jax.numpy.geomspaceΒΆ

jax.numpy.geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0)[source]ΒΆ

Return numbers spaced evenly on a log scale (a geometric progression).

LAX-backend implementation of geomspace(). Original docstring below.

This is similar to logspace, but with endpoints specified directly. Each output sample is a constant multiple of the previous.

Changed in version 1.16.0: Non-scalar start and stop are now supported.

Parameters
  • start (array_like) – The starting value of the sequence.

  • stop (array_like) – The final value of the sequence, unless endpoint is False. In that case, num + 1 values are spaced over the interval in log-space, of which all but the last (a sequence of length num) are returned.

  • num (integer, optional) – Number of samples to generate. Default is 50.

  • endpoint (boolean, optional) – If true, stop is the last sample. Otherwise, it is not included. Default is True.

  • dtype (dtype) – The type of the output array. If dtype is not given, infer the data type from the other input arguments.

  • axis (int, optional) – The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end.

Returns

samples – num samples, equally spaced on a log scale.

Return type

ndarray

See also

logspace()

Similar to geomspace, but with endpoints specified using log and base.

linspace()

Similar to geomspace, but with arithmetic instead of geometric progression.

arange()

Similar to linspace, with the step size specified instead of the number of samples.

Notes

If the inputs or dtype are complex, the output will follow a logarithmic spiral in the complex plane. (There are an infinite number of spirals passing through two points; the output will follow the shortest such path.)

Examples

>>> np.geomspace(1, 1000, num=4)
array([    1.,    10.,   100.,  1000.])
>>> np.geomspace(1, 1000, num=3, endpoint=False)
array([   1.,   10.,  100.])
>>> np.geomspace(1, 1000, num=4, endpoint=False)
array([   1.        ,    5.62341325,   31.6227766 ,  177.827941  ])
>>> np.geomspace(1, 256, num=9)
array([   1.,    2.,    4.,    8.,   16.,   32.,   64.,  128.,  256.])

Note that the above may not produce exact integers:

>>> np.geomspace(1, 256, num=9, dtype=int)
array([  1,   2,   4,   7,  16,  32,  63, 127, 256])
>>> np.around(np.geomspace(1, 256, num=9)).astype(int)
array([  1,   2,   4,   8,  16,  32,  64, 128, 256])

Negative, decreasing, and complex inputs are allowed:

>>> np.geomspace(1000, 1, num=4)
array([1000.,  100.,   10.,    1.])
>>> np.geomspace(-1000, -1, num=4)
array([-1000.,  -100.,   -10.,    -1.])
>>> np.geomspace(1j, 1000j, num=4)  # Straight line
array([0.   +1.j, 0.  +10.j, 0. +100.j, 0.+1000.j])
>>> np.geomspace(-1+0j, 1+0j, num=5)  # Circle
array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,
        6.12323400e-17+1.00000000e+00j,  7.07106781e-01+7.07106781e-01j,
        1.00000000e+00+0.00000000e+00j])

Graphical illustration of endpoint parameter:

>>> import matplotlib.pyplot as plt
>>> N = 10
>>> y = np.zeros(N)
>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.axis([0.5, 2000, 0, 3])
[0.5, 2000, 0, 3]
>>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
>>> plt.show()