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Module « numpy.matlib »

Fonction geomspace - module numpy.matlib

Signature de la fonction geomspace

def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0) 

Description

help(numpy.matlib.geomspace)

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

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

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, the data type
    is inferred from `start` and `stop`. The inferred dtype will never be
    an integer; `float` is chosen even if the arguments would produce an
    array of integers.
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 : ndarray
    `num` samples, equally spaced on a log scale.

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.
:ref:`how-to-partition`

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
--------
>>> import numpy as np
>>> 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()

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