471 lines
16 KiB
Python
471 lines
16 KiB
Python
|
from __future__ import division, absolute_import, print_function
|
||
|
|
||
|
import functools
|
||
|
import warnings
|
||
|
import operator
|
||
|
|
||
|
from . import numeric as _nx
|
||
|
from .numeric import (result_type, NaN, shares_memory, MAY_SHARE_BOUNDS,
|
||
|
TooHardError, asanyarray, ndim)
|
||
|
from numpy.core.multiarray import add_docstring
|
||
|
from numpy.core import overrides
|
||
|
|
||
|
__all__ = ['logspace', 'linspace', 'geomspace']
|
||
|
|
||
|
|
||
|
array_function_dispatch = functools.partial(
|
||
|
overrides.array_function_dispatch, module='numpy')
|
||
|
|
||
|
|
||
|
def _index_deprecate(i, stacklevel=2):
|
||
|
try:
|
||
|
i = operator.index(i)
|
||
|
except TypeError:
|
||
|
msg = ("object of type {} cannot be safely interpreted as "
|
||
|
"an integer.".format(type(i)))
|
||
|
i = int(i)
|
||
|
stacklevel += 1
|
||
|
warnings.warn(msg, DeprecationWarning, stacklevel=stacklevel)
|
||
|
return i
|
||
|
|
||
|
|
||
|
def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None,
|
||
|
dtype=None, axis=None):
|
||
|
return (start, stop)
|
||
|
|
||
|
|
||
|
@array_function_dispatch(_linspace_dispatcher)
|
||
|
def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None,
|
||
|
axis=0):
|
||
|
"""
|
||
|
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.
|
||
|
|
||
|
.. versionchanged:: 1.16.0
|
||
|
Non-scalar `start` and `stop` are now supported.
|
||
|
|
||
|
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, infer the data
|
||
|
type from the other input arguments.
|
||
|
|
||
|
.. versionadded:: 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.
|
||
|
|
||
|
.. versionadded:: 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()
|
||
|
|
||
|
"""
|
||
|
# 2016-02-25, 1.12
|
||
|
num = _index_deprecate(num)
|
||
|
if num < 0:
|
||
|
raise ValueError("Number of samples, %s, must be non-negative." % num)
|
||
|
div = (num - 1) if endpoint else num
|
||
|
|
||
|
# Convert float/complex array scalars to float, gh-3504
|
||
|
# and make sure one can use variables that have an __array_interface__, gh-6634
|
||
|
start = asanyarray(start) * 1.0
|
||
|
stop = asanyarray(stop) * 1.0
|
||
|
|
||
|
dt = result_type(start, stop, float(num))
|
||
|
if dtype is None:
|
||
|
dtype = dt
|
||
|
|
||
|
delta = stop - start
|
||
|
y = _nx.arange(0, num, dtype=dt).reshape((-1,) + (1,) * ndim(delta))
|
||
|
# In-place multiplication y *= delta/div is faster, but prevents the multiplicant
|
||
|
# from overriding what class is produced, and thus prevents, e.g. use of Quantities,
|
||
|
# see gh-7142. Hence, we multiply in place only for standard scalar types.
|
||
|
_mult_inplace = _nx.isscalar(delta)
|
||
|
if num > 1:
|
||
|
step = delta / div
|
||
|
if _nx.any(step == 0):
|
||
|
# Special handling for denormal numbers, gh-5437
|
||
|
y /= div
|
||
|
if _mult_inplace:
|
||
|
y *= delta
|
||
|
else:
|
||
|
y = y * delta
|
||
|
else:
|
||
|
if _mult_inplace:
|
||
|
y *= step
|
||
|
else:
|
||
|
y = y * step
|
||
|
else:
|
||
|
# 0 and 1 item long sequences have an undefined step
|
||
|
step = NaN
|
||
|
# Multiply with delta to allow possible override of output class.
|
||
|
y = y * delta
|
||
|
|
||
|
y += start
|
||
|
|
||
|
if endpoint and num > 1:
|
||
|
y[-1] = stop
|
||
|
|
||
|
if axis != 0:
|
||
|
y = _nx.moveaxis(y, 0, axis)
|
||
|
|
||
|
if retstep:
|
||
|
return y.astype(dtype, copy=False), step
|
||
|
else:
|
||
|
return y.astype(dtype, copy=False)
|
||
|
|
||
|
|
||
|
def _logspace_dispatcher(start, stop, num=None, endpoint=None, base=None,
|
||
|
dtype=None, axis=None):
|
||
|
return (start, stop)
|
||
|
|
||
|
|
||
|
@array_function_dispatch(_logspace_dispatcher)
|
||
|
def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None,
|
||
|
axis=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).
|
||
|
|
||
|
.. versionchanged:: 1.16.0
|
||
|
Non-scalar `start` and `stop` are now supported.
|
||
|
|
||
|
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 : 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.
|
||
|
dtype : dtype
|
||
|
The type of the output array. If `dtype` is not given, infer the data
|
||
|
type from the other input arguments.
|
||
|
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.
|
||
|
|
||
|
.. versionadded:: 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()
|
||
|
|
||
|
"""
|
||
|
y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis)
|
||
|
if dtype is None:
|
||
|
return _nx.power(base, y)
|
||
|
return _nx.power(base, y).astype(dtype, copy=False)
|
||
|
|
||
|
|
||
|
def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None,
|
||
|
axis=None):
|
||
|
return (start, stop)
|
||
|
|
||
|
|
||
|
@array_function_dispatch(_geomspace_dispatcher)
|
||
|
def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0):
|
||
|
"""
|
||
|
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.
|
||
|
|
||
|
.. versionchanged:: 1.16.0
|
||
|
Non-scalar `start` and `stop` are now supported.
|
||
|
|
||
|
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, infer the data
|
||
|
type from the other input arguments.
|
||
|
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.
|
||
|
|
||
|
.. versionadded:: 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()
|
||
|
|
||
|
"""
|
||
|
start = asanyarray(start)
|
||
|
stop = asanyarray(stop)
|
||
|
if _nx.any(start == 0) or _nx.any(stop == 0):
|
||
|
raise ValueError('Geometric sequence cannot include zero')
|
||
|
|
||
|
dt = result_type(start, stop, float(num), _nx.zeros((), dtype))
|
||
|
if dtype is None:
|
||
|
dtype = dt
|
||
|
else:
|
||
|
# complex to dtype('complex128'), for instance
|
||
|
dtype = _nx.dtype(dtype)
|
||
|
|
||
|
# Promote both arguments to the same dtype in case, for instance, one is
|
||
|
# complex and another is negative and log would produce NaN otherwise.
|
||
|
# Copy since we may change things in-place further down.
|
||
|
start = start.astype(dt, copy=True)
|
||
|
stop = stop.astype(dt, copy=True)
|
||
|
|
||
|
out_sign = _nx.ones(_nx.broadcast(start, stop).shape, dt)
|
||
|
# Avoid negligible real or imaginary parts in output by rotating to
|
||
|
# positive real, calculating, then undoing rotation
|
||
|
if _nx.issubdtype(dt, _nx.complexfloating):
|
||
|
all_imag = (start.real == 0.) & (stop.real == 0.)
|
||
|
if _nx.any(all_imag):
|
||
|
start[all_imag] = start[all_imag].imag
|
||
|
stop[all_imag] = stop[all_imag].imag
|
||
|
out_sign[all_imag] = 1j
|
||
|
|
||
|
both_negative = (_nx.sign(start) == -1) & (_nx.sign(stop) == -1)
|
||
|
if _nx.any(both_negative):
|
||
|
_nx.negative(start, out=start, where=both_negative)
|
||
|
_nx.negative(stop, out=stop, where=both_negative)
|
||
|
_nx.negative(out_sign, out=out_sign, where=both_negative)
|
||
|
|
||
|
log_start = _nx.log10(start)
|
||
|
log_stop = _nx.log10(stop)
|
||
|
result = out_sign * logspace(log_start, log_stop, num=num,
|
||
|
endpoint=endpoint, base=10.0, dtype=dtype)
|
||
|
if axis != 0:
|
||
|
result = _nx.moveaxis(result, 0, axis)
|
||
|
|
||
|
return result.astype(dtype, copy=False)
|
||
|
|
||
|
|
||
|
#always succeed
|
||
|
def _add_docstring(obj, doc):
|
||
|
try:
|
||
|
add_docstring(obj, doc)
|
||
|
except Exception:
|
||
|
pass
|
||
|
|
||
|
|
||
|
def add_newdoc(place, obj, doc):
|
||
|
"""
|
||
|
Adds documentation to obj which is in module place.
|
||
|
|
||
|
If doc is a string add it to obj as a docstring
|
||
|
|
||
|
If doc is a tuple, then the first element is interpreted as
|
||
|
an attribute of obj and the second as the docstring
|
||
|
(method, docstring)
|
||
|
|
||
|
If doc is a list, then each element of the list should be a
|
||
|
sequence of length two --> [(method1, docstring1),
|
||
|
(method2, docstring2), ...]
|
||
|
|
||
|
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.
|
||
|
"""
|
||
|
new = getattr(__import__(place, globals(), {}, [obj]), obj)
|
||
|
if isinstance(doc, str):
|
||
|
_add_docstring(new, doc.strip())
|
||
|
elif isinstance(doc, tuple):
|
||
|
_add_docstring(getattr(new, doc[0]), doc[1].strip())
|
||
|
elif isinstance(doc, list):
|
||
|
for val in doc:
|
||
|
_add_docstring(getattr(new, val[0]), val[1].strip())
|