def splint(a, b, tck, full_output=0):
"""
Evaluate the definite integral of a B-spline.
Given the knots and coefficients of a B-spline, evaluate the definite
integral of the smoothing polynomial between two given points.
Parameters
----------
a, b : float
The end-points of the integration interval.
tck : tuple
A tuple (t,c,k) containing the vector of knots, the B-spline
coefficients, and the degree of the spline (see `splev`).
full_output : int, optional
Non-zero to return optional output.
Returns
-------
integral : float
The resulting integral.
wrk : ndarray
An array containing the integrals of the normalized B-splines
defined on the set of knots.
See Also
--------
splprep, splrep, sproot, spalde, splev
bisplrep, bisplev
UnivariateSpline, BivariateSpline
References
----------
.. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
J. Inst. Maths Applics, 17, p.37-41, 1976.
.. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs
on Numerical Analysis, Oxford University Press, 1993.
"""
t, c, k = tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(
map(lambda c, a=a, b=b, t=t, k=k: splint(a, b, [t, c, k]), c))
else:
aint, wrk = _fitpack._splint(t, c, k, a, b)
if full_output: return aint, wrk
else: return aint
def splint(a,b,tck,full_output=0):
"""
Evaluate the definite integral of a B-spline.
Given the knots and coefficients of a B-spline, evaluate the definite
integral of the smoothing polynomial between two given points.
Parameters
----------
a, b : float
The end-points of the integration interval.
tck : tuple
A tuple (t,c,k) containing the vector of knots, the B-spline
coefficients, and the degree of the spline (see `splev`).
full_output : int, optional
Non-zero to return optional output.
Returns
-------
integral : float
The resulting integral.
wrk : ndarray
An array containing the integrals of the normalized B-splines
defined on the set of knots.
See Also
--------
splprep, splrep, sproot, spalde, splev
bisplrep, bisplev
UnivariateSpline, BivariateSpline
References
----------
.. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
J. Inst. Maths Applics, 17, p.37-41, 1976.
.. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs
on Numerical Analysis, Oxford University Press, 1993.
"""
t,c,k=tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c))
else:
aint,wrk=_fitpack._splint(t,c,k,a,b)
if full_output: return aint,wrk
else: return aint
def splint(a,b,tck,full_output=0):
"""
Evaluate the definite integral of a B-spline.
Given the knots and coefficients of a B-spline, evaluate the definite
integral of the smoothing polynomial between two given points.
Parameters
----------
a, b -- The end-points of the integration interval.
tck -- A length 3 sequence describing the given spline (See splev).
full_output -- Non-zero to return optional output.
Returns
-------
integral -- The resulting integral.
wrk -- An array containing the integrals of the
normalized B-splines defined on the set of knots.
See Also
--------
splprep, splrep, sproot, spalde, splev : evaluation, roots, integral
bisplrep, bisplev : bivariate splines
UnivariateSpline, BivariateSpline :
An alternative wrapping of the FITPACK functions.
References
----------
.. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
J. Inst. Maths Applics, 17, p.37-41, 1976.
.. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs
on Numerical Analysis, Oxford University Press, 1993.
"""
t,c,k=tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c))
else:
aint,wrk=_fitpack._splint(t,c,k,a,b)
if full_output: return aint,wrk
else: return aint
def splint(a,b,tck,full_output=0):
"""Evaluate the definite integral of a B-spline.
Description:
Given the knots and coefficients of a B-spline, evaluate the definite
integral of the smoothing polynomial between two given points.
Inputs:
a, b -- The end-points of the integration interval.
tck -- A length 3 sequence describing the given spline (See splev).
full_output -- Non-zero to return optional output.
Outputs: (integral, {wrk})
integral -- The resulting integral.
wrk -- An array containing the integrals of the normalized B-splines defined
on the set of knots.
See also:
splprep, splrep, sproot, spalde, splev - evaluation, roots, integral
bisplrep, bisplev - bivariate splines
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
"""
t,c,k=tck
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c))
else:
aint,wrk=_fitpack._splint(t,c,k,a,b)
if full_output: return aint,wrk
else: return aint