Mathpack

This gem includes a collection of mathematical methods

Installation

Add this line to your application's Gemfile:

gem 'mathpack'

And then execute:

$ bundle

Or install it yourself as:

$ gem install mathpack

Information

Gem mathpack allows to count statistical functions through Statistics class, solve nonlinear equations through Equation module solve method, solve systems of linear equations through SLE module solve method.

Statistics

Statistics class have following methods

• number - returns a number of elements in series
• mean - returns a mean of series
• variance - returns a variance of series
• skewness - returns a skewness of series
• kurtosis - returns a kurtosis
• min - returns the minimal element of series
• max - returns the maxinal element of series
• raw_moment - returns the nth raw moment of series
• central_moment - returns the nth central moment of series
• empirical_cdf - returns empirical distribution function value in some point
• empirical_pdf - returns empirical probability density function value in some point
• print_empirical_cdf_to_csv - allows to print empirical_cdf line chart values to .csv file with name filename
• print_empirical_cdf_to_csv - allows to print empirical_cdf line chart values to .csv file with name filename

Usage

stat = Mathpack::Statistics.new([1, 2, 5, 6])
stat.number() #=> 4
stat.mean() #=> 3.5
stat.variance() #=> 4.25
stat.kurtosis() #=> 1.221453287197232
stat.skewness() #=> 0.0
stat.min() #=> 1
stat.max() #=> 6
stat.raw_moment(3) #=> 87.5
stat.central_moment(4) #=> 22.0625
stat.empirical_cdf(5.5) #=> 0.75
stat.empirical_pdf(3) #=> 0.07639393483317147
stat.print_empirical_cdf_to_csv('cdf.csv') #=> nil
stat.print_empirical_pdf_to_csv('pdf.csv') #=> nil

Equation

Equation module has only one method

• solve - method, which allows to solve nonlinear equations. Neccessary params are eps representing calculations accuraccy and start representing point to start root search

Usage

Now you have no problems solving nonlinear equations. If you want, for example, to solve equation

You need to complete the following steps:

• Equation should look like
• For our equation
• Choose the calculations accurracy. For example
• Choose some point near the expected root of equation. For example

Then to solve equation you should call

Mathpack::Equation.solve(start: 0, eps: 0.00001){|x| x**2 - Math.sin(x+1)})

Here is some examples of solve function usage

Mathpack::Equation.solve(start: 0, eps: 0.00001){|x| x**2 - Math.sin(x+1)})
Mathpack::Equation.solve(start: 0.01, eps: 0.00001){|x| 1/x - Math.log(x)})
Mathpack::Equation.solve(start: 0.01, eps: 0.00001){|x| x**2 - 2*x + 1})
Mathpack::Equation.solve(start: 0.01, eps: 0.00001){|x| Math.exp(x-2) - Math.sin(x)})

SLE

SLE module has only one method

• solve - method, which allows to solve system of linear equations. Neccessary params are matrix representing system matrix and f. Params can be Array or Matrix class. If the system can't be solved, method raise exception

Usage

Let's solve some system of linear equations. It can be written as

where A is n*n matrix, X - vector of unknown, B - vector

If you want to solve this system you should call

Mathpack::SLE.solve(matrix: A, f: B)

Parameter A can be Array or Matrix class. If Array is given result will be Array class. If Matrix is given result will be Matrix class.

a = [[1, 2, 3], [4, 5, 6],[3, 5, 2]]
b = [15, 30, 15]
Mathpack::SLE.solve(matrix: a, f: b) #=> [-1.0, 2.0, 4.0]
a = Matrix[[1, 2, 3], [4, 5, 6],[3, 5, 2]]
b = Matrix.row_vector [15, 30, 15]
Mathpack::SLE.solve(matrix: a, f: b) #=> Matrix[[-1.0, 2.0, 4.0]]

Contributing

1. Fork it ( https://github.com/[my-github-username]/mathpack/fork )
2. Create your feature branch (git checkout -b my-new-feature)
3. Commit your changes (git commit -am 'Add some feature')
4. Push to the branch (git push origin my-new-feature)
5. Create a new Pull Request