359 lines
12 KiB
Python
359 lines
12 KiB
Python
from __future__ import division, absolute_import, print_function
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import warnings
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import operator
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from . import numeric as _nx
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from .numeric import (result_type, NaN, shares_memory, MAY_SHARE_BOUNDS,
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TooHardError,asanyarray)
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__all__ = ['logspace', 'linspace', 'geomspace']
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def _index_deprecate(i, stacklevel=2):
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try:
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i = operator.index(i)
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except TypeError:
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msg = ("object of type {} cannot be safely interpreted as "
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"an integer.".format(type(i)))
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i = int(i)
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stacklevel += 1
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warnings.warn(msg, DeprecationWarning, stacklevel=stacklevel)
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return i
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def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None):
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"""
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Return evenly spaced numbers over a specified interval.
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Returns `num` evenly spaced samples, calculated over the
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interval [`start`, `stop`].
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The endpoint of the interval can optionally be excluded.
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Parameters
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----------
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start : scalar
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The starting value of the sequence.
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stop : scalar
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The end value of the sequence, unless `endpoint` is set to False.
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In that case, the sequence consists of all but the last of ``num + 1``
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evenly spaced samples, so that `stop` is excluded. Note that the step
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size changes when `endpoint` is False.
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num : int, optional
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Number of samples to generate. Default is 50. Must be non-negative.
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endpoint : bool, optional
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If True, `stop` is the last sample. Otherwise, it is not included.
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Default is True.
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retstep : bool, optional
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If True, return (`samples`, `step`), where `step` is the spacing
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between samples.
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dtype : dtype, optional
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The type of the output array. If `dtype` is not given, infer the data
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type from the other input arguments.
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.. versionadded:: 1.9.0
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Returns
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-------
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samples : ndarray
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There are `num` equally spaced samples in the closed interval
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``[start, stop]`` or the half-open interval ``[start, stop)``
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(depending on whether `endpoint` is True or False).
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step : float, optional
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Only returned if `retstep` is True
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Size of spacing between samples.
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See Also
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--------
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arange : Similar to `linspace`, but uses a step size (instead of the
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number of samples).
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logspace : Samples uniformly distributed in log space.
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Examples
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--------
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>>> np.linspace(2.0, 3.0, num=5)
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array([ 2. , 2.25, 2.5 , 2.75, 3. ])
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>>> np.linspace(2.0, 3.0, num=5, endpoint=False)
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array([ 2. , 2.2, 2.4, 2.6, 2.8])
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>>> np.linspace(2.0, 3.0, num=5, retstep=True)
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(array([ 2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)
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Graphical illustration:
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>>> import matplotlib.pyplot as plt
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>>> N = 8
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>>> y = np.zeros(N)
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>>> x1 = np.linspace(0, 10, N, endpoint=True)
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>>> x2 = np.linspace(0, 10, N, endpoint=False)
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>>> plt.plot(x1, y, 'o')
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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.plot(x2, y + 0.5, 'o')
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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.ylim([-0.5, 1])
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(-0.5, 1)
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>>> plt.show()
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"""
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# 2016-02-25, 1.12
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num = _index_deprecate(num)
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if num < 0:
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raise ValueError("Number of samples, %s, must be non-negative." % num)
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div = (num - 1) if endpoint else num
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# Convert float/complex array scalars to float, gh-3504
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# and make sure one can use variables that have an __array_interface__, gh-6634
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start = asanyarray(start) * 1.0
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stop = asanyarray(stop) * 1.0
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dt = result_type(start, stop, float(num))
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if dtype is None:
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dtype = dt
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y = _nx.arange(0, num, dtype=dt)
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delta = stop - start
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# In-place multiplication y *= delta/div is faster, but prevents the multiplicant
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# from overriding what class is produced, and thus prevents, e.g. use of Quantities,
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# see gh-7142. Hence, we multiply in place only for standard scalar types.
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_mult_inplace = _nx.isscalar(delta)
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if num > 1:
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step = delta / div
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if step == 0:
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# Special handling for denormal numbers, gh-5437
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y /= div
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if _mult_inplace:
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y *= delta
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else:
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y = y * delta
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else:
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if _mult_inplace:
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y *= step
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else:
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y = y * step
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else:
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# 0 and 1 item long sequences have an undefined step
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step = NaN
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# Multiply with delta to allow possible override of output class.
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y = y * delta
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y += start
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if endpoint and num > 1:
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y[-1] = stop
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if retstep:
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return y.astype(dtype, copy=False), step
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else:
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return y.astype(dtype, copy=False)
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def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None):
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"""
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Return numbers spaced evenly on a log scale.
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In linear space, the sequence starts at ``base ** start``
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(`base` to the power of `start`) and ends with ``base ** stop``
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(see `endpoint` below).
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Parameters
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----------
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start : float
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``base ** start`` is the starting value of the sequence.
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stop : float
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``base ** stop`` is the final value of the sequence, unless `endpoint`
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is False. In that case, ``num + 1`` values are spaced over the
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interval in log-space, of which all but the last (a sequence of
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length `num`) are returned.
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num : integer, optional
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Number of samples to generate. Default is 50.
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endpoint : boolean, optional
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If true, `stop` is the last sample. Otherwise, it is not included.
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Default is True.
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base : float, optional
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The base of the log space. The step size between the elements in
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``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
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Default is 10.0.
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dtype : dtype
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The type of the output array. If `dtype` is not given, infer the data
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type from the other input arguments.
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Returns
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-------
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samples : ndarray
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`num` samples, equally spaced on a log scale.
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See Also
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--------
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arange : Similar to linspace, with the step size specified instead of the
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number of samples. Note that, when used with a float endpoint, the
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endpoint may or may not be included.
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linspace : Similar to logspace, but with the samples uniformly distributed
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in linear space, instead of log space.
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geomspace : Similar to logspace, but with endpoints specified directly.
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Notes
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-----
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Logspace is equivalent to the code
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>>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
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... # doctest: +SKIP
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>>> power(base, y).astype(dtype)
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... # doctest: +SKIP
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Examples
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--------
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>>> np.logspace(2.0, 3.0, num=4)
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array([ 100. , 215.443469 , 464.15888336, 1000. ])
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>>> np.logspace(2.0, 3.0, num=4, endpoint=False)
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array([ 100. , 177.827941 , 316.22776602, 562.34132519])
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>>> np.logspace(2.0, 3.0, num=4, base=2.0)
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array([ 4. , 5.0396842 , 6.34960421, 8. ])
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Graphical illustration:
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>>> import matplotlib.pyplot as plt
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>>> N = 10
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>>> x1 = np.logspace(0.1, 1, N, endpoint=True)
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>>> x2 = np.logspace(0.1, 1, N, endpoint=False)
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>>> y = np.zeros(N)
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>>> plt.plot(x1, y, 'o')
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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.plot(x2, y + 0.5, 'o')
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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.ylim([-0.5, 1])
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(-0.5, 1)
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>>> plt.show()
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"""
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y = linspace(start, stop, num=num, endpoint=endpoint)
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if dtype is None:
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return _nx.power(base, y)
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return _nx.power(base, y).astype(dtype)
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def geomspace(start, stop, num=50, endpoint=True, dtype=None):
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"""
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Return numbers spaced evenly on a log scale (a geometric progression).
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This is similar to `logspace`, but with endpoints specified directly.
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Each output sample is a constant multiple of the previous.
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Parameters
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----------
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start : scalar
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The starting value of the sequence.
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stop : scalar
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The final value of the sequence, unless `endpoint` is False.
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In that case, ``num + 1`` values are spaced over the
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interval in log-space, of which all but the last (a sequence of
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length `num`) are returned.
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num : integer, optional
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Number of samples to generate. Default is 50.
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endpoint : boolean, optional
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If true, `stop` is the last sample. Otherwise, it is not included.
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Default is True.
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dtype : dtype
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The type of the output array. If `dtype` is not given, infer the data
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type from the other input arguments.
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Returns
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-------
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samples : ndarray
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`num` samples, equally spaced on a log scale.
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See Also
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--------
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logspace : Similar to geomspace, but with endpoints specified using log
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and base.
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linspace : Similar to geomspace, but with arithmetic instead of geometric
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progression.
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arange : Similar to linspace, with the step size specified instead of the
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number of samples.
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Notes
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-----
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If the inputs or dtype are complex, the output will follow a logarithmic
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spiral in the complex plane. (There are an infinite number of spirals
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passing through two points; the output will follow the shortest such path.)
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Examples
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--------
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>>> np.geomspace(1, 1000, num=4)
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array([ 1., 10., 100., 1000.])
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>>> np.geomspace(1, 1000, num=3, endpoint=False)
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array([ 1., 10., 100.])
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>>> np.geomspace(1, 1000, num=4, endpoint=False)
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array([ 1. , 5.62341325, 31.6227766 , 177.827941 ])
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>>> np.geomspace(1, 256, num=9)
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array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.])
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Note that the above may not produce exact integers:
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>>> np.geomspace(1, 256, num=9, dtype=int)
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array([ 1, 2, 4, 7, 16, 32, 63, 127, 256])
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>>> np.around(np.geomspace(1, 256, num=9)).astype(int)
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array([ 1, 2, 4, 8, 16, 32, 64, 128, 256])
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Negative, decreasing, and complex inputs are allowed:
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>>> np.geomspace(1000, 1, num=4)
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array([ 1000., 100., 10., 1.])
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>>> np.geomspace(-1000, -1, num=4)
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array([-1000., -100., -10., -1.])
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>>> np.geomspace(1j, 1000j, num=4) # Straight line
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array([ 0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j])
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>>> np.geomspace(-1+0j, 1+0j, num=5) # Circle
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array([-1.00000000+0.j , -0.70710678+0.70710678j,
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0.00000000+1.j , 0.70710678+0.70710678j,
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1.00000000+0.j ])
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Graphical illustration of ``endpoint`` parameter:
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>>> import matplotlib.pyplot as plt
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>>> N = 10
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>>> y = np.zeros(N)
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>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
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>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
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>>> plt.axis([0.5, 2000, 0, 3])
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>>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
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>>> plt.show()
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"""
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if start == 0 or stop == 0:
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raise ValueError('Geometric sequence cannot include zero')
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dt = result_type(start, stop, float(num))
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if dtype is None:
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dtype = dt
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else:
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# complex to dtype('complex128'), for instance
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dtype = _nx.dtype(dtype)
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# Avoid negligible real or imaginary parts in output by rotating to
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# positive real, calculating, then undoing rotation
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out_sign = 1
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if start.real == stop.real == 0:
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start, stop = start.imag, stop.imag
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out_sign = 1j * out_sign
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if _nx.sign(start) == _nx.sign(stop) == -1:
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start, stop = -start, -stop
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out_sign = -out_sign
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# Promote both arguments to the same dtype in case, for instance, one is
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# complex and another is negative and log would produce NaN otherwise
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start = start + (stop - stop)
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stop = stop + (start - start)
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if _nx.issubdtype(dtype, _nx.complexfloating):
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start = start + 0j
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stop = stop + 0j
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log_start = _nx.log10(start)
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log_stop = _nx.log10(stop)
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result = out_sign * logspace(log_start, log_stop, num=num,
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endpoint=endpoint, base=10.0, dtype=dtype)
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return result.astype(dtype)
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