Using trapz function to provide answers using loop

Hey,

I am trying to use the trapz function in a loop:

y_approx = zeros ([21 1]);

for i = 1:length(x)

y_approx = trapz(x(i),y)

end

It is providing me the 21 answers but they are incorrect. I think it is using the 21 y for each iteration of x. 21 y values for 1 x value, 21 y values for 2 x values etc. How do I alter the code to make it use the same number of y values as x values?

Answer 1

[Chunru]

% The way to use trapz
x= 1:20;                    % x
y = randn(20, 1);           % y

ytrapz = trapz(x, y)        % integral y dx

ytrapz = -0.0920

[Dyl]

I understand how to use trapz, I am trying to calculate an answer for each point of x. Using trapz that way only provides the answer for the whole domain. ie. x =20. I am trying to caculate answers for x=1, x=2, ... x=19, x=20 using a loop.

[Chunru]

So this is what you want? You don't need trapz function

x= 1:20;                    % x
y = randn(20, 1);           % y
ytrapz = trapz(x, y)        % integral y dx

ytrapz = 0.2045

yloop = zeros(size(x));
for i=2:length(x)
    yloop(i) = yloop(i-1) + (y(i) + y(i-1))/2*(x(i)-x(i-1));
end
yloop([1:3 end-3:end])

ans = 1×7

0 -0.7630 -0.5163 -0.4795 -0.0430 0.0183 0.2045

[Dyl]

I need the trapz fuction as I am estimating y values using the trapezoidal method. Basically, I need a loop that does:

y2 = trapz(x(1:2),y(1:2))

y3 = trapz(x(1:3),y(1:3))

...

y19 = trapz(x(1:20),y(1:20))

y20 = trapz(x(1:21),y(1:21))

[Chunru]

That is not really necessary since the looping code above is doing the trapz job in a more efficient way when you want the intermidiate results.

However, if you insisit, you can do the following (definitely not recommended):

x= 1:20;                    % x
y = randn(20, 1);           % y
ytrapz = trapz(x, y)        % integral y dx

ytrapz = 3.5232

yloop = zeros(size(x));
for i=2:length(x)
    yloop(i) = yloop(i-1) + (y(i) + y(i-1))/2*(x(i)-x(i-1));
end
yloop([1:3 end-3:end])

ans = 1×7

0 -0.7511 -0.5029 5.0386 4.9629 4.9692 3.5232

% Not recommended:
yloop1 = zeros(size(x));
for i=2:length(x)
    yloop1(i) = trapz(x(1:i), y(1:i));
end
yloop1([1:3 end-3:end])

ans = 1×7

0 -0.7511 -0.5029 5.0386 4.9629 4.9692 3.5232