Trapezoidal rule for integral function

I need to apply trapezoidal rule for this Function and put it inside that tanh

: F=1-b*integral{K(s) v(x+s)}+d*integral{K(s) ur(x+s)} where K(s)=1/0.01*sqrt(2pi)*exp-s^2*/2*sigma^2 where a=0, b=1. i got error because of array. see the attached please

Answer 1

[Walter Roberson]

x=xl:dx:xr;

That is a numeric vector, that is not integers

K(x)=1/(0.05*sqrt(2*pi))*exp(-0.5*(x/0.05).^2);
y(x)= b*K(x)*v+d*K(x)*ur;

x is a numeric vector that is not integers. K is not defined at that point, so K(x) on the left side means that you are creating a variable and indexing it at those non-integer locations, which is an error.

You appear to trying to define a formula for K and y. In MATLAB, in order to define a formula using the syntax you are using, the indexing variable on the left needs to be a symbolic variable created with sym() or syms()

The non-symbolic way to define a formula in MATLAB is to use anonymous functions. That would look like

K = @(x) 1/(0.05*sqrt(2*pi))*exp(-0.5*(x/0.05).^2);
y = @(x) b*K(x)*v+d*K(x)*ur;

[lulu]

I see. Thank yoy for your comment. I did according to your advise but still has error regarding the integral.

[lulu]

How I can use the trapezoidal rule for the integral of y?. I tried as we can see in the attached file but it is not working.

[Torsten]

Didn't you read Walter's response ?

K and y have to be defined as function handles:

K = @(x) 1/(0.05*sqrt(2*pi))*exp(-0.5*(x/0.05).^2);
y = @(x) b*K(x)*v+d*K(x)*ur;

not as

K(x)=1/(0.05*sqrt(2*pi))*exp(-0.5*(x/0.05).^2);
y(x)= b*K(x)*v+d*K(x)*ur;

Then you can evaluate them as

xnum=xl:dx:xr;
ynum = y(x);
I = trapz(xnum,ynum)

[lulu]

Thank you for replaying, I saw his responce but I got error when I applied trapezoidal rule there (xnum=xl:dx:xr;

ynum = y(x);

I = trapz(xnum,ynum));

>> trapezoidal

Error using trapz (line 66)

Point spacing must be a scalar specifying uniform spacing or a vector of x-coordinates for each data point.

Error in trapezoidal (line 62)

I = trapz(ynum,xnum);

[Walter Roberson]

ur=zeros(J+1,Nt);
ul=zeros(J+1,Nt);
vr=zeros(J+1,Nt);
vl=zeros(J+1,Nt);
v=zeros(J+1,Nt);

Those are all arrays of zeros.

%%%%%%%%%%%%%%%%%%%%%%%%
K = @(x)1./(0.05*sqrt(2*pi)).*exp(-0.5*(x/0.05).^2);
y = @(x)b*K(x)*v+d*K(x)*ur;

The anonymous function definition for y captures the all-zero v and ur and freezes those arrays into the definition of y. y will not use the current value of v and ur as v and ur are updated.

For scalar inputs, K will return a scalar. b and d are scalars. So y will be scalar * array + scalar * array and the result of that is going to be an array.

Question: why do you calculate K(x) twice? Why did you not define

y = @(x) K(x) * (b * v + d * ur)

and then since b and v and d and ur are constants relative to the function, why did you not do

bvdur = (b * v + d * ur);
y = @(x) K(x) * bvdur;

?

F = int(y,w);

y is a function handle, but w is vector of 100 elements. int() is symbolic integration, not numeric integration. But int() requires that the second parameter be the name of a symbolic variable to integrate over.

What was your intention for integrating the function passing in a vector ? Especially since you seem to be doing indefinite integration rather than definite integration.

Q=trapz(F,w);

w is your vector of independent values. trapz() expects the vector of independent values to be the first parameter, so like

Q = trapz(w, F);

You do not use K or y later in the code after you have changed ur and v... and with v and ur being intialized to all 0, (b * v + d * ur) is going to be all 0, and so your y is going to return an array of zeros.

[Torsten]

@ima Kindy

According to the error message, your call to trapz is

I = trapz(ynum,xnum);

This is wrong. The input arguments must be reversed:

I = trapz(xnum,ynum);