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.