Numeripy

Numeripy is a numerical methods package that includes various numerical methods often encountered in senior year Numerical Analysis + Optimization courses. It is written with the motivation to provide flexibility to the user in selecting a certain scheme and having a good precision control. It also helps one compare and contrast the performances of different schemes for a certain problem. Another potential avenue of use would be for pedagogical purposes - with a pre-compiled library, real time analysis of rather involved methods in class is made possible

Ver 0.1 comes with

ODE solvers

numeripy.ODE_solvers

Methods included

• Euler
• Modified Euler
• Taylor (orders 2,3, 4 and 5)
• Runge-Kutta
  • Orders 3, 4 and 6
  • Adaptable to systems of ODE (and therefore, higher order ODE)
• Runge-Kutta Fehlberg (R-K with variable step size)
• Adam-Bashforth m-step explicit method (m = 2, 3, 4 or 5)
• (multi-step) Predictor Corrector schemes
  • Predictor: Adam-Bashforth; Corrector: Adam-Moulton
  • Predictor steps supported: m = 2, 3, 4 or 5
  • Corrector steps supported: m = 2, 3 or 4
  • Accomodates variable step size with
    • Predictor: 4 step Adam-Bashforth
    • Corrector: 3 step Adam-Moulton

Matrix methods

numeripy.matrix_methods

Methods included

• Matrix multiplication
• Determinant
• Gaussian Elimination by backward substitution (GEBS)
  • Normal GEBS
  • GEBS with partial pivoting
  • GEBS with scaled pivoting
• Factorization
  • LU factorization
  • LDL^T factorization
  • Cholesky factorization
• Iterative matrix methods
  • Jacobi
  • Gauss-Seidel
  • Successive order relaxation (SOR)

numeripy also comes with some post-processing tools for numerical ODE solutions.

• numeripy.Latexit() creates latex formatted tables (when passed with array inputs)
• numeripy.plotit() plots all the solutions (when passed with ODE solutions as inputs)

Getting numeripy

(Assuming, the user already has pip installed - otherwise, follow this first to get pip)

Getting numeripy is as simple as opening command prompt and entering

$ pip install numeripy

Working with numeripy

Dependencies

numeripy requires

• numpy
• matplotlib
• tabulate

to be able to function properly

numeripy.help()

numeripy.help() takes a keyword argument about any of the above methods and prints the subdirectory that needs to be imported along with information pertaining to function input and output. .help() can also be accessed from any of the subdirectory (that is to say, numeripy.help() provides information about all functionality inside numeripy, whereas, numeripy.matrix_methods.help() provides information only about the matrix methods.)

What to expect in numeripy 0.2

Optimization schemes

numeripy plans to include a subdirectory containing standard optimization algorithms such as Gradient descent, Gradient descent for higher order multidimensional problems, Secant method, Line search, Newton's method and a few others.

Example problem set

numeripy also plans to include a folder with many example problems that the user is invited to try out. The Examples folder will be located along with the user's numeripy installation. (This update will be released shortly).