insert(x, tck, m=1, per=0)

Given the knots and coefficients of a B-spline representation, create a new B-spline with a knot inserted m times at point x. This is a wrapper around the FORTRAN routine insert of FITPACK.

Notes

Based on algorithms from and .

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

Parameters

x (u) : array_like

A 1-D point at which to insert a new knot(s). If :None:None:`tck` was returned from splprep , then the parameter values, u should be given.

tck : a `BSpline` instance or a tuple

If tuple, then it is expected to be a tuple (t,c,k) containing the vector of knots, the B-spline coefficients, and the degree of the spline.

m : int, optional

The number of times to insert the given knot (its multiplicity). Default is 1.

per : int, optional

If non-zero, the input spline is considered periodic.

Returns

BSpline instance or a tuple

A new B-spline with knots t, coefficients c, and degree k. t(k+1) <= x <= t(n-k) , where k is the degree of the spline. In case of a periodic spline ( per != 0 ) there must be either at least k interior knots t(j) satisfying t(k+1)<t(j)<=x or at least k interior knots t(j) satisfying x<=t(j)<t(n-k) . A tuple is returned iff the input argument :None:None:`tck` is a tuple, otherwise a BSpline object is constructed and returned.

Insert knots into a B-spline.

Examples

You can insert knots into a B-spline.

>>> from scipy.interpolate import splrep, insert
... x = np.linspace(0, 10, 5)
... y = np.sin(x)
... tck = splrep(x, y)
... tck[0]
array([ 0.,  0.,  0.,  0.,  5., 10., 10., 10., 10.])

A knot is inserted:

>>> tck_inserted = insert(3, tck)
... tck_inserted[0]
array([ 0.,  0.,  0.,  0.,  3.,  5., 10., 10., 10., 10.])

Some knots are inserted:

>>> tck_inserted2 = insert(8, tck, m=3)
... tck_inserted2[0]
array([ 0.,  0.,  0.,  0.,  5.,  8.,  8.,  8., 10., 10., 10., 10.])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.interpolate._fitpack_py.insert

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