def spalde(x, tck):
"""Evaluate all derivatives of a B-spline.
Description:
Given the knots and coefficients of a cubic B-spline compute all
derivatives up to order k at a point (or set of points).
Inputs:
tck -- A length 3 sequence describing the given spline (See splev).
x -- A point or a set of points at which to evaluate the derivatives.
Note that t(k) <= x <= t(n-k+1) must hold for each x.
Outputs: (results, )
results -- An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
See also:
splprep, splrep, splint, sproot, splev - evaluation, roots, integral
bisplrep, bisplev - bivariate splines
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
Notes:
Based on algorithms from:
de Boor C : On calculating with b-splines, J. Approximation Theory
6 (1972) 50-62.
Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths
applics 10 (1972) 134-149.
Dierckx P. : 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, x=x, t=t, k=k: spalde(x, [t, c, k]), c))
else:
try:
x = x.tolist()
except:
try:
x = list(x)
except:
x = [x]
if len(x) > 1:
return map(lambda x, tck=tck: spalde(x, tck), x)
d, ier = _fitpack._spalde(t, c, k, x[0])
if ier == 0: return d
if ier == 10:
raise TypeError, "Invalid input data. t(k)<=x<=t(n-k+1) must hold."
raise TypeError, "Unknown error"
def spalde(x,tck):
"""
Evaluate all derivatives of a B-spline.
Given the knots and coefficients of a cubic B-spline compute all
derivatives up to order k at a point (or set of points).
Parameters
----------
tck : tuple
A tuple (t,c,k) containing the vector of knots,
the B-spline coefficients, and the degree of the spline.
x : array_like
A point or a set of points at which to evaluate the derivatives.
Note that ``t(k) <= x <= t(n-k+1)`` must hold for each `x`.
Returns
-------
results : array_like
An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
See Also
--------
splprep, splrep, splint, sproot, splev, bisplrep, bisplev,
UnivariateSpline, BivariateSpline
References
----------
.. [1] de Boor C : On calculating with b-splines, J. Approximation Theory
6 (1972) 50-62.
.. [2] Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths
applics 10 (1972) 134-149.
.. [3] Dierckx P. : 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,x=x,t=t,k=k:spalde(x,[t,c,k]),c))
else:
x = myasarray(x)
if len(x)>1:
return map(lambda x,tck=tck:spalde(x,tck),x)
d,ier=_fitpack._spalde(t,c,k,x[0])
if ier==0: return d
if ier==10:
raise TypeError,"Invalid input data. t(k)<=x<=t(n-k+1) must hold."
raise TypeError,"Unknown error"
def spalde(x, tck):
"""
Evaluate all derivatives of a B-spline.
Given the knots and coefficients of a cubic B-spline compute all
derivatives up to order k at a point (or set of points).
Parameters
----------
tck : tuple
A tuple (t,c,k) containing the vector of knots,
the B-spline coefficients, and the degree of the spline.
x : array_like
A point or a set of points at which to evaluate the derivatives.
Note that ``t(k) <= x <= t(n-k+1)`` must hold for each `x`.
Returns
-------
results : array_like
An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
See Also
--------
splprep, splrep, splint, sproot, splev, bisplrep, bisplev,
UnivariateSpline, BivariateSpline
References
----------
.. [1] de Boor C : On calculating with b-splines, J. Approximation Theory
6 (1972) 50-62.
.. [2] Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths
applics 10 (1972) 134-149.
.. [3] Dierckx P. : 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, x=x, t=t, k=k: spalde(x, [t, c, k]), c))
else:
x = myasarray(x)
if len(x) > 1:
return map(lambda x, tck=tck: spalde(x, tck), x)
d, ier = _fitpack._spalde(t, c, k, x[0])
if ier == 0: return d
if ier == 10:
raise TypeError("Invalid input data. t(k)<=x<=t(n-k+1) must hold.")
raise TypeError("Unknown error")
def spalde(x,tck):
"""Evaluate all derivatives of a B-spline.
Description:
Given the knots and coefficients of a cubic B-spline compute all
derivatives up to order k at a point (or set of points).
Inputs:
tck -- A length 3 sequence describing the given spline (See splev).
x -- A point or a set of points at which to evaluate the derivatives.
Note that t(k) <= x <= t(n-k+1) must hold for each x.
Outputs: (results, )
results -- An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
See also:
splprep, splrep, splint, sproot, splev - evaluation, roots, integral
bisplrep, bisplev - bivariate splines
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
Notes:
Based on algorithms from:
de Boor C : On calculating with b-splines, J. Approximation Theory
6 (1972) 50-62.
Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths
applics 10 (1972) 134-149.
Dierckx P. : 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,x=x,t=t,k=k:spalde(x,[t,c,k]),c))
else:
try: x=x.tolist()
except:
try: x=list(x)
except: x=[x]
if len(x)>1:
return map(lambda x,tck=tck:spalde(x,tck),x)
d,ier=_fitpack._spalde(t,c,k,x[0])
if ier==0: return d
if ier==10:
raise TypeError,"Invalid input data. t(k)<=x<=t(n-k+1) must hold."
raise TypeError,"Unknown error"
def spalde(x,tck):
"""Evaluate all derivatives of a B-spline.
Description:
Given the knots and coefficients of a cubic B-spline compute all
derivatives up to order k at a point (or set of points).
Inputs:
tck -- A length 3 sequence describing the given spline (See splev).
x -- A point or a set of points at which to evaluate the derivatives.
Note that t(k) <= x <= t(n-k+1) must hold for each x.
Outputs: (results, )
results -- An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
See also:
splprep, splrep, splint, sproot, 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,x=x,t=t,k=k:spalde(x,[t,c,k]),c))
else:
try: x=x.tolist()
except:
try: x=list(x)
except: x=[x]
if len(x)>1:
return map(lambda x,tck=tck:spalde(x,tck),x)
d,ier=_fitpack._spalde(t,c,k,x[0])
if ier==0: return d
if ier==10:
raise TypeError,"Invalid input data. t(k)<=x<=t(n-k+1) must hold."
raise TypeError,"Unknown error"
