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Finding Toeplitz matrix using SciPy

Overview:

  • A Toeplitz matrix is a matrix whose diagonal elements are constant. i.e, The value of the diagonal elements are equal. Toeplitz matrix is named after the mathematician Otto Toeplitz.
  • Toeplitz matrices have their applications in several scientific fields including finding solutions to differential equations and integral equations, signal processing, image processing, spline functions and queuing theory.
  • Given the first colulmn and the first row of the output matrix, the function toeplitz() from the linalg module of the scipy library returns a Toeplitz matrix as an ndarray. If the first row is not given its is taken as the conjucate of the given first column.

Example:

# Example Python program that creates a
# Toeplitz matrix using the scipy module
# scipy.linalg

import scipy.linalg as sclg

firstColumn = [1, 3, 5]
firstRow     = [1, 2, 4]

# Create a Toeplitz matrix with the given first column and
# the first row
toeplitzMatrix = sclg.toeplitz(firstColumn, firstRow)

print("First column:")
print(firstColumn)

print("First row:")
print(firstRow)

print("Toeplitz matrix:")
print(type(toeplitzMatrix))
print(toeplitzMatrix)

Output:

First column:
[1, 3, 5]
First row:
[1, 2, 4]
Toeplitz matrix:
<class 'numpy.ndarray'>
[[1 2 4]
 [3 1 2]
 [5 3 1]]

 


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