How to fit hyperbola to scatter plot?

I have attached data I want to fit with hyperbola. As you can see in attached picture, the fit is appearing behind the scattered plot, however, I want it above the scatter plot. Here is the code I am using,

XLSdatafile = 'b46.csv';
XLIM = [0.4     0.24  ];  % beginning/end of yellow selection region
YLIM = [0.12     0.4  ];  % beginning/end of yellow selection region
INITIAL_FIT_GUESS = 0.0200; % initial ecd guess
INITIAL_2FIT_GUESS = 2.35 * INITIAL_FIT_GUESS;
if ~exist('XLSdatafile_loaded','var') || ~strcmp(XLSdatafile, XLSdatafile_loaded)
  M = load(XLSdatafile);
  XLSdatafile_loaded = XLSdatafile;  
  X = M(:,1);
  Y = M(:,2);
end
f3=figure;
bins=75;
xi = linspace(min(X(:)),max(X(:)),bins);
yi = linspace(min(Y(:)),max(Y(:)),bins);
xr = interp1(xi,1:numel(xi),X,'nearest')';
yr = interp1(yi,1:numel(yi),Y,'nearest')';
scatter2dheat = log10(accumarray([xr' yr'], 1, [bins bins]));
scatter2dheat(isinf(scatter2dheat))=0; % replace inf with 0
pp3 = surf(xi,yi,scatter2dheat');
%this is a nice colormap
colormap([1 1 1;0.949999988079071 1 1;0.899999976158142 1 1;0.850000023841858 1 1;0.800000011920929 1 1;0.75 1 
1;0.699999988079071 1 1;0.649999976158142 1 1;0.600000023841858 1 1;0.550000011920929 1 1;0.5 1 1;0.449999988079071 1 
1;0.400000005960464 1 1;0.349999994039536 1 1;0.300000011920929 1 1;0.25 1 1;0.200000002980232 1 1;0.150000005960464 1 
1;0.100000001490116 1 1;0.0500000007450581 1 1;0 1 1;0.0476190485060215 1 0.952380955219269;0.095238097012043 1 
0.904761910438538;0.142857149243355 1 0.857142865657806;0.190476194024086 1 0.809523820877075;0.238095238804817 1 
0.761904776096344;0.28571429848671 1 0.714285731315613;0.333333343267441 1 0.666666686534882;0.380952388048172 1 
0.61904764175415;0.428571432828903 1 0.571428596973419;0.476190477609634 1 0.523809552192688;0.523809552192688 1 
0.476190477609634;0.571428596973419 1 0.428571432828903;0.61904764175415 1 0.380952388048172;0.666666686534882 1 
0.333333343267441;0.714285731315613 1 0.28571429848671;0.761904776096344 1 0.238095238804817;0.809523820877075 1 
0.190476194024086;0.857142865657806 1 0.142857149243355;0.904761910438538 1 0.095238097012043;0.952380955219269 1 
0.0476190485060215;1 1 0;1 0.954545438289642 0;1 0.909090936183929 0;1 0.863636374473572 0;1 0.818181812763214 0;1 
0.772727251052856 0;1 0.727272748947144 0;1 0.681818187236786 0;1 0.636363625526428 0;1 0.590909063816071 0;1 
0.545454561710358 0;1 0.5 0;1 0.454545468091965 0;1 0.409090906381607 0;1 0.363636374473572 0;1 0.318181812763214 0;1 
0.272727280855179 0;1 0.227272734045982 0;1 0.181818187236786 0;1 0.136363640427589 0;1 0.0909090936183929 0;1 
0.0454545468091965 0;1 0 0]);
set(gca,'Clim',[max(min(scatter2dheat(:)),1e-3) max(scatter2dheat(:))]);
view(2)
grid off
shading flat
axis([min(X) max(X) min(Y) max(Y)]);  
hold on  
fit_const =  INITIAL_FIT_GUESS;
time    = 0.01:0.001:0.3;
current = fit_const./time;
figure(f3)
hold on
p_fit1 = plot(time,current,'r-');
set(gca,'ylim',[0.05,0.5]);
hold on
fit_const =  INITIAL_2FIT_GUESS;
time    = 0.01:0.001:0.5;
current = fit_const./time;
figure(f3)
hold on
p_fit1 = plot(time,current,'r-');

Hyperbola fit is my only choice. Could anyone suggest a fitting code?

Answer 1

[Ameer Hamza]

The problem is happening because you are viewing 3D plot from a 2D projection. In order to bring the line to the front, you need to give them z values greater the then the scatter plot points. You can use the following code to get the desired results

XLSdatafile = 'b46.csv';
XLIM = [0.4     0.24  ];  % beginning/end of yellow selection region
YLIM = [0.12     0.4  ];  % beginning/end of yellow selection region
INITIAL_FIT_GUESS = 0.0200; % initial ecd guess
INITIAL_2FIT_GUESS = 2.35 * INITIAL_FIT_GUESS;
if ~exist('XLSdatafile_loaded','var') || ~strcmp(XLSdatafile, XLSdatafile_loaded)
M = load(XLSdatafile);
XLSdatafile_loaded = XLSdatafile;  
X = M(:,1);
Y = M(:,2);
end
f3=figure;
bins=75;
xi = linspace(min(X(:)),max(X(:)),bins);
yi = linspace(min(Y(:)),max(Y(:)),bins);
xr = interp1(xi,1:numel(xi),X,'nearest')';
yr = interp1(yi,1:numel(yi),Y,'nearest')';
scatter2dheat = log10(accumarray([xr' yr'], 1, [bins bins]));
scatter2dheat(isinf(scatter2dheat))=0; % replace inf with 0
pp3 = surf(xi,yi,scatter2dheat');
set(gca,'Clim',[max(min(scatter2dheat(:)),1e-3) max(scatter2dheat(:))]);
view(2)
grid off
shading flat
axis([min(X) max(X) min(Y) max(Y)]);  
hold on  
fit_const =  INITIAL_FIT_GUESS;
time    = 0.01:0.001:0.3;
current = fit_const./time;
figure(f3)
hold on
p_fit1 = plot3(time,current, max(max(scatter2dheat))*ones(size(time)),'r-', 'LineWidth', 4);
hold on
fit_const =  INITIAL_2FIT_GUESS;
time    = 0.01:0.001:0.5;
current = fit_const./time;
figure(f3)
hold on
p_fit2 = plot3(time,current,  max(max(scatter2dheat))*ones(size(time)), 'r-','LineWidth', 4);

I have removed the colormap to keep code compact. You can add a color map of your choice.

To get the optimal parameters for your hyperbole, you can use lsqcurvefit().