Coverage for /usr/lib/python3/dist-packages/numpy/core/function_base.py : 51%

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) 

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,) * delta.ndim) 

# 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([-1.00000000+0.j , -0.70710678+0.70710678j, 

0.00000000+1.j , 0.70710678+0.70710678j, 

1.00000000+0.j ]) 

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') 

>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o') 

>>> plt.axis([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_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. 

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. 

""" 

try: 

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()) 

except Exception: 

pass