Python numpy.inexact() Examples

def around(a, decimals=0):  # pylint: disable=missing-docstring
  a = asarray(a)
  dtype = a.dtype
  factor = math.pow(10, decimals)
  if np.issubdtype(dtype, np.inexact):
    factor = tf.cast(factor, dtype)
  else:
    # Use float as the working dtype when a.dtype is exact (e.g. integer),
    # because `decimals` can be negative.
    float_dtype = dtypes.default_float_type()
    a = a.astype(float_dtype).data
    factor = tf.cast(factor, float_dtype)
  a = tf.multiply(a, factor)
  a = tf.round(a)
  a = tf.math.divide(a, factor)
  return utils.tensor_to_ndarray(a).astype(dtype) 

def _scalar(tf_fn, x, promote_to_float=False):
  """Computes the tf_fn(x) for each element in `x`.

  Args:
    tf_fn: function that takes a single Tensor argument.
    x: array_like. Could be an ndarray, a Tensor or any object that can
      be converted to a Tensor using `tf.convert_to_tensor`.
    promote_to_float: whether to cast the argument to a float dtype
      (`dtypes.default_float_type`) if it is not already.

  Returns:
    An ndarray with the same shape as `x`. The default output dtype is
    determined by `dtypes.default_float_type`, unless x is an ndarray with a
    floating point type, in which case the output type is same as x.dtype.
  """
  x = array_ops.asarray(x)
  if promote_to_float and not np.issubdtype(x.dtype, np.inexact):
    x = x.astype(dtypes.default_float_type())
  return utils.tensor_to_ndarray(tf_fn(x.data)) 

def _init_traces(trace_funcs, init_state, n_iter, memmap_enabled,
                 memmap_path, chain_index):
    """Initialize dictionary of chain trace arrays."""
    traces = {}
    for trace_func in trace_funcs:
        for key, val in trace_func(init_state).items():
            val = np.array(val) if np.isscalar(val) else val
            init = np.nan if np.issubdtype(val.dtype, np.inexact) else 0
            if memmap_enabled:
                filename = _generate_memmap_filename(
                    memmap_path, 'trace', key, chain_index)
                traces[key] = _open_new_memmap(
                    filename, (n_iter,) + val.shape, init, val.dtype)
            else:
                traces[key] = np.full((n_iter,) + val.shape, init, val.dtype)
    return traces 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

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 test_both_abstract(self):
        assert_(np.issubdtype(np.floating, np.inexact))
        assert_(not np.issubdtype(np.inexact, np.floating)) 

def __call__(self, series, dtype):
        if dtype is None:
            inferred_dtype = None
            if callable(self._arg):
                # arg is a function, try to inspect the signature
                sig = inspect.signature(self._arg)
                return_type = sig.return_annotation
                if return_type is not inspect._empty:
                    inferred_dtype = np.dtype(return_type)
            else:
                if isinstance(self._arg, MutableMapping):
                    inferred_dtype = pd.Series(self._arg).dtype
                else:
                    inferred_dtype = self._arg.dtype
            if inferred_dtype is not None and np.issubdtype(inferred_dtype, np.number):
                if np.issubdtype(inferred_dtype, np.inexact):
                    # for the inexact e.g. float
                    # we can make the decision,
                    # but for int, due to the nan which may occur,
                    # we cannot infer the dtype
                    dtype = inferred_dtype
            else:
                dtype = inferred_dtype

        if dtype is None:
            raise ValueError('cannot infer dtype, '
                             'it needs to be specified manually for `map`')
        else:
            dtype = np.int64 if dtype is int else dtype
            dtype = np.dtype(dtype)

        inputs = [series]
        if isinstance(self._arg, SERIES_TYPE):
            inputs.append(self._arg)
        return self.new_series(inputs, shape=series.shape, dtype=dtype,
                               index_value=series.index_value, name=series.name) 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

def _divide_sparse(self, other):
        """
        Divide this matrix by a second sparse matrix.
        """
        if other.shape != self.shape:
            raise ValueError('inconsistent shapes')

        r = self._binopt(other, '_eldiv_')

        if np.issubdtype(r.dtype, np.inexact):
            # Eldiv leaves entries outside the combined sparsity
            # pattern empty, so they must be filled manually.
            # Everything outside of other's sparsity is NaN, and everything
            # inside it is either zero or defined by eldiv.
            out = np.empty(self.shape, dtype=self.dtype)
            out.fill(np.nan)
            row, col = other.nonzero()
            out[row, col] = 0
            r = r.tocoo()
            out[r.row, r.col] = r.data
            out = np.matrix(out)
        else:
            # integers types go with nan <-> 0
            out = r

        return out 

def _as_inexact(x):
    """Return `x` as an array, of either floats or complex floats"""
    x = asarray(x)
    if not np.issubdtype(x.dtype, np.inexact):
        return asarray(x, dtype=np.float_)
    return x 

def __init__(self, rdiff=None, method='lgmres', inner_maxiter=20,
                 inner_M=None, outer_k=10, **kw):
        self.preconditioner = inner_M
        self.rdiff = rdiff
        self.method = dict(
            bicgstab=scipy.sparse.linalg.bicgstab,
            gmres=scipy.sparse.linalg.gmres,
            lgmres=scipy.sparse.linalg.lgmres,
            cgs=scipy.sparse.linalg.cgs,
            minres=scipy.sparse.linalg.minres,
            ).get(method, method)

        self.method_kw = dict(maxiter=inner_maxiter, M=self.preconditioner)

        if self.method is scipy.sparse.linalg.gmres:
            # Replace GMRES's outer iteration with Newton steps
            self.method_kw['restrt'] = inner_maxiter
            self.method_kw['maxiter'] = 1
        elif self.method is scipy.sparse.linalg.lgmres:
            self.method_kw['outer_k'] = outer_k
            # Replace LGMRES's outer iteration with Newton steps
            self.method_kw['maxiter'] = 1
            # Carry LGMRES's `outer_v` vectors across nonlinear iterations
            self.method_kw.setdefault('outer_v', [])
            self.method_kw.setdefault('prepend_outer_v', True)
            # But don't carry the corresponding Jacobian*v products, in case
            # the Jacobian changes a lot in the nonlinear step
            #
            # XXX: some trust-region inspired ideas might be more efficient...
            #      See eg. Brown & Saad. But needs to be implemented separately
            #      since it's not an inexact Newton method.
            self.method_kw.setdefault('store_outer_Av', False)

        for key, value in kw.items():
            if not key.startswith('inner_'):
                raise ValueError("Unknown parameter %s" % key)
            self.method_kw[key[6:]] = value 

def get_tolerances(self, dtype):
        if not np.issubdtype(dtype, np.inexact):
            dtype = np.dtype(float)
        info = np.finfo(dtype)
        rtol, atol = self.rtol, self.atol
        if rtol is None:
            rtol = 5*info.eps
        if atol is None:
            atol = 5*info.tiny
        return rtol, atol 

def _replace_nan(a, val):
    """
    If `a` is of inexact type, make a copy of `a`, replace NaNs with
    the `val` value, and return the copy together with a boolean mask
    marking the locations where NaNs were present. If `a` is not of
    inexact type, do nothing and return `a` together with a mask of None.

    Note that scalars will end up as array scalars, which is important
    for using the result as the value of the out argument in some
    operations.

    Parameters
    ----------
    a : array-like
        Input array.
    val : float
        NaN values are set to val before doing the operation.

    Returns
    -------
    y : ndarray
        If `a` is of inexact type, return a copy of `a` with the NaNs
        replaced by the fill value, otherwise return `a`.
    mask: {bool, None}
        If `a` is of inexact type, return a boolean mask marking locations of
        NaNs, otherwise return None.

    """
    is_new = not isinstance(a, np.ndarray)
    if is_new:
        a = np.array(a)
    if not issubclass(a.dtype.type, np.inexact):
        return a, None
    if not is_new:
        # need copy
        a = np.array(a, subok=True)

    mask = np.isnan(a)
    np.copyto(a, val, where=mask)
    return a, mask 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

def _replace_nan(a, val):
    """
    If `a` is of inexact type, make a copy of `a`, replace NaNs with
    the `val` value, and return the copy together with a boolean mask
    marking the locations where NaNs were present. If `a` is not of
    inexact type, do nothing and return `a` together with a mask of None.

    Note that scalars will end up as array scalars, which is important
    for using the result as the value of the out argument in some
    operations.

    Parameters
    ----------
    a : array-like
        Input array.
    val : float
        NaN values are set to val before doing the operation.

    Returns
    -------
    y : ndarray
        If `a` is of inexact type, return a copy of `a` with the NaNs
        replaced by the fill value, otherwise return `a`.
    mask: {bool, None}
        If `a` is of inexact type, return a boolean mask marking locations of
        NaNs, otherwise return None.

    """
    is_new = not isinstance(a, np.ndarray)
    if is_new:
        a = np.array(a)
    if not issubclass(a.dtype.type, np.inexact):
        return a, None
    if not is_new:
        # need copy
        a = np.array(a, subok=True)

    mask = np.isnan(a)
    np.copyto(a, val, where=mask)
    return a, mask 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

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 test_both_abstract(self):
        assert_(np.issubdtype(np.floating, np.inexact))
        assert_(not np.issubdtype(np.inexact, np.floating)) 

def _replace_nan(a, val):
    """
    If `a` is of inexact type, make a copy of `a`, replace NaNs with
    the `val` value, and return the copy together with a boolean mask
    marking the locations where NaNs were present. If `a` is not of
    inexact type, do nothing and return `a` together with a mask of None.

    Parameters
    ----------
    a : array-like
        Input array.
    val : float
        NaN values are set to val before doing the operation.

    Returns
    -------
    y : ndarray
        If `a` is of inexact type, return a copy of `a` with the NaNs
        replaced by the fill value, otherwise return `a`.
    mask: {bool, None}
        If `a` is of inexact type, return a boolean mask marking locations of
        NaNs, otherwise return None.

    """
    is_new = not isinstance(a, np.ndarray)
    if is_new:
        a = np.array(a)
    if not issubclass(a.dtype.type, np.inexact):
        return a, None
    if not is_new:
        # need copy
        a = np.array(a, subok=True)

    mask = np.isnan(a)
    np.copyto(a, val, where=mask)
    return a, mask 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

def _as_inexact(x):
    """Return `x` as an array, of either floats or complex floats"""
    x = asarray(x)
    if not np.issubdtype(x.dtype, np.inexact):
        return asarray(x, dtype=np.float_)
    return x 

def __init__(self, rdiff=None, method='lgmres', inner_maxiter=20,
                 inner_M=None, outer_k=10, **kw):
        self.preconditioner = inner_M
        self.rdiff = rdiff
        self.method = dict(
            bicgstab=scipy.sparse.linalg.bicgstab,
            gmres=scipy.sparse.linalg.gmres,
            lgmres=scipy.sparse.linalg.lgmres,
            cgs=scipy.sparse.linalg.cgs,
            minres=scipy.sparse.linalg.minres,
            ).get(method, method)

        self.method_kw = dict(maxiter=inner_maxiter, M=self.preconditioner)

        if self.method is scipy.sparse.linalg.gmres:
            # Replace GMRES's outer iteration with Newton steps
            self.method_kw['restrt'] = inner_maxiter
            self.method_kw['maxiter'] = 1
        elif self.method is scipy.sparse.linalg.lgmres:
            self.method_kw['outer_k'] = outer_k
            # Replace LGMRES's outer iteration with Newton steps
            self.method_kw['maxiter'] = 1
            # Carry LGMRES's `outer_v` vectors across nonlinear iterations
            self.method_kw.setdefault('outer_v', [])
            # But don't carry the corresponding Jacobian*v products, in case
            # the Jacobian changes a lot in the nonlinear step
            #
            # XXX: some trust-region inspired ideas might be more efficient...
            #      See eg. Brown & Saad. But needs to be implemented separately
            #      since it's not an inexact Newton method.
            self.method_kw.setdefault('store_outer_Av', False)

        for key, value in kw.items():
            if not key.startswith('inner_'):
                raise ValueError("Unknown parameter %s" % key)
            self.method_kw[key[6:]] = value 

def get_tolerances(self, dtype):
        if not np.issubdtype(dtype, np.inexact):
            dtype = np.dtype(float)
        info = np.finfo(dtype)
        rtol, atol = self.rtol, self.atol
        if rtol is None:
            rtol = 5*info.eps
        if atol is None:
            atol = 5*info.tiny
        return rtol, atol 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe') 

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 test_both_abstract(self):
        assert_(np.issubdtype(np.floating, np.inexact))
        assert_(not np.issubdtype(np.inexact, np.floating)) 

def heaviside(x1, x2):
  def f(x1, x2):
    return tf.where(x1 < 0, tf.constant(0, dtype=x2.dtype),
                    tf.where(x1 > 0, tf.constant(1, dtype=x2.dtype), x2))
  y = _bin_op(f, x1, x2)
  if not np.issubdtype(y.dtype, np.inexact):
    y = y.astype(dtypes.default_float_type())
  return y 

def isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False):  # pylint: disable=missing-docstring
  def f(a, b):  # pylint: disable=missing-docstring
    dtype = a.dtype
    if np.issubdtype(dtype.as_numpy_dtype, np.inexact):
      rtol_ = tf.convert_to_tensor(rtol, dtype.real_dtype)
      atol_ = tf.convert_to_tensor(atol, dtype.real_dtype)
      result = (tf.math.abs(a - b) <= atol_ + rtol_ * tf.math.abs(b))
      if equal_nan:
        result = result | (tf.math.is_nan(a) & tf.math.is_nan(b))
      return result
    else:
      return a == b
  return _bin_op(f, a, b) 

def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe')