# Evaluate a 2D Legendre series on the Cartesian product of x and y with 3d array of coefficient in Python

To evaluate a 2D Legendre series on the Cartesian product of x and y, use the polynomial.legendre.leggrid2d() method in Python Numpy. The method returns the values of the two dimensional Chebyshev series at points in the Cartesian product of x and y. If c has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.

The 1st parameter is x, y. The two dimensional series is evaluated at the points in the Cartesian product of x and y. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar. The 2nd parameter is c. Array of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in c[i,j]. If c has dimension greater than two the remaining indices enumerate multiple sets of coefficients.

## Steps

At first, import the required library −

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

Create a 3d array of coefficients −

c = np.arange(24).reshape(2,2,6)

Display the array −

print("Our Array...\n",c)

Check the Dimensions −

print("\nDimensions of our Array...\n",c.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",c.dtype)

Get the Shape −

print("\nShape of our Array object...\n",c.shape)

To evaluate a 2D Legendre series on the Cartesian product of x and y, use the polynomial.legendre.leggrid2d() method in Python. The method returns the values of the two dimensional Chebyshev series at points in the Cartesian product of x and y −

print("\nResult...\n",L.leggrid2d([1,2],[1,2],c))

## Example

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

# Create a 3d array of coefficients
c = np.arange(24).reshape(2,2,6)

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

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

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

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

# To evaluate a 2D Legendre series on the Cartesian product of x and y, use the polynomial.legendre.leggrid2d() method in Python Numpy
print("\nResult...\n",L.leggrid2d([1,2],[1,2],c))

## Output

Our Array...
[[[ 0 1 2 3 4 5]
[ 6 7 8 9 10 11]]

[[12 13 14 15 16 17]
[18 19 20 21 22 23]]]

Dimensions of our Array...
3

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2, 6)

Result...
[[[ 36. 60.]
[ 66. 108.]]

[[ 40. 66.]
[ 72. 117.]]

[[ 44. 72.]
[ 78. 126.]]

[[ 48. 78.]
[ 84. 135.]]

[[ 52. 84.]
[ 90. 144.]]

[[ 56. 90.]
[ 96. 153.]]]

Updated on: 07-Mar-2022

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