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Evaluate a 2-D polynomial on the Cartesian product of x and y with 3d array of coefficient in Python
To evaluate a 2-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid2d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y.
The 1st parameter, x and y, are 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, c is an array of coefficients ordered so that the coefficients for terms of degree i,j are contained in c[i,j]. If c has dimension greater than two the remaining indices enumerate multiple sets of coefficients.
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.
Steps
At first, import the required library −
import numpy as np from numpy.polynomial.polynomial import polygrid2d
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 2-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid2d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y −
print("\nResult...\n",polygrid2d([1,2],[1,2], c))Example
import numpy as np
from numpy.polynomial.polynomial import polygrid2d
# 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 2-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid2d(x, y, c) method in Python
print("\nResult...\n",polygrid2d([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.]]]
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