Python - numpy.vander() Method with Examples

Learn about the numpy.vander() method, how does it work?
By Pranit Sharma Last updated : December 25, 2023

Python - numpy.vander() Method

The numpy.vander() method is used to generate a Vandermonde matrix. A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials, and the reconstruction of a statistical distribution from the distribution's moments. A Vandermonde matrix of order is of the following form:

numpy.vander() Method

The columns of the output matrix are powers of the input vector. The order of the powers is determined by the increasing boolean argument. Specifically, when increasing is False, the i-th output column is the input vector raised element-wise to the power of N - i - 1.

Syntax of numpy.vander() Method

Below is the syntax of numpy.vander() method:

numpy.vander(x, N=None, increasing=False)

Parameters of numpy.vander() Method

Below are the parameters of numpy.vander() method:

  • x: input array (1D)
  • n: int values which represent the number of columns in the output.
  • increasing: Order of the powers of the columns.

Return Value of numpy.vander() Method

The method returns vandermonde matrix. If increasing is False, the first column is x^(N-1), the second x^(N-2) and so forth. If increasing is True, the columns are x^0, x^1, ..., x^(N-1). [Source]

Let us understand with the help of an example,

The numpy.vander() Method Examples

Practice the below example to understand the use of numpy.vander() method:

Example 1: Python program to demonstrate the example of numpy.vander() Method

# Import numpy
import numpy as np

# Creating a numpy array
arr = np.array([1, 2, 3, 5])

# Display original array
print("Original Array:\n",arr,"\n")

# Creating a vandermonde matrix
res = np.vander(arr,3)

# Display result


Example: numpy.vander() Method with Example

Example 2

# Importing numpy module
import numpy as np

# Creating an array
arr = np.array([9, 29, 19])

# Printing the array
print("The arr is:\n", arr)

# Performing np.vander()
result = np.vander(arr)

# Printing the result
print("Vandermonde Matrix (result):\n", result)


The arr is:
 [ 9 29 19]
Vandermonde Matrix (result):
 [[ 81   9   1]
 [841  29   1]
 [361  19   1]]

Web References

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