## Gaussian ellipses constant probability curves

Version 1.0.0.0 (2.52 KB) by
Construct data points of ellipses representing contour curves of bivariate Gaussian distributions.
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Updated 22 Apr 2014

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Ellipsedata V1.001
Construct data points of ellipses representing contour curves of Gaussian distributions with any covariance and mean value.

Example

In this example, the funcion ellipsedata constructs three ellipses of 100 points each representing the contour curves corresponding to standard deviations of 1, 2 and 3 for a Gaussian distribution with covariance matrix given by [4,1;1,1] and mean value given by [3,3].

elpt=ellipsedata([4,1;1,1],[3,3],100,[1,2,3]);

The results can be plot as follows

plot(elpt(:,1:2:end),elpt(:,2:2:end));

Input arguments

covmat:
Covariance matrix of a bivariate Gaussian distribution. Must be of size 2x2, symmetric and positive definite. If the format is not correct, an error is triggered. If the matrix is not symmetric, it is symmetrized by adding its transpose and dividing by 2.

center:
The center (mean value) of the bivariate Gaussian distribution. If the format is not correct, it is set to [0,0].

numpoints:
The number of points that each ellipse will be composed of. Must be a positive integer number. If it is not numeric or positive, it is set to 100. If it is not integer, it is converted to integer using the function ceil.

sigmarule:
Vector of real numbers indicating the proportion of standard deviation surrounded by each ellipse.

varargin (later assigned to "zeroprecision"):
A real number indicating the maximum difference after which two numbers are considered different. This value is used for assessing whether covmat is symmetric. If not specified, it is set to 1E-12

Output arguments

elpt:
Matrix in which each consecutive pair of columns represent an ellipse corresponding to a different value of sigmarule, in the order they were given in the input.

Version control

V1.001: Changes are: (1) Previous version trigger an error if the matrix was not symmetric. In this version, if the matrix is not symmetric, it is symmetrized. (2) The last input argument is assigned to a variable called "zeroprecision" which controls the extent to which two numbers are considered different or equal. This value is used to assess whether covmat is symmetric or not.

Please, report any bugs to Hugo.Eyherabide@cs.helsinki.fi

Copyright (c) 2014, Hugo Gabriel Eyherabide, Department of Mathematics and Statistics, Department of Computer Science and Helsinki Institute for Information Technology, University of Helsinki, Finland.
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

### Cite As

Hugo (2024). Gaussian ellipses constant probability curves (https://www.mathworks.com/matlabcentral/fileexchange/46324-gaussian-ellipses-constant-probability-curves), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2013a
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.0.0.0