def basis(self, x, d=0, lower=None, upper=None):
"""
Evaluate the basis of the BSpline or its derivative.
If lower or upper is specified, then only
the [lower:upper] elements of the basis are returned.
INPUTS:
x -- x values at which to evaluate the basis element
i -- which element of the BSpline to return
d -- the order of derivative
lower -- optional lower limit of the set of basis
elements
upper -- optional upper limit of the set of basis
elements
OUTPUTS: y
y -- value of d-th derivative of the basis elements
of the BSpline at specified x values
"""
x = N.asarray(x)
_shape = x.shape
if _shape == ():
x.shape = (1,)
x.shape = (N.product(_shape,axis=0),)
if upper is None:
upper = self.tau.shape[0] - self.m
if lower is None:
lower = 0
upper = min(upper, self.tau.shape[0] - self.m)
lower = max(0, lower)
d = N.asarray(d)
if d.shape == ():
v = _bspline.evaluate(x, self.tau, self.m, int(d), lower, upper)
else:
if d.shape[0] != 2:
raise ValueError, "if d is not an integer, expecting a jx2 \
array with first row indicating order \
of derivative, second row coefficient in front."
v = 0
for i in range(d.shape[1]):
v += d[1,i] * _bspline.evaluate(x, self.tau, self.m, d[0,i], lower, upper)
v.shape = (upper-lower,) + _shape
if upper == self.tau.shape[0] - self.m:
v[-1] = N.where(N.equal(x, self.tau[-1]), 1, v[-1])
return v
def basis_element(self, x, i, d=0):
"""
Evaluate a particular basis element of the BSpline,
or its derivative.
INPUTS:
x -- x values at which to evaluate the basis element
i -- which element of the BSpline to return
d -- the order of derivative
OUTPUTS: y
y -- value of d-th derivative of the i-th basis element
of the BSpline at specified x values
"""
x = N.asarray(x, N.float64)
_shape = x.shape
if _shape == ():
x.shape = (1,)
x.shape = (N.product(_shape,axis=0),)
if i < self.tau.shape[0] - 1:
## TODO: OWNDATA flags...
v = _bspline.evaluate(x, self.tau, self.m, d, i, i+1)
else:
return N.zeros(x.shape, N.float64)
if (i == self.tau.shape[0] - self.m):
v = N.where(N.equal(x, self.tau[-1]), 1, v)
v.shape = _shape
return v
