diff options
Diffstat (limited to 'numpy/lib/function_base.py')
| -rw-r--r-- | numpy/lib/function_base.py | 95 |
1 files changed, 77 insertions, 18 deletions
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py index 0bb41c270..783d45c2f 100644 --- a/numpy/lib/function_base.py +++ b/numpy/lib/function_base.py @@ -1496,26 +1496,40 @@ def angle(z, deg=False): return a -def _unwrap_dispatcher(p, discont=None, axis=None): +def _unwrap_dispatcher(p, discont=None, axis=None, *, period=None): return (p,) @array_function_dispatch(_unwrap_dispatcher) -def unwrap(p, discont=pi, axis=-1): - """ - Unwrap by changing deltas between values to 2*pi complement. +def unwrap(p, discont=None, axis=-1, *, period=2*pi): + r""" + Unwrap by taking the complement of large deltas with respect to the period. + + This unwraps a signal `p` by changing elements which have an absolute + difference from their predecessor of more than ``max(discont, period/2)`` + to their `period`-complementary values. - Unwrap radian phase `p` by changing absolute jumps greater than - `discont` to their 2*pi complement along the given axis. + For the default case where `period` is :math:`2\pi` and is `discont` is + :math:`\pi`, this unwraps a radian phase `p` such that adjacent differences + are never greater than :math:`\pi` by adding :math:`2k\pi` for some + integer :math:`k`. Parameters ---------- p : array_like Input array. discont : float, optional - Maximum discontinuity between values, default is ``pi``. + Maximum discontinuity between values, default is ``period/2``. + Values below ``period/2`` are treated as if they were ``period/2``. + To have an effect different from the default, `discont` should be + larger than ``period/2``. axis : int, optional Axis along which unwrap will operate, default is the last axis. + period: float, optional + Size of the range over which the input wraps. By default, it is + ``2 pi``. + + .. versionadded:: 1.21.0 Returns ------- @@ -1528,9 +1542,9 @@ def unwrap(p, discont=pi, axis=-1): Notes ----- - If the discontinuity in `p` is smaller than ``pi``, but larger than - `discont`, no unwrapping is done because taking the 2*pi complement - would only make the discontinuity larger. + If the discontinuity in `p` is smaller than ``period/2``, + but larger than `discont`, no unwrapping is done because taking + the complement would only make the discontinuity larger. Examples -------- @@ -1540,19 +1554,44 @@ def unwrap(p, discont=pi, axis=-1): array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) # may vary >>> np.unwrap(phase) array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) # may vary - + >>> np.unwrap([0, 1, 2, -1, 0], period=4) + array([0, 1, 2, 3, 4]) + >>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6) + array([1, 2, 3, 4, 5, 6, 7, 8, 9]) + >>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4) + array([2, 3, 4, 5, 6, 7, 8, 9]) + >>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180 + >>> np.unwrap(phase_deg, period=360) + array([-180., -140., -100., -60., -20., 20., 60., 100., 140., + 180., 220., 260., 300., 340., 380., 420., 460., 500., + 540.]) """ p = asarray(p) nd = p.ndim dd = diff(p, axis=axis) + if discont is None: + discont = period/2 slice1 = [slice(None, None)]*nd # full slices slice1[axis] = slice(1, None) slice1 = tuple(slice1) - ddmod = mod(dd + pi, 2*pi) - pi - _nx.copyto(ddmod, pi, where=(ddmod == -pi) & (dd > 0)) + dtype = np.result_type(dd, period) + if _nx.issubdtype(dtype, _nx.integer): + interval_high, rem = divmod(period, 2) + boundary_ambiguous = rem == 0 + else: + interval_high = period / 2 + boundary_ambiguous = True + interval_low = -interval_high + ddmod = mod(dd - interval_low, period) + interval_low + if boundary_ambiguous: + # for `mask = (abs(dd) == period/2)`, the above line made + # `ddmod[mask] == -period/2`. correct these such that + # `ddmod[mask] == sign(dd[mask])*period/2`. + _nx.copyto(ddmod, interval_high, + where=(ddmod == interval_low) & (dd > 0)) ph_correct = ddmod - dd _nx.copyto(ph_correct, 0, where=abs(dd) < discont) - up = array(p, copy=True, dtype='d') + up = array(p, copy=True, dtype=dtype) up[slice1] = p[slice1] + ph_correct.cumsum(axis) return up @@ -4089,11 +4128,18 @@ def _trapz_dispatcher(y, x=None, dx=None, axis=None): @array_function_dispatch(_trapz_dispatcher) def trapz(y, x=None, dx=1.0, axis=-1): - """ + r""" Integrate along the given axis using the composite trapezoidal rule. - Integrate `y` (`x`) along given axis. - + If `x` is provided, the integration happens in sequence along its + elements - they are not sorted. + + Integrate `y` (`x`) along each 1d slice on the given axis, compute + :math:`\int y(x) dx`. + When `x` is specified, this integrates along the parametric curve, + computing :math:`\int_t y(t) dt = + \int_t y(t) \left.\frac{dx}{dt}\right|_{x=x(t)} dt`. + Parameters ---------- y : array_like @@ -4143,6 +4189,20 @@ def trapz(y, x=None, dx=1.0, axis=-1): 8.0 >>> np.trapz([1,2,3], dx=2) 8.0 + + Using a decreasing `x` corresponds to integrating in reverse: + + >>> np.trapz([1,2,3], x=[8,6,4]) + -8.0 + + More generally `x` is used to integrate along a parametric curve. + This finds the area of a circle, noting we repeat the sample which closes + the curve: + + >>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True) + >>> np.trapz(np.cos(theta), x=np.sin(theta)) + 3.141571941375841 + >>> a = np.arange(6).reshape(2, 3) >>> a array([[0, 1, 2], @@ -4151,7 +4211,6 @@ def trapz(y, x=None, dx=1.0, axis=-1): array([1.5, 2.5, 3.5]) >>> np.trapz(a, axis=1) array([2., 8.]) - """ y = asanyarray(y) if x is None: |