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__all__ = ['logspace', 'linspace']
import numeric as _nx from numeric import array
def linspace(start, stop, num=50, endpoint=True, retstep=False): """ Return evenly spaced numbers over a specified interval.
Returns `num` evenly spaced samples, calculated over the interval [`start`, `stop` ].
The endpoint of the interval can optionally be excluded.
Parameters ---------- start : scalar The starting value of the sequence. stop : scalar 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. 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.
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 (only if `retstep` is True) Size of spacing between samples.
See Also -------- arange : Similiar to `linspace`, but uses a step size (instead of the number of samples). logspace : Samples uniformly distributed in log space.
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') >>> plt.plot(x2, y + 0.5, 'o') >>> plt.ylim([-0.5, 1]) >>> plt.show()
""" num = int(num) if num <= 0: return array([], float) if endpoint: if num == 1: return array([float(start)]) step = (stop-start)/float((num-1)) y = _nx.arange(0, num) * step + start y[-1] = stop else: step = (stop-start)/float(num) y = _nx.arange(0, num) * step + start if retstep: return y, step else: return y
def logspace(start,stop,num=50,endpoint=True,base=10.0): """ Return numbers spaced evenly on a log scale.
In linear space, the sequence starts at ``base ** start`` (`base` to the power of `start`) and ends with ``base ** stop`` (see `endpoint` below).
Parameters ---------- start : float ``base ** start`` is the starting value of the sequence. stop : float ``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 : float, 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.
Returns ------- samples : ndarray `num` samples, equally spaced on a log scale.
See Also -------- arange : Similiar 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.
Notes ----- Logspace is equivalent to the code
>>> y = linspace(start, stop, num=num, endpoint=endpoint) >>> power(base, y)
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') >>> plt.plot(x2, y + 0.5, 'o') >>> plt.ylim([-0.5, 1]) >>> plt.show()
""" y = linspace(start,stop,num=num,endpoint=endpoint) return _nx.power(base,y)
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