MATLAB: Definite integral of numerical vectors

integrationvectors

i'm looking for to solve a definite integral of two vectors

I know: z vector of numbers and G(z) vector of numbers. The limits of integration are zmin and zmax

I should to calculate: Integral between zmin,zmax of [G(z) * z^(7/6)] dz

Best Answer

I think you have to use numerial method of integration such as simpson rule or trapezoidal rule. Make a routine for either of these methods and calculate them for each z values and add up. If sum over them, you will get the answer. I hope it works for you. Let me know if you have problem on making subroutine.

Goof luck.

Related Solutions

MATLAB: Multiple integrals with limits as variables

function_of_scalar_z_only = @(z)integral2(@(w,l)f(z,w,l),0,L,0,@(w)w);
g = @(z)arrayfun(function_of_scalar_z_only,z);

Depending on how f is written, you may need to manually expand the scalar z.

function_of_scalar_z_only = @(z)integral(@(w,l)f(z*ones(size(w)),w,l),0,L,0,@(w)w);
g = @(z)arrayfun(function_of_scalar_z_only,z);

As the long function name suggests, that first function is only good for a scalar input. The ARRAYFUN modification "vectorizes" it so you can do all the usual things with g that you want, e.g. things like

x = linspace(zmin,zmax);
y = g(x);
plot(x,y);

MATLAB: Numerical integration

This turned out to be surprisingly tricky, but here is the solution. First, define a function

function fzv = integrateOverSecondPair(fun,x,y,zmin,zmax,vmin,vmax)
% DBLQUAD evaluates FUN for a vector x and scalar y. The backwards loop is
% Matt Fig's dynamic preallocation.
for ii=numel(x):-1:1
  g = @(z,v) fun(x(ii),y,z,v);
  fzv(ii) = dblquad(g,zmin,zmax,vmin,vmax);
end

Then use the commands

fzv = @(x,y) integrateOverSecondPair(@f,x,y,zmin,zmax,vmin,vmax);
fxyzv = dblquad(fzv,xmin,xmax,ymin,ymax);

Best Answer

Related Solutions

MATLAB: Multiple integrals with limits as variables

MATLAB: Numerical integration

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