NumPy spacing()
The numpy.spacing() function returns the distance between a given number and the nearest adjacent floating-point number, which is useful for understanding numerical precision and floating-point representation.
Syntax
numpy.spacing(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True)Parameters
| Parameter | Type | Description |
|---|---|---|
x | array_like | Values to find the spacing of (i.e., the difference between the given value and its nearest floating-point neighbor). |
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 should be computed. Elements where where=False retain their original value. |
casting | str, optional | Defines the casting behavior when computing the spacing. |
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 or a scalar representing the spacing of values in x. If x is a scalar, a scalar is returned.
Examples
1. Finding Spacing of a Single Value
Here, we compute the spacing of a single floating-point number.
import numpy as np
# Define a single floating-point number
value = 1.0
# Compute the spacing
spacing_value = np.spacing(value)
# Print the result
print("Spacing of 1.0:", spacing_value)Output:
Spacing of 1.0: 2.220446049250313e-16
The output represents the smallest positive number that can be added to 1.0 to produce a different floating-point value.
2. Finding Spacing for an Array of Values
We compute the spacing values for multiple floating-point numbers.
import numpy as np
# Define an array of numbers
values = np.array([0.1, 1.0, 10.0, 100.0])
# Compute the spacing for each value
spacing_values = np.spacing(values)
# Print the results
print("Input values:", values)
print("Spacing values:", spacing_values)Output:
Input values: [ 0.1 1. 10. 100. ]
Spacing values: [1.38777878e-17 2.22044605e-16 1.77635684e-15 1.42108547e-14]
3. Using the out Parameter
Storing the output in a pre-allocated array instead of creating a new one.
import numpy as np
# Define an array of values
values = np.array([1.0, 2.0, 3.0, 4.0])
# Create an output array
output_array = np.empty_like(values)
# Compute spacing and store the result in output_array
np.spacing(values, out=output_array)
# Print the results
print("Computed spacing values:", output_array)Output:
Computed spacing values: [2.22044605e-16 4.44089210e-16 4.44089210e-16 8.88178420e-16]
4. Using the where Parameter
Computing spacing only for selected elements based on a condition.
import numpy as np
# Define an array of values
values = np.array([0.1, 1.0, 10.0, 100.0])
# Define a mask (compute spacing only where mask is True)
mask = np.array([True, False, True, False])
# Compute spacing values where mask is True
result = np.spacing(values, where=mask)
# Print the results
print("Computed spacing values with mask:", result)Output:
Computed spacing values with mask: [1.38777878e-17 0.00000000e+00 1.77635684e-15 0.00000000e+00]
The spacing values are computed only for elements where mask=True. The other values remain unchanged.