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# Accessing collections abstract classes from collections # has been deprecated since Python 3.3 except ImportError: import collections as collections_abc
_fastCopyAndTranspose as fastCopyAndTranspose, ALLOW_THREADS, BUFSIZE, CLIP, MAXDIMS, MAY_SHARE_BOUNDS, MAY_SHARE_EXACT, RAISE, WRAP, arange, array, broadcast, can_cast, compare_chararrays, concatenate, copyto, dot, dtype, empty, empty_like, flatiter, frombuffer, fromfile, fromiter, fromstring, inner, int_asbuffer, lexsort, matmul, may_share_memory, min_scalar_type, ndarray, nditer, nested_iters, promote_types, putmask, result_type, set_numeric_ops, shares_memory, vdot, where, zeros, normalize_axis_index) from .multiarray import newbuffer, getbuffer
ERR_IGNORE, ERR_WARN, ERR_RAISE, ERR_CALL, ERR_PRINT, ERR_LOG, ERR_DEFAULT, PINF, NAN)
else: import pickle else: import cPickle as pickle import __builtin__ as builtins
overrides.array_function_dispatch, module='numpy')
# NumPy 1.15.0, 2017-12-10 warnings.warn( "np.core.numeric.loads is deprecated, use pickle.loads instead", DeprecationWarning, stacklevel=2) return pickle.loads(*args, **kwargs)
'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc', 'arange', 'array', 'zeros', 'count_nonzero', 'empty', 'broadcast', 'dtype', 'fromstring', 'fromfile', 'frombuffer', 'int_asbuffer', 'where', 'argwhere', 'copyto', 'concatenate', 'fastCopyAndTranspose', 'lexsort', 'set_numeric_ops', 'can_cast', 'promote_types', 'min_scalar_type', 'result_type', 'asarray', 'asanyarray', 'ascontiguousarray', 'asfortranarray', 'isfortran', 'empty_like', 'zeros_like', 'ones_like', 'correlate', 'convolve', 'inner', 'dot', 'outer', 'vdot', 'roll', 'rollaxis', 'moveaxis', 'cross', 'tensordot', 'little_endian', 'require', 'fromiter', 'array_equal', 'array_equiv', 'indices', 'fromfunction', 'isclose', 'load', 'loads', 'isscalar', 'binary_repr', 'base_repr', 'ones', 'identity', 'allclose', 'compare_chararrays', 'putmask', 'seterr', 'geterr', 'setbufsize', 'getbufsize', 'seterrcall', 'geterrcall', 'errstate', 'flatnonzero', 'Inf', 'inf', 'infty', 'Infinity', 'nan', 'NaN', 'False_', 'True_', 'bitwise_not', 'CLIP', 'RAISE', 'WRAP', 'MAXDIMS', 'BUFSIZE', 'ALLOW_THREADS', 'ComplexWarning', 'full', 'full_like', 'matmul', 'shares_memory', 'may_share_memory', 'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'TooHardError', 'AxisError']
__all__.extend(['getbuffer', 'newbuffer'])
""" The warning raised when casting a complex dtype to a real dtype.
As implemented, casting a complex number to a real discards its imaginary part, but this behavior may not be what the user actually wants.
"""
return (a,)
""" Return an array of zeros with the same shape and type as a given array.
Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result.
.. versionadded:: 1.6.0 order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible.
.. versionadded:: 1.6.0 subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True.
Returns ------- out : ndarray Array of zeros with the same shape and type as `a`.
See Also -------- empty_like : Return an empty array with shape and type of input. ones_like : Return an array of ones with shape and type of input. full_like : Return a new array with shape of input filled with value. zeros : Return a new array setting values to zero.
Examples -------- >>> x = np.arange(6) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.zeros_like(x) array([[0, 0, 0], [0, 0, 0]])
>>> y = np.arange(3, dtype=float) >>> y array([ 0., 1., 2.]) >>> np.zeros_like(y) array([ 0., 0., 0.])
""" # needed instead of a 0 to get same result as zeros for for string dtypes
""" Return a new array of given shape and type, filled with ones.
Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional, default: C Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory.
Returns ------- out : ndarray Array of ones with the given shape, dtype, and order.
See Also -------- ones_like : Return an array of ones with shape and type of input. empty : Return a new uninitialized array. zeros : Return a new array setting values to zero. full : Return a new array of given shape filled with value.
Examples -------- >>> np.ones(5) array([ 1., 1., 1., 1., 1.])
>>> np.ones((5,), dtype=int) array([1, 1, 1, 1, 1])
>>> np.ones((2, 1)) array([[ 1.], [ 1.]])
>>> s = (2,2) >>> np.ones(s) array([[ 1., 1.], [ 1., 1.]])
"""
return (a,)
""" Return an array of ones with the same shape and type as a given array.
Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result.
.. versionadded:: 1.6.0 order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible.
.. versionadded:: 1.6.0 subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True.
Returns ------- out : ndarray Array of ones with the same shape and type as `a`.
See Also -------- empty_like : Return an empty array with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full_like : Return a new array with shape of input filled with value. ones : Return a new array setting values to one.
Examples -------- >>> x = np.arange(6) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.ones_like(x) array([[1, 1, 1], [1, 1, 1]])
>>> y = np.arange(3, dtype=float) >>> y array([ 0., 1., 2.]) >>> np.ones_like(y) array([ 1., 1., 1.])
""" res = empty_like(a, dtype=dtype, order=order, subok=subok) multiarray.copyto(res, 1, casting='unsafe') return res
""" Return a new array of given shape and type, filled with `fill_value`.
Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. fill_value : scalar Fill value. dtype : data-type, optional The desired data-type for the array The default, `None`, means `np.array(fill_value).dtype`. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory.
Returns ------- out : ndarray Array of `fill_value` with the given shape, dtype, and order.
See Also -------- full_like : Return a new array with shape of input filled with value. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero.
Examples -------- >>> np.full((2, 2), np.inf) array([[ inf, inf], [ inf, inf]]) >>> np.full((2, 2), 10) array([[10, 10], [10, 10]])
"""
return (a,)
""" Return a full array with the same shape and type as a given array.
Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. fill_value : scalar Fill value. dtype : data-type, optional Overrides the data type of the result. order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True.
Returns ------- out : ndarray Array of `fill_value` with the same shape and type as `a`.
See Also -------- empty_like : Return an empty array with shape and type of input. ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full : Return a new array of given shape filled with value.
Examples -------- >>> x = np.arange(6, dtype=int) >>> np.full_like(x, 1) array([1, 1, 1, 1, 1, 1]) >>> np.full_like(x, 0.1) array([0, 0, 0, 0, 0, 0]) >>> np.full_like(x, 0.1, dtype=np.double) array([ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) >>> np.full_like(x, np.nan, dtype=np.double) array([ nan, nan, nan, nan, nan, nan])
>>> y = np.arange(6, dtype=np.double) >>> np.full_like(y, 0.1) array([ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
"""
return (a,)
""" Counts the number of non-zero values in the array ``a``.
The word "non-zero" is in reference to the Python 2.x built-in method ``__nonzero__()`` (renamed ``__bool__()`` in Python 3.x) of Python objects that tests an object's "truthfulness". For example, any number is considered truthful if it is nonzero, whereas any string is considered truthful if it is not the empty string. Thus, this function (recursively) counts how many elements in ``a`` (and in sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()`` method evaluated to ``True``.
Parameters ---------- a : array_like The array for which to count non-zeros. axis : int or tuple, optional Axis or tuple of axes along which to count non-zeros. Default is None, meaning that non-zeros will be counted along a flattened version of ``a``.
.. versionadded:: 1.12.0
Returns ------- count : int or array of int Number of non-zero values in the array along a given axis. Otherwise, the total number of non-zero values in the array is returned.
See Also -------- nonzero : Return the coordinates of all the non-zero values.
Examples -------- >>> np.count_nonzero(np.eye(4)) 4 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]]) 5 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=0) array([1, 1, 1, 1, 1]) >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=1) array([2, 3])
"""
a = asanyarray(a)
# TODO: this works around .astype(bool) not working properly (gh-9847) if np.issubdtype(a.dtype, np.character): a_bool = a != a.dtype.type() else: a_bool = a.astype(np.bool_, copy=False)
return a_bool.sum(axis=axis, dtype=np.intp)
"""Convert the input to an array.
Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major (C-style) or column-major (Fortran-style) memory representation. Defaults to 'C'.
Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray with matching dtype and order. If `a` is a subclass of ndarray, a base class ndarray is returned.
See Also -------- asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions.
Examples -------- Convert a list into an array:
>>> a = [1, 2] >>> np.asarray(a) array([1, 2])
Existing arrays are not copied:
>>> a = np.array([1, 2]) >>> np.asarray(a) is a True
If `dtype` is set, array is copied only if dtype does not match:
>>> a = np.array([1, 2], dtype=np.float32) >>> np.asarray(a, dtype=np.float32) is a True >>> np.asarray(a, dtype=np.float64) is a False
Contrary to `asanyarray`, ndarray subclasses are not passed through:
>>> issubclass(np.recarray, np.ndarray) True >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) >>> np.asarray(a) is a False >>> np.asanyarray(a) is a True
"""
"""Convert the input to an ndarray, but pass ndarray subclasses through.
Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes scalars, lists, lists of tuples, tuples, tuples of tuples, tuples of lists, and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major (C-style) or column-major (Fortran-style) memory representation. Defaults to 'C'.
Returns ------- out : ndarray or an ndarray subclass Array interpretation of `a`. If `a` is an ndarray or a subclass of ndarray, it is returned as-is and no copy is performed.
See Also -------- asarray : Similar function which always returns ndarrays. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions.
Examples -------- Convert a list into an array:
>>> a = [1, 2] >>> np.asanyarray(a) array([1, 2])
Instances of `ndarray` subclasses are passed through as-is:
>>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) >>> np.asanyarray(a) is a True
"""
""" Return a contiguous array (ndim >= 1) in memory (C order).
Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional Data-type of returned array.
Returns ------- out : ndarray Contiguous array of same shape and content as `a`, with type `dtype` if specified.
See Also -------- asfortranarray : Convert input to an ndarray with column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array.
Examples -------- >>> x = np.arange(6).reshape(2,3) >>> np.ascontiguousarray(x, dtype=np.float32) array([[ 0., 1., 2.], [ 3., 4., 5.]], dtype=float32) >>> x.flags['C_CONTIGUOUS'] True
Note: This function returns an array with at least one-dimension (1-d) so it will not preserve 0-d arrays.
""" return array(a, dtype, copy=False, order='C', ndmin=1)
""" Return an array (ndim >= 1) laid out in Fortran order in memory.
Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional By default, the data-type is inferred from the input data.
Returns ------- out : ndarray The input `a` in Fortran, or column-major, order.
See Also -------- ascontiguousarray : Convert input to a contiguous (C order) array. asanyarray : Convert input to an ndarray with either row or column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array.
Examples -------- >>> x = np.arange(6).reshape(2,3) >>> y = np.asfortranarray(x) >>> x.flags['F_CONTIGUOUS'] False >>> y.flags['F_CONTIGUOUS'] True
Note: This function returns an array with at least one-dimension (1-d) so it will not preserve 0-d arrays.
""" return array(a, dtype, copy=False, order='F', ndmin=1)
""" Return an ndarray of the provided type that satisfies requirements.
This function is useful to be sure that an array with the correct flags is returned for passing to compiled code (perhaps through ctypes).
Parameters ---------- a : array_like The object to be converted to a type-and-requirement-satisfying array. dtype : data-type The required data-type. If None preserve the current dtype. If your application requires the data to be in native byteorder, include a byteorder specification as a part of the dtype specification. requirements : str or list of str The requirements list can be any of the following
* 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array * 'ALIGNED' ('A') - ensure a data-type aligned array * 'WRITEABLE' ('W') - ensure a writable array * 'OWNDATA' ('O') - ensure an array that owns its own data * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass
See Also -------- asarray : Convert input to an ndarray. asanyarray : Convert to an ndarray, but pass through ndarray subclasses. ascontiguousarray : Convert input to a contiguous array. asfortranarray : Convert input to an ndarray with column-major memory order. ndarray.flags : Information about the memory layout of the array.
Notes ----- The returned array will be guaranteed to have the listed requirements by making a copy if needed.
Examples -------- >>> x = np.arange(6).reshape(2,3) >>> x.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : False WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False
>>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F']) >>> y.flags C_CONTIGUOUS : False F_CONTIGUOUS : True OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False
""" possible_flags = {'C': 'C', 'C_CONTIGUOUS': 'C', 'CONTIGUOUS': 'C', 'F': 'F', 'F_CONTIGUOUS': 'F', 'FORTRAN': 'F', 'A': 'A', 'ALIGNED': 'A', 'W': 'W', 'WRITEABLE': 'W', 'O': 'O', 'OWNDATA': 'O', 'E': 'E', 'ENSUREARRAY': 'E'} if not requirements: return asanyarray(a, dtype=dtype) else: requirements = {possible_flags[x.upper()] for x in requirements}
if 'E' in requirements: requirements.remove('E') subok = False else: subok = True
order = 'A' if requirements >= {'C', 'F'}: raise ValueError('Cannot specify both "C" and "F" order') elif 'F' in requirements: order = 'F' requirements.remove('F') elif 'C' in requirements: order = 'C' requirements.remove('C')
arr = array(a, dtype=dtype, order=order, copy=False, subok=subok)
for prop in requirements: if not arr.flags[prop]: arr = arr.copy(order) break return arr
def isfortran(a): """ Returns True if the array is Fortran contiguous but *not* C contiguous.
This function is obsolete and, because of changes due to relaxed stride checking, its return value for the same array may differ for versions of NumPy >= 1.10.0 and previous versions. If you only want to check if an array is Fortran contiguous use ``a.flags.f_contiguous`` instead.
Parameters ---------- a : ndarray Input array.
Examples --------
np.array allows to specify whether the array is written in C-contiguous order (last index varies the fastest), or FORTRAN-contiguous order in memory (first index varies the fastest).
>>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False
>>> b = np.array([[1, 2, 3], [4, 5, 6]], order='FORTRAN') >>> b array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(b) True
The transpose of a C-ordered array is a FORTRAN-ordered array.
>>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False >>> b = a.T >>> b array([[1, 4], [2, 5], [3, 6]]) >>> np.isfortran(b) True
C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.
>>> np.isfortran(np.array([1, 2], order='FORTRAN')) False
""" return a.flags.fnc
return (a,)
def argwhere(a): """ Find the indices of array elements that are non-zero, grouped by element.
Parameters ---------- a : array_like Input data.
Returns ------- index_array : ndarray Indices of elements that are non-zero. Indices are grouped by element.
See Also -------- where, nonzero
Notes ----- ``np.argwhere(a)`` is the same as ``np.transpose(np.nonzero(a))``.
The output of ``argwhere`` is not suitable for indexing arrays. For this purpose use ``nonzero(a)`` instead.
Examples -------- >>> x = np.arange(6).reshape(2,3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.argwhere(x>1) array([[0, 2], [1, 0], [1, 1], [1, 2]])
""" return transpose(nonzero(a))
return (a,)
def flatnonzero(a): """ Return indices that are non-zero in the flattened version of a.
This is equivalent to np.nonzero(np.ravel(a))[0].
Parameters ---------- a : array_like Input data.
Returns ------- res : ndarray Output array, containing the indices of the elements of `a.ravel()` that are non-zero.
See Also -------- nonzero : Return the indices of the non-zero elements of the input array. ravel : Return a 1-D array containing the elements of the input array.
Examples -------- >>> x = np.arange(-2, 3) >>> x array([-2, -1, 0, 1, 2]) >>> np.flatnonzero(x) array([0, 1, 3, 4])
Use the indices of the non-zero elements as an index array to extract these elements:
>>> x.ravel()[np.flatnonzero(x)] array([-2, -1, 1, 2])
""" return np.nonzero(np.ravel(a))[0]
's': 1, 'f': 2}
return mode
return (a, v)
""" Cross-correlation of two 1-dimensional sequences.
This function computes the correlation as generally defined in signal processing texts::
c_{av}[k] = sum_n a[n+k] * conj(v[n])
with a and v sequences being zero-padded where necessary and conj being the conjugate.
Parameters ---------- a, v : array_like Input sequences. mode : {'valid', 'same', 'full'}, optional Refer to the `convolve` docstring. Note that the default is 'valid', unlike `convolve`, which uses 'full'. old_behavior : bool `old_behavior` was removed in NumPy 1.10. If you need the old behavior, use `multiarray.correlate`.
Returns ------- out : ndarray Discrete cross-correlation of `a` and `v`.
See Also -------- convolve : Discrete, linear convolution of two one-dimensional sequences. multiarray.correlate : Old, no conjugate, version of correlate.
Notes ----- The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is::
c'_{av}[k] = sum_n a[n] conj(v[n+k])
which is related to ``c_{av}[k]`` by ``c'_{av}[k] = c_{av}[-k]``.
Examples -------- >>> np.correlate([1, 2, 3], [0, 1, 0.5]) array([ 3.5]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same") array([ 2. , 3.5, 3. ]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full") array([ 0.5, 2. , 3.5, 3. , 0. ])
Using complex sequences:
>>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full') array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])
Note that you get the time reversed, complex conjugated result when the two input sequences change places, i.e., ``c_{va}[k] = c^{*}_{av}[-k]``:
>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full') array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])
""" mode = _mode_from_name(mode) return multiarray.correlate2(a, v, mode)
return (a, v)
""" Returns the discrete, linear convolution of two one-dimensional sequences.
The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [1]_. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions.
If `v` is longer than `a`, the arrays are swapped before computation.
Parameters ---------- a : (N,) array_like First one-dimensional input array. v : (M,) array_like Second one-dimensional input array. mode : {'full', 'valid', 'same'}, optional 'full': By default, mode is 'full'. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen.
'same': Mode 'same' returns output of length ``max(M, N)``. Boundary effects are still visible.
'valid': Mode 'valid' returns output of length ``max(M, N) - min(M, N) + 1``. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect.
Returns ------- out : ndarray Discrete, linear convolution of `a` and `v`.
See Also -------- scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier Transform. scipy.linalg.toeplitz : Used to construct the convolution operator. polymul : Polynomial multiplication. Same output as convolve, but also accepts poly1d objects as input.
Notes ----- The discrete convolution operation is defined as
.. math:: (a * v)[n] = \\sum_{m = -\\infty}^{\\infty} a[m] v[n - m]
It can be shown that a convolution :math:`x(t) * y(t)` in time/space is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier domain, after appropriate padding (padding is necessary to prevent circular convolution). Since multiplication is more efficient (faster) than convolution, the function `scipy.signal.fftconvolve` exploits the FFT to calculate the convolution of large data-sets.
References ---------- .. [1] Wikipedia, "Convolution", https://en.wikipedia.org/wiki/Convolution
Examples -------- Note how the convolution operator flips the second array before "sliding" the two across one another:
>>> np.convolve([1, 2, 3], [0, 1, 0.5]) array([ 0. , 1. , 2.5, 4. , 1.5])
Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account:
>>> np.convolve([1,2,3],[0,1,0.5], 'same') array([ 1. , 2.5, 4. ])
The two arrays are of the same length, so there is only one position where they completely overlap:
>>> np.convolve([1,2,3],[0,1,0.5], 'valid') array([ 2.5])
""" raise ValueError('a cannot be empty') raise ValueError('v cannot be empty')
return (a, b, out)
""" Compute the outer product of two vectors.
Given two vectors, ``a = [a0, a1, ..., aM]`` and ``b = [b0, b1, ..., bN]``, the outer product [1]_ is::
[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]
Parameters ---------- a : (M,) array_like First input vector. Input is flattened if not already 1-dimensional. b : (N,) array_like Second input vector. Input is flattened if not already 1-dimensional. out : (M, N) ndarray, optional A location where the result is stored
.. versionadded:: 1.9.0
Returns ------- out : (M, N) ndarray ``out[i, j] = a[i] * b[j]``
See also -------- inner einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent. ufunc.outer : A generalization to N dimensions and other operations. ``np.multiply.outer(a.ravel(), b.ravel())`` is the equivalent.
References ---------- .. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8.
Examples -------- Make a (*very* coarse) grid for computing a Mandelbrot set:
>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5)) >>> rl array([[-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.]]) >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,))) >>> im array([[ 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j], [ 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j], [ 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]]) >>> grid = rl + im >>> grid array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j], [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j], [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j], [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j], [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])
An example using a "vector" of letters:
>>> x = np.array(['a', 'b', 'c'], dtype=object) >>> np.outer(x, [1, 2, 3]) array([[a, aa, aaa], [b, bb, bbb], [c, cc, ccc]], dtype=object)
""" a = asarray(a) b = asarray(b) return multiply(a.ravel()[:, newaxis], b.ravel()[newaxis, :], out)
return (a, b)
""" Compute tensor dot product along specified axes for arrays >= 1-D.
Given two tensors (arrays of dimension greater than or equal to one), `a` and `b`, and an array_like object containing two array_like objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s elements (components) over the axes specified by ``a_axes`` and ``b_axes``. The third argument can be a single non-negative integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions of `a` and the first ``N`` dimensions of `b` are summed over.
Parameters ---------- a, b : array_like, len(shape) >= 1 Tensors to "dot".
axes : int or (2,) array_like * integer_like If an int N, sum over the last N axes of `a` and the first N axes of `b` in order. The sizes of the corresponding axes must match. * (2,) array_like Or, a list of axes to be summed over, first sequence applying to `a`, second to `b`. Both elements array_like must be of the same length.
See Also -------- dot, einsum
Notes ----- Three common use cases are: * ``axes = 0`` : tensor product :math:`a\\otimes b` * ``axes = 1`` : tensor dot product :math:`a\\cdot b` * ``axes = 2`` : (default) tensor double contraction :math:`a:b`
When `axes` is integer_like, the sequence for evaluation will be: first the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and Nth axis in `b` last.
When there is more than one axis to sum over - and they are not the last (first) axes of `a` (`b`) - the argument `axes` should consist of two sequences of the same length, with the first axis to sum over given first in both sequences, the second axis second, and so forth.
Examples -------- A "traditional" example:
>>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> c = np.tensordot(a,b, axes=([1,0],[0,1])) >>> c.shape (5, 2) >>> c array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> # A slower but equivalent way of computing the same... >>> d = np.zeros((5,2)) >>> for i in range(5): ... for j in range(2): ... for k in range(3): ... for n in range(4): ... d[i,j] += a[k,n,i] * b[n,k,j] >>> c == d array([[ True, True], [ True, True], [ True, True], [ True, True], [ True, True]])
An extended example taking advantage of the overloading of + and \\*:
>>> a = np.array(range(1, 9)) >>> a.shape = (2, 2, 2) >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) >>> A.shape = (2, 2) >>> a; A array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) array([[a, b], [c, d]], dtype=object)
>>> np.tensordot(a, A) # third argument default is 2 for double-contraction array([abbcccdddd, aaaaabbbbbbcccccccdddddddd], dtype=object)
>>> np.tensordot(a, A, 1) array([[[acc, bdd], [aaacccc, bbbdddd]], [[aaaaacccccc, bbbbbdddddd], [aaaaaaacccccccc, bbbbbbbdddddddd]]], dtype=object)
>>> np.tensordot(a, A, 0) # tensor product (result too long to incl.) array([[[[[a, b], [c, d]], ...
>>> np.tensordot(a, A, (0, 1)) array([[[abbbbb, cddddd], [aabbbbbb, ccdddddd]], [[aaabbbbbbb, cccddddddd], [aaaabbbbbbbb, ccccdddddddd]]], dtype=object)
>>> np.tensordot(a, A, (2, 1)) array([[[abb, cdd], [aaabbbb, cccdddd]], [[aaaaabbbbbb, cccccdddddd], [aaaaaaabbbbbbbb, cccccccdddddddd]]], dtype=object)
>>> np.tensordot(a, A, ((0, 1), (0, 1))) array([abbbcccccddddddd, aabbbbccccccdddddddd], dtype=object)
>>> np.tensordot(a, A, ((2, 1), (1, 0))) array([acccbbdddd, aaaaacccccccbbbbbbdddddddd], dtype=object)
""" try: iter(axes) except Exception: axes_a = list(range(-axes, 0)) axes_b = list(range(0, axes)) else: axes_a, axes_b = axes try: na = len(axes_a) axes_a = list(axes_a) except TypeError: axes_a = [axes_a] na = 1 try: nb = len(axes_b) axes_b = list(axes_b) except TypeError: axes_b = [axes_b] nb = 1
a, b = asarray(a), asarray(b) as_ = a.shape nda = a.ndim bs = b.shape ndb = b.ndim equal = True if na != nb: equal = False else: for k in range(na): if as_[axes_a[k]] != bs[axes_b[k]]: equal = False break if axes_a[k] < 0: axes_a[k] += nda if axes_b[k] < 0: axes_b[k] += ndb if not equal: raise ValueError("shape-mismatch for sum")
# Move the axes to sum over to the end of "a" # and to the front of "b" notin = [k for k in range(nda) if k not in axes_a] newaxes_a = notin + axes_a N2 = 1 for axis in axes_a: N2 *= as_[axis] newshape_a = (int(multiply.reduce([as_[ax] for ax in notin])), N2) olda = [as_[axis] for axis in notin]
notin = [k for k in range(ndb) if k not in axes_b] newaxes_b = axes_b + notin N2 = 1 for axis in axes_b: N2 *= bs[axis] newshape_b = (N2, int(multiply.reduce([bs[ax] for ax in notin]))) oldb = [bs[axis] for axis in notin]
at = a.transpose(newaxes_a).reshape(newshape_a) bt = b.transpose(newaxes_b).reshape(newshape_b) res = dot(at, bt) return res.reshape(olda + oldb)
return (a,)
""" Roll array elements along a given axis.
Elements that roll beyond the last position are re-introduced at the first.
Parameters ---------- a : array_like Input array. shift : int or tuple of ints The number of places by which elements are shifted. If a tuple, then `axis` must be a tuple of the same size, and each of the given axes is shifted by the corresponding number. If an int while `axis` is a tuple of ints, then the same value is used for all given axes. axis : int or tuple of ints, optional Axis or axes along which elements are shifted. By default, the array is flattened before shifting, after which the original shape is restored.
Returns ------- res : ndarray Output array, with the same shape as `a`.
See Also -------- rollaxis : Roll the specified axis backwards, until it lies in a given position.
Notes ----- .. versionadded:: 1.12.0
Supports rolling over multiple dimensions simultaneously.
Examples -------- >>> x = np.arange(10) >>> np.roll(x, 2) array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])
>>> x2 = np.reshape(x, (2,5)) >>> x2 array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> np.roll(x2, 1) array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]) >>> np.roll(x2, 1, axis=0) array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]) >>> np.roll(x2, 1, axis=1) array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])
""" return roll(a.ravel(), shift, 0).reshape(a.shape)
else: raise ValueError( "'shift' and 'axis' should be scalars or 1D sequences")
# (original, result), (original, result) (slice(-offset, None), slice(None, offset)))
return (a,)
""" Roll the specified axis backwards, until it lies in a given position.
This function continues to be supported for backward compatibility, but you should prefer `moveaxis`. The `moveaxis` function was added in NumPy 1.11.
Parameters ---------- a : ndarray Input array. axis : int The axis to roll backwards. The positions of the other axes do not change relative to one another. start : int, optional The axis is rolled until it lies before this position. The default, 0, results in a "complete" roll.
Returns ------- res : ndarray For NumPy >= 1.10.0 a view of `a` is always returned. For earlier NumPy versions a view of `a` is returned only if the order of the axes is changed, otherwise the input array is returned.
See Also -------- moveaxis : Move array axes to new positions. roll : Roll the elements of an array by a number of positions along a given axis.
Examples -------- >>> a = np.ones((3,4,5,6)) >>> np.rollaxis(a, 3, 1).shape (3, 6, 4, 5) >>> np.rollaxis(a, 2).shape (5, 3, 4, 6) >>> np.rollaxis(a, 1, 4).shape (3, 5, 6, 4)
""" start += n raise AxisError(msg % ('start', -n, 'start', n + 1, start)) # it's been removed start -= 1 axes = list(range(0, n)) axes.remove(axis) axes.insert(start, axis) return a.transpose(axes)
""" Normalizes an axis argument into a tuple of non-negative integer axes.
This handles shorthands such as ``1`` and converts them to ``(1,)``, as well as performing the handling of negative indices covered by `normalize_axis_index`.
By default, this forbids axes from being specified multiple times.
Used internally by multi-axis-checking logic.
.. versionadded:: 1.13.0
Parameters ---------- axis : int, iterable of int The un-normalized index or indices of the axis. ndim : int The number of dimensions of the array that `axis` should be normalized against. argname : str, optional A prefix to put before the error message, typically the name of the argument. allow_duplicate : bool, optional If False, the default, disallow an axis from being specified twice.
Returns ------- normalized_axes : tuple of int The normalized axis index, such that `0 <= normalized_axis < ndim`
Raises ------ AxisError If any axis provided is out of range ValueError If an axis is repeated
See also -------- normalize_axis_index : normalizing a single scalar axis """ # Optimization to speed-up the most common cases. except TypeError: pass # Going via an iterator directly is slower than via list comprehension. if argname: raise ValueError('repeated axis in `{}` argument'.format(argname)) else: raise ValueError('repeated axis')
return (a,)
def moveaxis(a, source, destination): """ Move axes of an array to new positions.
Other axes remain in their original order.
.. versionadded:: 1.11.0
Parameters ---------- a : np.ndarray The array whose axes should be reordered. source : int or sequence of int Original positions of the axes to move. These must be unique. destination : int or sequence of int Destination positions for each of the original axes. These must also be unique.
Returns ------- result : np.ndarray Array with moved axes. This array is a view of the input array.
See Also -------- transpose: Permute the dimensions of an array. swapaxes: Interchange two axes of an array.
Examples --------
>>> x = np.zeros((3, 4, 5)) >>> np.moveaxis(x, 0, -1).shape (4, 5, 3) >>> np.moveaxis(x, -1, 0).shape (5, 3, 4)
These all achieve the same result:
>>> np.transpose(x).shape (5, 4, 3) >>> np.swapaxes(x, 0, -1).shape (5, 4, 3) >>> np.moveaxis(x, [0, 1], [-1, -2]).shape (5, 4, 3) >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape (5, 4, 3)
""" # allow duck-array types if they define transpose except AttributeError: a = asarray(a) transpose = a.transpose
raise ValueError('`source` and `destination` arguments must have ' 'the same number of elements')
# fix hack in scipy which imports this function return moveaxis(a, axis, 0)
return (a, b)
""" Return the cross product of two (arrays of) vectors.
The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors are defined by the last axis of `a` and `b` by default, and these axes can have dimensions 2 or 3. Where the dimension of either `a` or `b` is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly. In cases where both input vectors have dimension 2, the z-component of the cross product is returned.
Parameters ---------- a : array_like Components of the first vector(s). b : array_like Components of the second vector(s). axisa : int, optional Axis of `a` that defines the vector(s). By default, the last axis. axisb : int, optional Axis of `b` that defines the vector(s). By default, the last axis. axisc : int, optional Axis of `c` containing the cross product vector(s). Ignored if both input vectors have dimension 2, as the return is scalar. By default, the last axis. axis : int, optional If defined, the axis of `a`, `b` and `c` that defines the vector(s) and cross product(s). Overrides `axisa`, `axisb` and `axisc`.
Returns ------- c : ndarray Vector cross product(s).
Raises ------ ValueError When the dimension of the vector(s) in `a` and/or `b` does not equal 2 or 3.
See Also -------- inner : Inner product outer : Outer product. ix_ : Construct index arrays.
Notes ----- .. versionadded:: 1.9.0
Supports full broadcasting of the inputs.
Examples -------- Vector cross-product.
>>> x = [1, 2, 3] >>> y = [4, 5, 6] >>> np.cross(x, y) array([-3, 6, -3])
One vector with dimension 2.
>>> x = [1, 2] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3])
Equivalently:
>>> x = [1, 2, 0] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3])
Both vectors with dimension 2.
>>> x = [1,2] >>> y = [4,5] >>> np.cross(x, y) -3
Multiple vector cross-products. Note that the direction of the cross product vector is defined by the `right-hand rule`.
>>> x = np.array([[1,2,3], [4,5,6]]) >>> y = np.array([[4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[-3, 6, -3], [ 3, -6, 3]])
The orientation of `c` can be changed using the `axisc` keyword.
>>> np.cross(x, y, axisc=0) array([[-3, 3], [ 6, -6], [-3, 3]])
Change the vector definition of `x` and `y` using `axisa` and `axisb`.
>>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]]) >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[ -6, 12, -6], [ 0, 0, 0], [ 6, -12, 6]]) >>> np.cross(x, y, axisa=0, axisb=0) array([[-24, 48, -24], [-30, 60, -30], [-36, 72, -36]])
""" axisa, axisb, axisc = (axis,) * 3 # Check axisa and axisb are within bounds
# Move working axis to the end of the shape "(dimension must be 2 or 3)") raise ValueError(msg)
# Create the output array # Check axisc is within bounds
# create local aliases for readability
if b.shape[-1] == 2: # a0 * b1 - a1 * b0 multiply(a0, b1, out=cp) cp -= a1 * b0 return cp else: assert b.shape[-1] == 3 # cp0 = a1 * b2 - 0 (a2 = 0) # cp1 = 0 - a0 * b2 (a2 = 0) # cp2 = a0 * b1 - a1 * b0 multiply(a1, b2, out=cp0) multiply(a0, b2, out=cp1) negative(cp1, out=cp1) multiply(a0, b1, out=cp2) cp2 -= a1 * b0 else: # cp0 = a1 * b2 - a2 * b1 # cp1 = a2 * b0 - a0 * b2 # cp2 = a0 * b1 - a1 * b0 else: assert b.shape[-1] == 2 # cp0 = 0 - a2 * b1 (b2 = 0) # cp1 = a2 * b0 - 0 (b2 = 0) # cp2 = a0 * b1 - a1 * b0 multiply(a2, b1, out=cp0) negative(cp0, out=cp0) multiply(a2, b0, out=cp1) multiply(a0, b1, out=cp2) cp2 -= a1 * b0
""" Return an array representing the indices of a grid.
Compute an array where the subarrays contain index values 0,1,... varying only along the corresponding axis.
Parameters ---------- dimensions : sequence of ints The shape of the grid. dtype : dtype, optional Data type of the result.
Returns ------- grid : ndarray The array of grid indices, ``grid.shape = (len(dimensions),) + tuple(dimensions)``.
See Also -------- mgrid, meshgrid
Notes ----- The output shape is obtained by prepending the number of dimensions in front of the tuple of dimensions, i.e. if `dimensions` is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is ``(N,r0,...,rN-1)``.
The subarrays ``grid[k]`` contains the N-D array of indices along the ``k-th`` axis. Explicitly::
grid[k,i0,i1,...,iN-1] = ik
Examples -------- >>> grid = np.indices((2, 3)) >>> grid.shape (2, 2, 3) >>> grid[0] # row indices array([[0, 0, 0], [1, 1, 1]]) >>> grid[1] # column indices array([[0, 1, 2], [0, 1, 2]])
The indices can be used as an index into an array.
>>> x = np.arange(20).reshape(5, 4) >>> row, col = np.indices((2, 3)) >>> x[row, col] array([[0, 1, 2], [4, 5, 6]])
Note that it would be more straightforward in the above example to extract the required elements directly with ``x[:2, :3]``.
""" dimensions = tuple(dimensions) N = len(dimensions) shape = (1,)*N res = empty((N,)+dimensions, dtype=dtype) for i, dim in enumerate(dimensions): res[i] = arange(dim, dtype=dtype).reshape( shape[:i] + (dim,) + shape[i+1:] ) return res
def fromfunction(function, shape, **kwargs): """ Construct an array by executing a function over each coordinate.
The resulting array therefore has a value ``fn(x, y, z)`` at coordinate ``(x, y, z)``.
Parameters ---------- function : callable The function is called with N parameters, where N is the rank of `shape`. Each parameter represents the coordinates of the array varying along a specific axis. For example, if `shape` were ``(2, 2)``, then the parameters would be ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])`` shape : (N,) tuple of ints Shape of the output array, which also determines the shape of the coordinate arrays passed to `function`. dtype : data-type, optional Data-type of the coordinate arrays passed to `function`. By default, `dtype` is float.
Returns ------- fromfunction : any The result of the call to `function` is passed back directly. Therefore the shape of `fromfunction` is completely determined by `function`. If `function` returns a scalar value, the shape of `fromfunction` would not match the `shape` parameter.
See Also -------- indices, meshgrid
Notes ----- Keywords other than `dtype` are passed to `function`.
Examples -------- >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) array([[ True, False, False], [False, True, False], [False, False, True]])
>>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) array([[0, 1, 2], [1, 2, 3], [2, 3, 4]])
""" dtype = kwargs.pop('dtype', float) args = indices(shape, dtype=dtype) return function(*args, **kwargs)
return frombuffer(buf, dtype=dtype).reshape(shape, order=order)
def isscalar(num): """ Returns True if the type of `num` is a scalar type.
Parameters ---------- num : any Input argument, can be of any type and shape.
Returns ------- val : bool True if `num` is a scalar type, False if it is not.
See Also -------- ndim : Get the number of dimensions of an array
Notes ----- In almost all cases ``np.ndim(x) == 0`` should be used instead of this function, as that will also return true for 0d arrays. This is how numpy overloads functions in the style of the ``dx`` arguments to `gradient` and the ``bins`` argument to `histogram`. Some key differences:
+--------------------------------------+---------------+-------------------+ | x |``isscalar(x)``|``np.ndim(x) == 0``| +======================================+===============+===================+ | PEP 3141 numeric objects (including | ``True`` | ``True`` | | builtins) | | | +--------------------------------------+---------------+-------------------+ | builtin string and buffer objects | ``True`` | ``True`` | +--------------------------------------+---------------+-------------------+ | other builtin objects, like | ``False`` | ``True`` | | `pathlib.Path`, `Exception`, | | | | the result of `re.compile` | | | +--------------------------------------+---------------+-------------------+ | third-party objects like | ``False`` | ``True`` | | `matplotlib.figure.Figure` | | | +--------------------------------------+---------------+-------------------+ | zero-dimensional numpy arrays | ``False`` | ``True`` | +--------------------------------------+---------------+-------------------+ | other numpy arrays | ``False`` | ``False`` | +--------------------------------------+---------------+-------------------+ | `list`, `tuple`, and other sequence | ``False`` | ``False`` | | objects | | | +--------------------------------------+---------------+-------------------+
Examples -------- >>> np.isscalar(3.1) True >>> np.isscalar(np.array(3.1)) False >>> np.isscalar([3.1]) False >>> np.isscalar(False) True >>> np.isscalar('numpy') True
NumPy supports PEP 3141 numbers:
>>> from fractions import Fraction >>> isscalar(Fraction(5, 17)) True >>> from numbers import Number >>> isscalar(Number()) True
""" or type(num) in ScalarType or isinstance(num, numbers.Number))
""" Return the binary representation of the input number as a string.
For negative numbers, if width is not given, a minus sign is added to the front. If width is given, the two's complement of the number is returned, with respect to that width.
In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.
Parameters ---------- num : int Only an integer decimal number can be used. width : int, optional The length of the returned string if `num` is positive, or the length of the two's complement if `num` is negative, provided that `width` is at least a sufficient number of bits for `num` to be represented in the designated form.
If the `width` value is insufficient, it will be ignored, and `num` will be returned in binary (`num` > 0) or two's complement (`num` < 0) form with its width equal to the minimum number of bits needed to represent the number in the designated form. This behavior is deprecated and will later raise an error.
.. deprecated:: 1.12.0
Returns ------- bin : str Binary representation of `num` or two's complement of `num`.
See Also -------- base_repr: Return a string representation of a number in the given base system. bin: Python's built-in binary representation generator of an integer.
Notes ----- `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x faster.
References ---------- .. [1] Wikipedia, "Two's complement", https://en.wikipedia.org/wiki/Two's_complement
Examples -------- >>> np.binary_repr(3) '11' >>> np.binary_repr(-3) '-11' >>> np.binary_repr(3, width=4) '0011'
The two's complement is returned when the input number is negative and width is specified:
>>> np.binary_repr(-3, width=3) '101' >>> np.binary_repr(-3, width=5) '11101'
""" def warn_if_insufficient(width, binwidth): if width is not None and width < binwidth: warnings.warn( "Insufficient bit width provided. This behavior " "will raise an error in the future.", DeprecationWarning, stacklevel=3)
if num == 0: return '0' * (width or 1)
elif num > 0: binary = bin(num)[2:] binwidth = len(binary) outwidth = (binwidth if width is None else max(binwidth, width)) warn_if_insufficient(width, binwidth) return binary.zfill(outwidth)
else: if width is None: return '-' + bin(-num)[2:]
else: poswidth = len(bin(-num)[2:])
# See gh-8679: remove extra digit # for numbers at boundaries. if 2**(poswidth - 1) == -num: poswidth -= 1
twocomp = 2**(poswidth + 1) + num binary = bin(twocomp)[2:] binwidth = len(binary)
outwidth = max(binwidth, width) warn_if_insufficient(width, binwidth) return '1' * (outwidth - binwidth) + binary
""" Return a string representation of a number in the given base system.
Parameters ---------- number : int The value to convert. Positive and negative values are handled. base : int, optional Convert `number` to the `base` number system. The valid range is 2-36, the default value is 2. padding : int, optional Number of zeros padded on the left. Default is 0 (no padding).
Returns ------- out : str String representation of `number` in `base` system.
See Also -------- binary_repr : Faster version of `base_repr` for base 2.
Examples -------- >>> np.base_repr(5) '101' >>> np.base_repr(6, 5) '11' >>> np.base_repr(7, base=5, padding=3) '00012'
>>> np.base_repr(10, base=16) 'A' >>> np.base_repr(32, base=16) '20'
""" digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ' if base > len(digits): raise ValueError("Bases greater than 36 not handled in base_repr.") elif base < 2: raise ValueError("Bases less than 2 not handled in base_repr.")
num = abs(number) res = [] while num: res.append(digits[num % base]) num //= base if padding: res.append('0' * padding) if number < 0: res.append('-') return ''.join(reversed(res or '0'))
""" Wrapper around cPickle.load which accepts either a file-like object or a filename.
Note that the NumPy binary format is not based on pickle/cPickle anymore. For details on the preferred way of loading and saving files, see `load` and `save`.
See Also -------- load, save
""" # NumPy 1.15.0, 2017-12-10 warnings.warn( "np.core.numeric.load is deprecated, use pickle.load instead", DeprecationWarning, stacklevel=2) if isinstance(file, type("")): file = open(file, "rb") return pickle.load(file)
# These are all essentially abbreviations # These might wind up in a special abbreviations module
dt = dtype(descr) # Place val in all scalar tuples: fields = dt.fields if fields is None: return val else: res = [_maketup(fields[name][0], val) for name in dt.names] return tuple(res)
""" Return the identity array.
The identity array is a square array with ones on the main diagonal.
Parameters ---------- n : int Number of rows (and columns) in `n` x `n` output. dtype : data-type, optional Data-type of the output. Defaults to ``float``.
Returns ------- out : ndarray `n` x `n` array with its main diagonal set to one, and all other elements 0.
Examples -------- >>> np.identity(3) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])
"""
return (a, b)
""" Returns True if two arrays are element-wise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`.
If either array contains one or more NaNs, False is returned. Infs are treated as equal if they are in the same place and of the same sign in both arrays.
Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN's as equal. If True, NaN's in `a` will be considered equal to NaN's in `b` in the output array.
.. versionadded:: 1.10.0
Returns ------- allclose : bool Returns True if the two arrays are equal within the given tolerance; False otherwise.
See Also -------- isclose, all, any, equal
Notes ----- If the following equation is element-wise True, then allclose returns True.
absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))
The above equation is not symmetric in `a` and `b`, so that ``allclose(a, b)`` might be different from ``allclose(b, a)`` in some rare cases.
The comparison of `a` and `b` uses standard broadcasting, which means that `a` and `b` need not have the same shape in order for ``allclose(a, b)`` to evaluate to True. The same is true for `equal` but not `array_equal`.
Examples -------- >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8]) False >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9]) True >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) True
""" res = all(isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)) return bool(res)
return (a, b)
""" Returns a boolean array where two arrays are element-wise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`.
.. warning:: The default `atol` is not appropriate for comparing numbers that are much smaller than one (see Notes).
Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN's as equal. If True, NaN's in `a` will be considered equal to NaN's in `b` in the output array.
Returns ------- y : array_like Returns a boolean array of where `a` and `b` are equal within the given tolerance. If both `a` and `b` are scalars, returns a single boolean value.
See Also -------- allclose
Notes ----- .. versionadded:: 1.7.0
For finite values, isclose uses the following equation to test whether two floating point values are equivalent.
absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))
Unlike the built-in `math.isclose`, the above equation is not symmetric in `a` and `b` -- it assumes `b` is the reference value -- so that `isclose(a, b)` might be different from `isclose(b, a)`. Furthermore, the default value of atol is not zero, and is used to determine what small values should be considered close to zero. The default value is appropriate for expected values of order unity: if the expected values are significantly smaller than one, it can result in false positives. `atol` should be carefully selected for the use case at hand. A zero value for `atol` will result in `False` if either `a` or `b` is zero.
Examples -------- >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8]) array([True, False]) >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9]) array([True, True]) >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([True, True]) >>> np.isclose([1e-8, 1e-7], [0.0, 0.0]) array([ True, False], dtype=bool) >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0) array([False, False], dtype=bool) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0]) array([ True, True], dtype=bool) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0) array([False, True], dtype=bool) """
# Make sure y is an inexact type to avoid bad behavior on abs(MIN_INT). # This will cause casting of x later. Also, make sure to allow subclasses # (e.g., for numpy.ma).
else: finite = xfin & yfin cond = zeros_like(finite, subok=True) # Because we're using boolean indexing, x & y must be the same shape. # Ideally, we'd just do x, y = broadcast_arrays(x, y). It's in # lib.stride_tricks, though, so we can't import it here. x = x * ones_like(cond) y = y * ones_like(cond) # Avoid subtraction with infinite/nan values... cond[finite] = within_tol(x[finite], y[finite], atol, rtol) # Check for equality of infinite values... cond[~finite] = (x[~finite] == y[~finite]) if equal_nan: # Make NaN == NaN both_nan = isnan(x) & isnan(y)
# Needed to treat masked arrays correctly. = True would not work. cond[both_nan] = both_nan[both_nan]
return cond[()] # Flatten 0d arrays to scalars
return (a1, a2)
def array_equal(a1, a2): """ True if two arrays have the same shape and elements, False otherwise.
Parameters ---------- a1, a2 : array_like Input arrays.
Returns ------- b : bool Returns True if the arrays are equal.
See Also -------- allclose: Returns True if two arrays are element-wise equal within a tolerance. array_equiv: Returns True if input arrays are shape consistent and all elements equal.
Examples -------- >>> np.array_equal([1, 2], [1, 2]) True >>> np.array_equal(np.array([1, 2]), np.array([1, 2])) True >>> np.array_equal([1, 2], [1, 2, 3]) False >>> np.array_equal([1, 2], [1, 4]) False
""" except Exception: return False return False
return (a1, a2)
def array_equiv(a1, a2): """ Returns True if input arrays are shape consistent and all elements equal.
Shape consistent means they are either the same shape, or one input array can be broadcasted to create the same shape as the other one.
Parameters ---------- a1, a2 : array_like Input arrays.
Returns ------- out : bool True if equivalent, False otherwise.
Examples -------- >>> np.array_equiv([1, 2], [1, 2]) True >>> np.array_equiv([1, 2], [1, 3]) False
Showing the shape equivalence:
>>> np.array_equiv([1, 2], [[1, 2], [1, 2]]) True >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]]) False
>>> np.array_equiv([1, 2], [[1, 2], [1, 3]]) False
""" try: a1, a2 = asarray(a1), asarray(a2) except Exception: return False try: multiarray.broadcast(a1, a2) except Exception: return False
return bool(asarray(a1 == a2).all())
_errdict = {"ignore": ERR_IGNORE, "warn": ERR_WARN, "raise": ERR_RAISE, "call": ERR_CALL, "print": ERR_PRINT, "log": ERR_LOG}
""" Set how floating-point errors are handled.
Note that operations on integer scalar types (such as `int16`) are handled like floating point, and are affected by these settings.
Parameters ---------- all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Set treatment for all types of floating-point errors at once:
- ignore: Take no action when the exception occurs. - warn: Print a `RuntimeWarning` (via the Python `warnings` module). - raise: Raise a `FloatingPointError`. - call: Call a function specified using the `seterrcall` function. - print: Print a warning directly to ``stdout``. - log: Record error in a Log object specified by `seterrcall`.
The default is not to change the current behavior. divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for division by zero. over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point overflow. under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point underflow. invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for invalid floating-point operation.
Returns ------- old_settings : dict Dictionary containing the old settings.
See also -------- seterrcall : Set a callback function for the 'call' mode. geterr, geterrcall, errstate
Notes ----- The floating-point exceptions are defined in the IEEE 754 standard [1]_:
- Division by zero: infinite result obtained from finite numbers. - Overflow: result too large to be expressed. - Underflow: result so close to zero that some precision was lost. - Invalid operation: result is not an expressible number, typically indicates that a NaN was produced.
.. [1] https://en.wikipedia.org/wiki/IEEE_754
Examples -------- >>> old_settings = np.seterr(all='ignore') #seterr to known value >>> np.seterr(over='raise') {'over': 'ignore', 'divide': 'ignore', 'invalid': 'ignore', 'under': 'ignore'} >>> np.seterr(**old_settings) # reset to default {'over': 'raise', 'divide': 'ignore', 'invalid': 'ignore', 'under': 'ignore'}
>>> np.int16(32000) * np.int16(3) 30464 >>> old_settings = np.seterr(all='warn', over='raise') >>> np.int16(32000) * np.int16(3) Traceback (most recent call last): File "<stdin>", line 1, in <module> FloatingPointError: overflow encountered in short_scalars
>>> old_settings = np.seterr(all='print') >>> np.geterr() {'over': 'print', 'divide': 'print', 'invalid': 'print', 'under': 'print'} >>> np.int16(32000) * np.int16(3) Warning: overflow encountered in short_scalars 30464
"""
(_errdict[over] << SHIFT_OVERFLOW) + (_errdict[under] << SHIFT_UNDERFLOW) + (_errdict[invalid] << SHIFT_INVALID))
def geterr(): """ Get the current way of handling floating-point errors.
Returns ------- res : dict A dictionary with keys "divide", "over", "under", and "invalid", whose values are from the strings "ignore", "print", "log", "warn", "raise", and "call". The keys represent possible floating-point exceptions, and the values define how these exceptions are handled.
See Also -------- geterrcall, seterr, seterrcall
Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`.
Examples -------- >>> np.geterr() {'over': 'warn', 'divide': 'warn', 'invalid': 'warn', 'under': 'ignore'} >>> np.arange(3.) / np.arange(3.) array([ NaN, 1., 1.])
>>> oldsettings = np.seterr(all='warn', over='raise') >>> np.geterr() {'over': 'raise', 'divide': 'warn', 'invalid': 'warn', 'under': 'warn'} >>> np.arange(3.) / np.arange(3.) __main__:1: RuntimeWarning: invalid value encountered in divide array([ NaN, 1., 1.])
"""
def setbufsize(size): """ Set the size of the buffer used in ufuncs.
Parameters ---------- size : int Size of buffer.
""" if size > 10e6: raise ValueError("Buffer size, %s, is too big." % size) if size < 5: raise ValueError("Buffer size, %s, is too small." % size) if size % 16 != 0: raise ValueError("Buffer size, %s, is not a multiple of 16." % size)
pyvals = umath.geterrobj() old = getbufsize() pyvals[0] = size umath.seterrobj(pyvals) return old
def getbufsize(): """ Return the size of the buffer used in ufuncs.
Returns ------- getbufsize : int Size of ufunc buffer in bytes.
""" return umath.geterrobj()[0]
def seterrcall(func): """ Set the floating-point error callback function or log object.
There are two ways to capture floating-point error messages. The first is to set the error-handler to 'call', using `seterr`. Then, set the function to call using this function.
The second is to set the error-handler to 'log', using `seterr`. Floating-point errors then trigger a call to the 'write' method of the provided object.
Parameters ---------- func : callable f(err, flag) or object with write method Function to call upon floating-point errors ('call'-mode) or object whose 'write' method is used to log such message ('log'-mode).
The call function takes two arguments. The first is a string describing the type of error (such as "divide by zero", "overflow", "underflow", or "invalid value"), and the second is the status flag. The flag is a byte, whose four least-significant bits indicate the type of error, one of "divide", "over", "under", "invalid"::
[0 0 0 0 divide over under invalid]
In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.
If an object is provided, its write method should take one argument, a string.
Returns ------- h : callable, log instance or None The old error handler.
See Also -------- seterr, geterr, geterrcall
Examples -------- Callback upon error:
>>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ...
>>> saved_handler = np.seterrcall(err_handler) >>> save_err = np.seterr(all='call')
>>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([ Inf, Inf, Inf])
>>> np.seterrcall(saved_handler) <function err_handler at 0x...> >>> np.seterr(**save_err) {'over': 'call', 'divide': 'call', 'invalid': 'call', 'under': 'call'}
Log error message:
>>> class Log(object): ... def write(self, msg): ... print("LOG: %s" % msg) ...
>>> log = Log() >>> saved_handler = np.seterrcall(log) >>> save_err = np.seterr(all='log')
>>> np.array([1, 2, 3]) / 0.0 LOG: Warning: divide by zero encountered in divide <BLANKLINE> array([ Inf, Inf, Inf])
>>> np.seterrcall(saved_handler) <__main__.Log object at 0x...> >>> np.seterr(**save_err) {'over': 'log', 'divide': 'log', 'invalid': 'log', 'under': 'log'}
""" if func is not None and not isinstance(func, collections_abc.Callable): if not hasattr(func, 'write') or not isinstance(func.write, collections_abc.Callable): raise ValueError("Only callable can be used as callback") pyvals = umath.geterrobj() old = geterrcall() pyvals[2] = func umath.seterrobj(pyvals) return old
def geterrcall(): """ Return the current callback function used on floating-point errors.
When the error handling for a floating-point error (one of "divide", "over", "under", or "invalid") is set to 'call' or 'log', the function that is called or the log instance that is written to is returned by `geterrcall`. This function or log instance has been set with `seterrcall`.
Returns ------- errobj : callable, log instance or None The current error handler. If no handler was set through `seterrcall`, ``None`` is returned.
See Also -------- seterrcall, seterr, geterr
Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`.
Examples -------- >>> np.geterrcall() # we did not yet set a handler, returns None
>>> oldsettings = np.seterr(all='call') >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) >>> oldhandler = np.seterrcall(err_handler) >>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([ Inf, Inf, Inf])
>>> cur_handler = np.geterrcall() >>> cur_handler is err_handler True
""" return umath.geterrobj()[2]
""" errstate(**kwargs)
Context manager for floating-point error handling.
Using an instance of `errstate` as a context manager allows statements in that context to execute with a known error handling behavior. Upon entering the context the error handling is set with `seterr` and `seterrcall`, and upon exiting it is reset to what it was before.
Parameters ---------- kwargs : {divide, over, under, invalid} Keyword arguments. The valid keywords are the possible floating-point exceptions. Each keyword should have a string value that defines the treatment for the particular error. Possible values are {'ignore', 'warn', 'raise', 'call', 'print', 'log'}.
See Also -------- seterr, geterr, seterrcall, geterrcall
Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`.
Examples -------- >>> olderr = np.seterr(all='ignore') # Set error handling to known state.
>>> np.arange(3) / 0. array([ NaN, Inf, Inf]) >>> with np.errstate(divide='warn'): ... np.arange(3) / 0. ... __main__:2: RuntimeWarning: divide by zero encountered in divide array([ NaN, Inf, Inf])
>>> np.sqrt(-1) nan >>> with np.errstate(invalid='raise'): ... np.sqrt(-1) Traceback (most recent call last): File "<stdin>", line 2, in <module> FloatingPointError: invalid value encountered in sqrt
Outside the context the error handling behavior has not changed:
>>> np.geterr() {'over': 'warn', 'divide': 'warn', 'invalid': 'warn', 'under': 'ignore'}
""" # Note that we don't want to run the above doctests because they will fail # without a from __future__ import with_statement
self.oldcall = seterrcall(self.call)
seterrcall(self.oldcall)
# set the default values
|