numpy.core.function_base

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.

New in version 1.16.0.

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.

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()

Parameters

start : array_like

The starting value of the sequence.

stop : array_like

The end value of the sequence, unless endpoint is set to False. In that case, the sequence consists of all but the last of num + 1 evenly spaced samples, so that stop is excluded. Note that the step size changes when endpoint is False.

num : int, optional

Number of samples to generate. Default is 50. Must be non-negative.

endpoint : bool, optional

If True, stop is the last sample. Otherwise, it is not included. Default is True.

retstep : bool, optional

If True, return (samples, step), where step is the spacing between samples.

dtype : dtype, optional

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.

New in version 1.9.0.

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.

New in version 1.16.0.

Returns

samples : ndarray

There are num equally spaced samples in the closed interval [start, stop] or the half-open interval [start, stop) (depending on whether endpoint is True or False).

step : float, optional

Only returned if retstep is True

Size of spacing between samples.

See Also

arange : Similar to linspace, but uses a step size (instead of the

number of samples).

geomspace : Similar to linspace, but with numbers spaced evenly on a log

scale (a geometric progression).

logspace : Similar to geomspace, but with the end points specified as

logarithms.

Examples

>>> np.linspace(2.0, 3.0, num=5)
array([2.  , 2.25, 2.5 , 2.75, 3.  ])
>>> np.linspace(2.0, 3.0, num=5, endpoint=False)
array([2. ,  2.2,  2.4,  2.6,  2.8])
>>> np.linspace(2.0, 3.0, num=5, retstep=True)
(array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)

Graphical illustration:

>>> import matplotlib.pyplot as plt
>>> N = 8
>>> y = np.zeros(N)
>>> x1 = np.linspace(0, 10, N, endpoint=True)
>>> x2 = np.linspace(0, 10, N, endpoint=False)
>>> plt.plot(x1, y, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(x2, y + 0.5, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.ylim([-0.5, 1])
(-0.5, 1)
>>> plt.show()

Parameters

start : array_like

base ** start is the starting value of the sequence.

stop : array_like

base ** stop is 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.

base : array_like, optional

The base of the log space. The step size between the elements in ln(samples) / ln(base) (or log_base(samples)) is uniform. Default is 10.0.

dtype : dtype

The type of the output array. If dtype is not given, the data type is inferred from start and stop. The inferred type 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.

New in version 1.16.0.

Returns

samples : ndarray

num samples, equally spaced on a log scale.

See Also

arange : Similar to linspace, with the step size specified instead of the

number of samples. Note that, when used with a float endpoint, the endpoint may or may not be included.

linspace : Similar to logspace, but with the samples uniformly distributed

in linear space, instead of log space.

geomspace : Similar to logspace, but with endpoints specified directly.

Notes

Logspace is equivalent to the code

>>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
... # doctest: +SKIP
>>> power(base, y).astype(dtype)
... # doctest: +SKIP

Examples

>>> np.logspace(2.0, 3.0, num=4)
array([ 100.        ,  215.443469  ,  464.15888336, 1000.        ])
>>> np.logspace(2.0, 3.0, num=4, endpoint=False)
array([100.        ,  177.827941  ,  316.22776602,  562.34132519])
>>> np.logspace(2.0, 3.0, num=4, base=2.0)
array([4.        ,  5.0396842 ,  6.34960421,  8.        ])

Graphical illustration:

>>> import matplotlib.pyplot as plt
>>> N = 10
>>> x1 = np.logspace(0.1, 1, N, endpoint=True)
>>> x2 = np.logspace(0.1, 1, N, endpoint=False)
>>> y = np.zeros(N)
>>> plt.plot(x1, y, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(x2, y + 0.5, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.ylim([-0.5, 1])
(-0.5, 1)
>>> plt.show()