import functools import warnings import operator import types import numpy as np from . import numeric as _nx from .numeric import result_type, NaN, asanyarray, ndim from numpy.core.multiarray import add_docstring from numpy.core import overrides __all__ = ['logspace', 'linspace', 'geomspace'] array_function_dispatch = functools.partial( overrides.array_function_dispatch, module='numpy') def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None, dtype=None, axis=None): return (start, stop) @array_function_dispatch(_linspace_dispatcher) def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0): """ Return evenly spaced numbers over a specified interval. Returns `num` evenly spaced samples, calculated over the interval [`start`, `stop`]. The endpoint of the interval can optionally be excluded. .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. .. versionchanged:: 1.20.0 Values are rounded towards ``-inf`` instead of ``0`` when an integer ``dtype`` is specified. The old behavior can still be obtained with ``np.linspace(start, stop, num).astype(int)`` Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The end value of the sequence, unless `endpoint` is set to False. In that case, the sequence consists of all but the last of ``num + 1`` evenly spaced samples, so that `stop` is excluded. Note that the step size changes when `endpoint` is False. num : int, optional Number of samples to generate. Default is 50. Must be non-negative. endpoint : bool, optional If True, `stop` is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional If True, return (`samples`, `step`), where `step` is the spacing between samples. dtype : dtype, optional The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. .. versionadded:: 1.9.0 axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray There are `num` equally spaced samples in the closed interval ``[start, stop]`` or the half-open interval ``[start, stop)`` (depending on whether `endpoint` is True or False). step : float, optional Only returned if `retstep` is True Size of spacing between samples. See Also -------- arange : Similar to `linspace`, but uses a step size (instead of the number of samples). geomspace : Similar to `linspace`, but with numbers spaced evenly on a log scale (a geometric progression). logspace : Similar to `geomspace`, but with the end points specified as logarithms. :ref:`how-to-partition` Examples -------- >>> np.linspace(2.0, 3.0, num=5) array([2. , 2.25, 2.5 , 2.75, 3. ]) >>> np.linspace(2.0, 3.0, num=5, endpoint=False) array([2. , 2.2, 2.4, 2.6, 2.8]) >>> np.linspace(2.0, 3.0, num=5, retstep=True) (array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 8 >>> y = np.zeros(N) >>> x1 = np.linspace(0, 10, N, endpoint=True) >>> x2 = np.linspace(0, 10, N, endpoint=False) >>> plt.plot(x1, y, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.plot(x2, y + 0.5, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() """ num = operator.index(num) if num < 0: raise ValueError("Number of samples, %s, must be non-negative." % num) div = (num - 1) if endpoint else num # Convert float/complex array scalars to float, gh-3504 # and make sure one can use variables that have an __array_interface__, gh-6634 start = asanyarray(start) * 1.0 stop = asanyarray(stop) * 1.0 dt = result_type(start, stop, float(num)) if dtype is None: dtype = dt integer_dtype = False else: integer_dtype = _nx.issubdtype(dtype, _nx.integer) delta = stop - start y = _nx.arange(0, num, dtype=dt).reshape((-1,) + (1,) * ndim(delta)) # In-place multiplication y *= delta/div is faster, but prevents the multiplicant # from overriding what class is produced, and thus prevents, e.g. use of Quantities, # see gh-7142. Hence, we multiply in place only for standard scalar types. if div > 0: _mult_inplace = _nx.isscalar(delta) step = delta / div any_step_zero = ( step == 0 if _mult_inplace else _nx.asanyarray(step == 0).any()) if any_step_zero: # Special handling for denormal numbers, gh-5437 y /= div if _mult_inplace: y *= delta else: y = y * delta else: if _mult_inplace: y *= step else: y = y * step else: # sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0) # have an undefined step step = NaN # Multiply with delta to allow possible override of output class. y = y * delta y += start if endpoint and num > 1: y[-1, ...] = stop if axis != 0: y = _nx.moveaxis(y, 0, axis) if integer_dtype: _nx.floor(y, out=y) if retstep: return y.astype(dtype, copy=False), step else: return y.astype(dtype, copy=False) def _logspace_dispatcher(start, stop, num=None, endpoint=None, base=None, dtype=None, axis=None): return (start, stop, base) @array_function_dispatch(_logspace_dispatcher) def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0): """ Return numbers spaced evenly on a log scale. In linear space, the sequence starts at ``base ** start`` (`base` to the power of `start`) and ends with ``base ** stop`` (see `endpoint` below). .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. .. versionchanged:: 1.25.0 Non-scalar 'base` is now supported Parameters ---------- start : array_like ``base ** start`` is the starting value of the sequence. stop : array_like ``base ** stop`` is the final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. base : array_like, optional The base of the log space. The step size between the elements in ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. Default is 10.0. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred type will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start, stop, or base are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- arange : Similar to linspace, with the step size specified instead of the number of samples. Note that, when used with a float endpoint, the endpoint may or may not be included. linspace : Similar to logspace, but with the samples uniformly distributed in linear space, instead of log space. geomspace : Similar to logspace, but with endpoints specified directly. :ref:`how-to-partition` Notes ----- If base is a scalar, logspace is equivalent to the code >>> y = np.linspace(start, stop, num=num, endpoint=endpoint) ... # doctest: +SKIP >>> power(base, y).astype(dtype) ... # doctest: +SKIP Examples -------- >>> np.logspace(2.0, 3.0, num=4) array([ 100. , 215.443469 , 464.15888336, 1000. ]) >>> np.logspace(2.0, 3.0, num=4, endpoint=False) array([100. , 177.827941 , 316.22776602, 562.34132519]) >>> np.logspace(2.0, 3.0, num=4, base=2.0) array([4. , 5.0396842 , 6.34960421, 8. ]) >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1) array([[ 4. , 5.0396842 , 6.34960421, 8. ], [ 9. , 12.98024613, 18.72075441, 27. ]]) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 10 >>> x1 = np.logspace(0.1, 1, N, endpoint=True) >>> x2 = np.logspace(0.1, 1, N, endpoint=False) >>> y = np.zeros(N) >>> plt.plot(x1, y, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.plot(x2, y + 0.5, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() """ ndmax = np.broadcast(start, stop, base).ndim start, stop, base = ( np.array(a, copy=False, subok=True, ndmin=ndmax) for a in (start, stop, base) ) y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis) base = np.expand_dims(base, axis=axis) if dtype is None: return _nx.power(base, y) return _nx.power(base, y).astype(dtype, copy=False) def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None, axis=None): return (start, stop) @array_function_dispatch(_geomspace_dispatcher) def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0): """ Return numbers spaced evenly on a log scale (a geometric progression). This is similar to `logspace`, but with endpoints specified directly. Each output sample is a constant multiple of the previous. .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- logspace : Similar to geomspace, but with endpoints specified using log and base. linspace : Similar to geomspace, but with arithmetic instead of geometric progression. arange : Similar to linspace, with the step size specified instead of the number of samples. :ref:`how-to-partition` Notes ----- If the inputs or dtype are complex, the output will follow a logarithmic spiral in the complex plane. (There are an infinite number of spirals passing through two points; the output will follow the shortest such path.) Examples -------- >>> np.geomspace(1, 1000, num=4) array([ 1., 10., 100., 1000.]) >>> np.geomspace(1, 1000, num=3, endpoint=False) array([ 1., 10., 100.]) >>> np.geomspace(1, 1000, num=4, endpoint=False) array([ 1. , 5.62341325, 31.6227766 , 177.827941 ]) >>> np.geomspace(1, 256, num=9) array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.]) Note that the above may not produce exact integers: >>> np.geomspace(1, 256, num=9, dtype=int) array([ 1, 2, 4, 7, 16, 32, 63, 127, 256]) >>> np.around(np.geomspace(1, 256, num=9)).astype(int) array([ 1, 2, 4, 8, 16, 32, 64, 128, 256]) Negative, decreasing, and complex inputs are allowed: >>> np.geomspace(1000, 1, num=4) array([1000., 100., 10., 1.]) >>> np.geomspace(-1000, -1, num=4) array([-1000., -100., -10., -1.]) >>> np.geomspace(1j, 1000j, num=4) # Straight line array([0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j]) >>> np.geomspace(-1+0j, 1+0j, num=5) # Circle array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j, 6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j, 1.00000000e+00+0.00000000e+00j]) Graphical illustration of `endpoint` parameter: >>> import matplotlib.pyplot as plt >>> N = 10 >>> y = np.zeros(N) >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o') [<matplotlib.lines.Line2D object at 0x...>] >>> plt.axis([0.5, 2000, 0, 3]) [0.5, 2000, 0, 3] >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both') >>> plt.show() """ start = asanyarray(start) stop = asanyarray(stop) if _nx.any(start == 0) or _nx.any(stop == 0): raise ValueError('Geometric sequence cannot include zero') dt = result_type(start, stop, float(num), _nx.zeros((), dtype)) if dtype is None: dtype = dt else: # complex to dtype('complex128'), for instance dtype = _nx.dtype(dtype) # Promote both arguments to the same dtype in case, for instance, one is # complex and another is negative and log would produce NaN otherwise. # Copy since we may change things in-place further down. start = start.astype(dt, copy=True) stop = stop.astype(dt, copy=True) out_sign = _nx.ones(_nx.broadcast(start, stop).shape, dt) # Avoid negligible real or imaginary parts in output by rotating to # positive real, calculating, then undoing rotation if _nx.issubdtype(dt, _nx.complexfloating): all_imag = (start.real == 0.) & (stop.real == 0.) if _nx.any(all_imag): start[all_imag] = start[all_imag].imag stop[all_imag] = stop[all_imag].imag out_sign[all_imag] = 1j both_negative = (_nx.sign(start) == -1) & (_nx.sign(stop) == -1) if _nx.any(both_negative): _nx.negative(start, out=start, where=both_negative) _nx.negative(stop, out=stop, where=both_negative) _nx.negative(out_sign, out=out_sign, where=both_negative) log_start = _nx.log10(start) log_stop = _nx.log10(stop) result = logspace(log_start, log_stop, num=num, endpoint=endpoint, base=10.0, dtype=dtype) # Make sure the endpoints match the start and stop arguments. This is # necessary because np.exp(np.log(x)) is not necessarily equal to x. if num > 0: result[0] = start if num > 1 and endpoint: result[-1] = stop result = out_sign * result if axis != 0: result = _nx.moveaxis(result, 0, axis) return result.astype(dtype, copy=False) def _needs_add_docstring(obj): """ Returns true if the only way to set the docstring of `obj` from python is via add_docstring. This function errs on the side of being overly conservative. """ Py_TPFLAGS_HEAPTYPE = 1 << 9 if isinstance(obj, (types.FunctionType, types.MethodType, property)): return False if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE: return False return True def _add_docstring(obj, doc, warn_on_python): if warn_on_python and not _needs_add_docstring(obj): warnings.warn( "add_newdoc was used on a pure-python object {}. " "Prefer to attach it directly to the source." .format(obj), UserWarning, stacklevel=3) try: add_docstring(obj, doc) except Exception: pass def add_newdoc(place, obj, doc, warn_on_python=True): """ Add documentation to an existing object, typically one defined in C The purpose is to allow easier editing of the docstrings without requiring a re-compile. This exists primarily for internal use within numpy itself. Parameters ---------- place : str The absolute name of the module to import from obj : str The name of the object to add documentation to, typically a class or function name doc : {str, Tuple[str, str], List[Tuple[str, str]]} If a string, the documentation to apply to `obj` If a tuple, then the first element is interpreted as an attribute of `obj` and the second as the docstring to apply - ``(method, docstring)`` If a list, then each element of the list should be a tuple of length two - ``[(method1, docstring1), (method2, docstring2), ...]`` warn_on_python : bool If True, the default, emit `UserWarning` if this is used to attach documentation to a pure-python object. Notes ----- This routine never raises an error if the docstring can't be written, but will raise an error if the object being documented does not exist. 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. Since this function grabs the ``char *`` from a c-level str object and puts it into the ``tp_doc`` slot of the type of `obj`, it violates a number of C-API best-practices, by: - modifying a `PyTypeObject` after calling `PyType_Ready` - calling `Py_INCREF` on the str and losing the reference, so the str will never be released If possible it should be avoided. """ new = getattr(__import__(place, globals(), {}, [obj]), obj) if isinstance(doc, str): _add_docstring(new, doc.strip(), warn_on_python) elif isinstance(doc, tuple): attr, docstring = doc _add_docstring(getattr(new, attr), docstring.strip(), warn_on_python) elif isinstance(doc, list): for attr, docstring in doc: _add_docstring(getattr(new, attr), docstring.strip(), warn_on_python)