"""Automatically adapted for numpy Sep 19, 2005 by convertcode.py """ import functools __all__ = ['iscomplexobj', 'isrealobj', 'imag', 'iscomplex', 'isreal', 'nan_to_num', 'real', 'real_if_close', 'typename', 'asfarray', 'mintypecode', 'common_type'] from .._utils import set_module import numpy.core.numeric as _nx from numpy.core.numeric import asarray, asanyarray, isnan, zeros from numpy.core import overrides, getlimits from .ufunclike import isneginf, isposinf array_function_dispatch = functools.partial( overrides.array_function_dispatch, module='numpy') _typecodes_by_elsize = 'GDFgdfQqLlIiHhBb?' @set_module('numpy') def mintypecode(typechars, typeset='GDFgdf', default='d'): """ Return the character for the minimum-size type to which given types can be safely cast. The returned type character must represent the smallest size dtype such that an array of the returned type can handle the data from an array of all types in `typechars` (or if `typechars` is an array, then its dtype.char). Parameters ---------- typechars : list of str or array_like If a list of strings, each string should represent a dtype. If array_like, the character representation of the array dtype is used. typeset : str or list of str, optional The set of characters that the returned character is chosen from. The default set is 'GDFgdf'. default : str, optional The default character, this is returned if none of the characters in `typechars` matches a character in `typeset`. Returns ------- typechar : str The character representing the minimum-size type that was found. See Also -------- dtype, sctype2char, maximum_sctype Examples -------- >>> np.mintypecode(['d', 'f', 'S']) 'd' >>> x = np.array([1.1, 2-3.j]) >>> np.mintypecode(x) 'D' >>> np.mintypecode('abceh', default='G') 'G' """ typecodes = ((isinstance(t, str) and t) or asarray(t).dtype.char for t in typechars) intersection = set(t for t in typecodes if t in typeset) if not intersection: return default if 'F' in intersection and 'd' in intersection: return 'D' return min(intersection, key=_typecodes_by_elsize.index) def _asfarray_dispatcher(a, dtype=None): return (a,) @array_function_dispatch(_asfarray_dispatcher) def asfarray(a, dtype=_nx.float_): """ Return an array converted to a float type. Parameters ---------- a : array_like The input array. dtype : str or dtype object, optional Float type code to coerce input array `a`. If `dtype` is one of the 'int' dtypes, it is replaced with float64. Returns ------- out : ndarray The input `a` as a float ndarray. Examples -------- >>> np.asfarray([2, 3]) array([2., 3.]) >>> np.asfarray([2, 3], dtype='float') array([2., 3.]) >>> np.asfarray([2, 3], dtype='int8') array([2., 3.]) """ if not _nx.issubdtype(dtype, _nx.inexact): dtype = _nx.float_ return asarray(a, dtype=dtype) def _real_dispatcher(val): return (val,) @array_function_dispatch(_real_dispatcher) def real(val): """ Return the real part of the complex argument. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray or scalar The real component of the complex argument. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real_if_close, imag, angle Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.real array([1., 3., 5.]) >>> a.real = 9 >>> a array([9.+2.j, 9.+4.j, 9.+6.j]) >>> a.real = np.array([9, 8, 7]) >>> a array([9.+2.j, 8.+4.j, 7.+6.j]) >>> np.real(1 + 1j) 1.0 """ try: return val.real except AttributeError: return asanyarray(val).real def _imag_dispatcher(val): return (val,) @array_function_dispatch(_imag_dispatcher) def imag(val): """ Return the imaginary part of the complex argument. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray or scalar The imaginary component of the complex argument. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real, angle, real_if_close Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.imag array([2., 4., 6.]) >>> a.imag = np.array([8, 10, 12]) >>> a array([1. +8.j, 3.+10.j, 5.+12.j]) >>> np.imag(1 + 1j) 1.0 """ try: return val.imag except AttributeError: return asanyarray(val).imag def _is_type_dispatcher(x): return (x,) @array_function_dispatch(_is_type_dispatcher) def iscomplex(x): """ Returns a bool array, where True if input element is complex. What is tested is whether the input has a non-zero imaginary part, not if the input type is complex. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray of bools Output array. See Also -------- isreal iscomplexobj : Return True if x is a complex type or an array of complex numbers. Examples -------- >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([ True, False, False, False, False, True]) """ ax = asanyarray(x) if issubclass(ax.dtype.type, _nx.complexfloating): return ax.imag != 0 res = zeros(ax.shape, bool) return res[()] # convert to scalar if needed @array_function_dispatch(_is_type_dispatcher) def isreal(x): """ Returns a bool array, where True if input element is real. If element has complex type with zero complex part, the return value for that element is True. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray, bool Boolean array of same shape as `x`. Notes ----- `isreal` may behave unexpectedly for string or object arrays (see examples) See Also -------- iscomplex isrealobj : Return True if x is not a complex type. Examples -------- >>> a = np.array([1+1j, 1+0j, 4.5, 3, 2, 2j], dtype=complex) >>> np.isreal(a) array([False, True, True, True, True, False]) The function does not work on string arrays. >>> a = np.array([2j, "a"], dtype="U") >>> np.isreal(a) # Warns about non-elementwise comparison False Returns True for all elements in input array of ``dtype=object`` even if any of the elements is complex. >>> a = np.array([1, "2", 3+4j], dtype=object) >>> np.isreal(a) array([ True, True, True]) isreal should not be used with object arrays >>> a = np.array([1+2j, 2+1j], dtype=object) >>> np.isreal(a) array([ True, True]) """ return imag(x) == 0 @array_function_dispatch(_is_type_dispatcher) def iscomplexobj(x): """ Check for a complex type or an array of complex numbers. The type of the input is checked, not the value. Even if the input has an imaginary part equal to zero, `iscomplexobj` evaluates to True. Parameters ---------- x : any The input can be of any type and shape. Returns ------- iscomplexobj : bool The return value, True if `x` is of a complex type or has at least one complex element. See Also -------- isrealobj, iscomplex Examples -------- >>> np.iscomplexobj(1) False >>> np.iscomplexobj(1+0j) True >>> np.iscomplexobj([3, 1+0j, True]) True """ try: dtype = x.dtype type_ = dtype.type except AttributeError: type_ = asarray(x).dtype.type return issubclass(type_, _nx.complexfloating) @array_function_dispatch(_is_type_dispatcher) def isrealobj(x): """ Return True if x is a not complex type or an array of complex numbers. The type of the input is checked, not the value. So even if the input has an imaginary part equal to zero, `isrealobj` evaluates to False if the data type is complex. Parameters ---------- x : any The input can be of any type and shape. Returns ------- y : bool The return value, False if `x` is of a complex type. See Also -------- iscomplexobj, isreal Notes ----- The function is only meant for arrays with numerical values but it accepts all other objects. Since it assumes array input, the return value of other objects may be True. >>> np.isrealobj('A string') True >>> np.isrealobj(False) True >>> np.isrealobj(None) True Examples -------- >>> np.isrealobj(1) True >>> np.isrealobj(1+0j) False >>> np.isrealobj([3, 1+0j, True]) False """ return not iscomplexobj(x) #----------------------------------------------------------------------------- def _getmaxmin(t): from numpy.core import getlimits f = getlimits.finfo(t) return f.max, f.min def _nan_to_num_dispatcher(x, copy=None, nan=None, posinf=None, neginf=None): return (x,) @array_function_dispatch(_nan_to_num_dispatcher) def nan_to_num(x, copy=True, nan=0.0, posinf=None, neginf=None): """ Replace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the `nan`, `posinf` and/or `neginf` keywords. If `x` is inexact, NaN is replaced by zero or by the user defined value in `nan` keyword, infinity is replaced by the largest finite floating point values representable by ``x.dtype`` or by the user defined value in `posinf` keyword and -infinity is replaced by the most negative finite floating point values representable by ``x.dtype`` or by the user defined value in `neginf` keyword. For complex dtypes, the above is applied to each of the real and imaginary components of `x` separately. If `x` is not inexact, then no replacements are made. Parameters ---------- x : scalar or array_like Input data. copy : bool, optional Whether to create a copy of `x` (True) or to replace values in-place (False). The in-place operation only occurs if casting to an array does not require a copy. Default is True. .. versionadded:: 1.13 nan : int, float, optional Value to be used to fill NaN values. If no value is passed then NaN values will be replaced with 0.0. .. versionadded:: 1.17 posinf : int, float, optional Value to be used to fill positive infinity values. If no value is passed then positive infinity values will be replaced with a very large number. .. versionadded:: 1.17 neginf : int, float, optional Value to be used to fill negative infinity values. If no value is passed then negative infinity values will be replaced with a very small (or negative) number. .. versionadded:: 1.17 Returns ------- out : ndarray `x`, with the non-finite values replaced. If `copy` is False, this may be `x` itself. See Also -------- isinf : Shows which elements are positive or negative infinity. isneginf : Shows which elements are negative infinity. isposinf : Shows which elements are positive infinity. isnan : Shows which elements are Not a Number (NaN). isfinite : Shows which elements are finite (not NaN, not infinity) Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Examples -------- >>> np.nan_to_num(np.inf) 1.7976931348623157e+308 >>> np.nan_to_num(-np.inf) -1.7976931348623157e+308 >>> np.nan_to_num(np.nan) 0.0 >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128]) >>> np.nan_to_num(x) array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary -1.28000000e+002, 1.28000000e+002]) >>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333) array([ 3.3333333e+07, 3.3333333e+07, -9.9990000e+03, -1.2800000e+02, 1.2800000e+02]) >>> y = np.array([complex(np.inf, np.nan), np.nan, complex(np.nan, np.inf)]) array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary -1.28000000e+002, 1.28000000e+002]) >>> np.nan_to_num(y) array([ 1.79769313e+308 +0.00000000e+000j, # may vary 0.00000000e+000 +0.00000000e+000j, 0.00000000e+000 +1.79769313e+308j]) >>> np.nan_to_num(y, nan=111111, posinf=222222) array([222222.+111111.j, 111111. +0.j, 111111.+222222.j]) """ x = _nx.array(x, subok=True, copy=copy) xtype = x.dtype.type isscalar = (x.ndim == 0) if not issubclass(xtype, _nx.inexact): return x[()] if isscalar else x iscomplex = issubclass(xtype, _nx.complexfloating) dest = (x.real, x.imag) if iscomplex else (x,) maxf, minf = _getmaxmin(x.real.dtype) if posinf is not None: maxf = posinf if neginf is not None: minf = neginf for d in dest: idx_nan = isnan(d) idx_posinf = isposinf(d) idx_neginf = isneginf(d) _nx.copyto(d, nan, where=idx_nan) _nx.copyto(d, maxf, where=idx_posinf) _nx.copyto(d, minf, where=idx_neginf) return x[()] if isscalar else x #----------------------------------------------------------------------------- def _real_if_close_dispatcher(a, tol=None): return (a,) @array_function_dispatch(_real_if_close_dispatcher) def real_if_close(a, tol=100): """ If input is complex with all imaginary parts close to zero, return real parts. "Close to zero" is defined as `tol` * (machine epsilon of the type for `a`). Parameters ---------- a : array_like Input array. tol : float Tolerance in machine epsilons for the complex part of the elements in the array. If the tolerance is <=1, then the absolute tolerance is used. Returns ------- out : ndarray If `a` is real, the type of `a` is used for the output. If `a` has complex elements, the returned type is float. See Also -------- real, imag, angle Notes ----- Machine epsilon varies from machine to machine and between data types but Python floats on most platforms have a machine epsilon equal to 2.2204460492503131e-16. You can use 'np.finfo(float).eps' to print out the machine epsilon for floats. Examples -------- >>> np.finfo(float).eps 2.2204460492503131e-16 # may vary >>> np.real_if_close([2.1 + 4e-14j, 5.2 + 3e-15j], tol=1000) array([2.1, 5.2]) >>> np.real_if_close([2.1 + 4e-13j, 5.2 + 3e-15j], tol=1000) array([2.1+4.e-13j, 5.2 + 3e-15j]) """ a = asanyarray(a) type_ = a.dtype.type if not issubclass(type_, _nx.complexfloating): return a if tol > 1: f = getlimits.finfo(type_) tol = f.eps * tol if _nx.all(_nx.absolute(a.imag) < tol): a = a.real return a #----------------------------------------------------------------------------- _namefromtype = {'S1': 'character', '?': 'bool', 'b': 'signed char', 'B': 'unsigned char', 'h': 'short', 'H': 'unsigned short', 'i': 'integer', 'I': 'unsigned integer', 'l': 'long integer', 'L': 'unsigned long integer', 'q': 'long long integer', 'Q': 'unsigned long long integer', 'f': 'single precision', 'd': 'double precision', 'g': 'long precision', 'F': 'complex single precision', 'D': 'complex double precision', 'G': 'complex long double precision', 'S': 'string', 'U': 'unicode', 'V': 'void', 'O': 'object' } @set_module('numpy') def typename(char): """ Return a description for the given data type code. Parameters ---------- char : str Data type code. Returns ------- out : str Description of the input data type code. See Also -------- dtype, typecodes Examples -------- >>> typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q', ... 'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q'] >>> for typechar in typechars: ... print(typechar, ' : ', np.typename(typechar)) ... S1 : character ? : bool B : unsigned char D : complex double precision G : complex long double precision F : complex single precision I : unsigned integer H : unsigned short L : unsigned long integer O : object Q : unsigned long long integer S : string U : unicode V : void b : signed char d : double precision g : long precision f : single precision i : integer h : short l : long integer q : long long integer """ return _namefromtype[char] #----------------------------------------------------------------------------- #determine the "minimum common type" for a group of arrays. array_type = [[_nx.half, _nx.single, _nx.double, _nx.longdouble], [None, _nx.csingle, _nx.cdouble, _nx.clongdouble]] array_precision = {_nx.half: 0, _nx.single: 1, _nx.double: 2, _nx.longdouble: 3, _nx.csingle: 1, _nx.cdouble: 2, _nx.clongdouble: 3} def _common_type_dispatcher(*arrays): return arrays @array_function_dispatch(_common_type_dispatcher) def common_type(*arrays): """ Return a scalar type which is common to the input arrays. The return type will always be an inexact (i.e. floating point) scalar type, even if all the arrays are integer arrays. If one of the inputs is an integer array, the minimum precision type that is returned is a 64-bit floating point dtype. All input arrays except int64 and uint64 can be safely cast to the returned dtype without loss of information. Parameters ---------- array1, array2, ... : ndarrays Input arrays. Returns ------- out : data type code Data type code. See Also -------- dtype, mintypecode Examples -------- >>> np.common_type(np.arange(2, dtype=np.float32)) <class 'numpy.float32'> >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2)) <class 'numpy.float64'> >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0])) <class 'numpy.complex128'> """ is_complex = False precision = 0 for a in arrays: t = a.dtype.type if iscomplexobj(a): is_complex = True if issubclass(t, _nx.integer): p = 2 # array_precision[_nx.double] else: p = array_precision.get(t, None) if p is None: raise TypeError("can't get common type for non-numeric array") precision = max(precision, p) if is_complex: return array_type[1][precision] else: return array_type[0][precision]