diff options
Diffstat (limited to 'numpy/lib/function_base.py')
| -rw-r--r-- | numpy/lib/function_base.py | 204 |
1 files changed, 143 insertions, 61 deletions
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py index 95edb95fa..75a39beaa 100644 --- a/numpy/lib/function_base.py +++ b/numpy/lib/function_base.py @@ -27,10 +27,11 @@ from numpy.core.fromnumeric import ( ravel, nonzero, sort, partition, mean, any, sum ) from numpy.core.numerictypes import typecodes, number +from numpy.core.function_base import add_newdoc from numpy.lib.twodim_base import diag from .utils import deprecate from numpy.core.multiarray import ( - _insert, add_docstring, digitize, bincount, normalize_axis_index, + _insert, add_docstring, bincount, normalize_axis_index, _monotonicity, interp as compiled_interp, interp_complex as compiled_interp_complex ) from numpy.core.umath import _add_newdoc_ufunc as add_newdoc_ufunc @@ -1308,7 +1309,7 @@ def interp(x, xp, fp, left=None, right=None, period=None): return interp_func(x, xp, fp, left, right) -def angle(z, deg=0): +def angle(z, deg=False): """ Return the angle of the complex argument. @@ -1324,6 +1325,9 @@ def angle(z, deg=0): angle : ndarray or scalar The counterclockwise angle from the positive real axis on the complex plane, with dtype as numpy.float64. + + ..versionchanged:: 1.16.0 + This function works on subclasses of ndarray like `ma.array`. See Also -------- @@ -1338,18 +1342,18 @@ def angle(z, deg=0): 45.0 """ - if deg: - fact = 180/pi - else: - fact = 1.0 - z = asarray(z) - if (issubclass(z.dtype.type, _nx.complexfloating)): + z = asanyarray(z) + if issubclass(z.dtype.type, _nx.complexfloating): zimag = z.imag zreal = z.real else: zimag = 0 zreal = z - return arctan2(zimag, zreal) * fact + + a = arctan2(zimag, zreal) + if deg: + a *= 180/pi + return a def unwrap(p, discont=pi, axis=-1): @@ -1649,7 +1653,7 @@ def disp(mesg, device=None, linefeed=True): return -# See http://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html +# See https://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html _DIMENSION_NAME = r'\w+' _CORE_DIMENSION_LIST = '(?:{0:}(?:,{0:})*)?'.format(_DIMENSION_NAME) _ARGUMENT = r'\({}\)'.format(_CORE_DIMENSION_LIST) @@ -1906,7 +1910,7 @@ class vectorize(object): References ---------- .. [1] NumPy Reference, section `Generalized Universal Function API - <http://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html>`_. + <https://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html>`_. """ def __init__(self, pyfunc, otypes=None, doc=None, excluded=None, @@ -2561,7 +2565,7 @@ def bartlett(M): .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal Processing", Prentice-Hall, 1999, pp. 468-471. .. [4] Wikipedia, "Window function", - http://en.wikipedia.org/wiki/Window_function + https://en.wikipedia.org/wiki/Window_function .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 429. @@ -2661,7 +2665,7 @@ def hanning(M): .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 106-108. .. [3] Wikipedia, "Window function", - http://en.wikipedia.org/wiki/Window_function + https://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. @@ -2759,7 +2763,7 @@ def hamming(M): .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] Wikipedia, "Window function", - http://en.wikipedia.org/wiki/Window_function + https://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. @@ -3036,7 +3040,7 @@ def kaiser(M, beta): .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 177-178. .. [3] Wikipedia, "Window function", - http://en.wikipedia.org/wiki/Window_function + https://en.wikipedia.org/wiki/Window_function Examples -------- @@ -3124,7 +3128,7 @@ def sinc(x): .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html .. [2] Wikipedia, "Sinc function", - http://en.wikipedia.org/wiki/Sinc_function + https://en.wikipedia.org/wiki/Sinc_function Examples -------- @@ -3398,9 +3402,9 @@ def _median(a, axis=None, out=None, overwrite_input=False): def percentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False): """ - Compute the qth percentile of the data along the specified axis. + Compute the q-th percentile of the data along the specified axis. - Returns the qth percentile(s) of the array elements. + Returns the q-th percentile(s) of the array elements. Parameters ---------- @@ -3467,7 +3471,7 @@ def percentile(a, q, axis=None, out=None, Notes ----- - Given a vector ``V`` of length ``N``, the ``q``-th percentile of + Given a vector ``V`` of length ``N``, the q-th percentile of ``V`` is the value ``q/100`` of the way from the minimum to the maximum in a sorted copy of ``V``. The values and distances of the two nearest neighbors as well as the `interpolation` parameter @@ -3543,7 +3547,7 @@ def percentile(a, q, axis=None, out=None, def quantile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False): """ - Compute the `q`th quantile of the data along the specified axis. + Compute the q-th quantile of the data along the specified axis. ..versionadded:: 1.15.0 Parameters @@ -3569,6 +3573,7 @@ def quantile(a, q, axis=None, out=None, This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points ``i < j``: + * linear: ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. @@ -3602,7 +3607,7 @@ def quantile(a, q, axis=None, out=None, Notes ----- - Given a vector ``V`` of length ``N``, the ``q``-th quantile of + Given a vector ``V`` of length ``N``, the q-th quantile of ``V`` is the value ``q`` of the way from the minimum to the maximum in a sorted copy of ``V``. The values and distances of the two nearest neighbors as well as the `interpolation` parameter @@ -3720,7 +3725,7 @@ def _quantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False, indices = concatenate((indices, [-1])) ap.partition(indices, axis=axis) - # ensure axis with qth is first + # ensure axis with q-th is first ap = np.moveaxis(ap, axis, 0) axis = 0 @@ -3753,7 +3758,7 @@ def _quantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False, ap.partition(concatenate((indices_below, indices_above)), axis=axis) - # ensure axis with qth is first + # ensure axis with q-th is first ap = np.moveaxis(ap, axis, 0) weights_below = np.moveaxis(weights_below, axis, 0) weights_above = np.moveaxis(weights_above, axis, 0) @@ -3767,7 +3772,7 @@ def _quantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False, x1 = take(ap, indices_below, axis=axis) * weights_below x2 = take(ap, indices_above, axis=axis) * weights_above - # ensure axis with qth is first + # ensure axis with q-th is first x1 = np.moveaxis(x1, axis, 0) x2 = np.moveaxis(x2, axis, 0) @@ -3840,10 +3845,10 @@ def trapz(y, x=None, dx=1.0, axis=-1): References ---------- - .. [1] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule + .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule .. [2] Illustration image: - http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png + https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png Examples -------- @@ -3891,41 +3896,6 @@ def trapz(y, x=None, dx=1.0, axis=-1): return ret -#always succeed -def add_newdoc(place, obj, doc): - """ - Adds documentation to obj which is in module place. - - If doc is a string add it to obj as a docstring - - If doc is a tuple, then the first element is interpreted as - an attribute of obj and the second as the docstring - (method, docstring) - - If doc is a list, then each element of the list should be a - sequence of length two --> [(method1, docstring1), - (method2, docstring2), ...] - - This routine never raises an error. - - This routine cannot modify read-only docstrings, as appear - in new-style classes or built-in functions. Because this - routine never raises an error the caller must check manually - that the docstrings were changed. - """ - try: - new = getattr(__import__(place, globals(), {}, [obj]), obj) - if isinstance(doc, str): - add_docstring(new, doc.strip()) - elif isinstance(doc, tuple): - add_docstring(getattr(new, doc[0]), doc[1].strip()) - elif isinstance(doc, list): - for val in doc: - add_docstring(getattr(new, val[0]), val[1].strip()) - except Exception: - pass - - # Based on scitools meshgrid def meshgrid(*xi, **kwargs): """ @@ -4022,11 +3992,13 @@ def meshgrid(*xi, **kwargs): `meshgrid` is very useful to evaluate functions on a grid. + >>> import matplotlib.pyplot as plt >>> x = np.arange(-5, 5, 0.1) >>> y = np.arange(-5, 5, 0.1) >>> xx, yy = np.meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z) + >>> plt.show() """ ndim = len(xi) @@ -4526,3 +4498,113 @@ def append(arr, values, axis=None): values = ravel(values) axis = arr.ndim-1 return concatenate((arr, values), axis=axis) + + +def digitize(x, bins, right=False): + """ + Return the indices of the bins to which each value in input array belongs. + + ========= ============= ============================ + `right` order of bins returned index `i` satisfies + ========= ============= ============================ + ``False`` increasing ``bins[i-1] <= x < bins[i]`` + ``True`` increasing ``bins[i-1] < x <= bins[i]`` + ``False`` decreasing ``bins[i-1] > x >= bins[i]`` + ``True`` decreasing ``bins[i-1] >= x > bins[i]`` + ========= ============= ============================ + + If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is + returned as appropriate. + + Parameters + ---------- + x : array_like + Input array to be binned. Prior to NumPy 1.10.0, this array had to + be 1-dimensional, but can now have any shape. + bins : array_like + Array of bins. It has to be 1-dimensional and monotonic. + right : bool, optional + Indicating whether the intervals include the right or the left bin + edge. Default behavior is (right==False) indicating that the interval + does not include the right edge. The left bin end is open in this + case, i.e., bins[i-1] <= x < bins[i] is the default behavior for + monotonically increasing bins. + + Returns + ------- + indices : ndarray of ints + Output array of indices, of same shape as `x`. + + Raises + ------ + ValueError + If `bins` is not monotonic. + TypeError + If the type of the input is complex. + + See Also + -------- + bincount, histogram, unique, searchsorted + + Notes + ----- + If values in `x` are such that they fall outside the bin range, + attempting to index `bins` with the indices that `digitize` returns + will result in an IndexError. + + .. versionadded:: 1.10.0 + + `np.digitize` is implemented in terms of `np.searchsorted`. This means + that a binary search is used to bin the values, which scales much better + for larger number of bins than the previous linear search. It also removes + the requirement for the input array to be 1-dimensional. + + For monotonically _increasing_ `bins`, the following are equivalent:: + + np.digitize(x, bins, right=True) + np.searchsorted(bins, x, side='left') + + Note that as the order of the arguments are reversed, the side must be too. + The `searchsorted` call is marginally faster, as it does not do any + monotonicity checks. Perhaps more importantly, it supports all dtypes. + + Examples + -------- + >>> x = np.array([0.2, 6.4, 3.0, 1.6]) + >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) + >>> inds = np.digitize(x, bins) + >>> inds + array([1, 4, 3, 2]) + >>> for n in range(x.size): + ... print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]) + ... + 0.0 <= 0.2 < 1.0 + 4.0 <= 6.4 < 10.0 + 2.5 <= 3.0 < 4.0 + 1.0 <= 1.6 < 2.5 + + >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) + >>> bins = np.array([0, 5, 10, 15, 20]) + >>> np.digitize(x,bins,right=True) + array([1, 2, 3, 4, 4]) + >>> np.digitize(x,bins,right=False) + array([1, 3, 3, 4, 5]) + """ + x = _nx.asarray(x) + bins = _nx.asarray(bins) + + # here for compatibility, searchsorted below is happy to take this + if np.issubdtype(x.dtype, _nx.complexfloating): + raise TypeError("x may not be complex") + + mono = _monotonicity(bins) + if mono == 0: + raise ValueError("bins must be monotonically increasing or decreasing") + + # this is backwards because the arguments below are swapped + side = 'left' if right else 'right' + if mono == -1: + # reverse the bins, and invert the results + return len(bins) - _nx.searchsorted(bins[::-1], x, side=side) + else: + return _nx.searchsorted(bins, x, side=side) |