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I am struggling in finding a way to write a code which can let me do the following:

I have a nonlinear ODE called fy.

fy = g1*p1+g2*p2+g3*p3; % g1,g2,g3 are real-valued numbers and p1,p2,p3 are vectors

g1, g2 and g3 are constants found by the method of linear regression.

g1 = 591.5121
g2 = 35.1352
g3 = 107.5798

the vectors p1, p2 and p3 are given as follow: (sorry than I am not giving the hole vector p1, p2 and p3 since they have 1500 rows:

[ p1        p2        p3] =
-0.8714   -0.0527   -0.3103
-0.3154   -0.0101    0.0874
-0.1972   -0.0029    0.1247
-0.1449   -0.0001    0.1294
-0.1151    0.0012    0.1271
-0.0959    0.0020    0.1231
-0.0824    0.0025    0.1187
-0.0723    0.0028    0.1144
-0.0646    0.0030    0.1104
-0.0584    0.0032    0.1068
-0.0533    0.0033    0.1034
-0.0491    0.0034    0.1003
-0.0455    0.0035    0.0975
-0.0425    0.0035    0.0949
-0.0398    0.0036    0.0925
-0.0375    0.0036    0.0903
-0.0355    0.0036    0.0882
-0.0336    0.0036    0.0863
-0.0320    0.0037    0.0845
-0.0305    0.0037    0.0828
-0.0292    0.0037    0.0812
-0.0280    0.0037    0.0797
-0.0268    0.0037    0.0783
-0.0258    0.0037    0.0769
-0.0249    0.0037    0.0757
-0.0240    0.0037    0.0745
-0.0232    0.0037    0.0733
-0.0224    0.0037    0.0722
-0.0217    0.0037    0.0712
-0.0211    0.0037    0.0702
   .         .          .
   .         .          .
   .         .          .

I am solving the ODE as follows:

fy = g1*p1+g2*p2+g3*p3;                     (1)
y= xj; % here has xj the same dim. than fy
f = @(yq)interp1(y, fy, yq);
tspan = 0:0.02:1;
x0 = 0.2;
[~, xt] = ode45(@(t,y)f(y), tspan, x0);

And I get a very nice curve.

My problem is: I have a Library:

Library = [L1 L2 L3]; % L1, L2, L3 are vectors of same size than p1, p2, p3

This Library contains potential triples, and ONE SET of these triples (given in row...lets say 568) can allow me to get the same nice curve I am getting from (1). In other words, if I change g1, g2 and g3 with l1, l2 and l3 (which are found in the row 586 from Library) I should have almost the same results as in (1).

I need to find a way to find this SET of triples!

The only information to my disposal is the information from (1) and the curve I get. It would be awful if I have to compare all the curves to the one I get from (1)... because my Library has 1500 triples which implies 1500 curves... After I have my triples I could solve the following system in the same way as I did it with (1).

 fy = l1*p1+l2*p2+l3*p3;                 (2)
 y= xj; % xj % has the same dim than fy
 f = @(yq)interp1(y, fy, yq);
 tspan = 0:0.02:1;
 x0 = 0.2;
 [~, xt2] = ode45(@(t,y)f(y), tspan, x0);

fy from (1) should be approximate to fy from (2).

some more info: From linear regression I was supposed to get a set of triples that are/exits in my library, but this is not the case... my system is, because of this, sloppy. For this reason I have to find a way to connect in some way these two outputs. (the g's and the l's).

Sergio Haram
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1 Answers1

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You may use dsearchn to find the closest triplet.

x = rand(1000,3);
xi = rand(1,3);
k = dsearchn(x,xi);

Alternatively, you may compare all the 1500 generated curves with the original one. There are several techniques such as the ones described here how to find the similarity between two curves and the score of similarity?

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marsei
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  • Hi @Macduff, thanks for tour quick answer, I will try your suggestion and check the link you are posting. – Sergio Haram Feb 21 '14 at 12:31
  • Hi @Macduff, I have examined your suggestion (and try it). My problem is that none of my `g`-values are/exists in `Library`. In other words, I don't have any `xi` in my `x`. Can I still use `dsearchn`? – Sergio Haram Feb 21 '14 at 13:01
  • You mean that you can't find any closest triplet? You can also try a distance of your choice and find its minimum (minimum of the euclidian distance for example) – marsei Feb 21 '14 at 13:06
  • Hi again @Macduff. Yes, I do not have any triple which is close to my `g`-values. That is my problem, I get a nice curve with the `g's` and I have to find the `l`-values that can help me reproduce the same curve. Nevertheless, `g` and `l` doesn't need to be close to each other. And the are not. – Sergio Haram Feb 21 '14 at 13:28
  • By the way, I have try this problem where I have control of the `g's` and `l's` and it works, but I need to find a way to make it work with out manipulating my `g`-values. – Sergio Haram Feb 21 '14 at 13:29