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DOC: stats, interpolate: Fix some minor docstring issues. #18000

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merged 1 commit into from Feb 20, 2023
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DOC: stats, interpolate: Fix some minor docstring issues. #18000

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65 changes: 35 additions & 30 deletions scipy/interpolate/_bsplines.py
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Expand Up @@ -236,7 +236,7 @@ def __init__(self, t, c, k, extrapolate=True, axis=0):
raise ValueError("Knot vector must be one-dimensional.")
if n < self.k + 1:
raise ValueError("Need at least %d knots for degree %d" %
(2*k + 2, k))
(2*k + 2, k))
if (np.diff(self.t) < 0).any():
raise ValueError("Knots must be in a non-decreasing order.")
if len(np.unique(self.t[k:n+1])) < 2:
Expand Down Expand Up @@ -510,7 +510,7 @@ def __call__(self, x, nu=0, extrapolate=None):

def _evaluate(self, xp, nu, extrapolate, out):
_bspl.evaluate_spline(self.t, self.c.reshape(self.c.shape[0], -1),
self.k, xp, nu, extrapolate, out)
self.k, xp, nu, extrapolate, out)

def _ensure_c_contiguous(self):
"""
Expand Down Expand Up @@ -549,7 +549,7 @@ def derivative(self, nu=1):
c = np.r_[c, np.zeros((ct,) + c.shape[1:])]
tck = _fitpack_impl.splder((self.t, c, self.k), nu)
return self.construct_fast(*tck, extrapolate=self.extrapolate,
axis=self.axis)
axis=self.axis)

def antiderivative(self, nu=1):
"""Return a B-spline representing the antiderivative.
Expand Down Expand Up @@ -876,6 +876,7 @@ def _process_deriv_spec(deriv):
ords, vals = [], []
return np.atleast_1d(ords, vals)


def _woodbury_algorithm(A, ur, ll, b, k):
'''
Solve a cyclic banded linear system with upper right
Expand All @@ -885,7 +886,7 @@ def _woodbury_algorithm(A, ur, ll, b, k):
Parameters
----------
A : 2-D array, shape(k, n)
Matrix of diagonals of original matrix(see
Matrix of diagonals of original matrix (see
``solve_banded`` documentation).
ur : 2-D array, shape(bs, bs)
Upper right block matrix.
Expand Down Expand Up @@ -944,11 +945,11 @@ def _woodbury_algorithm(A, ur, ll, b, k):
U = np.zeros((n - 1, k_mod))
VT = np.zeros((k_mod, n - 1)) # V transpose

# upper right block
# upper right block
U[:bs, :bs] = ur
VT[np.arange(bs), np.arange(bs) - bs] = 1

# lower left block
# lower left block
U[-bs:, -bs:] = ll
VT[np.arange(bs) - bs, np.arange(bs)] = 1

Expand All @@ -961,6 +962,7 @@ def _woodbury_algorithm(A, ur, ll, b, k):

return c


def _periodic_knots(x, k):
'''
returns vector of nodes on circle
Expand All @@ -969,7 +971,7 @@ def _periodic_knots(x, k):
n = len(xc)
if k % 2 == 0:
dx = np.diff(xc)
xc[1: -1] -= dx[:-1] / 2
xc[1: -1] -= dx[:-1] / 2
dx = np.diff(xc)
t = np.zeros(n + 2 * k)
t[k: -k] = xc
Expand Down Expand Up @@ -1043,6 +1045,7 @@ def _make_interp_per_full_matr(x, y, t, k):
c = solve(matr, b)
return c


def _make_periodic_spline(x, y, t, k, axis):
'''
Compute the (coefficients of) interpolating B-spline with periodic
Expand Down Expand Up @@ -1131,6 +1134,7 @@ def _make_periodic_spline(x, y, t, k, axis):
c = np.ascontiguousarray(c.reshape((n + k - 1,) + y.shape[1:]))
return BSpline.construct_fast(t, c, k, extrapolate='periodic', axis=axis)


def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
check_finite=True):
"""Compute the (coefficients of) interpolating B-spline.
Expand Down Expand Up @@ -1180,6 +1184,14 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
-------
b : a BSpline object of the degree ``k`` and with knots ``t``.

See Also
--------
BSpline : base class representing the B-spline objects
CubicSpline : a cubic spline in the polynomial basis
make_lsq_spline : a similar factory function for spline fitting
UnivariateSpline : a wrapper over FITPACK spline fitting routines
splrep : a wrapper over FITPACK spline fitting routines

Examples
--------

Expand Down Expand Up @@ -1253,14 +1265,6 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
>>> ax.scatter3D(x, *y, color='red')
>>> plt.show()

See Also
--------
BSpline : base class representing the B-spline objects
CubicSpline : a cubic spline in the polynomial basis
make_lsq_spline : a similar factory function for spline fitting
UnivariateSpline : a wrapper over FITPACK spline fitting routines
splrep : a wrapper over FITPACK spline fitting routines

"""
# convert string aliases for the boundary conditions
if bc_type is None or bc_type == 'not-a-knot' or bc_type == 'periodic':
Expand Down Expand Up @@ -1317,7 +1321,8 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,

if bc_type == 'periodic' and t is not None:
raise NotImplementedError("For periodic case t is constructed "
"automatically and can not be passed manually")
"automatically and can not be passed "
"manually")

# come up with a sensible knot vector, if needed
if t is None:
Expand All @@ -1329,8 +1334,8 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
# 2nd and 2nd-to-last points, a la not-a-knot
t = (x[1:] + x[:-1]) / 2.
t = np.r_[(x[0],)*(k+1),
t[1:-1],
(x[-1],)*(k+1)]
t[1:-1],
(x[-1],)*(k+1)]
else:
t = _not_a_knot(x, k)
else:
Expand Down Expand Up @@ -1381,7 +1386,7 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
_bspl._handle_lhs_derivatives(t, k, x[0], ab, kl, ku, deriv_l_ords)
if nright > 0:
_bspl._handle_lhs_derivatives(t, k, x[-1], ab, kl, ku, deriv_r_ords,
offset=nt-nright)
offset=nt-nright)

# set up the RHS: values to interpolate (+ derivative values, if any)
extradim = prod(y.shape[1:])
Expand All @@ -1397,7 +1402,7 @@ def make_interp_spline(x, y, k=3, t=None, bc_type=None, axis=0,
ab, rhs = map(np.asarray_chkfinite, (ab, rhs))
gbsv, = get_lapack_funcs(('gbsv',), (ab, rhs))
lu, piv, c, info = gbsv(kl, ku, ab, rhs,
overwrite_ab=True, overwrite_b=True)
overwrite_ab=True, overwrite_b=True)

if info > 0:
raise LinAlgError("Collocation matrix is singular.")
Expand Down Expand Up @@ -1451,6 +1456,13 @@ def make_lsq_spline(x, y, t, k=3, w=None, axis=0, check_finite=True):
-------
b : a BSpline object of the degree ``k`` with knots ``t``.

See Also
--------
BSpline : base class representing the B-spline objects
make_interp_spline : a similar factory function for interpolating splines
LSQUnivariateSpline : a FITPACK-based spline fitting routine
splrep : a FITPACK-based fitting routine

Notes
-----
The number of data points must be larger than the spline degree ``k``.
Expand Down Expand Up @@ -1507,13 +1519,6 @@ def make_lsq_spline(x, y, t, k=3, w=None, axis=0, check_finite=True):
Notice the need to replace a ``nan`` by a numerical value (precise value
does not matter as long as the corresponding weight is zero.)

See Also
--------
BSpline : base class representing the B-spline objects
make_interp_spline : a similar factory function for interpolating splines
LSQUnivariateSpline : a FITPACK-based spline fitting routine
splrep : a FITPACK-based fitting routine

"""
x = _as_float_array(x, check_finite)
y = _as_float_array(y, check_finite)
Expand Down Expand Up @@ -1555,9 +1560,9 @@ def make_lsq_spline(x, y, t, k=3, w=None, axis=0, check_finite=True):
ab = np.zeros((k+1, n), dtype=np.float_, order='F')
rhs = np.zeros((n, extradim), dtype=y.dtype, order='F')
_bspl._norm_eq_lsq(x, t, k,
y.reshape(-1, extradim),
w,
ab, rhs)
y.reshape(-1, extradim),
w,
ab, rhs)
rhs = rhs.reshape((n,) + y.shape[1:])

# have observation matrix & rhs, can solve the LSQ problem
Expand Down
11 changes: 5 additions & 6 deletions scipy/interpolate/_cubic.py
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Expand Up @@ -227,7 +227,6 @@ class PchipInterpolator(CubicHermiteSpline):
.. [2] see, e.g., C. Moler, Numerical Computing with Matlab, 2004.
:doi:`10.1137/1.9780898717952`


"""

def __init__(self, x, y, axis=0, extrapolate=None):
Expand Down Expand Up @@ -328,14 +327,14 @@ def pchip_interpolate(xi, yi, x, der=0, axis=0):
axis : int, optional
Axis in the yi array corresponding to the x-coordinate values.

See Also
--------
PchipInterpolator : PCHIP 1-D monotonic cubic interpolator.

Returns
-------
y : scalar or array_like
The result, of length R or length M or M by R,
The result, of length R or length M or M by R.

See Also
--------
PchipInterpolator : PCHIP 1-D monotonic cubic interpolator.

Examples
--------
Expand Down
19 changes: 9 additions & 10 deletions scipy/interpolate/_fitpack_impl.py
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Expand Up @@ -625,17 +625,17 @@ def splint(a, b, tck, full_output=0):
An array containing the integrals of the normalized B-splines
defined on the set of knots.

Notes
-----
splint silently assumes that the spline function is zero outside the data
interval (a, b).

See Also
--------
splprep, splrep, sproot, spalde, splev
bisplrep, bisplev
UnivariateSpline, BivariateSpline

Notes
-----
splint silently assumes that the spline function is zero outside the data
interval (a, b).

References
----------
.. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
Expand Down Expand Up @@ -689,7 +689,6 @@ def sproot(tck, mest=10):
bisplrep, bisplev
UnivariateSpline, BivariateSpline


References
----------
.. [1] C. de Boor, "On calculating with b-splines", J. Approximation
Expand Down Expand Up @@ -1166,15 +1165,15 @@ def splder(tck, n=1):
Spline of order k2=k-n representing the derivative
of the input spline.

See Also
--------
splantider, splev, spalde

Notes
-----

.. versionadded:: 0.13.0

See Also
--------
splantider, splev, spalde

Examples
--------
This can be used for finding maxima of a curve:
Expand Down
41 changes: 20 additions & 21 deletions scipy/interpolate/_fitpack_py.py
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Expand Up @@ -328,17 +328,17 @@ def splev(x, tck, der=0, ext=0):
the points in `x`. If `tck` was returned from `splprep`, then this
is a list of arrays representing the curve in an N-D space.

Notes
-----
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using `BSpline` objects.

See Also
--------
splprep, splrep, sproot, spalde, splint
bisplrep, bisplev
BSpline

Notes
-----
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using `BSpline` objects.

References
----------
.. [1] C. de Boor, "On calculating with b-splines", J. Approximation
Expand Down Expand Up @@ -395,6 +395,12 @@ def splint(a, b, tck, full_output=0):
defined on the set of knots.
(Only returned if `full_output` is non-zero)

See Also
--------
splprep, splrep, sproot, spalde, splev
bisplrep, bisplev
BSpline

Notes
-----
`splint` silently assumes that the spline function is zero outside the data
Expand All @@ -403,12 +409,6 @@ def splint(a, b, tck, full_output=0):
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using the `BSpline` objects.

See Also
--------
splprep, splrep, sproot, spalde, splev
bisplrep, bisplev
BSpline

References
----------
.. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
Expand Down Expand Up @@ -459,17 +459,16 @@ def sproot(tck, mest=10):
zeros : ndarray
An array giving the roots of the spline.

Notes
-----
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using the `BSpline` objects.

See Also
--------
splprep, splrep, splint, spalde, splev
bisplrep, bisplev
BSpline

Notes
-----
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using the `BSpline` objects.

References
----------
Expand Down Expand Up @@ -684,16 +683,16 @@ def splder(tck, n=1):
A tuple is returned iff the input argument `tck` is a tuple, otherwise
a BSpline object is constructed and returned.

Notes
-----

.. versionadded:: 0.13.0

See Also
--------
splantider, splev, spalde
BSpline

Notes
-----

.. versionadded:: 0.13.0

Examples
--------
This can be used for finding maxima of a curve:
Expand Down