Python numpy.complexfloating() Examples

def test_basic_property(self):
        # Check A = L L^H
        shapes = [(1, 1), (2, 2), (3, 3), (50, 50), (3, 10, 10)]
        dtypes = (np.float32, np.float64, np.complex64, np.complex128)

        for shape, dtype in itertools.product(shapes, dtypes):
            np.random.seed(1)
            a = np.random.randn(*shape)
            if np.issubdtype(dtype, np.complexfloating):
                a = a + 1j*np.random.randn(*shape)

            t = list(range(len(shape)))
            t[-2:] = -1, -2

            a = np.matmul(a.transpose(t).conj(), a)
            a = np.asarray(a, dtype=dtype)

            c = np.linalg.cholesky(a)

            b = np.matmul(c, c.transpose(t).conj())
            assert_allclose(b, a,
                            err_msg="{} {}\n{}\n{}".format(shape, dtype, a, c),
                            atol=500 * a.shape[0] * np.finfo(dtype).eps) 

def check_arguments(fun, y0, support_complex):
    """Helper function for checking arguments common to all solvers."""
    y0 = np.asarray(y0)
    if np.issubdtype(y0.dtype, np.complexfloating):
        if not support_complex:
            raise ValueError("`y0` is complex, but the chosen solver does "
                             "not support integration in a complex domain.")
        dtype = complex
    else:
        dtype = float
    y0 = y0.astype(dtype, copy=False)

    if y0.ndim != 1:
        raise ValueError("`y0` must be 1-dimensional.")

    def fun_wrapped(t, y):
        return np.asarray(fun(t, y), dtype=dtype)

    return fun_wrapped, y0 

def test_basic_property(self):
        # Check A = L L^H
        shapes = [(1, 1), (2, 2), (3, 3), (50, 50), (3, 10, 10)]
        dtypes = (np.float32, np.float64, np.complex64, np.complex128)

        for shape, dtype in itertools.product(shapes, dtypes):
            np.random.seed(1)
            a = np.random.randn(*shape)
            if np.issubdtype(dtype, np.complexfloating):
                a = a + 1j*np.random.randn(*shape)

            t = list(range(len(shape)))
            t[-2:] = -1, -2

            a = np.matmul(a.transpose(t).conj(), a)
            a = np.asarray(a, dtype=dtype)

            c = np.linalg.cholesky(a)

            b = np.matmul(c, c.transpose(t).conj())
            assert_allclose(b, a,
                            err_msg="{} {}\n{}\n{}".format(shape, dtype, a, c),
                            atol=500 * a.shape[0] * np.finfo(dtype).eps) 

def get_test_array(shape, tp, val_range=None):
    dtype = tp_dtype(tp)
    if val_range is None:
        nmin, nmax = tp_limits(tp)
    else:
        nmin, nmax = val_range

    if numpy.issubdtype(dtype, numpy.integer):
        return numpy.random.randint(nmin, nmax, dtype=dtype, size=shape)
    elif numpy.issubdtype(dtype, numpy.floating):
        return numpy.random.uniform(nmin, nmax, size=shape).astype(dtype)
    elif numpy.issubdtype(dtype, numpy.complexfloating):
        return (
            numpy.random.uniform(nmin, nmax, size=shape)
            + 1j * numpy.random.uniform(nmin, nmax, size=shape)).astype(dtype)
    else:
        raise NotImplementedError(dtype) 

def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes):
        np.random.seed(1234)
        if np.issubdtype(dtype, np.complexfloating):
            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
        else:
            data = np.random.randn(*shape)
        data = data.astype(dtype)

        for type in [1, 2, 3]:
            for overwrite_x in [True, False]:
                for norm in [None, 'ortho']:
                    if type == 1 and norm == 'ortho':
                        continue

                    should_overwrite = (overwrite_x
                                        and dtype in overwritable_dtypes
                                        and (len(shape) == 1 or
                                             (axis % len(shape) == len(shape)-1
                                              )))
                    self._check(data, routine, type, None, axis, norm,
                                overwrite_x, should_overwrite) 

def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes):
        np.random.seed(1234)
        if np.issubdtype(dtype, np.complexfloating):
            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
        else:
            data = np.random.randn(*shape)
        data = data.astype(dtype)

        for fftsize in [8, 16, 32]:
            for overwrite_x in [True, False]:
                should_overwrite = (overwrite_x
                                    and dtype in overwritable_dtypes
                                    and fftsize <= shape[axis]
                                    and (len(shape) == 1 or
                                         (axis % len(shape) == len(shape)-1
                                          and fftsize == shape[axis])))
                self._check(data, routine, fftsize, axis,
                            overwrite_x=overwrite_x,
                            should_overwrite=should_overwrite) 

def test_mu(self):
        self.__arith_init()

        # basic tests
        assert_array_equal((self.__Asp*self.__Bsp.T).todense(),self.__A*self.__B.T)

        for x in supported_dtypes:
            A = self.__A.astype(x)
            Asp = self.spmatrix(A)
            for y in supported_dtypes:
                if np.issubdtype(y, np.complexfloating):
                    B = self.__B.astype(y)
                else:
                    B = self.__B.real.astype(y)
                Bsp = self.spmatrix(B)

                D1 = A * B.T
                S1 = Asp * Bsp.T

                assert_array_equal(S1.todense(),D1)
                assert_equal(S1.dtype,D1.dtype) 

def __init__(self, scipy_func, mpmath_func, arg_spec, name=None,
                 dps=None, prec=None, n=5000, rtol=1e-7, atol=1e-300,
                 ignore_inf_sign=False):
        self.scipy_func = scipy_func
        self.mpmath_func = mpmath_func
        self.arg_spec = arg_spec
        self.dps = dps
        self.prec = prec
        self.n = n
        self.rtol = rtol
        self.atol = atol
        self.ignore_inf_sign = ignore_inf_sign
        if isinstance(self.arg_spec, np.ndarray):
            self.is_complex = np.issubdtype(self.arg_spec.dtype, np.complexfloating)
        else:
            self.is_complex = any([isinstance(arg, ComplexArg) for arg in self.arg_spec])
        self.ignore_inf_sign = ignore_inf_sign
        if not name or name == '<lambda>':
            name = getattr(scipy_func, '__name__', None)
        if not name or name == '<lambda>':
            name = getattr(mpmath_func, '__name__', None)
        self.name = name 

def test_basic_property(self):
        # Check A = L L^H
        shapes = [(1, 1), (2, 2), (3, 3), (50, 50), (3, 10, 10)]
        dtypes = (np.float32, np.float64, np.complex64, np.complex128)

        for shape, dtype in itertools.product(shapes, dtypes):
            np.random.seed(1)
            a = np.random.randn(*shape)
            if np.issubdtype(dtype, np.complexfloating):
                a = a + 1j*np.random.randn(*shape)

            t = list(range(len(shape)))
            t[-2:] = -1, -2

            a = np.matmul(a.transpose(t).conj(), a)
            a = np.asarray(a, dtype=dtype)

            c = np.linalg.cholesky(a)

            b = np.matmul(c, c.transpose(t).conj())
            assert_allclose(b, a,
                            err_msg="{} {}\n{}\n{}".format(shape, dtype, a, c),
                            atol=500 * a.shape[0] * np.finfo(dtype).eps) 

def _rand_dtype(rand, shape, dtype, scale=1., post=lambda x: x):
  """Produce random values given shape, dtype, scale, and post-processor.

  Args:
    rand: a function for producing random values of a given shape, e.g. a
      bound version of either onp.RandomState.randn or onp.RandomState.rand.
    shape: a shape value as a tuple of positive integers.
    dtype: a numpy dtype.
    scale: optional, a multiplicative scale for the random values (default 1).
    post: optional, a callable for post-processing the random values (default
      identity).

  Returns:
    An ndarray of the given shape and dtype using random values based on a call
    to rand but scaled, converted to the appropriate dtype, and post-processed.
  """
  r = lambda: onp.asarray(scale * rand(*_dims_of_shape(shape)), dtype)
  if onp.issubdtype(dtype, onp.complexfloating):
    vals = r() + 1.0j * r()
  else:
    vals = r()
  return _cast_to_shape(onp.asarray(post(vals), dtype), shape, dtype) 

def real(self):
        ret_type = numpy.real(numpy.zeros((),dtype=self.dtype)).dtype
        shape = list(self.shape)
        if not numpy.issubdtype(self.dtype, numpy.complexfloating):
            return self

        shape[-1] *= 2
        dims = numpy.array(pu.c2f(shape),dtype=pu.dim_t)
        s = arrayfire.Array()
        arrayfire.backend.get().af_device_array(ctypes.pointer(s.arr),
                                                ctypes.c_void_p(self.d_array.device_ptr()),
                                                self.ndim,
                                                ctypes.c_void_p(dims.ctypes.data),
                                                pu.typemap(ret_type).value)
        arrayfire.backend.get().af_retain_array(ctypes.pointer(s.arr),s.arr)
        a = ndarray(shape, dtype=ret_type, af_array=s)
        ret = a[...,::2]
        ret._base = a
        ret._base_index = (Ellipsis, slice(None,None,2))
        return ret 

def imag(self):
        ret_type = numpy.real(numpy.zeros((),dtype=self.dtype)).dtype
        shape = list(self.shape)
        if not numpy.issubdtype(self.dtype, numpy.complexfloating):
            return afnumpy.zeros(self.shape)
        shape[-1] *= 2
        dims = numpy.array(pu.c2f(shape),dtype=pu.dim_t)
        s = arrayfire.Array()
        arrayfire.backend.get().af_device_array(ctypes.pointer(s.arr),
                                                ctypes.c_void_p(self.d_array.device_ptr()),
                                                self.ndim,
                                                ctypes.c_void_p(dims.ctypes.data),
                                                pu.typemap(ret_type).value)
        arrayfire.backend.get().af_retain_array(ctypes.pointer(s.arr),s.arr)
        a = ndarray(shape, dtype=ret_type, af_array=s)
        ret = a[...,1::2]
        ret._base = a
        ret._base_index = (Ellipsis, slice(1,None,2))
        return ret 

def test_basic_property(self):
        # Check A = L L^H
        shapes = [(1, 1), (2, 2), (3, 3), (50, 50), (3, 10, 10)]
        dtypes = (np.float32, np.float64, np.complex64, np.complex128)

        for shape, dtype in itertools.product(shapes, dtypes):
            np.random.seed(1)
            a = np.random.randn(*shape)
            if np.issubdtype(dtype, np.complexfloating):
                a = a + 1j*np.random.randn(*shape)

            t = list(range(len(shape)))
            t[-2:] = -1, -2

            a = np.matmul(a.transpose(t).conj(), a)
            a = np.asarray(a, dtype=dtype)

            c = np.linalg.cholesky(a)

            b = np.matmul(c, c.transpose(t).conj())
            assert_allclose(b, a,
                            err_msg="{} {}\n{}\n{}".format(shape, dtype, a, c),
                            atol=500 * a.shape[0] * np.finfo(dtype).eps) 

def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes):
        np.random.seed(1234)
        if np.issubdtype(dtype, np.complexfloating):
            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
        else:
            data = np.random.randn(*shape)
        data = data.astype(dtype)

        for type in [1, 2, 3]:
            for overwrite_x in [True, False]:
                for norm in [None, 'ortho']:
                    if type == 1 and norm == 'ortho':
                        continue

                    should_overwrite = (overwrite_x
                                        and dtype in overwritable_dtypes
                                        and (len(shape) == 1 or
                                             (axis % len(shape) == len(shape)-1
                                              )))
                    self._check(data, routine, type, None, axis, norm,
                                overwrite_x, should_overwrite) 

def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes):
        np.random.seed(1234)
        if np.issubdtype(dtype, np.complexfloating):
            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
        else:
            data = np.random.randn(*shape)
        data = data.astype(dtype)

        for fftsize in [8, 16, 32]:
            for overwrite_x in [True, False]:
                should_overwrite = (overwrite_x
                                    and dtype in overwritable_dtypes
                                    and fftsize <= shape[axis]
                                    and (len(shape) == 1 or
                                         (axis % len(shape) == len(shape)-1
                                          and fftsize == shape[axis])))
                self._check(data, routine, fftsize, axis,
                            overwrite_x=overwrite_x,
                            should_overwrite=should_overwrite) 

def conj(self, copy=True):
        """Element-wise complex conjugation.

        If the matrix is of non-complex data type and `copy` is False,
        this method does nothing and the data is not copied.

        Parameters
        ----------
        copy : bool, optional
            If True, the result is guaranteed to not share data with self.

        Returns
        -------
        A : The element-wise complex conjugate.

        """
        if np.issubdtype(self.dtype, np.complexfloating):
            return self.tocsr(copy=copy).conj(copy=False)
        elif copy:
            return self.copy()
        else:
            return self 

def test_mu(self):
        self.__arith_init()

        # basic tests
        assert_array_equal((self.__Asp*self.__Bsp.T).todense(),self.__A*self.__B.T)

        for x in supported_dtypes:
            A = self.__A.astype(x)
            Asp = self.spmatrix(A)
            for y in supported_dtypes:
                if np.issubdtype(y, np.complexfloating):
                    B = self.__B.astype(y)
                else:
                    B = self.__B.real.astype(y)
                Bsp = self.spmatrix(B)

                D1 = A * B.T
                S1 = Asp * Bsp.T

                assert_allclose(S1.todense(), D1,
                                atol=1e-14*abs(D1).max())
                assert_equal(S1.dtype,D1.dtype) 

def test_dtype_cast(self):
        A_real = scipy.sparse.csr_matrix([[1, 2, 0],
                                          [0, 0, 3],
                                          [4, 0, 5]])
        A_complex = scipy.sparse.csr_matrix([[1, 2, 0],
                                             [0, 0, 3],
                                             [4, 0, 5 + 1j]])
        b_real = np.array([1,1,1])
        b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
        x = spsolve(A_real, b_real)
        assert_(np.issubdtype(x.dtype, np.floating))
        x = spsolve(A_real, b_complex)
        assert_(np.issubdtype(x.dtype, np.complexfloating))
        x = spsolve(A_complex, b_real)
        assert_(np.issubdtype(x.dtype, np.complexfloating))
        x = spsolve(A_complex, b_complex)
        assert_(np.issubdtype(x.dtype, np.complexfloating)) 

def _get_format_function(data, **options):
    """
    find the right formatting function for the dtype_
    """
    dtype_ = data.dtype
    dtypeobj = dtype_.type
    formatdict = _get_formatdict(data, **options)
    if issubclass(dtypeobj, _nt.bool_):
        return formatdict['bool']()
    elif issubclass(dtypeobj, _nt.integer):
        if issubclass(dtypeobj, _nt.timedelta64):
            return formatdict['timedelta']()
        else:
            return formatdict['int']()
    elif issubclass(dtypeobj, _nt.floating):
        if issubclass(dtypeobj, _nt.longfloat):
            return formatdict['longfloat']()
        else:
            return formatdict['float']()
    elif issubclass(dtypeobj, _nt.complexfloating):
        if issubclass(dtypeobj, _nt.clongfloat):
            return formatdict['longcomplexfloat']()
        else:
            return formatdict['complexfloat']()
    elif issubclass(dtypeobj, (_nt.unicode_, _nt.string_)):
        return formatdict['numpystr']()
    elif issubclass(dtypeobj, _nt.datetime64):
        return formatdict['datetime']()
    elif issubclass(dtypeobj, _nt.object_):
        return formatdict['object']()
    elif issubclass(dtypeobj, _nt.void):
        if dtype_.names is not None:
            return StructuredVoidFormat.from_data(data, **options)
        else:
            return formatdict['void']()
    else:
        return formatdict['numpystr']() 

def test_abstract(self):
        assert_(issubclass(np.number, numbers.Number))

        assert_(issubclass(np.inexact, numbers.Complex))
        assert_(issubclass(np.complexfloating, numbers.Complex))
        assert_(issubclass(np.floating, numbers.Real))

        assert_(issubclass(np.integer, numbers.Integral))
        assert_(issubclass(np.signedinteger, numbers.Integral))
        assert_(issubclass(np.unsignedinteger, numbers.Integral)) 

def _is_py3_complex_incompat(result, expected):
    return (PY3 and isinstance(expected, (complex, np.complexfloating)) and
            np.isnan(result)) 

def _can_hold_element(self, element):
        tipo = maybe_infer_dtype_type(element)
        if tipo is not None:
            return issubclass(tipo.type,
                              (np.floating, np.integer, np.complexfloating))
        return (
            isinstance(
                element,
                (float, int, complex, np.float_, np.int_, compat.long))
            and not isinstance(element, (bool, np.bool_))) 

def should_store(self, value):
        return not (issubclass(value.dtype.type,
                               (np.integer, np.floating, np.complexfloating,
                                np.datetime64, np.bool_)) or
                    # TODO(ExtensionArray): remove is_extension_type
                    # when all extension arrays have been ported.
                    is_extension_type(value) or
                    is_extension_array_dtype(value)) 

def is_complex_dtype(arr_or_dtype):
    """
    Check whether the provided array or dtype is of a complex dtype.

    Parameters
    ----------
    arr_or_dtype : array-like
        The array or dtype to check.

    Returns
    -------
    boolean : Whether or not the array or dtype is of a compex dtype.

    Examples
    --------
    >>> is_complex_dtype(str)
    False
    >>> is_complex_dtype(int)
    False
    >>> is_complex_dtype(np.complex)
    True
    >>> is_complex_dtype(np.array(['a', 'b']))
    False
    >>> is_complex_dtype(pd.Series([1, 2]))
    False
    >>> is_complex_dtype(np.array([1 + 1j, 5]))
    True
    """

    return _is_dtype_type(arr_or_dtype, classes(np.complexfloating)) 

def _get_format_function(data, **options):
    """
    find the right formatting function for the dtype_
    """
    dtype_ = data.dtype
    dtypeobj = dtype_.type
    formatdict = _get_formatdict(data, **options)
    if issubclass(dtypeobj, _nt.bool_):
        return formatdict['bool']()
    elif issubclass(dtypeobj, _nt.integer):
        if issubclass(dtypeobj, _nt.timedelta64):
            return formatdict['timedelta']()
        else:
            return formatdict['int']()
    elif issubclass(dtypeobj, _nt.floating):
        if issubclass(dtypeobj, _nt.longfloat):
            return formatdict['longfloat']()
        else:
            return formatdict['float']()
    elif issubclass(dtypeobj, _nt.complexfloating):
        if issubclass(dtypeobj, _nt.clongfloat):
            return formatdict['longcomplexfloat']()
        else:
            return formatdict['complexfloat']()
    elif issubclass(dtypeobj, (_nt.unicode_, _nt.string_)):
        return formatdict['numpystr']()
    elif issubclass(dtypeobj, _nt.datetime64):
        return formatdict['datetime']()
    elif issubclass(dtypeobj, _nt.object_):
        return formatdict['object']()
    elif issubclass(dtypeobj, _nt.void):
        if dtype_.names is not None:
            return StructuredVoidFormat.from_data(data, **options)
        else:
            return formatdict['void']()
    else:
        return formatdict['numpystr']() 

def _sparse_frobenius_norm(x):
    if np.issubdtype(x.dtype, np.complexfloating):
        sqnorm = abs(x).power(2).sum()
    else:
        sqnorm = x.power(2).sum()
    return sqrt(sqnorm) 

def __init__(self, M):
        self.M_lu = splu(M)
        self.shape = M.shape
        self.dtype = M.dtype
        self.isreal = not np.issubdtype(self.dtype, np.complexfloating) 

def _matvec(self, x):
        # careful here: splu.solve will throw away imaginary
        # part of x if M is real
        x = np.asarray(x)
        if self.isreal and np.issubdtype(x.dtype, np.complexfloating):
            return (self.M_lu.solve(np.real(x).astype(self.dtype))
                    + 1j * self.M_lu.solve(np.imag(x).astype(self.dtype)))
        else:
            return self.M_lu.solve(x.astype(self.dtype)) 

def get_OPinv_matvec(A, M, sigma, symmetric=False, tol=0):
    if sigma == 0:
        return get_inv_matvec(A, symmetric=symmetric, tol=tol)

    if M is None:
        #M is the identity matrix
        if isdense(A):
            if (np.issubdtype(A.dtype, np.complexfloating)
                    or np.imag(sigma) == 0):
                A = np.copy(A)
            else:
                A = A + 0j
            A.flat[::A.shape[1] + 1] -= sigma
            return LuInv(A).matvec
        elif isspmatrix(A):
            A = A - sigma * eye(A.shape[0])
            if symmetric and isspmatrix_csr(A):
                A = A.T
            return SpLuInv(A.tocsc()).matvec
        else:
            return IterOpInv(_aslinearoperator_with_dtype(A),
                              M, sigma, tol=tol).matvec
    else:
        if ((not isdense(A) and not isspmatrix(A)) or
                (not isdense(M) and not isspmatrix(M))):
            return IterOpInv(_aslinearoperator_with_dtype(A),
                              _aslinearoperator_with_dtype(M),
                              sigma, tol=tol).matvec
        elif isdense(A) or isdense(M):
            return LuInv(A - sigma * M).matvec
        else:
            OP = A - sigma * M
            if symmetric and isspmatrix_csr(OP):
                OP = OP.T
            return SpLuInv(OP.tocsc()).matvec


# ARPACK is not threadsafe or reentrant (SAVE variables), so we need a
# lock and a re-entering check. 

def _set_dtype(self, dtype, union=False):
        if np.issubdtype(dtype, np.complexfloating) \
               or np.issubdtype(self.dtype, np.complexfloating):
            self.dtype = np.complex_
        else:
            if not union or self.dtype != np.complex_:
                self.dtype = np.float_