numpy.logspace() in Python

The numpy.logspace() function is used to generate numbers that are evenly spaced on a logarithmic scale. Instead of creating values with equal linear differences, this function generates values that are evenly spaced according to powers of a base value.

Example: The following example demonstrates how to generate logarithmically spaced values using logspace().

import numpy as np
a = np.logspace(2, 3, num=5)
print(a)

[ 100.          177.827941    316.22776602  562.34132519 1000.        ]

Explanation:

• start=2 represents 10² and stop=3 represents 10³
• num=5 generates five values between 10² and 10³
• The values increase logarithmically, not linearly.

Syntax

numpy.logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None)

Parameters:

• start: Starting exponent of the sequence (base ** start).
• stop: Ending exponent of the sequence (base ** stop).
• num: Number of values to generate (default is 50).
• endpoint: Includes the stop value if True (default True).
• base: Base of the logarithm (default is 10).
• dtype: Data type of the output array.

Return Type: ndarray

Using Different Base Values

By default, logspace() uses base 10. This can be changed using the base parameter.

import numpy as np
b = np.logspace(2, 3, num=5, base=11)
print(b)

[ 121.          220.36039471  401.31159963  730.8527479  1331.        ]

Explanation:

• base=11 generates values as powers of 11 instead of 10.
• start=2 and stop=3 create values from 11² to 11³.
• num=5 specifies the total number of values.

Specifying Data Type

The output array can be converted to a specific data type using the dtype parameter.

import numpy as np
c = np.logspace(2, 3, num=5, dtype=int)
print(c)

[ 100  177  316  562 1000]

Explanation: dtype=int converts float values to integers and decimal values are removed during conversion.

Visualizing logspace() Output

This example demonstrate how to visualize logarithmically spaced values using pylab for a better visualized understanding of their distribution.

import numpy as np
import pylab as p

x1 = np.logspace(0, 1, 10)
y1 = np.zeros(10)

x2 = np.logspace(0.1, 1.5, 12)
y2 = np.zeros(12)

p.plot(x1, y1 + 0.05, 'o')
p.plot(x2, y2, 'x')
p.xlim(-0.2, 18)
p.ylim(-0.5, 1)
p.show()

Output

Explanation:

• np.logspace(0, 1, 10) creates 10 logarithmically spaced values between 10⁰ and 10¹.
• np.logspace(0.1, 1.5, 12) creates 12 values between 10⁰·¹ and 10¹·⁵.
• p.plot(x1, ..., 'o') and p.plot(x2, ..., 'x') plot these values using different markers.
• The increasing gaps between plotted points show the exponential growth of values produced by logspace().