Trapezoidal rule for integral function
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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
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Walter Roberson
2022-9-11
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;
6 个评论
lulu
2022-9-11
lulu
2022-9-11
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
2022-9-12
Walter Roberson
2022-9-12
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
2022-9-12
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);
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