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- bisplev(x, y, tck, dx=0, dy=0)
- Evaluate a bivariate B-spline and its derivatives.
Description:
Return a rank-2 array of spline function values (or spline derivative
values) at points given by the cross-product of the rank-1 arrays x and y.
In special cases, return an array or just a float if either x or y or
both are floats.
Inputs:
x, y -- Rank-1 arrays specifying the domain over which to evaluate the
spline or its derivative.
tck -- A sequence of length 5 returned by bisplrep containing the knot
locations, the coefficients, and the degree of the spline:
[tx, ty, c, kx, ky].
dx, dy -- The orders of the partial derivatives in x and y respectively.
Outputs: (vals, )
vals -- The B-pline or its derivative evaluated over the set formed by
the cross-product of x and y.
- bisplrep(x, y, z, w=None, xb=None, xe=None, yb=None, ye=None, kx=3, ky=3, task=0, s=None, eps=9.9999999999999998e-17, tx=None, ty=None, full_output=0, nxest=None, nyest=None, quiet=1)
- Find a bivariate B-spline representation of a surface.
Description:
Given a set of data points (x[i], y[i], z[i]) representing a surface
z=f(x,y), compute a B-spline representation of the surface.
Inputs:
x, y, z -- Rank-1 arrays of data points.
w -- Rank-1 array of weights. By default w=ones(len(x)).
xb, xe -- End points of approximation interval in x.
yb, ye -- End points of approximation interval in y.
By default xb, xe, yb, ye = x[0], x[-1], y[0], y[-1]
kx, ky -- The degrees of the spline (1 <= kx, ky <= 5). Third order
(kx=ky=3) is recommended.
task -- If task=0, find knots in x and y and coefficients for a given
smoothing factor, s.
If task=1, find knots and coefficients for another value of the
smoothing factor, s. bisplrep must have been previously called
with task=0 or task=1.
If task=-1, find coefficients for a given set of knots tx, ty.
s -- A non-negative smoothing factor. If weights correspond to the inverse
of the standard-deviation of the errors in z, then a good s-value
should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m=len(x)
eps -- A threshold for determining the effective rank of an over-determined
linear system of equations (0 < eps < 1) --- not likely to need
changing.
tx, ty -- Rank-1 arrays of the knots of the spline for task=-1
full_output -- Non-zero to return optional outputs.
nxest, nyest -- Over-estimates of the total number of knots. If None then
nxest = max(kx+sqrt(m/2),2*kx+3),
nyest = max(ky+sqrt(m/2),2*ky+3)
quiet -- Non-zero to suppress printing of messages.
Outputs: (tck, {fp, ier, msg})
tck -- A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
coefficients (c) of the bivariate B-spline representation of the
surface along with the degree of the spline.
fp -- The weighted sum of squared residuals of the spline approximation.
ier -- An integer flag about splrep success. Success is indicated if
ier<=0. If ier in [1,2,3] an error occurred but was not raised.
Otherwise an error is raised.
msg -- A message corresponding to the integer flag, ier.
Remarks:
SEE bisplev to evaluate the value of the B-spline given its tck
representation.
- myasarray(a)
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