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530 lines
19 KiB
530 lines
19 KiB
import functools
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import warnings
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import operator
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import types
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from . import numeric as _nx
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from .numeric import result_type, NaN, asanyarray, ndim
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from numpy.core.multiarray import add_docstring
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from numpy.core import overrides
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__all__ = ['logspace', 'linspace', 'geomspace']
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array_function_dispatch = functools.partial(
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overrides.array_function_dispatch, module='numpy')
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def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None,
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dtype=None, axis=None):
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return (start, stop)
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@array_function_dispatch(_linspace_dispatcher)
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def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None,
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axis=0):
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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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.. versionchanged:: 1.16.0
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Non-scalar `start` and `stop` are now supported.
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.. versionchanged:: 1.20.0
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Values are rounded towards ``-inf`` instead of ``0`` when an
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integer ``dtype`` is specified. The old behavior can
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still be obtained with ``np.linspace(start, stop, num).astype(int)``
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Parameters
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----------
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start : array_like
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The starting value of the sequence.
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stop : array_like
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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, the data type
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is inferred from `start` and `stop`. The inferred dtype will never be
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an integer; `float` is chosen even if the arguments would produce an
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array of integers.
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.. versionadded:: 1.9.0
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axis : int, optional
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The axis in the result to store the samples. Relevant only if start
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or stop are array-like. By default (0), the samples will be along a
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new axis inserted at the beginning. Use -1 to get an axis at the end.
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.. versionadded:: 1.16.0
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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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geomspace : Similar to `linspace`, but with numbers spaced evenly on a log
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scale (a geometric progression).
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logspace : Similar to `geomspace`, but with the end points specified as
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logarithms.
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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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num = operator.index(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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delta = stop - start
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y = _nx.arange(0, num, dtype=dt).reshape((-1,) + (1,) * ndim(delta))
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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 div > 0:
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step = delta / div
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if _nx.any(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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# sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0)
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# 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 axis != 0:
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y = _nx.moveaxis(y, 0, axis)
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if _nx.issubdtype(dtype, _nx.integer):
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_nx.floor(y, out=y)
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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_dispatcher(start, stop, num=None, endpoint=None, base=None,
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dtype=None, axis=None):
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return (start, stop)
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@array_function_dispatch(_logspace_dispatcher)
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def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None,
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axis=0):
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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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.. versionchanged:: 1.16.0
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Non-scalar `start` and `stop` are now supported.
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Parameters
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----------
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start : array_like
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``base ** start`` is the starting value of the sequence.
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stop : array_like
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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 : array_like, 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, the data type
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is inferred from `start` and `stop`. The inferred type will never be
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an integer; `float` is chosen even if the arguments would produce an
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array of integers.
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axis : int, optional
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The axis in the result to store the samples. Relevant only if start
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or stop are array-like. By default (0), the samples will be along a
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new axis inserted at the beginning. Use -1 to get an axis at the end.
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.. versionadded:: 1.16.0
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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, axis=axis)
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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, copy=False)
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def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None,
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axis=None):
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return (start, stop)
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@array_function_dispatch(_geomspace_dispatcher)
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def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0):
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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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.. versionchanged:: 1.16.0
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Non-scalar `start` and `stop` are now supported.
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Parameters
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----------
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start : array_like
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The starting value of the sequence.
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stop : array_like
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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, the data type
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is inferred from `start` and `stop`. The inferred dtype will never be
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an integer; `float` is chosen even if the arguments would produce an
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array of integers.
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axis : int, optional
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The axis in the result to store the samples. Relevant only if start
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or stop are array-like. By default (0), the samples will be along a
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new axis inserted at the beginning. Use -1 to get an axis at the end.
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.. versionadded:: 1.16.0
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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([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,
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6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j,
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1.00000000e+00+0.00000000e+00j])
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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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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
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[<matplotlib.lines.Line2D object at 0x...>]
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>>> plt.axis([0.5, 2000, 0, 3])
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[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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start = asanyarray(start)
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stop = asanyarray(stop)
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if _nx.any(start == 0) or _nx.any(stop == 0):
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raise ValueError('Geometric sequence cannot include zero')
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dt = result_type(start, stop, float(num), _nx.zeros((), dtype))
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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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# 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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# Copy since we may change things in-place further down.
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start = start.astype(dt, copy=True)
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stop = stop.astype(dt, copy=True)
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out_sign = _nx.ones(_nx.broadcast(start, stop).shape, dt)
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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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if _nx.issubdtype(dt, _nx.complexfloating):
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all_imag = (start.real == 0.) & (stop.real == 0.)
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if _nx.any(all_imag):
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start[all_imag] = start[all_imag].imag
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stop[all_imag] = stop[all_imag].imag
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out_sign[all_imag] = 1j
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both_negative = (_nx.sign(start) == -1) & (_nx.sign(stop) == -1)
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if _nx.any(both_negative):
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_nx.negative(start, out=start, where=both_negative)
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_nx.negative(stop, out=stop, where=both_negative)
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_nx.negative(out_sign, out=out_sign, where=both_negative)
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log_start = _nx.log10(start)
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log_stop = _nx.log10(stop)
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result = logspace(log_start, log_stop, num=num,
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endpoint=endpoint, base=10.0, dtype=dtype)
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# Make sure the endpoints match the start and stop arguments. This is
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# necessary because np.exp(np.log(x)) is not necessarily equal to x.
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if num > 0:
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result[0] = start
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if num > 1 and endpoint:
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result[-1] = stop
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result = out_sign * result
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if axis != 0:
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result = _nx.moveaxis(result, 0, axis)
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return result.astype(dtype, copy=False)
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def _needs_add_docstring(obj):
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"""
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Returns true if the only way to set the docstring of `obj` from python is
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via add_docstring.
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This function errs on the side of being overly conservative.
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"""
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Py_TPFLAGS_HEAPTYPE = 1 << 9
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if isinstance(obj, (types.FunctionType, types.MethodType, property)):
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return False
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if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE:
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return False
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return True
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def _add_docstring(obj, doc, warn_on_python):
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if warn_on_python and not _needs_add_docstring(obj):
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warnings.warn(
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"add_newdoc was used on a pure-python object {}. "
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"Prefer to attach it directly to the source."
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.format(obj),
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UserWarning,
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stacklevel=3)
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try:
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add_docstring(obj, doc)
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except Exception:
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pass
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def add_newdoc(place, obj, doc, warn_on_python=True):
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"""
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Add documentation to an existing object, typically one defined in C
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The purpose is to allow easier editing of the docstrings without requiring
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a re-compile. This exists primarily for internal use within numpy itself.
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Parameters
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----------
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place : str
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The absolute name of the module to import from
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obj : str
|
|
The name of the object to add documentation to, typically a class or
|
|
function name
|
|
doc : {str, Tuple[str, str], List[Tuple[str, str]]}
|
|
If a string, the documentation to apply to `obj`
|
|
|
|
If a tuple, then the first element is interpreted as an attribute of
|
|
`obj` and the second as the docstring to apply - ``(method, docstring)``
|
|
|
|
If a list, then each element of the list should be a tuple of length
|
|
two - ``[(method1, docstring1), (method2, docstring2), ...]``
|
|
warn_on_python : bool
|
|
If True, the default, emit `UserWarning` if this is used to attach
|
|
documentation to a pure-python object.
|
|
|
|
Notes
|
|
-----
|
|
This routine never raises an error if the docstring can't be written, but
|
|
will raise an error if the object being documented does not exist.
|
|
|
|
This routine cannot modify read-only docstrings, as appear
|
|
in new-style classes or built-in functions. Because this
|
|
routine never raises an error the caller must check manually
|
|
that the docstrings were changed.
|
|
|
|
Since this function grabs the ``char *`` from a c-level str object and puts
|
|
it into the ``tp_doc`` slot of the type of `obj`, it violates a number of
|
|
C-API best-practices, by:
|
|
|
|
- modifying a `PyTypeObject` after calling `PyType_Ready`
|
|
- calling `Py_INCREF` on the str and losing the reference, so the str
|
|
will never be released
|
|
|
|
If possible it should be avoided.
|
|
"""
|
|
new = getattr(__import__(place, globals(), {}, [obj]), obj)
|
|
if isinstance(doc, str):
|
|
_add_docstring(new, doc.strip(), warn_on_python)
|
|
elif isinstance(doc, tuple):
|
|
attr, docstring = doc
|
|
_add_docstring(getattr(new, attr), docstring.strip(), warn_on_python)
|
|
elif isinstance(doc, list):
|
|
for attr, docstring in doc:
|
|
_add_docstring(getattr(new, attr), docstring.strip(), warn_on_python)
|