dydx= spline(y, x)
-or- yp= spline(dydx, y, x, xp)
-or- yp= spline(y, x, xp)
computes the cubic spline curve passing through the points (X, Y).
With two arguments, Y and X, spline returns the derivatives DYDX at
the points, an array of the same length as X and Y. The DYDX values
are chosen so that the piecewise cubic function returned by the four
argument call will have a continuous second derivative.
The X array must be strictly monotonic; it may either increase or
The values Y and the derivatives DYDX uniquely determine a piecewise
cubic function, whose value is returned in the four argument form.
In this form, spline is analogous to the piecewise linear interpolator
interp; usually you will regard it as a continuous function of its
fourth argument, XP. The first argument, DYDX, will normally have
been computed by a previous call to the two argument spline function.
However, this need not be the case; another DYDX will generate a
piecewise cubic function with continuous first derivative, but a
discontinuous second derivative. For XP outside the extreme values
of X, spline is linear (if DYDX1 or DYDX0 keywords were specified,
the function will NOT have continuous second derivative at the
The XP array may have any dimensionality; the result YP will have
the same dimensions as XP.
If you only want the spline evaluated at a single set of XP, use the
three argument form. This is equivalent to:
yp= spline(spline(y,x), y, x, xp)
The keywords DYDX1 and DYDX0 can be used to set the values of the
returned DYDX(1) and DYDX(0) -- the first and last values of the
slope, respectively. If either is not specified or nil, the slope at
that end will be chosen so that the second derivative is zero there.
The function tspline (tensioned spline) gives an interpolation
function which lies between spline and interp, at the cost of
requiring you to specify another parameter (the tension).
interpreted function, defined at i/spline.i line 10