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SymScriptPinTaun

PURPOSE ^

Script for symbolic expressions for the lowest orders pi_n and tau_n angular functions

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 Script for symbolic expressions for the lowest orders pi_n and tau_n angular functions
 pi_n and tau_n are defined as in Bohren and Huffman (Ref. 146).
 See also the SPlaC supplementary information.
 This script requires the Matlab symbolic toolbox to run.

 This file is part of the SPlaC v1.0 package (copyright 2008)
 Check the README file for further information

EXAMPLE OF OUTPUT ^

Example figure output

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 nNmax=8;
0002 syms t positive; % t for theta
0003 
0004 % This code follows the method of PwePinTaun
0005 
0006 mu=cos(t);
0007 nrows=1; % only one theta here
0008 % Initialize recurrence pi_0=0, pi_1=1
0009 % pinm1 contains pi_{n-1} n=1..nNmax+1
0010 pinm1=zeros(nrows,nNmax+1) * t; % for symbolic zeros
0011 pinm1(:,2)=zeros(nrows,1) * t +1; % for symbolic ones
0012 
0013 % Get pi_2 to pi_nNmax by recurrence (see SPlaC guide)
0014 % pi_n is pinm1(:,n+1)
0015 for n=2:(nNmax)
0016     pinm1(:,n+1)=(2*n-1)/(n-1)*mu.*pinm1(:,n)-n/(n-1)*pinm1(:,n-1);
0017 end;
0018 
0019 % return pi_n matrix (except n=0)
0020 pin=pinm1(:,2:(nNmax+1));
0021 
0022 % return tau_n matrix
0023 nmat=repmat(1:nNmax,nrows,1);
0024 mumat=repmat(mu,1,nNmax);
0025 taun=nmat.*mumat.*pin - (nmat+1).*pinm1(:,1:nNmax);
0026 
0027 % Write output:
0028 disp(' ')
0029 for n=1:(nNmax)
0030     disp(['pi_' int2str(n) '(t)= ' char(factor(pin(1,n)))])
0031     disp(['tau_' int2str(n) '(t)= ' char(factor(taun(1,n)))])
0032     disp(' ')
0033 end;

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