int main(void)
{
char txt[MAXSTR];
int i,j,m,n,nval;
float fac,val,x;
FILE *fp;
if ((fp = fopen("fncval.dat","r")) == NULL)
nrerror("Data file fncval.dat not found\n");
fgets(txt,MAXSTR,fp);
while (strncmp(txt,"Legendre Polynomials",20)) {
fgets(txt,MAXSTR,fp);
if (feof(fp)) nrerror("Data not found in fncval.dat\n");
}
fscanf(fp,"%d %*s",&nval);
printf("\n%s\n",txt);
printf("%4s %4s %10s %17s %24s\n","n",
"m","x","actual","plgndr(n,m,x)");
for (i=1;i<=nval;i++) {
fscanf(fp,"%d %d %f %f",&n,&m,&x,&val);
fac=1.0;
if (m > 0)
for (j=n-m+1;j<=n+m;j++) fac *= j;
fac *= 2.0/(2.0*n+1.0);
val *= sqrt(fac);
printf("%4d %4d %13.6f %19.6e %19.6e\n",
n,m,x,val,plgndr(n,m,x));
}
fclose(fp);
return 0;
}
void ylm(int l, int m, double theta, double phi,
double *re, double *im)
{
int i;
double coeff = 1.0;
double plm, ylm;
int sign = 1;
if (m < 0.0)
{
sign *= -1;
}
m = abs(m);
for (i = l-m; i > 1; i--)
{
coeff *= i;
}
for (i = l+m; i > 1; i--)
{
coeff /= i;
}
coeff *= (2.0*l+1.0)/4.0/M_PI;
coeff = sqrt(coeff);
/*
printf("coeff: %e\n", coeff);
*/
plm = plgndr(l, m , cos(theta));
ylm = coeff * plm;
*re = ylm * cos(m*phi);
*im = ylm * sin(m*phi);
if (sign < 0)
{
*im *= -1;
if (m % 2 == 1)
{
*re *= -1;
*im *= -1;
}
}
}
int main(void) /* Program sfroid */
{
float plgndr(int l, int m, float x);
void solvde(int itmax, float conv, float slowc, float scalv[],
int indexv[], int ne, int nb, int m, float **y, float ***c, float **s);
int i,itmax,k,indexv[NE+1];
float conv,deriv,fac1,fac2,q1,slowc,scalv[NE+1];
float **y,**s,***c;
y=matrix(1,NYJ,1,NYK);
s=matrix(1,NSI,1,NSJ);
c=f3tensor(1,NCI,1,NCJ,1,NCK);
itmax=100;
conv=5.0e-6;
slowc=1.0;
h=1.0/(M-1);
printf("\nenter m n\n");
scanf("%d %d",&mm,&n);
if (n+mm & 1) {
indexv[1]=1;
indexv[2]=2;
indexv[3]=3;
} else {
indexv[1]=2;
indexv[2]=1;
indexv[3]=3;
}
anorm=1.0;
if (mm) {
q1=n;
for (i=1;i<=mm;i++) anorm = -0.5*anorm*(n+i)*(q1--/i);
}
for (k=1;k<=(M-1);k++) {
x[k]=(k-1)*h;
fac1=1.0-x[k]*x[k];
fac2=exp((-mm/2.0)*log(fac1));
y[1][k]=plgndr(n,mm,x[k])*fac2;
deriv = -((n-mm+1)*plgndr(n+1,mm,x[k])-
(n+1)*x[k]*plgndr(n,mm,x[k]))/fac1;
y[2][k]=mm*x[k]*y[1][k]/fac1+deriv*fac2;
y[3][k]=n*(n+1)-mm*(mm+1);
}
x[M]=1.0;
y[1][M]=anorm;
y[3][M]=n*(n+1)-mm*(mm+1);
y[2][M]=(y[3][M]-c2)*y[1][M]/(2.0*(mm+1.0));
scalv[1]=fabs(anorm);
scalv[2]=(y[2][M] > scalv[1] ? y[2][M] : scalv[1]);
scalv[3]=(y[3][M] > 1.0 ? y[3][M] : 1.0);
for (;;) {
printf("\nEnter c**2 or 999 to end.\n");
scanf("%f",&c2);
if (c2 == 999) {
free_f3tensor(c,1,NCI,1,NCJ,1,NCK);
free_matrix(s,1,NSI,1,NSJ);
free_matrix(y,1,NYJ,1,NYK);
return 0;
}
solvde(itmax,conv,slowc,scalv,indexv,NE,NB,M,y,c,s);
printf("\n %s %2d %s %2d %s %7.3f %s %10.6f\n",
"m =",mm," n =",n," c**2 =",c2,
" lamda =",y[3][1]+mm*(mm+1));
}
}
