NumPy arctan()
The numpy.arctan() function computes the trigonometric inverse tangent (arctangent) of each element in an input array.
The inverse tangent function returns values in the range [-π/2, π/2].
Syntax
numpy.arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True)Parameters
| Parameter | Type | Description |
|---|---|---|
x | array_like | Input values for which the inverse tangent is computed. |
out | ndarray, None, or tuple of ndarray and None, optional | Optional output array where the result is stored. If None, a new array is created. |
where | array_like, optional | Boolean mask specifying which elements to compute. Elements where where=False retain their original value. |
casting | str, optional | Defines the casting behavior when computing the function. |
order | str, optional | Memory layout order of the output array. |
dtype | data-type, optional | Defines the data type of the output array. |
subok | bool, optional | Determines if subclasses of ndarray are preserved in the output. |
Return Value
Returns an array with the inverse tangent values of the input elements. If the input is a scalar, a scalar is returned.
The output values are in the range [-π/2, π/2].
Examples
1. Computing Arctangent of a Single Value
Here, we compute the inverse tangent of a single value.
import numpy as np
# Define a value
value = 1.0
# Compute the inverse tangent (arctan) of the value
result = np.arctan(value)
# Print the result
print("Arctan of 1:", result)Output:
Arctan of 1: 0.7853981633974483
The result is approximately 0.785, which is equivalent to π/4.
2. Computing Arctangent for an Array of Values
We compute the arctangent values for multiple input values in an array.
import numpy as np
# Define an array of values
values = np.array([-1, 0, 1, np.tan(np.pi/3)])
# Compute the inverse tangent of each value
arctan_values = np.arctan(values)
# Print the results
print("Input values:", values)
print("Arctan values:", arctan_values)Output:
Input values: [-1. 0. 1. 1.73205081]
Arctan values: [-0.78539816 0. 0.78539816 1.04719755]
The results show that arctan(-1) is -π/4, arctan(0) is 0, arctan(1) is π/4, and arctan(√3) is π/3.
3. Using the out Parameter
Using an output array to store results instead of creating a new array.
import numpy as np
# Define an array of values
values = np.array([-1, 0, 1])
# Create an output array with the same shape
output_array = np.ndarray(shape=[1, 3])
# Compute arctan and store the result in output_array
np.arctan(values, out=output_array)
# Print the results
print("Computed arctan values:", output_array)Output:
Computed arctan values: [-0.78539816 0. 0.78539816]
4. Using the where Parameter
Using a condition to compute arctangent only for selected elements.
import numpy as np
# Define an array of values
values = np.array([-1, 0, 1, 10])
# Define a mask (compute arctan only where mask is True)
mask = np.array([True, False, True, False])
# Compute arctan values where mask is True
result = np.arctan(values, where=mask)
# Print the results
print("Computed arctan values with mask:", result)Output:
Computed arctan values with mask: [-7.85398163e-001 0.00000000e+000 7.85398163e-001 4.95242130e+223]
The arctangent is computed only for elements where mask=True. The other values remain unchanged.