Spherical harmonics should be ok. Note, that there are some difference from...

Samo Penic

2011-03-19 af3bad5b0ffbe0f19b0f85519c85a385326dec03

Spherical harmonics should be ok. Note, that there are some difference from proposed theoretical scheme. Is Miha's theory wrong?

 src/sh.c

@@ -64,11 +64,11 @@
        fatal("Error using shY function!",1);

    fac1=1.0;
    for(i=1; i<=l-m;i++){
    for(i=1; i<=l-abs(m);i++){
        fac1 *= i;
    }
    fac2=1.0;
    for(i=1; i<=l+m;i++){
    for(i=1; i<=l+abs(m);i++){
        fac2 *= i;
    }

@@ -81,9 +81,9 @@
    else {
        //K=pow(-1.0,abs(m))*sqrt(1.0/(2.0*M_PI))*cos(m*fi);
        if(abs(m)%2==0)
        K=sqrt(1.0/(M_PI))*sin(m*fi);
        K=sqrt(1.0/(M_PI))*cos(m*fi);
        else
        K=-sqrt(1.0/(M_PI))*sin(m*fi);
        K=-sqrt(1.0/(M_PI))*cos(m*fi);
    }
    
    return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta));    

 src/shdiscover.c

@@ -24,14 +24,15 @@
ts_fprintf(stdout,"P(0,0,0.5)=%f (%f)\n",plgndr(0,0,0.5),1.0);
ts_fprintf(stdout,"P(1,0,0.5)=%f (%f)\n",plgndr(1,0,0.5),0.5);
ts_fprintf(stdout,"P(2,0,0.5)=%f (%f)\n",plgndr(2,0,0.5),0.5*(3*0.5*0.5-1));
ts_fprintf(stdout,"P(2,2,0.5)=%f (ni to:%f)\n",plgndr(2,2,0.5),0.5*(3*0.5*0.5-1));

ts_fprintf(stdout,"Y(0,0,pi/6,pi/4)=%f (%f)\n",shY(0,0,M_PI/6,M_PI/4),sqrt(1/(4*M_PI)));
ts_fprintf(stdout,"Y(1,0,pi/6,pi/4)=%f (%f)\n",shY(1,0,M_PI/6,M_PI/4),sqrt(3/(4*M_PI))*cos(M_PI/6));
ts_fprintf(stdout,"Y(1,0,4*pi/6,6*pi/4)=%f (%f)\n",shY(1,0,4*M_PI/6,6*M_PI/4),sqrt(3/(4*M_PI))*cos(4*M_PI/6));
ts_fprintf(stdout,"Y(1,1,pi/6,pi/4)=%f (%f)\n",shY(1,1,M_PI/6,M_PI/4),-sqrt(3/(8*M_PI))*sin(M_PI/6)*sin(M_PI/4));
ts_fprintf(stdout,"Y(1,1,pi/6,pi/4)=%f (%f)\n",shY(1,1,M_PI/6,M_PI/4),-sqrt(3/(8*M_PI))*sin(M_PI/6)*cos(M_PI/4));
ts_fprintf(stdout,"Y(2,0,pi/6,pi/4)=%f (%f)\n",shY(2,0,M_PI/6,M_PI/4),sqrt(5/(4*M_PI))*(3.0/2.0*cos(M_PI/6)*cos(M_PI/6)-1.0/2.0));
ts_fprintf(stdout,"Y(2,-2,pi/6,pi/4)=%f (0)\n",shY(2,-2,M_PI/6,M_PI/4));
ts_fprintf(stdout,"Y(2,2,pi/6,pi/4)=%f (0)\n",shY(2,2,M_PI/6,M_PI/4));
ts_fprintf(stdout,"Y(2,2,pi/6,pi/3)=%f (%f)\n",shY(2,2,M_PI/6,M_PI/3), sqrt(15.0/(32.0*M_PI))*sin(M_PI/6)*sin(M_PI/6)*cos(2*M_PI/3));
    
    for(j=1;j<argc;j++){
        l=(int)sqrt(j-1); /* determine l from dataline */