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# 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.]]]