Integral of a matrix (x = integration(v)dt) to find x in each time step - how to get it?

Dear altruists,

I have these (5x1 size) time steps -

t1 = 5.000;
t2 = 5.005;
t3 = 5.015;
t4 = 5.020;
t5 = 5.025;

For each of these time steps, I have this (8x5 size) velocity matrix -

0.223886255942431	0.766594808762019	0.777477860918720	1.46402363417739	NaN
NaN	                0.666581311838176	0.440897758695197	0.786687514042304	NaN
NaN	                0.760744913959832	0.726179926996350	1.04378898162688	0.222809516150796
NaN	                0.275556537143772	0.805109395242995	0.500274785771561	1.14165961699158
NaN	                0.388113337549528	0.895797227421048	0.868957410079128	0.906645475357619
0.514726870663309	1.37194840648291	1.17901149918237	0.267171163532900	0.679251749599892
0.700833065925187	0.843516259310205	0.692695783390200	0.206484971298492	0.773597719024071
0.748304643154520	0.433574718009251	0.551547292426642	0.346941328685530	0.738716957530404

How can I intigrate it (x = integration(v)dt) in such way that I get the position of x in every time step? I mean, I want x1,x2,x3,x4, and x5 :)

Thank you so much!

[Torsten]

I suspect that the five columns correspond to the velocities at the five time instants that you gave.

But what are the seven rows ? Seven different sprinters starting at the same position and having unequal speed ?

And it should be clear that you will have to remove the NaN values somehow in your matrix to get reasonable results.

And what is the initial x0 the races start from ?

[Ashfaq Ahmed]

Yes, you interpreted it right. Those are 7 different person's data. There are NaN values in the problem, but they were some other values (say, 0) how would I do the calculation?

[Ashfaq Ahmed]

And the innitial x0 is 0 for all the rows.

Answer 1

[Torsten]

After replacing the NaN values in the matrix, just do

T = [5 5.005 5.015 5.020 5.025];
A = [0.223886255942431	0.766594808762019	0.777477860918720	1.46402363417739	0 
    0	                0.666581311838176	0.440897758695197	0.786687514042304	0 
    0	                0.760744913959832	0.726179926996350	1.04378898162688	0.222809516150796
    0	                0.275556537143772	0.805109395242995	0.500274785771561	1.14165961699158
    0	                0.388113337549528	0.895797227421048	0.868957410079128	0.906645475357619
    0.514726870663309	1.37194840648291	1.17901149918237	0.267171163532900	0.679251749599892
    0.700833065925187	0.843516259310205	0.692695783390200	0.206484971298492	0.773597719024071
    0.748304643154520	0.433574718009251	0.551547292426642	0.346941328685530	0.738716957530404];
X0 = zeros(size(A,1),1);
for i = 1:size(A,1)
    X(i,:) = X0(i) + cumtrapz(T,A(i,:));
end
X

[Ashfaq Ahmed]

Yes, that's exactly what I wanted! Thank you so much Torsten :) You are amazing!