Integrate a Hermite series over specific axis in Python

To integrate a Hermite series, use the hermite.hermint() method in Python. This method integrates Hermite series coefficients over a specified axis, making it useful for polynomial integration in scientific computing.

Syntax

numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0)

Parameters

Example

Let's create a multidimensional array and integrate along different axes ?

import numpy as np
from numpy.polynomial import hermite as H

# Create a multidimensional array of coefficients
c = np.arange(4).reshape(2,2)

# 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 integrate a Hermite series, use the hermite.hermint() method in Python
print("\nResult (axis=1)...\n",H.hermint(c, axis = 1))

Our Array...
 [[0 1]
 [2 3]]

Dimensions of our Array...
2

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2)

Result (axis=1)...
 [[0.5 0.  0.25]
 [1.5 1.  0.75]]

Integration Along Different Axes

Compare integration along axis 0 vs axis 1 ?

import numpy as np
from numpy.polynomial import hermite as H

c = np.arange(6).reshape(2,3)
print("Original array:")
print(c)

print("\nIntegration along axis=0:")
print(H.hermint(c, axis=0))

print("\nIntegration along axis=1:")
print(H.hermint(c, axis=1))

Original array:
[[0 1 2]
 [3 4 5]]

Integration along axis=0:
[[1.5 0.  2.5 1.  3.5]]

Integration along axis=1:
[[0.5 0.  0.25 0.  0.5 ]
 [2.5 1.5 1.   0.75 1.25]]

Using Integration Constants

Add integration constants using the k parameter ?

import numpy as np
from numpy.polynomial import hermite as H

c = np.array([1, 2, 3])
print("Coefficients:", c)

# Integration with constant k=5
result_with_k = H.hermint(c, k=5)
print("With integration constant k=5:")
print(result_with_k)

# Integration without constant (default k=[])
result_default = H.hermint(c)
print("Without integration constant:")
print(result_default)

Coefficients: [1 2 3]
With integration constant k=5:
[5.  0.5 1.  0.75]
Without integration constant:
[0.  0.5 1.  0.75]

Conclusion

The hermite.hermint() method provides flexible integration of Hermite series with control over axes, integration order, and constants. Use the axis parameter to specify which dimension to integrate along in multidimensional arrays.