linear algebra benchmarks

linalg_benchmarks.py

from numpy import linalg
import numpy as np
import time

""" This will generate a random NxN invertible matrix [1] """
def generate_mat(n):
    mat = list()
    for k in range(n):
        rv = np.linspace(1,1,n)
        rv = rv*np.random.random(n)
        rv[k] = rv[k]*(k+1)
        mat.append(rv)
    return np.array(mat)
    
""" Some benchmarks worth trying out """
N = 2000

# Time to construct matrix A
s=time.time(); A=generate_mat(N); e=time.time(); print (e-s)    # my machine:  0.184283971 sec

# Time to compute inverse of A
s=time.time(); result=linalg.inv(A); e=time.time(); print (e-s) # my machine:  2.667845010 sec

# Time to compute eigen[values/vectors] of A
s=time.time(); result=linalg.eig(A); e=time.time(); print (e-s) # my machine: 29.871132135 sec

# Time to compute Singular Value Decomposition of A
s=time.time(); result=linalg.svd(A); e=time.time(); print (e-s) # my machine: 15.854166984 sec
    

CPU starts to choke on my machine (Ubuntu 14.04 on virtualized Intel Core i7-3687U with 12 GB RAM running Python 2.7.6) when N >= 2000

References:
[1] https://matthewhr.wordpress.com/2013/09/01/how-to-construct-an-invertible-matrix-just-choose-large-diagonals/