
1.41
|
||||
0.99
|
||||
0.66
|
||||
0.50
|
||||
0.22
|
||||
0.71
|
||||
-0.16
|
||||
0.38
|
||||
0.00
|
||||
-1.11
|
||||
-1.04
|
||||
0.05
|
||||
-0.64
|
||||
-0.34
|
||||
-0.50
|
||||
-1.85
|
||||
-0.94
|
||||
-0.78
|
||||
0.29
|
||||
0.27
|
||||
0.69
|
||||
-0.06
|
||||
-0.83
|
||||
-0.80
|
||||
-1.02
|
||||
-0.96
|
||||
-0.09
|
||||
0.62
|
||||
0.87
|
||||
1.03
|
||||
0.70
|
||||
-0.10
|
||||
-0.31
|
||||
0.04
|
||||
-0.46
|
||||
0.04
|
||||
0.24
|
||||
-0.08
|
||||
-0.28
|
||||
0.06
|
||||
0.05
|
||||
-0.31
|
||||
0.11
|
||||
0.27
|
||||
0.26
|
||||
0.04
|
||||
0.12
|
||||
1.11
|
||||
1.53
|
||||
1.23
|
||||
0.17
|
||||
-0.18
|
||||
-0.56
|
||||
0.05
|
||||
0.41
|
||||
0.22
|
||||
0.04
|
||||
-0.19
|
||||
-0.46
|
||||
-0.65
|
||||
-1.06
|
||||
-0.54
|
||||
0.14
|
||||
0.25
|
||||
-0.21
|
||||
-0.73
|
||||
-0.43
|
||||
0.48
|
||||
0.26
|
||||
0.05
|
||||
0.11
|
||||
-0.27
|
||||
-0.08
|
||||
-0.10
|
||||
0.29
|
||||
-0.15
|
||||
-0.28
|
||||
-0.55
|
||||
-0.44
|
||||
-1.40
|
||||
-0.55
|
||||
-0.69
|
||||
0.58
|
||||
0.37
|
||||
0.42
|
||||
1.83
|
||||
1.23
|
||||
0.65
|
||||
0.41
|
||||
1.03
|
||||
0.64
|
||||
-0.07
|
||||
0.98
|
||||
0.36
|
||||
-0.30
|
||||
-1.33
|
||||
-1.39
|
||||
-0.94
|
||||
0.34
|
||||
-0.00
|
||||
-0.15
|
||||
0.06
|
||||
0.39
|
||||
0.36
|
||||
-0.49
|
||||
-0.53
|
||||
0.35
|
||||
0.07
|
||||
-0.24
|
||||
0.20
|
||||
-0.22
|
||||
-0.68
|
||||
-0.44
|
||||
0.02
|
||||
-0.22
|
||||
-0.30
|
||||
-0.59
|
||||
0.10
|
||||
-0.02
|
||||
-0.27
|
||||
-0.60
|
||||
-0.48
|
||||
-0.37
|
||||
-0.53
|
||||
-1.35
|
||||
-1.22
|
||||
-0.99
|
||||
-0.34
|
||||
-0.79
|
||||
-0.24
|
||||
0.02
|
||||
0.69
|
||||
0.78
|
||||
0.17
|
||||
-0.17
|
||||
-0.29
|
||||
-0.27
|
||||
0.31
|
||||
0.44
|
||||
0.38
|
||||
0.24
|
||||
-0.13
|
||||
-0.89
|
||||
-0.76
|
||||
-0.71
|
||||
-0.37
|
||||
-0.59
|
||||
-0.63
|
||||
-1.47
|
||||
-0.40
|
||||
-0.18
|
||||
-0.37
|
||||
-0.43
|
||||
-0.06
|
||||
0.61
|
||||
1.33
|
||||
1.19
|
||||
1.13
|
||||
0.31
|
||||
0.14
|
||||
0.03
|
||||
0.21
|
||||
0.15
|
||||
-0.22
|
||||
-0.02
|
||||
0.03
|
||||
-0.17
|
||||
0.12
|
||||
-0.35
|
||||
-0.06
|
||||
0.38
|
||||
-0.45
|
||||
-0.32
|
||||
-0.33
|
||||
-0.49
|
||||
-0.14
|
||||
-0.56
|
||||
-0.18
|
||||
0.46
|
||||
1.09
|
||||
1.04
|
||||
0.23
|
||||
-0.99
|
||||
-0.59
|
||||
-0.92
|
||||
-0.28
|
||||
0.52
|
||||
1.31
|
||||
1.45
|
||||
0.61
|
||||
-0.11
|
||||
-0.18
|
||||
-0.39
|
||||
-0.39
|
||||
-0.36
|
||||
-0.50
|
||||
-0.81
|
||||
-1.10
|
||||
-0.29
|
||||
0.57
|
||||
0.68
|
||||
0.78
|
||||
0.78
|
||||
0.63
|
||||
0.98
|
||||
0.49
|
||||
-0.42
|
||||
-1.34
|
||||
-1.20
|
||||
-1.18
|
||||
-0.65
|
||||
-0.42
|
||||
-0.97
|
||||
-0.28
|
||||
0.77
|
||||
1.77
|
||||
2.22
|
||||
1.05
|
||||
-0.67
|
||||
-0.99
|
||||
-1.52
|
||||
-1.17
|
||||
-0.22
|
||||
-0.04
|
||||
-0.45
|
||||
-0.46
|
||||
-0.75
|
||||
-0.70
|
||||
-1.38
|
||||
-1.15
|
||||
-0.01
|
||||
0.97
|
||||
1.10
|
||||
0.68
|
||||
-0.02
|
||||
-0.04
|
||||
0.47
|
||||
0.30
|
||||
-0.55
|
||||
-0.51
|
||||
-0.09
|
||||
-0.01
|
||||
0.34
|
||||
0.61
|
||||
0.58
|
||||
0.33
|
||||
0.38
|
||||
0.10
|
||||
0.18
|
||||
-0.30
|
||||
-0.06
|
||||
-0.28
|
||||
0.12
|
||||
0.58
|
||||
0.89
|
||||
0.93
|
||||
2.39
|
||||
2.44
|
||||
1.92
|
||||
0.64
|
||||
-0.24
|
||||
0.27
|
||||
-0.13
|
||||
-0.16
|
||||
-0.54
|
||||
-0.13
|
||||
-0.37
|
||||
-0.78
|
||||
-0.22
|
||||
0.03
|
||||
0.25
|
||||
0.31
|
||||
1.03
|
||||
1.10
|
||||
1.05
|
||||
1.11
|
||||
1.28
|
||||
0.57
|
||||
-0.55
|
||||
-1.16
|
||||
-0.99
|
||||
-0.38
|
||||
0.01
|
||||
-0.29
|
||||
0.09
|
||||
0.46
|
||||
0.57
|
||||
0.24
|
||||
0.39
|
||||
0.49
|
||||
0.86
|
||||
0.51
|
||||
0.95
|
||||
1.25
|
||||
1.33
|
||||
-0.00
|
||||
0.34
|
||||
0.66
|
||||
1.11
|
||||
0.34
|
||||
0.48
|
||||
0.56
|
||||
0.39
|
||||
-0.17
|
||||
1.04
|
||||
0.77
|
||||
0.12
|
||||
-0.35
|
||||
-0.22
|
||||
0.08
|
||||
-0.08
|
||||
-0.18
|
||||
-0.06
|
||||
@ -98,6 +98,17 @@ double RMS_Error(double *data, double *rec, int N) {
|
||||
return sqrt(sum/((double)N-1));
|
||||
}
|
||||
|
||||
double REL_Error(double *data, double *rec, int N) {
|
||||
int i;
|
||||
double sum1 = 0;
|
||||
double sum2 = 0;
|
||||
for (i = 0; i < N; ++i) {
|
||||
sum1 += (data[i] - rec[i])*(data[i] - rec[i]);
|
||||
sum2 += data[i] * data[i];
|
||||
}
|
||||
return sqrt(sum1)/sqrt(sum2);
|
||||
}
|
||||
|
||||
void ReconstructionTest()
|
||||
{
|
||||
|
||||
@ -334,6 +345,77 @@ void DWPTReconstructionTest()
|
||||
free(inp);
|
||||
}
|
||||
|
||||
void CWTReconstructionTest() {
|
||||
int i, j,N, J,subscale,a0,iter;
|
||||
double *inp,*oup;
|
||||
double dt, dj,s0, pi,t;
|
||||
double val, epsilon;
|
||||
int it1,it2;
|
||||
cwt_object wt;
|
||||
|
||||
|
||||
char *wave[3];
|
||||
wave[0] = (char*) "morl";
|
||||
wave[1] =(char*) "paul";
|
||||
wave[2] = (char*) "dog";
|
||||
double param[30] = {4.5,5,5.5,6,6.5,8,10,13,17,20,
|
||||
4,5,7,8,10,12,13,14,17,20,2,4,6,8,10,12,14,16,18,20};
|
||||
char *type = (char*) "pow";
|
||||
|
||||
epsilon = 0.01;
|
||||
N = 2048;
|
||||
dt = 0.000125;
|
||||
subscale = 20;
|
||||
dj = 1.0 / (double) subscale;
|
||||
s0 = dt/32;
|
||||
J = 32 * subscale;
|
||||
a0 = 2;//power
|
||||
|
||||
|
||||
inp = (double*)malloc(sizeof(double)* N);
|
||||
oup = (double*)malloc(sizeof(double)* N);
|
||||
|
||||
pi = 4.0 * atan(1.0);
|
||||
|
||||
|
||||
for (i = 0; i < N; ++i) {
|
||||
t = dt * i;
|
||||
inp[i] = sin(2 * pi * 500 * t) + sin(2 * pi * 1000 * t) + 0.1 * sin(2 * pi * 8 * t);
|
||||
if (i == 1200 || i ==1232) {
|
||||
inp[i] += 5.0;
|
||||
}
|
||||
}
|
||||
|
||||
for(it1 = 0; it1 < 3;++it1) {
|
||||
for(it2 = 0; it2 < 10;++it2) {
|
||||
|
||||
wt = cwt_init(wave[it1], param[it1*10+it2], N,dt, J);
|
||||
|
||||
setCWTScales(wt, s0, dj, type, a0);
|
||||
|
||||
cwt(wt, inp);
|
||||
|
||||
|
||||
icwt(wt, oup);
|
||||
|
||||
|
||||
//printf("\nWavelet : %s Parameter %g Error %g \n", wave[it1],param[it1*10+it2],REL_Error(inp,oup, wt->siglength));
|
||||
if (REL_Error(inp,oup, wt->siglength) > epsilon) {
|
||||
printf("\n ERROR : DWPT Reconstruction Unit Test Failed. Exiting. \n");
|
||||
exit(-1);
|
||||
}
|
||||
|
||||
cwt_free(wt);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
free(inp);
|
||||
free(oup);
|
||||
|
||||
}
|
||||
|
||||
|
||||
void DBCoefTests()
|
||||
{
|
||||
@ -569,6 +651,9 @@ int main() {
|
||||
printf("Running DWPT ReconstructionTests ... ");
|
||||
DWPTReconstructionTest();
|
||||
printf("DONE \n");
|
||||
printf("Running CWT ReconstructionTests ... ");
|
||||
CWTReconstructionTest();
|
||||
printf("DONE \n");
|
||||
printf("\n\nUnit Tests Successful\n\n");
|
||||
return 0;
|
||||
|
||||
|
||||
BIN
wavelib-doc.pdf
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Reference in New Issue
Block a user