How to get X values given an Y from a Spline

Hey guys, I obtained a bunch of splines (given one at a time from a for cycle). From this curves I would like to know the values of x at random y points, example for ymin:ymax:10 and store each one of these points from each spline for later use.

My code is this (the for cycles leading up to the spline functionare there to change the data from errors and small deviations):

                      z1 = zeros(1,numWls);
                      z = zeros(1,numWls);
                      ymin = newSec.FOB;
                      ymax = newSec.DWL;
                      xx=zeros(1,numWls+2);
                      yy=zeros(1,numWls);
                      y = linspace(ymin , ymax , numWls);
                      for j=1:numWls                            
                              z(j) = z1(j);
                              z1(j) = newSec.FSectBWL(y(j));
                      end;
                      xx=(y);
                      yy=z1;
                      for j=2:numWls-1
                          if yy(j)<= yy(j-1)
                              yy(j)=(yy(j+1)+yy(j-1))/2.0;
                          end
                      end
                      for j=1:numWls
                          if xx(j)>newSec.FOB
                              if yy(j)<0
                                  yy(j)=0.001;
                              end
                          else
                              yy(j)=(1-newSec.KeelRise);
                          end
                      end
                      cs=spline(xx,[tan(deg2rad(newSec.KeelSlope)) yy tan(deg2rad(newSec.DwlSlope))]);
                      intx=linspace(newSec.FOB,newSec.DWL,numWls);
                      for j=1:numWls
                          if intx(j)<newSec.FOB
                              y = 0;
                          elseif intx(j)>=newSec.FOB
                              y = ppval(cs,intx);
                          end
                      end
                      plot(intx,y,intx,0.9);
                      grid on;

Answer 1

[John D'Errico]

I provide code for this in my SLM toolbox , which provides additional tools for computations with splines that also work on pp form functions returned from spline or pchip. All that you need is the slmsolve utility, which generates all the roots (in case there are multiple solutions.)

For example...

x = 0:.25:5;
y = sin(x);
pp = spline(x,y);
xsol = slmsolve(pp,.5)
xsol =
     0.5236        2.618

The values returned are those which produce the indicated function value, so effectively inverting the spline.

format long g
ppval(pp,xsol)
ans =
                     0.5                       0.5