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# Evaluate a 2D Legendre series on the Cartesian product of x and y with 1d 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 multidegree 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 1d array of coefficients −

c = np.array([3, 5])

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. 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 1d array of coefficients c = np.array([3, 5]) # 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... [3 5] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (2,) Result... [21. 34.]

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