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NumPy: Compute the condition number of a given matrix

NumPy: Linear Algebra Exercise-9 with Solution

Write a NumPy program to compute the condition number of a given matrix.

From Wikipedia, In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input. Very frequently, one is solving the inverse problem – given {\displaystyle f(x)=y,} f(x) = y, one is solving for x, and thus the condition number of the (local) inverse must be used. In linear regression the condition number can be used as a diagnostic for multicollinearity.

Sample Solution :

Python Code :

import numpy as np
from numpy import linalg as LA
a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
print("Original matrix:")
print(a)
print("The condition number of the said matrix:")
print(LA.cond(a))

Sample Output:

Original matrix:
[[ 1  0 -1]
 [ 0  1  0]
 [ 1  0  1]]
The condition number of the said matrix:
1.41421356237

Python-Numpy Code Editor:

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m