Evaluate a Laguerre series at points x broadcast over the columns of the coefficient in Python

To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python NumPy. This function broadcasts evaluation points over coefficient columns when tensor=False.

Syntax

numpy.polynomial.laguerre.lagval(x, c, tensor=True)

Parameters

The function accepts three parameters ?

• x − Array of points at which to evaluate the series. Can be scalar, list, or array
• c − Array of coefficients ordered so that coefficients for degree n are in c[n]. For multidimensional arrays, remaining indices enumerate multiple polynomials
• tensor − If True (default), extends coefficient shape. If False, broadcasts x over coefficient columns

Understanding Broadcasting with tensor=False

When tensor=False, each evaluation point in x corresponds to a column in the coefficient array c. This is useful for evaluating different polynomials at different points.

import numpy as np
from numpy.polynomial import laguerre as L

# Create a multidimensional array of coefficients
c = np.arange(4).reshape(2,2)

# Display the array
print("Our Array...")
print(c)

# Check the Dimensions
print("\nDimensions of our Array...")
print(c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...")
print(c.dtype)

# Get the Shape
print("\nShape of our Array object...")
print(c.shape)

# Evaluate Laguerre series with tensor=False
print("\nResult...")
print(L.lagval([1,2], c, tensor=False))

Our Array...
[[0 1]
 [2 3]]

Dimensions of our Array...
2

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2)

Result...
[ 0. -2.]

How It Works

With tensor=False, the evaluation works as follows ?

• Point x[0]=1 evaluates polynomial with coefficients c[:,0] = [0,2]
• Point x[1]=2 evaluates polynomial with coefficients c[:,1] = [1,3]

Comparison of tensor Parameter

import numpy as np
from numpy.polynomial import laguerre as L

c = np.array([[0, 1], [2, 3]])
x = [1, 2]

print("tensor=False (broadcast):")
print(L.lagval(x, c, tensor=False))

print("\ntensor=True (default):")
print(L.lagval(x, c, tensor=True))

tensor=False (broadcast):
[ 0. -2.]

tensor=True (default):
[[ 0. -1.]
 [-2. -5.]]

Conclusion

Use lagval() with tensor=False to evaluate different Laguerre polynomials at corresponding points. This broadcasting approach is efficient for paired evaluations of multiple polynomial series.