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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:

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
print("Result:\n",res)

Output

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)

Output

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

Web References

• Vandermonde matrix

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