#include<math.h>
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#include<stdlib.h>
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#include "general.h"
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#include "sh.h"
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/* Gives you legendre polynomials. Taken from NR, p. 254 */
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ts_double plgndr(ts_int l, ts_int m, ts_float x){
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ts_double fact, pll, pmm, pmmp1, somx2;
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ts_int i,ll;
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#ifdef TS_DOUBLE_DOUBLE
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if(m<0 || m>l || fabs(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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if(m<0 || m>l || fabsf(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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if(m<0 || m>l || fabsl(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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pmm=1.0;
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if (m>0) {
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#ifdef TS_DOUBLE_DOUBLE
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somx2=sqrt((1.0-x)*(1.0+x));
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#endif
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#ifdef TS_DOUBLE_FLOAT
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somx2=sqrtf((1.0-x)*(1.0+x));
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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somx2=sqrtl((1.0-x)*(1.0+x));
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#endif
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fact=1.0;
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for (i=1; i<=m;i++){
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pmm *= -fact*somx2;
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fact +=2.0;
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}
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}
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if (l == m) return pmm;
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else {
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pmmp1=x*(2*m+1)*pmm;
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if(l==(m+1)) return(pmmp1);
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else {
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pll=0; /* so it can not be uninitialized */
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for(ll=m+2;ll<=l;ll++){
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pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
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pmm=pmmp1;
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pmmp1=pll;
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}
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return(pll);
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}
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}
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}
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/*Computes Y(l,m,theta,fi) (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */
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ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){
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ts_double fac1, fac2, K;
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int i;
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if(l<0 || m>l || m<-l)
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fatal("Error using shY function!",1);
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fac1=1.0;
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for(i=1; i<=l-abs(m);i++){
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fac1 *= i;
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}
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fac2=1.0;
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for(i=1; i<=l+abs(m);i++){
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fac2 *= i;
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}
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if(m==0){
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K=sqrt(1.0/(2.0*M_PI));
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}
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else if (m>0) {
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K=sqrt(1.0/(M_PI))*cos(m*fi);
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}
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else {
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//K=pow(-1.0,abs(m))*sqrt(1.0/(2.0*M_PI))*cos(m*fi);
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if(abs(m)%2==0)
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K=sqrt(1.0/(M_PI))*cos(m*fi);
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else
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K=-sqrt(1.0/(M_PI))*cos(m*fi);
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}
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return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta));
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}
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