cupyx.scipy.interpolate.UnivariateSpline#
- class cupyx.scipy.interpolate.UnivariateSpline(x, y, w=None, bbox=[None, None], k=3, s=None, ext=0)[source]#
1-D smoothing spline fit to a given set of data points.
Fits a spline y = spl(x) of degree k to the provided x, y data. s specifies the number of knots by specifying a smoothing condition.
- Parameters:
x ((N,) array_like) – 1-D array of independent input data. Must be increasing; must be strictly increasing if s is 0.
y ((N,) array_like) – 1-D array of dependent input data, of the same length as x.
w ((N,) array_like, optional) – Weights for spline fitting. Must be positive. If w is None, weights are all 1. Default is None.
bbox ((2,) array_like, optional) – 2-sequence specifying the boundary of the approximation interval. If bbox is None,
bbox=[x[0], x[-1]]
. Default is None.k (int, optional) – Degree of the smoothing spline.
k = 3
is a cubic spline. Default is 3.s (float or None, optional) –
Positive smoothing factor used to choose the number of knots. Number of knots will be increased until the smoothing condition is satisfied:
sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) <= s
However, because of numerical issues, the actual condition is:
abs(sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) - s) < 0.001 * s
If s is None, s will be set as len(w) for a smoothing spline that uses all data points. If 0, spline will interpolate through all data points. This is equivalent to InterpolatedUnivariateSpline. Default is None. The user can use the s to control the tradeoff between closeness and smoothness of fit. Larger s means more smoothing while smaller values of s indicate less smoothing. Recommended values of s depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a good s value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m is the number of datapoints in x, y, and w. This means
s = len(w)
should be a good value if1/w[i]
is an estimate of the standard deviation ofy[i]
.Controls the extrapolation mode for elements not in the interval defined by the knot sequence.
if ext=0 or ‘extrapolate’, return the extrapolated value.
if ext=1 or ‘zeros’, return 0
if ext=2 or ‘raise’, raise a ValueError
if ext=3 or ‘const’, return the boundary value.
Default is 0.
See also
Methods
- __call__(x, nu=0, ext=None)[source]#
Evaluate spline (or its nu-th derivative) at positions x.
- Parameters:
x (ndarray) – A 1-D array of points at which to return the value of the smoothed spline or its derivatives. Note: x can be unordered but the evaluation is more efficient if x is (partially) ordered.
nu (int) – The order of derivative of the spline to compute.
ext (int) –
Controls the value returned for elements of x not in the interval defined by the knot sequence.
if ext=0 or ‘extrapolate’, return the extrapolated value.
if ext=1 or ‘zeros’, return 0
if ext=2 or ‘raise’, raise a ValueError
if ext=3 or ‘const’, return the boundary value.
The default value is 0, passed from the initialization of UnivariateSpline.
- antiderivative(n=1)[source]#
Construct a new spline representing the antiderivative of this spline.
- Parameters:
n (int, optional) – Order of antiderivative to evaluate. Default: 1
- Returns:
spline – Spline of order k2=k+n representing the antiderivative of this spline.
- Return type:
- derivative(n=1)[source]#
Construct a new spline representing the derivative of this spline.
- Parameters:
n (int, optional) – Order of derivative to evaluate. Default: 1
- Returns:
spline – Spline of order k2=k-n representing the derivative of this spline.
- Return type:
- get_knots()[source]#
Return positions of interior knots of the spline.
Internally, the knot vector contains
2*k
additional boundary knots.
- get_residual()[source]#
Return weighted sum of squared residuals of the spline approx.
This is equivalent to:
sum((w[i] * (y[i]-spl(x[i])))**2, axis=0
- set_smoothing_factor(s, t=None)[source]#
Continue spline computation with the given smoothing factor s and with the knots found at the last call.
This routine modifies the spline in place.
- __eq__(value, /)#
Return self==value.
- __ne__(value, /)#
Return self!=value.
- __lt__(value, /)#
Return self<value.
- __le__(value, /)#
Return self<=value.
- __gt__(value, /)#
Return self>value.
- __ge__(value, /)#
Return self>=value.