## splineInterp(xy, cond)

Constructs an interpolating spline.

 xy It is a matrix the first column of which contains the x values, the second contains the corresponding y values. The 'x' coordinates are assumed to be increasing. cond (Optional) Additional (linear) constraints. For details see description. return value Spline matching the spline and additional constraints.

The order of the spline will be the number of additional constraints plus one. In particular, (explicit) no constraints will imply a piece-wise linear function. However, the default is cubic interpolation with zero second derivatives at the two end points.

``` xy = [-100,4; 8,93; 42,-88; 444, 827]; xunit = 1J; yunit = 1V; xmin = min(xy[...;0]); xmax = max(xy[...;0]); eps = (xmin-xmax)/200; xmin -= 2*eps; xmax += 2*eps; x = (xmin..eps..xmax)*xunit; print("Default constraints").title() p = splineInterp(xy * [xunit,0;0,yunit]) y = (@(x) splineEval(p,x))(#x); [! xy[...;0]*xunit, (@(x) splineEval(p,x))(#(xy[...;0]*xunit))' !] plot(x,y) print("Piece-wise linear").title() p = splineInterp(xy * [xunit,0;0,yunit], []) y = (@(x) splineEval(p,x))(#x); plot(x,y) print("Random constaints").title() cond = [ // It will take 4 at 128 (but 128 is not a node for the spline) (@(s) splineEval(s,128J)), 4V; // The second derivative at 228 will be also 4 (without being a node) (@(s) splineEval(splineDiff(s,2),228J)*1J^2), 4V; // ...and some combination of the above two. (@(s) splineEval(splineDiff(s,3), 16J)*1J^3 - 2*splineEval(s,128J)), 42V]; p = splineInterp(xy * [xunit,0;0,yunit], cond) y = (@(x) splineEval(p,x))(#x); plot(x,y) ```