numpy.vander Method in Python



The numpy.vander() method is used to generate a Vandermonde (Vander) matrix. A Vander matrix contains a geometric progression in each row, for example,

$$\mathrm{A =\begin{bmatrix}1 & 2 & 4 \1 & 3 & 9 \1 & 5 &25\end{bmatrix} or\: B = \begin{bmatrix}1 & 4 & 16 \1 & 6 &36 \end{bmatrix}}$$

Syntax

Its syntax is as follows −

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

Parameters

It accepts the following parameters −

  • x - This is the input array.

  • N - It is the number of columns in the output. By default, it is None.

  • Increasing - If increasing=True, then the power increases from left to right. If increasing=False, then powers are reversed.

Example 1

Let us consider the following example −

# import numpy library
import numpy as np

# create an array
a = np.array([11, 12, 13])
print("Input Array :", a)

# Vander function
x = np.vander(a)
print("Vander Elements: 
", x)

Output

It will generate the following output −

Input Array : [11 12 13]
Vander Elements:
[[121 11 1]
[144 12 1]
[169 13 1]]

Example 2

Let us take another example −

# import numpy library
import numpy as np

# create an array
x = np.array([4, 5, 9])
print("Input Array :", x)

# vander function
y = np.vander(x, increasing=True)
print("Vander Elements: 
", y)

Output

It will generate the following output −

Input Array : [4 5 9]
Vander Elements:
[[ 1 4 16]
[ 1 5 25]
[ 1 9 81]]

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