Collection of methods for numerical analysis and scientific computing, including numerical root-finders, numerical integration, linear algebra, and data visualization.
from linearAlgebra import * n = 2 y = [1,0] w = [0,1] dp = dotProduct(y,w,n) print('the dot product is : ', dp)Output:
the dot product is : 0.0 from linearAlgebra import * n = 2 mat = [[1,0],[0,1]] vec = [0,1] prod = matVecMult(mat,vec,n) print('the product is : ', prod)Output:
the product is : [0.0, 1.0] Contained in solvers.py
from solvers import * from visualization import * f = lambda x: x**2 vec = fixedptVec(f, 0.5, 0.001, 100) # function, start point, tolerance, max iterations printFloatVec(vec,spacing=2) # improved list print function (see below)Output:
-------------------- f(x) = lambda x: x**2, Fixed point iteration: 0.25 0.0625 0.00391 1.53e-05 2.33e-10 Additional solvers include:
- Bisection
- Newton's Method
- Hybrid Bisection -> Newton solver (in progress)
from solvers import * from visualization import * f_vec = [ lambda x: x**2, lambda x: x**2 - x**4 ] for f in f_vec: # loop through functions and compute roots print('-'*20) print(lambdaToString(f),'\n') print("Fixed point iteration:") vec = fixedptVec(f, 0.5, 0.001, 100) printFloatVec(vec,precision=3,spacing=2,newLine=True)Output:
-------------------- f(x) = lambda x: x**2, Fixed point iteration: 0.25 0.0625 0.00391 1.53e-05 2.33e-10 -------------------- f(x) = lambda x: x**2 - x**4 Fixed point iteration: 0.188 0.0339 0.00115 1.32e-06 1.74e-12 Created for work in APPM4600 at University of Colorado Boulder.