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/*************************************************************************** |
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************************************************************************** |
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S2kit 1.0 |
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A lite version of Spherical Harmonic Transform Kit |
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Peter Kostelec, Dan Rockmore |
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{geelong,rockmore}@cs.dartmouth.edu |
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Contact: Peter Kostelec |
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geelong@cs.dartmouth.edu |
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Copyright 2004 Peter Kostelec, Dan Rockmore |
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This file is part of S2kit. |
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S2kit is free software; you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation; either version 2 of the License, or |
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(at your option) any later version. |
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S2kit is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU General Public License for more details. |
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You should have received a copy of the GNU General Public License |
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along with S2kit; if not, write to the Free Software |
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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See the accompanying LICENSE file for details. |
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************************************************************************ |
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************************************************************************/ |
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/* source code for generating cosine transforms |
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of Pml and Gml functions */ |
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#include <math.h> |
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#include <string.h> /* to declare memcpy */ |
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#include <stdlib.h> |
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#include <stdio.h> |
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#include "primitive.h" |
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/************************************************************************/ |
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/* generate all of the Pmls for a specified value of m. |
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storeplm points to a double array of size 2 * bw * (bw - m); |
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Workspace needs to be |
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16 * bw |
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P(m,l,j) respresents the associated Legendre function P_l^m |
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evaluated at the j-th Chebyshev point (for the bandwidth bw) |
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Cos((2 * j + 1) * PI / (2 * bw)). |
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The array is placed in storeplm as follows: |
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P(m,m,0) P(m,m,1) ... P(m,m,2*bw-1) |
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P(m,m+1,0) P(m,m+1,1)... P(m,m+1,2*bw-1) |
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P(m,m+2,0) P(m,m+2,1)... P(m,m+2,2*bw-1) |
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... |
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P(m,bw-1,0) P(m,bw-1,1) ... P(m,bw-1,2*bw-1) |
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This array will eventually be used by the naive transform algorithm. |
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This function will precompute the arrays necessary for the algorithm. |
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*/ |
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void PmlTableGen(int bw, |
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int m, |
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double *storeplm, |
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double *workspace) |
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{ |
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double *prev, *prevprev; |
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double *temp1, *temp2, *temp3, *temp4; |
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double *x_i, *eval_args; |
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int i; |
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prevprev = workspace; |
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prev = prevprev + (2*bw); |
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temp1 = prev + (2*bw); |
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temp2 = temp1 + (2*bw); |
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temp3 = temp2 + (2*bw); |
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temp4 = temp3 + (2*bw); |
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x_i = temp4 + (2*bw); |
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eval_args = x_i + (2*bw); |
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/* get the evaluation nodes */ |
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EvalPts(2*bw,x_i); |
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ArcCosEvalPts(2*bw,eval_args); |
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/* set initial values of first two Pmls */ |
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for (i=0; i<2*bw; i++) |
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prevprev[i] = 0.0; |
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if (m == 0) |
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for (i=0; i<2*bw; i++) |
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prev[i] = 0.707106781186547 ; |
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else |
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Pmm_L2(m, eval_args, 2*bw, prev); |
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memcpy(storeplm, prev, sizeof(double) * 2 * bw); |
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for(i = 0; i < bw - m - 1; i++) |
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{ |
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vec_mul(L2_cn(m,m+i),prevprev,temp1,2*bw); |
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vec_pt_mul(prev, x_i, temp2, 2*bw); |
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vec_mul(L2_an(m,m+i), temp2, temp3, 2*bw); |
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vec_add(temp3, temp1, temp4, 2*bw); /* temp4 now contains P(m,m+i+1) */ |
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storeplm += (2 * bw); |
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memcpy(storeplm, temp4, sizeof(double) * 2 * bw); |
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memcpy(prevprev, prev, sizeof(double) * 2 * bw); |
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memcpy(prev, temp4, sizeof(double) * 2 * bw); |
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} |
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} |
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