dreamchef / numerical-analysis-methods

Collection of methods for numerical analysis and scientific computing, including numerical root-finders, numerical integration, linear algebra, and data visualization. Created for APPM4600 at CU Boulder.

Scientific Computing and Numerical Analysis Methods

Collection of methods for numerical analysis and scientific computing, including numerical root-finders, numerical integration, linear algebra, and data visualization.

Linear Algebra

Dot Product

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

Matrix-Vector Multiplication

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]

Rooting-Finding: Numerical Solvers

Contained in solvers.py

Fixed Point Iteration

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)

Visualization Methods

Print Vector

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.