def splev(x,tck,der=0):
"""
Evaluate a B-spline and its derivatives.
Given the knots and coefficients of a B-spline representation, evaluate
the value of the smoothing polynomial and it's derivatives.
This is a wrapper around the FORTRAN routines splev and splder of FITPACK.
Parameters
----------
x (u) -- a 1-D array of points at which to return the value of the
smoothed spline or its derivatives. If tck was returned from
splprep, then the parameter values, u should be given.
tck -- A sequence of length 3 returned by splrep or splprep containg the
knots, coefficients, and degree of the spline.
der -- The order of derivative of the spline to compute (must be less than
or equal to k).
Returns
-------
y -- an array of values representing the spline function or curve.
If tck was returned from splrep, then this is a list of arrays
representing the curve in N-dimensional space.
See Also
--------
splprep, splrep, sproot, spalde, splint : 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
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return map(lambda c,x=x,t=t,k=k,der=der:splev(x,[t,c,k],der),c)
else:
if not (0<=der<=k):
raise ValueError,"0<=der=%d<=k=%d must hold"%(der,k)
x=myasarray(x)
y,ier=_fitpack._spl_(x,der,t,c,k)
if ier==10: raise ValueError,"Invalid input data"
if ier: raise TypeError,"An error occurred"
if len(y)>1: return y
return y[0]
def splev(x,tck,der=0):
"""Evaulate a B-spline and its derivatives.
Description:
Given the knots and coefficients of a B-spline representation, evaluate
the value of the smoothing polynomial and it's derivatives.
This is a wrapper around the FORTRAN routines splev and splder of FITPACK.
Inputs:
x (u) -- a 1-D array of points at which to return the value of the
smoothed spline or its derivatives. If tck was returned from
splprep, then the parameter values, u should be given.
tck -- A sequence of length 3 returned by splrep or splprep containg the
knots, coefficients, and degree of the spline.
der -- The order of derivative of the spline to compute (must be less than
or equal to k).
Outputs: (y, )
y -- an array of values representing the spline function or curve.
If tck was returned from splrep, then this is a list of arrays
representing the curve in N-dimensional space.
See also:
splprep, splrep, sproot, spalde, splint - 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 map(lambda c,x=x,t=t,k=k,der=der:splev(x,[t,c,k],der),c)
else:
if not (0<=der<=k):
raise ValueError,"0<=der=%d<=k=%d must hold"%(der,k)
x=myasarray(x)
y,ier=_fitpack._spl_(x,der,t,c,k)
if ier==10: raise ValueError,"Invalid input data"
if ier: raise TypeError,"An error occurred"
if len(y)>1: return y
return y[0]
def splev(x, tck, der=0, ext=0):
"""
Evaluate a B-spline or its derivatives.
Given the knots and coefficients of a B-spline representation, evaluate
the value of the smoothing polynomial and its derivatives. This is a
wrapper around the FORTRAN routines splev and splder of FITPACK.
Parameters
----------
x : array_like
A 1-D array of points at which to return the value of the smoothed
spline or its derivatives. If `tck` was returned from `splprep`,
then the parameter values, u should be given.
tck : tuple
A sequence of length 3 returned by `splrep` or `splprep` containing
the knots, coefficients, and degree of the spline.
der : int
The order of derivative of the spline to compute (must be less than
or equal to k).
ext : int
Controls the value returned for elements of ``x`` not in the
interval defined by the knot sequence.
* if ext=0, return the extrapolated value.
* if ext=1, return 0
* if ext=2, raise a ValueError
The default value is 0.
Returns
-------
y : ndarray or list of ndarrays
An array of values representing the spline function evaluated at
the points in ``x``. If `tck` was returned from splrep, then this
is a list of arrays representing the curve in N-dimensional space.
See Also
--------
splprep, splrep, sproot, spalde, splint
bisplrep, bisplev
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
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return map(lambda c, x=x, t=t, k=k, der=der : splev(x, [t,c,k], der), c)
else:
if not (0 <= der <= k):
raise ValueError("0<=der=%d<=k=%d must hold"%(der,k))
if not ext in (0,1,2):
raise ValueError("ext not in (0, 1, 2)")
x = myasarray(x)
y, ier =_fitpack._spl_(x, der, t, c, k, ext)
if ier == 10:
raise ValueError("Invalid input data")
if ier == 1:
raise ValueError("Found x value not in the domain")
if ier:
raise TypeError("An error occurred")
if len(y) > 1:
return y
return y[0]
def splev(x, tck, der=0, ext=0):
"""
Evaluate a B-spline or its derivatives.
Given the knots and coefficients of a B-spline representation, evaluate
the value of the smoothing polynomial and its derivatives. This is a
wrapper around the FORTRAN routines splev and splder of FITPACK.
Parameters
----------
x : array_like
A 1-D array of points at which to return the value of the smoothed
spline or its derivatives. If `tck` was returned from `splprep`,
then the parameter values, u should be given.
tck : tuple
A sequence of length 3 returned by `splrep` or `splprep` containing
the knots, coefficients, and degree of the spline.
der : int
The order of derivative of the spline to compute (must be less than
or equal to k).
ext : int
Controls the value returned for elements of ``x`` not in the
interval defined by the knot sequence.
* if ext=0, return the extrapolated value.
* if ext=1, return 0
* if ext=2, raise a ValueError
The default value is 0.
Returns
-------
y : ndarray or list of ndarrays
An array of values representing the spline function evaluated at
the points in ``x``. If `tck` was returned from splrep, then this
is a list of arrays representing the curve in N-dimensional space.
See Also
--------
splprep, splrep, sproot, spalde, splint
bisplrep, bisplev
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
try:
c[0][0]
parametric = True
except:
parametric = False
if parametric:
return map(
lambda c, x=x, t=t, k=k, der=der: splev(x, [t, c, k], der, ext), c)
else:
if not (0 <= der <= k):
raise ValueError("0<=der=%d<=k=%d must hold" % (der, k))
if not ext in (0, 1, 2):
raise ValueError("ext not in (0, 1, 2)")
x = asarray(x)
shape = x.shape
x = atleast_1d(x)
y, ier = _fitpack._spl_(x, der, t, c, k, ext)
if ier == 10:
raise ValueError("Invalid input data")
if ier == 1:
raise ValueError("Found x value not in the domain")
if ier:
raise TypeError("An error occurred")
return y.reshape(shape)