[Master Index]
[Index for PublicToolbox/regutools]
# parallax

## (PublicToolbox/regutools/parallax.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

[A,b] = parallax(n)

### Help Text

PARALLAX Stellar parallax problem with 28 fixed, real observations.
[A,b] = parallax(n)
Stellar parallax problem with 28 fixed, real observations.
The underlying problem is a Fredholm integral equation of the
first kind with kernel
K(s,t) = (1/sigma*sqrt(2*pi))*esp(-0.5*((s-t)/sigma)^2) ,
and it is discretized by means of a Galerkin method with n
orthonormal basis functions. The right-hand side consists of
a measured distribution function of stellar parallaxes, and its
length is fixed, m = 26. The exact solution, which represents
the true distribution of stellar parallaxes, in not known.

### Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\parallax.m

function [A,b] = parallax(n)
%PARALLAX Stellar parallax problem with 28 fixed, real observations.
%
% [A,b] = parallax(n)
%
% Stellar parallax problem with 28 fixed, real observations.
%
% The underlying problem is a Fredholm integral equation of the
% first kind with kernel
% K(s,t) = (1/sigma*sqrt(2*pi))*esp(-0.5*((s-t)/sigma)^2) ,
% and it is discretized by means of a Galerkin method with n
% orthonormal basis functions. The right-hand side consists of
% a measured distribution function of stellar parallaxes, and its
% length is fixed, m = 26. The exact solution, which represents
% the true distribution of stellar parallaxes, in not known.
% Reference: W. M. Smart, "Stellar Dynamics", Cambridge
% University Press, 1938; p. 30.
% Discretized by Galerkin method with orthonormal box functions;
% 2-D integration is done by means of the computational molecule:
% 1 4 1
% 4 16 1
% 1 4 1
% Per Christian Hansen, UNI-C, 09/16/92.
% Initialization.
a = 0; b = 0.1; m = 26; sigma = 0.014234;
hs = 0.130/m; hx = (b-a)/n; hsh = hs/2; hxh = hx/2;
ss = (-0.03 + [0:m-1]'*hs)*ones(1,n);
xx = ones(m,1)*(a + [0:n-1]*hx);
% Set up the matrix.
A = 16*exp(-0.5*((ss+hsh - xx-hxh)/sigma).^2);
A = A + 4*(exp(-0.5*((ss+hsh - xx )/sigma).^2) + ...
exp(-0.5*((ss+hsh - xx-hx )/sigma).^2) + ...
exp(-0.5*((ss - xx-hxh)/sigma).^2) + ...
exp(-0.5*((ss+hs - xx-hxh)/sigma).^2));
A = A + (exp(-0.5*((ss - xx )/sigma).^2) + ...
exp(-0.5*((ss+hs - xx )/sigma).^2) + ...
exp(-0.5*((ss - xx-hx )/sigma).^2) + ...
exp(-0.5*((ss+hs - xx-hx )/sigma).^2));
A = sqrt(hs*hx)/(36*sigma*sqrt(2*pi))*A;
% Set up the normalized right-hand side.
b = [3;7;7;17;27;39;46;51;56;50;43;45;43;32;33;29;...
21;12;17;13;15;12;6;6;5;5]/(sqrt(hs)*640);

Produced by color_mat2html, a customized BrainStorm 2.0 (Alpha) version of mat2html on Tue Oct 12 12:05:14 2004

Cross-Directory links are: ON