def sproot(tck,mest=10):
"""
Find the roots of a cubic B-spline.
Given the knots (>=8) and coefficients of a cubic B-spline return the
roots of the spline.
Parameters
----------
tck : tuple
A tuple (t,c,k) containing the vector of knots,
the B-spline coefficients, and the degree of the spline.
The number of knots must be >= 8.
The knots must be a montonically increasing sequence.
mest : int
An estimate of the number of zeros (Default is 10).
Returns
-------
zeros : ndarray
An array giving the roots of the spline.
See also
--------
splprep, splrep, splint, spalde, splev
bisplrep, bisplev
UnivariateSpline, BivariateSpline
References
----------
.. [1] C. de Boor, "On calculating with b-splines", J. Approximation
Theory, 6, p.50-62, 1972.
.. [2] M.G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths
Applics, 10, p.134-149, 1972.
.. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs
on Numerical Analysis, Oxford University Press, 1993.
"""
t,c,k=tck
if k==4: t=t[1:-1]
if k==5: t=t[2:-2]
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,t=t,k=k,mest=mest:sproot([t,c,k],mest),c))
else:
if len(t)<8:
raise TypeError,"The number of knots %d>=8"%(len(t))
z,ier=_fitpack._sproot(t,c,k,mest)
if ier==10:
raise TypeError,"Invalid input data. t1<=..<=t4<t5<..<tn-3<=..<=tn must hold."
if ier==0: return z
if ier==1:
print "Warning: the number of zeros exceeds mest"
return z
raise TypeError,"Unknown error"
def sproot(tck, mest=10):
"""Find the roots of a cubic B-spline.
Description:
Given the knots (>=8) and coefficients of a cubic B-spline return the
roots of the spline.
Inputs:
tck -- A length 3 sequence describing the given spline (See splev).
The number of knots must be >= 8. The knots must be a montonically
increasing sequence.
mest -- An estimate of the number of zeros (Default is 10).
Outputs: (zeros, )
zeros -- An array giving the roots of the spline.
See also:
splprep, splrep, splint, spalde, splev - evaluation, roots, integral
bisplrep, bisplev - bivariate splines
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
"""
t, c, k = tck
if k == 4: t = t[1:-1]
if k == 5: t = t[2:-2]
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(
map(lambda c, t=t, k=k, mest=mest: sproot([t, c, k], mest), c))
else:
if len(t) < 8:
raise TypeError, "The number of knots %d>=8" % (len(t))
z, ier = _fitpack._sproot(t, c, k, mest)
if ier == 10:
raise TypeError, "Invalid input data. t1<=..<=t4<t5<..<tn-3<=..<=tn must hold."
if ier == 0: return z
if ier == 1:
print "Warning: the number of zeros exceeds mest"
return z
raise TypeError, "Unknown error"
def sproot(tck,mest=10):
"""Find the roots of a cubic B-spline.
Description:
Given the knots (>=8) and coefficients of a cubic B-spline return the
roots of the spline.
Inputs:
tck -- A length 3 sequence describing the given spline (See splev).
The number of knots must be >= 8. The knots must be a montonically
increasing sequence.
mest -- An estimate of the number of zeros (Default is 10).
Outputs: (zeros, )
zeros -- An array giving the roots of the spline.
See also:
splprep, splrep, splint, spalde, splev - evaluation, roots, integral
bisplrep, bisplev - bivariate splines
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
"""
t,c,k=tck
if k==4: t=t[1:-1]
if k==5: t=t[2:-2]
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,t=t,k=k,mest=mest:sproot([t,c,k],mest),c))
else:
if len(t)<8:
raise TypeError,"The number of knots %d>=8"%(len(t))
z,ier=_fitpack._sproot(t,c,k,mest)
if ier==10:
raise TypeError,"Invalid input data. t1<=..<=t4<t5<..<tn-3<=..<=tn must hold."
if ier==0: return z
if ier==1:
print "Warning: the number of zeros exceeds mest"
return z
raise TypeError,"Unknown error"
def sproot(tck,mest=10):
"""
Find the roots of a cubic B-spline.
Given the knots (>=8) and coefficients of a cubic B-spline return the
roots of the spline.
Parameters
----------
tck -- A length 3 sequence describing the given spline (See splev).
The number of knots must be >= 8. The knots must be a montonically
increasing sequence.
mest -- An estimate of the number of zeros (Default is 10)
Returns
-------
zeros -- An array giving the roots of the spline.
See also
--------
splprep, splrep, splint, spalde, splev :
evaluation, roots, integral
bisplrep, bisplev :
bivariate splines
UnivariateSpline, BivariateSpline :
An alternative wrapping of the FITPACK functions.
References
----------
.. [1] C. de Boor, "On calculating with b-splines", J. Approximation
Theory, 6, p.50-62, 1972.
.. [2] M.G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths
Applics, 10, p.134-149, 1972.
.. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs
on Numerical Analysis, Oxford University Press, 1993.
"""
t,c,k=tck
if k==4: t=t[1:-1]
if k==5: t=t[2:-2]
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return _ntlist(map(lambda c,t=t,k=k,mest=mest:sproot([t,c,k],mest),c))
else:
if len(t)<8:
raise TypeError,"The number of knots %d>=8"%(len(t))
z,ier=_fitpack._sproot(t,c,k,mest)
if ier==10:
raise TypeError,"Invalid input data. t1<=..<=t4<t5<..<tn-3<=..<=tn must hold."
if ier==0: return z
if ier==1:
print "Warning: the number of zeros exceeds mest"
return z
raise TypeError,"Unknown error"
