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# Evaluate 2-D Hermite series on the Cartesian product of x and y with 1d array of coefficient using NumPy in Python

• Last Updated : 03 Jun, 2022

In this article, we will discuss how to Evaluate a 2-D Hermite series on the Cartesian product of x and y with a 1d array of coefficients in Python using NumPy.

## NumPy.polynomial.hermite.hermgrid2d method

Hermite polynomials are significant in approximation theory because the Hermite nodes are used as matching points for optimizing polynomial interpolation. To perform the Hermite cartesian product, NumPy provides a function called Hermite.hermgrid2d which can be used to evaluate the cartesian product of the 1D Hermite series. This function converts the parameters x and y to array only if they are tuples or a list, otherwise, it is left unchanged and, if it is not an array, it is treated as a scalar.

Syntax: polynomial.hermite.hermgrid2d(x, y, c)

Parameters:

• x,y: array_like
• c: array of coefficients

Returns: Two dimensional polynomials at points as cartesian products of x and y.

### Example 1:

In the first example. let us consider a 1D array c that has 5 elements.  Let us consider a 2D series [1,2],[1,2] to evaluate against the 1D array. Import the necessary packages as shown and pass the appropriate parameters as shown below.

## Python3

 `import` `numpy as np``from` `numpy.polynomial ``import` `hermite`` ` `# coefficient array``c ``=` `np.array([``1``, ``2``, ``3``, ``4``, ``5``])`` ` `print``(f``'The co.efficient array is {c}'``)``print``(f``'The shape of the array is {c.shape}'``)``print``(f``'The dimension of the array is {c.ndim}D'``)``print``(f``'The datatype of the array is {c.dtype}'``)`` ` `# evaluating 1d co.eff array with a 2d``# hermite series``res ``=` `hermite.hermgrid2d([``1``, ``2``], [``1``, ``2``], c)`` ` `# resultant array``print``(f``'Resultant series ---> {res}'``)`

Output:

```The co.efficient array is [1 2 3 4 5]
The shape of the array is (5,)
The dimension of the array is 1D
The datatype of the array is int64
Resultant series ---> [1077. 2259.]```

### Example 2:

In the first example. let us consider a 1D array c that has 10 elements.  Let us consider a 2D series [2,1],[2,1] to evaluate against the 1D array. Import the necessary packages as shown and pass the appropriate parameters as shown below.

## Python3

 `import` `numpy as np``from` `numpy.polynomial ``import` `hermite`` ` `# coefficient array``c ``=` `np.array([``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10``])`` ` `print``(f``'The co.efficient array is {c}'``)``print``(f``'The shape of the array is {c.shape}'``)``print``(f``'The dimension of the array is {c.ndim}D'``)``print``(f``'The datatype of the array is {c.dtype}'``)`` ` `# evaluating 1d coeff array with a 2d``# hermite series``res ``=` `hermite.hermgrid2d([``2``, ``1``], [``2``, ``1``], c)`` ` `# resultant array``print``(f``'Resultant series ---> {res}'``)`

Output:

```The co.efficient array is [ 1  2  3  4  5  6  7  8  9 10]
The shape of the array is (10,)
The dimension of the array is 1D
The datatype of the array is int64
Resultant series ---> [-45325. 189045.]```

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