import functools
import warnings
import operator
import types
import numpy as np
from . import numeric as _nx
from .numeric import result_type, NaN, 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 _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.
.. versionchanged:: 1.20.0
Values are rounded towards ``-inf`` instead of ``0`` when an
integer ``dtype`` is specified. The old behavior can
still be obtained with ``np.linspace(start, stop, num).astype(int)``
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.
.. 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.
:ref:`how-to-partition`
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()
"""
num = operator.index(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
integer_dtype = False
else:
integer_dtype = _nx.issubdtype(dtype, _nx.integer)
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.
if div > 0:
_mult_inplace = _nx.isscalar(delta)
step = delta / div
any_step_zero = (
step == 0 if _mult_inplace else _nx.asanyarray(step == 0).any())
if any_step_zero:
# 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:
# sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0)
# 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 integer_dtype:
_nx.floor(y, out=y)
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, base)
@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.
.. versionchanged:: 1.25.0
Non-scalar 'base` is 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 : 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,
stop, or base 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.
:ref:`how-to-partition`
Notes
-----
If base is a scalar, 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. ])
>>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1)
array([[ 4. , 5.0396842 , 6.34960421, 8. ],
[ 9. , 12.98024613, 18.72075441, 27. ]])
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()
"""
ndmax = np.broadcast(start, stop, base).ndim
start, stop, base = (
np.array(a, copy=False, subok=True, ndmin=ndmax)
for a in (start, stop, base)
)
y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis)
base = np.expand_dims(base, 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, 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.
.. 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.
:ref:`how-to-partition`
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 = logspace(log_start, log_stop, num=num,
endpoint=endpoint, base=10.0, dtype=dtype)
# Make sure the endpoints match the start and stop arguments. This is
# necessary because np.exp(np.log(x)) is not necessarily equal to x.
if num > 0:
result[0] = start
if num > 1 and endpoint:
result[-1] = stop
result = out_sign * result
if axis != 0:
result = _nx.moveaxis(result, 0, axis)
return result.astype(dtype, copy=False)
def _needs_add_docstring(obj):
"""
Returns true if the only way to set the docstring of `obj` from python is
via add_docstring.
This function errs on the side of being overly conservative.
"""
Py_TPFLAGS_HEAPTYPE = 1 << 9
if isinstance(obj, (types.FunctionType, types.MethodType, property)):
return False
if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE:
return False
return True
def _add_docstring(obj, doc, warn_on_python):
if warn_on_python and not _needs_add_docstring(obj):
warnings.warn(
"add_newdoc was used on a pure-python object {}. "
"Prefer to attach it directly to the source."
.format(obj),
UserWarning,
stacklevel=3)
try:
add_docstring(obj, doc)
except Exception:
pass
def add_newdoc(place, obj, doc, warn_on_python=True):
"""
Add documentation to an existing object, typically one defined in C
The purpose is to allow easier editing of the docstrings without requiring
a re-compile. This exists primarily for internal use within numpy itself.
Parameters
----------
place : str
The absolute name of the module to import from
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)