Indefinite integral for a step function with variable number of steps

Hello friends,

I have a function handle which is defined by interp1. Is there a way to find its indefinite integral?

For instance

x0=[1 2 5 7 10];y0=[2 1 3 2]; f=@(x)interp1(x0,y0,x,'previous');

Please note the above example is just a simple case (I know how to handle this easy case). My function is a step function with many steps where the number of steps are not known to me beforehand. So, in general my function is defined by f=@(x)interp1(mesh,c,x,'previous'); where mesh is my x-data, c is a vector of steps or y-data. How to find the indefinite integral of this function?

Thanks in advance!

Babak

Answer 1

[Torsten]

The definite integral between a and b where mesh(1) <= a < b <= mesh(end) can be computed as for every other function as

value_integral = integral(f,a,b)

where

f = @(x)interp1(mesh,c,x,'previous')

[Mohammad Shojaei Arani]

Unfortunately, even the definite integral fails. Try the following commands

x0=[1 2 5 7 10];y0=[2 1 3 2]; f=@(x)interp1(x0,y0,x,'previous');

value_integral = integral(f,2.5,3.6)

then I get the following error message

Error using interp1>reshapeAndSortXandV (line 445)

X and V must be of the same length.

Error in interp1 (line 128)

[X,V,orig_size_v] = reshapeAndSortXandV(X,V);

Error in @(x)interp1(x0,y0,x,'previous')

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

[Torsten]

y0 has only 4 elements. It must be of the same size as x0 - thus have 5 elements.

[Mohammad Shojaei Arani]

Thanks!