# Evaluate a 2-D polynomial at points (x, y) in Python

• Last Updated : 25 Apr, 2022

We use the polynomial.polyval2d() which is a numpy’s function in Python to assess a 2-D polynomial at the positions (x, y). The technique returns the values of the given two-dimensional polynomial at places produced by x and y pairs. x and y are parameters. At the points (x, y), the two-dimensional series is assessed, where x and y must have the same form. If x or y is a list or tuple, it is first transformed to an ndarray, otherwise, it is kept unmodified and is regarded as a scalar if it isn’t a ndarray.

The parameter ‘Arr’ is an Array of coefficients sorted so that Arr[i,j] contains the coefficient of the term of multidegree i,j. The remaining indices enumerate numerous sets of coefficients if ‘Arr’ has a dimension higher than two. If the form of ‘Arr’ has less than two dimensions, ones are implicitly added to make it two-dimensional. Arr .shape[2:] + x.shape is the shape of the result.

## Below are the steps to evaluate 2-D polynomial at point (x,y) :

Step 1: Import NumPy and polyval2d libraries as shown below :

## Python3

 `import` `numpy as np``from` `numpy.polynomial.polynomial ``import` `polyval2d`

Step 2: Now we have to create a multidimensional array ‘Arr’ of coefficients as shown below :

## Python3

 `Arr ``=` `np.arange(``4``).reshape(``2``,``2``)`

Step 3: Define x and y (the points at which we are evaluating 2-D polynomial) as shown below :

## Python3

 `x ``=` `[``1``,``2``]``y ``=` `[``2``,``3``]`

Step 3: Use the polynomial.polyval2d() function to assess a 2-D polynomial at locations (x, y) as shown below :

## Python3

 `print``(``"Result : \n"``,polyval2d(x,y, Arr))`

Example 1 :

## Python3

 `# importing numpy and polyval2d``import` `numpy as np``from` `numpy.polynomial.polynomial ``import` `polyval2d` `# Create a multidimensional array of``# coefficients or a matrix``Arr ``=` `np.matrix([[``4``, ``2``], [``6``, ``3``]])` `# Defining x and y``x ``=` `[``2``, ``3``]``y ``=` `[``1``, ``2``]` `# in order to evaluate a 2-D polynomial``# at points (x, y), we are using the``# polynomial.polyval2d() method in Python``# Numpy``print``(polyval2d(x, y, Arr))`

Output :

`[24. 44.]`

Example 2 :

## Python3

 `# import polyval2d from numpy``from` `numpy.polynomial.polynomial ``import` `polyval2d` `# create a 2 dimensional array``# of coefficient or a matrix``Arr ``=` `[[``4``,``2``], [``6``,``3``]]` `# evaluate the 2D polynomial at``# point (x,y) using polyval2d``# function and print the result``print``(polyval2d([``2``,``3``],[``1``,``2``],Arr))`

Output :

`[24. 44.]`

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