integral with vectoric varying coeficient

Hello , i have a basic function

exp(-x.^2).*log(x).^2

which i integrate in a certain interval.

i want to multiply my basic function with a vectoric coefficient called coef_vec that varies with the interval.

so if the integral is at 5 my basic function whould be multiplied with coef_vec(5).

i know that its some how turning the integral into a loop.

Is it possible in matlab?

Thanks.

coef_vec=linspace(1,10,100)
fun = @(x)coef_vec*exp(-x.^2).*log(x).^2;
q = integral(fun,1,10);

Answer 1

[Ameer Hamza]

You need to consider that value of x is not always an integer, it can be a floating-point too. In that case, coef_vec(x) will fail. You need to interpolate your vector to give value on that range. Try this code

coef_vec = linspace(1,10,100);
coef_fun = @(x) interp1(1:numel(coef_vec), coef_vec, x);
fun = @(x) coef_fun(x).*exp(-x.^2).*log(x).^2;
q = integral(fun,1,10);

[fima v]

Hello Ameer, actually my coefficient has a filter like shape and polifit if not work for it

because of the blank space of the filter.

I get a polinomial wich gives me a pointy hill ratther than a filter plot as shown bellow.

and i tried polyfit of 5 order

What could be done to interpolate such filter shape?

Thanks.

[Ameer Hamza]

polyfit, gives a single polynomial curve. interp1() interpolate locally. Please try to see if interp1() gives the required interpolation behavior?

[fima v]

Hello Ameer, but i need a continues formula to use in my integral.

vq = interp1(x,v,xq)

how do i convert my vq data into a contines formula?

Thanks.

[Ameer Hamza]

I have defined coef_fun as a function handle using interp1 so that it can be continually evaluated at all the points. If you just use interp1 alone, then you will again get a finite vector. The function handle allows the integral to evaluate interp1 at an arbitrary point.

Following code shows the difference between interp1 and polyfit

x = 0:0.1:10;
coef_vec = gensig('square', 2, 10, 0.1) + 0.1*rand(size(x)).';
coef_fun = @(xq) interp1(x, coef_vec, xq);

xq = linspace(0, 10, 200);

p = polyfit(x, coef_vec, 10);
figure;
plot(x, coef_vec, '+-', xq, polyval(p, xq), '-o')
title('Polyfit')
figure;
plot(x, coef_vec, '+-', xq, coef_fun(xq), '-o')
title('interp1')

[Ameer Hamza]

Try this

data = load('Default Dataset4.csv');
x = data(:,1);
y = data(:,2);

[x, index] = unique(x);
coef_fun = @(xq) interp1(x, y(index), xq);
xq = linspace(3.5,23,100000);
plot(xq, coef_fun(xq))
title('interp1')

Answer 2

[David Hill]

Why not do it after computing the integral since it is a constant.

fun = @(x)coef_vec*exp(-x.^2).*log(x).^2;
q = integral(fun,1,10);
q=q*linspace(1,10,100);

[fima v]

because i want the coeffecient to be tied to the interval

so it needs to be during the integration.