wavelib/src/wavefunc.c

#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(cwt_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]);
	}
}