| Name | py-num-methods JSON |
| Version |
0.1.2
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| home_page | None |
| Summary | Numerical Methods and Analysis Library in Python |
| upload_time | 2024-03-28 19:06:11 |
| maintainer | None |
| docs_url | None |
| author | JaidevSK |
| requires_python | None |
| license | MIT |
| keywords |
numerical
methods
|
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| bugtrack_url |
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No requirements were recorded.
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py_num_methods: This is the module for the Numerical Methods such as approximations, equation solving, solving sets of linear equations, interpolations, numerical integration, numerical differentiation, and ODE solving.
# Approximations:
### Euler's Method
import py_num_methods.approximations as pynma
x, y = pynma.euler_method(f, x0, y0, h, n)
'''
Parameters:
- f: The derivative function of the ODE.
- x0: The initial x value.
- y0: The initial y value.
- h: The step size.
- n: The number of iterations.
Returns:
- x: The array of x values.
- y: The array of y values.
'''
# Equation Solving:
import py_num_methods.eqn_solver as pynm_es
### Graphical Solver:
pynm_es.solve_equation_graphically(equation, x_range, y_range)
'''
Parameters:
- equation: function
- x_range: Tuple
- y_range: Tuple
Returns:
- None
- Plots the graph
'''
### Bisection Method:
ret = pynm_es.bisection_method(f, a, b, tol)
'''
Parameters:
- f: The function for which we want to find the root.
- a: The lower bound of the interval.
- b: The upper bound of the interval.
- tol: The tolerance level for the root.
Returns:
- The approximate root of the function within the specified tolerance level.
'''
### False Position Method:
ret = pynm_es.false_position_method(f, a, b, tol, max_iter)
'''
Parameters:
- f: The function for which we want to find the root.
- a and b: The initial interval endpoints.
- tol: The tolerance level for convergence.
- max_iter: The maximum number of iterations allowed.
Returns:
- The approximate root of the function.
'''
### Fixed Point Iterations:
ret = pynm_es.fixed_point_iteration(f, initial_guess, tolerance, max_iterations)
'''
Parameters:
- f: The function for which we want to find the root.
- initial_guess: The initial guess value.
- tolerance: The tolerance level for convergence.
- max_iterations: The maximum number of iterations allowed.
Returns:
- The approximate root of the function.
'''
# Simultaneous Linear Equation Solver:
import py_num_methods.sim_lin_eqn_solve as pynmsles
### Gaussian Elimination:
x = pynmsles.gaussian_elimination(A, b)
'''
Parameters:
- A: The A (coefficient) matrix in Ax=b
- b: The b (constant) matrix in Ax=b
Returns:
- x: Solution
'''
### LU Decomposition:
x = pynmsles.lu_decomposition(A, b)
'''
Parameters:
- A: The A (coefficient) matrix in Ax=b
- b: The b (constant) matrix in Ax=b
Returns:
- x: Solution
'''
### Tri Diagonal Matrix Algorithm:
x = pynmsles.solve_tdma(A, b)
'''
Parameters:
- A: The A (coefficient) matrix in Ax=b
- b: The b (constant) matrix in Ax=b
Returns:
- x: Solution
'''
### Gauss Seidel:
x = pynmsles.gauss_seidel(A, b, x0, max_iterations=100, tolerance=1e-6)
'''
Parameters:
- A: The A (coefficient) matrix in Ax=b
- b: The b (constant) matrix in Ax=b
- x0: Initial guess array
- max_iterations: Max number of iterations
- tolerance: Permissible tolerance in relative error
Returns:
- x: Solution
'''
# Interpolations:
import py_num_methods.interpolations as pynmi
### Quadratic Interpolations:
y = pynmi.quadratic_interpolation(x, x0, x1, x2, y0, y1, y2)
'''
Parameters:
- x : The point at which to estimate the value.
- x0, x1, x2 : The x-coordinates of the three data points.
- y0, y1, y2 : The y-coordinates of the three data points.
Returns:
- y = estimated value at point x.
'''
### Lagrange Interpolations:
x = pynmi.lagrange_interpolation(x, y, xi)
'''
Parameters:
- x, y : Arrays of data points
- xi : Value at which we want to approximate the function
Returns:
- yi = interpolated value at point xi
'''
# Numerical Integration:
import py_num_methods.numerical_integration as pynmni
### Trapezoidal Integration:
val = pynmni.trapezoidal_integration(f, a, b, n)
'''
Parameters:
- f: The function to be integrated.
- a: The lower limit of integration.
- b: The upper limit of integration.
- n: The number of subintervals to divide the integration interval into.
Returns:
- val = The approximate value of the integral.
'''
### Simpsons 1/3 method:
val = pynmni.simpsons_13(f, a, b, n)
'''
Parameters:
- f: The function to be integrated.
- a: The lower limit of integration.
- b: The upper limit of integration.
- n: The number of subintervals.
Returns:
- val = The approximate value of the definite integral.
'''
### Simpsons 3/8 method:
val = pynmni.simpsons_38(f, a, b, n)
'''
Parameters:
- f: The function to be integrated.
- a: The lower limit of integration.
- b: The upper limit of integration.
- n: The number of subintervals.
Returns:
- val = The approximate value of the definite integral.
'''
# Numerical Differentiation
import py_num_methods.numerical_differentiation as pynmnd
val = pynmnd.numerical_differentiation(f, x, h, method)
'''
Parameters:
- f: Function
- x: x values for finding slope at
- h: The value of interval size
- method: "central", "backward" and "forward" based on type of differentiation
Returns:
val = The approximate value of differentiated function at x
'''
# ODE Solver
import py_num_methods.ODE_solver as pynmode
### Predictor Corrector Method:
t, y = pynmode.predictor_corrector(f, y0, t0, tn, h)
'''
Parameters:
- f: The function defining the ODE dy/dt = f(t, y).
- y0: The initial condition y(t0) = y0.
- t0: The initial time.
- tn: The final time.
- h: The time step size.
Returns:
- t: An array of time values.
- y: An array of corresponding solution values.
'''
### Second Order Runge Kutta:
t, y = pynmode.runge_kutta_2(f, t0, y0, h, n)
'''
Parameters:
- f: The function defining the ODE dy/dt = f(t, y).
- t0: The initial value of the independent variable.
- y0: The initial value of the dependent variable.
- h: The step size.
- n: The number of steps.
Returns:
- t: The array of time values.
- y: The array of solution values.
'''
### Fourth Order Runge Kutta:
t, y = pynmode.runge_kutta_4(f, t0, y0, h, n)
'''
Parameters:
- f: The function defining the ODE dy/dt = f(t, y).
- t0: The initial value of the independent variable.
- y0: The initial value of the dependent variable.
- h: The step size.
- n: The number of steps.
Returns:
- t: The array of time values.
- y: The array of solution values.
'''
Change Log
==========
0.0.1 (10/12/2023)
-------------------
- First Release
0.1.0 (29/03/24)
-------------------
- Second Release
0.1.1 (29/03/24)
-------------------
- First Update
0.1.2 (29/03/24)
-------------------
- Second Update
Raw data
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"description": "py_num_methods: This is the module for the Numerical Methods such as approximations, equation solving, solving sets of linear equations, interpolations, numerical integration, numerical differentiation, and ODE solving.\r\n\r\n\r\n# Approximations:\r\n\r\n### Euler's Method\r\n\r\n import py_num_methods.approximations as pynma\r\n x, y = pynma.euler_method(f, x0, y0, h, n)\r\n \r\n '''\r\n Parameters:\r\n - f: The derivative function of the ODE.\r\n - x0: The initial x value.\r\n - y0: The initial y value.\r\n - h: The step size.\r\n - n: The number of iterations.\r\n \r\n Returns:\r\n - x: The array of x values.\r\n - y: The array of y values.\r\n '''\r\n\r\n# Equation Solving:\r\n\r\n import py_num_methods.eqn_solver as pynm_es\r\n\r\n### Graphical Solver:\r\n\r\n pynm_es.solve_equation_graphically(equation, x_range, y_range)\r\n \r\n '''\r\n Parameters:\r\n\t- equation: function\r\n\t- x_range: Tuple\r\n\t- y_range: Tuple\r\n\r\n Returns:\r\n\t- None\r\n\t- Plots the graph\r\n '''\r\n### Bisection Method:\r\n\r\n ret = pynm_es.bisection_method(f, a, b, tol)\r\n \r\n '''\r\n Parameters:\r\n - f: The function for which we want to find the root.\r\n - a: The lower bound of the interval.\r\n - b: The upper bound of the interval.\r\n - tol: The tolerance level for the root.\r\n \r\n Returns:\r\n - The approximate root of the function within the specified tolerance level.\r\n '''\r\n### False Position Method:\r\n\r\n ret = pynm_es.false_position_method(f, a, b, tol, max_iter)\r\n\r\n '''\r\n Parameters:\r\n - f: The function for which we want to find the root.\r\n - a and b: The initial interval endpoints.\r\n - tol: The tolerance level for convergence.\r\n - max_iter: The maximum number of iterations allowed.\r\n Returns:\r\n - The approximate root of the function.\r\n '''\r\n### Fixed Point Iterations:\r\n\r\n ret = pynm_es.fixed_point_iteration(f, initial_guess, tolerance, max_iterations)\r\n\r\n '''\r\n Parameters:\r\n - f: The function for which we want to find the root.\r\n - initial_guess: The initial guess value.\r\n - tolerance: The tolerance level for convergence.\r\n - max_iterations: The maximum number of iterations allowed.\r\n\r\n Returns:\r\n - The approximate root of the function.\r\n '''\r\n# Simultaneous Linear Equation Solver:\r\n\r\n import py_num_methods.sim_lin_eqn_solve as pynmsles\r\n\r\n### Gaussian Elimination:\r\n\r\n x = pynmsles.gaussian_elimination(A, b)\r\n\r\n '''\r\n Parameters:\r\n - A: The A (coefficient) matrix in Ax=b\r\n - b: The b (constant) matrix in Ax=b\r\n\r\n Returns:\r\n - x: Solution\r\n '''\r\n### LU Decomposition:\r\n\r\n x = pynmsles.lu_decomposition(A, b)\r\n\r\n '''\r\n Parameters:\r\n - A: The A (coefficient) matrix in Ax=b\r\n - b: The b (constant) matrix in Ax=b\r\n\r\n Returns:\r\n - x: Solution\r\n '''\r\n### Tri Diagonal Matrix Algorithm:\r\n\r\n x = pynmsles.solve_tdma(A, b)\r\n\r\n '''\r\n Parameters:\r\n - A: The A (coefficient) matrix in Ax=b\r\n - b: The b (constant) matrix in Ax=b\r\n\r\n Returns:\r\n - x: Solution\r\n '''\r\n### Gauss Seidel:\r\n\r\n x = pynmsles.gauss_seidel(A, b, x0, max_iterations=100, tolerance=1e-6)\r\n\r\n '''\r\n Parameters:\r\n - A: The A (coefficient) matrix in Ax=b\r\n - b: The b (constant) matrix in Ax=b\r\n - x0: Initial guess array\r\n - max_iterations: Max number of iterations\r\n - tolerance: Permissible tolerance in relative error\r\n\r\n Returns:\r\n - x: Solution\r\n '''\r\n# Interpolations:\r\n\r\n import py_num_methods.interpolations as pynmi\r\n\r\n### Quadratic Interpolations:\r\n\r\n y = pynmi.quadratic_interpolation(x, x0, x1, x2, y0, y1, y2)\r\n '''\r\n Parameters:\r\n - x : The point at which to estimate the value.\r\n - x0, x1, x2 : The x-coordinates of the three data points.\r\n - y0, y1, y2 : The y-coordinates of the three data points.\r\n\r\n Returns:\r\n - y = estimated value at point x.\r\n '''\r\n### Lagrange Interpolations:\r\n\r\n x = pynmi.lagrange_interpolation(x, y, xi)\r\n '''\r\n Parameters:\r\n - x, y : Arrays of data points\r\n - xi : Value at which we want to approximate the function\r\n\r\n Returns:\r\n - yi = interpolated value at point xi\r\n '''\r\n# Numerical Integration:\r\n\r\n import py_num_methods.numerical_integration as pynmni\r\n\r\n### Trapezoidal Integration:\r\n\r\n val = pynmni.trapezoidal_integration(f, a, b, n)\r\n '''\r\n Parameters:\r\n - f: The function to be integrated.\r\n - a: The lower limit of integration.\r\n - b: The upper limit of integration.\r\n - n: The number of subintervals to divide the integration interval into.\r\n \r\n Returns:\r\n - val = The approximate value of the integral.\r\n '''\r\n### Simpsons 1/3 method:\r\n\r\n val = pynmni.simpsons_13(f, a, b, n)\r\n '''\r\n Parameters:\r\n - f: The function to be integrated.\r\n - a: The lower limit of integration.\r\n - b: The upper limit of integration.\r\n - n: The number of subintervals.\r\n \r\n Returns:\r\n - val = The approximate value of the definite integral.\r\n '''\r\n### Simpsons 3/8 method:\r\n\r\n val = pynmni.simpsons_38(f, a, b, n)\r\n '''\r\n Parameters:\r\n - f: The function to be integrated.\r\n - a: The lower limit of integration.\r\n - b: The upper limit of integration.\r\n - n: The number of subintervals.\r\n \r\n Returns:\r\n - val = The approximate value of the definite integral.\r\n '''\r\n# Numerical Differentiation\r\n\r\n import py_num_methods.numerical_differentiation as pynmnd\r\n\r\n val = pynmnd.numerical_differentiation(f, x, h, method)\r\n '''\t\r\n Parameters:\r\n - f: Function\r\n - x: x values for finding slope at\r\n - h: The value of interval size\r\n - method: \"central\", \"backward\" and \"forward\" based on type of differentiation\r\n\r\n Returns:\r\n val = The approximate value of differentiated function at x\r\n '''\r\n# ODE Solver\r\n\r\n import py_num_methods.ODE_solver as pynmode\r\n\r\n### Predictor Corrector Method:\r\n\r\n t, y = pynmode.predictor_corrector(f, y0, t0, tn, h)\r\n '''\r\n Parameters:\r\n - f: The function defining the ODE dy/dt = f(t, y).\r\n - y0: The initial condition y(t0) = y0.\r\n - t0: The initial time.\r\n - tn: The final time.\r\n - h: The time step size.\r\n\r\n Returns:\r\n - t: An array of time values.\r\n - y: An array of corresponding solution values.\r\n '''\r\n### Second Order Runge Kutta:\r\n\r\n t, y = pynmode.runge_kutta_2(f, t0, y0, h, n)\r\n '''\r\n Parameters:\r\n - f: The function defining the ODE dy/dt = f(t, y).\r\n - t0: The initial value of the independent variable.\r\n - y0: The initial value of the dependent variable.\r\n - h: The step size.\r\n - n: The number of steps.\r\n\r\n Returns:\r\n - t: The array of time values.\r\n - y: The array of solution values.\r\n '''\r\n\r\n### Fourth Order Runge Kutta:\r\n\r\n t, y = pynmode.runge_kutta_4(f, t0, y0, h, n)\r\n '''\r\n Parameters:\r\n - f: The function defining the ODE dy/dt = f(t, y).\r\n - t0: The initial value of the independent variable.\r\n - y0: The initial value of the dependent variable.\r\n - h: The step size.\r\n - n: The number of steps.\r\n\r\n Returns:\r\n - t: The array of time values.\r\n - y: The array of solution values.\r\n '''\r\n \r\n\r\n\r\nChange Log\r\n==========\r\n\r\n0.0.1 (10/12/2023)\r\n-------------------\r\n- First Release\r\n\r\n0.1.0 (29/03/24)\r\n-------------------\r\n- Second Release\r\n\r\n0.1.1 (29/03/24)\r\n-------------------\r\n- First Update\r\n\r\n0.1.2 (29/03/24)\r\n-------------------\r\n- Second Update\r\n",
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