Rotation of the spherical harmonics

[Zkribbler]

Originally posted by MrFun
head hurts . . . . . reading this thread . . . . . . .

Even the KrazyHorse kitty avatar looks like it's cringing.

[KrazyHorse]

this is weird

[KrazyHorse]

can only post short messages

[KrazyHorse]

long messages refuse to load. help

[MrFun]

Originally posted by KrazyHorse
why?

The terminology you're using. I must say, I'm impressed with your knowledge in your area of interest.

[KrazyHorse]

help me. seriously can't post long posts

[KrazyHorse]

or upload files. this is really weird

[Zkribbler]

I'd guess that it's a problem with your ISP. Because we can write long posts. Really long posts. Much longer posts than your can post. So it's not an Apolyton problem. Nope. Not at all. No problem here at all. It's you; it's all you, you, you.

Rotation of the spherical harmonics, indeed! See what happens when you show off how smart you are? The gods get you. So, it's not only an ISP problem but it's also devine intervention. Man, you are up the creek without a paddle. Without the ablity to post either.

[KrazyHorse]

**** you

[KrazyHorse]

and your little dog too

[MrFun]

Originally posted by Zkribbler
I'd guess that it's a problem with your ISP. Because we can write long posts. Really long posts. Much longer posts than your can post. So it's not an Apolyton problem. Nope. Not at all. No problem here at all. It's you; it's all you, you, you.

Rotation of the spherical harmonics, indeed! See what happens when you show off how smart you are? The gods get you. So, it's not only an ISP problem but it's also devine intervention. Man, you are up the creek without a paddle. Without the ablity to post either.

Actually, it had to with my overloading KH's computer by sending too many banana files to him.

[Flip McWho]

Ok so what does the OP actually say in layman?

[Asher]

Originally posted by Flip McWho


Ok so what does the OP actually say in layman?

Isn't it obvious?

/************************************************************************/
/***
  In the relation

  P_{L+r} = A_r^L P_L + B_r^L P_{L-1}
  
  this routine generates B_r^L . Initial conditions are
  
  B_0^L = 0, B_{-1}^L = 1.
  
  m = order of the problem
  r = how much to shift
  l = where to start shift (i.e. l = L in above *)
  n = number of points desired
  
  result is double array of size n 
  workspace is double array of size 4 * n
  ***/

static void Bshifted( int m,
		      int r,
		      int l,
		      int n,
		      double *result,
		      double *workspace )
{
  double *cospts, *pi, *piminus1, *pcurr;
  double di, dn, aval, cval;
  int i, j;

  /* allocate work space */
  cospts = workspace;
  pi = cospts + n;
  piminus1 = pi + n;
  pcurr = piminus1 + n;

  /* generate sample points */
  dn = (double) n;
  for (i=0; i<n; i++) {
    di = (double) i;
    cospts[i] = cos(
		    (((2.0 * di)+1.0) * PI)/(2.0 * dn));
  }
  
  if (r < 0) {
      for (i=0; i<n; i++)
	result[i] = 1.0;
  }

  /* piminus1 starts off as all zeros */
  for (i=0; i<n; i++)
    piminus1[i] = 0.0;

  if (r == 0) {
      for (i=0; i<n; i++)
	result[i] = 0.0;
  }

  /* return (piminus1); */

  /* generate initial value of pi */
  for (i=0; i<n; i++)
    pi[i] = L2_cn(m,m+l);
  
  if (r == 1) {
      for (i=0; i<n; i++)
	result[i] = pi[i];
  }

  /* return(pi); */

  /* main loop */
  if (r > 1) {
      for (i=m+1; i<m+r; i++) {
	  aval = L2_an(m,i+l);
	  cval = L2_cn(m,i+l);
	  for (j=0; j<n; j++)
	    pcurr[j] = aval * cospts[j] * pi[j] +
	      cval * piminus1[j];
	  /* need to copy values */
	  memcpy(piminus1, pi, sizeof(double) * n);
	  memcpy(pi, pcurr, sizeof(double) * n);

      }
      memcpy(result, pcurr, sizeof(double) * n);
  }

/*  return (pcurr); */

}

static void A_revshifted( int m,
			  int r,
			  int l,
			  int n,
			  double *result,
			  double *workspace )
{
  double *cospts, *pi, *piplus1, *pcurr;
  double di, dn, aval, cval;
  int i, j;

  /* allocate work space */
  cospts = workspace;
  pi = cospts + n;
  piplus1 = pi + n;
  pcurr = piplus1 + n;

  /* generate sample points */
  dn = (double) n;
  for (i=0; i<n; i++) {
    di = (double) i;
    cospts[i] = cos((((2.0 * di)+1.0) * PI)/(2.0 * dn));
  }

  
  if (r < 0) {
      for (i=0; i<n; i++)
	result[i] = 0.0;
  }

  /* return (zeros(n)); */

  /* piplus1 starts off as all ones */
  for (i=0; i<n; i++)
    piplus1[i] = 1.0;

  if (r == 0) {
      for (i=0; i<n; i++)
	result[i] = 1.0;
  }

  /* return (piplus1); */

  /* generate initial value of pi */
  /* aval = -L2_an(m,m+l); */
  /* cval = 1.0 / L2_cn(m,m+l); */
  aval = L2_ancn(m,m+l); 
  for (i=0; i<n; i++)
    pi[i] = cospts[i] * aval;
  
  if (r == 1) {
      for (i=0; i<n; i++)
	result[i] = pi[i];
  }

  /* return(pi); */

  /* main loop */
  if (r > 1) {
    for(i = 1 ; i < r ; i ++){
      /* aval = -L2_an(m, m + l - i); */
      aval = L2_ancn(m, m + l - i);
      /* cval = 1.0/L2_cn(m, m + l - i); */
      cval = L2_cn_inv(m,m+l-i);
      for(j = 0 ; j < n ; j ++)
	pcurr[j] = aval * cospts[j] * pi[j] +
	  cval * piplus1[j];
      /* need to copy values */
      memcpy(piplus1, pi, sizeof(double) * n);
      memcpy(pi, pcurr, sizeof(double) * n);
    }
    /*** now copy the final result ***/
    memcpy(result, pcurr, sizeof(double) * n);
  }

/*  return (pcurr); */

}

BTW, KH: http://www.cs.dartmouth.edu/~geelong/sphere/

[Flip McWho]

The effort factor is through the roof.

[Asher]

Did that link help, KH?