function [y] = sumsqu(xx)
d = length(xx);
sum = 0;
for ii = 1:d
xi = xx(ii);
sum = sum + ii*xi^2;
end
y = sum;
end
Above is the code for d variables. Whenever I call the function I get the sum as expected. Now I want to find the numerical gradient of the function. But since the function is returning a scalar value, gradient returns 0 obviously. What can I do so that gradient first evaluates in its variable form then return an array corresponding to [x1 x2 x3....xd]?
As you can see in the picture, I want it in that order. And I also want d as a variable so that code can be generic. Hope you understood my problem.
Your function does exactly this:
y = sum(xx.^2 .* (1:numel(xx)));
The derivatives then are:
y = 2*xx .* (1:numel(xx));
(according to the hand-written equations).
You should avoid using sum as a variable name, you can see above that it is an important function, if you assign a value to sum, you hide the function and can no longer use it.
For your specific function, you can calculate the gradient analytically like:
g = 2*(1:length(xx)).*xx;
You can also replace the call for length(xx) by d if it is given.
Related
I have written a function called "tension.m" in which I have used if else condition as shown below.
function [T,T_earlyvalues,T_latervalues] = tension(u,sigma,G,N,K)
%the values of sigma,G,N,K can be taken arbitrary.
sigma=2; G=3;N=8;K=1; v=1;
w=2.2;
if u<w
T =v*sqrt(sigma+G^2/(N-K));
T_earlyvalues=T;
else
T=(2*v)*sqrt(sigma+G^2/(N+K));
T_latervalues=T;
end
Now in another script "myvalues.m" I need to call T_earlyvalues and T_latervalues separately.
%have some coding before this part
sigma0=2400; lambda=1.3; v=2; sigma=2; G=3;N=8;K=1;
u=0:0.01:5;
T=tension(u,sigma,G,N,K);
T_earlyvalues=tension(u,sigma,G,N,K);
T_latervalues=tension(u,sigma,G,N,K);
deltaA=T_earlyvalues*sigma0*pi;
deltaB=T_latervalue*lambda*pi/2;
%have some coding after this part
How could I call the said values which are under if-else statement from tension.m function to myvalues.m script?
You have defined the tension function such that it returns three outputs.
If you call that function by requiring only one output, the function returns the first value, in your case, T
This implies that
T=tension(u,sigma,G,N,K);
shoud work since T is the first output parameter
T_earlyvalues=tension(u,sigma,G,N,K);
T_latervalues=tension(u,sigma,G,N,K);
are not working, since, actually tension returns the first value (T, whjikle you are expecting the second and the third respectively.)
You can cahnge the two above calls this way:
[~,T_earlyvalues,~]=tension(u,sigma,G,N,K);
[~,~,T_latervalues]=tension(u,sigma,G,N,K);
The ~ allows to avoid the function return the output paraemter.
You can find additional information here
Notice that in your function T_earlyvalue is not set in the else block, same for T_latervalue in the if block.
This will generate an error such as
Output argument T_earlyvalue (and maybe others) not assigned during call to tension
or
Output argument T_latervalues (and maybe others) not assigned during call to tension
You can initialize the output values to default values, at the beginning of the function, for example:
T=NaN
T_earlyvalue=NaN
T_latervalues=NaN
You can then use these special values (or any other you want to use) to trace, for example, if the if block has been executed or the else.
There seem to be a number of issues here, not the least of which is some confusion about how output argument lists work when defining or calling functions. I suggest starting with this documentation to better understand how to create and call functions. However, this issue is somewhat moot because the larger problem is how you are using your conditional statement...
You are trying to pass a vector u to your function tension, and from what I can tell you want to return a vector T, where the values of T for u < w are computed with a different formula than the values of T for u >= w. Your conditional statement will not accomplish this for you. Instead, you will want to use logical indexing to write your function like so:
function [T, index] = tension(u, sigma, G, N, K)
T = zeros(size(u)); % Initialize T to a vector of zeroes
w = 2.2;
index = (u < w); % A logical vector, with true where u < w, false where u >= w
T(index) = u(index)*v*sqrt(sigma+G^2/(N-K)); % Formula for u < w
T(~index) = 2*(u(~index)-v)*sqrt(sigma+G^2/(N+K)); % Formula for u >= w
end
Now you can call this function, capturing the second output argument to use for identifying "early" versus "late" values:
sigma0 = 2400; lambda = 1.3; v = 2; sigma = 2; G = 3; N = 8; K = 1;
u = 0:0.01:5;
[T, earlyIndex] = tension(u, sigma, G, N, K); % Call function
T_earlyvalues = T(earlyIndex); % Use logical index to get early T values
T_latervalues = T(~earlyIndex); % Use negated logical index to get later T values
And you can then use the subvectors T_earlyvalues and T_latervalues however you like.
I am working on an assignment that requires me to use the trapz function in MATLAB in order to evaluate an integral. I believe I have written the code correctly, but the program returns answers that are wildly incorrect. I am attempting to find the integral of e^(-x^2) from 0 to 1.
x = linspace(0,1,2000);
y = zeros(1,2000);
for iCnt = 1:2000
y(iCnt) = e.^(-(x(iCnt)^2));
end
a = trapz(y);
disp(a);
This code currently returns
1.4929e+03
What am I doing incorrectly?
You need to just specify also the x values:
x = linspace(0,1,2000);
y = exp(-x.^2);
a = trapz(x,y)
a =
0.7468
More details:
First of all, in MATLAB you can use vectors to avoid for-loops for performing operation on arrays (vectors). So the whole four lines of code
y = zeros(1,2000);
for iCnt = 1:2000
y(iCnt) = exp(-(x(iCnt)^2));
end
will be translated to one line:
y = exp(-x.^2)
You defined x = linspace(0,1,2000) it means that you need to calculate the integral of the given function in range [0 1]. So there is a mistake in the way you calculate y which returns it to be in range [1 2000] and that is why you got the big number as the result.
In addition, in MATLAB you should use exp there is not function as e in MATLAB.
Also, if you plot the function in the range, you will see that the result makes sense because the whole page has an area of 1x1.
How can I change the variables in MATLAB numeric function?
for example, the original function is:
function y = myfile1(a,b,c)
y = a*b*c
end
and I want to convert it into this form:
function y = myfile2(x)
y = x(1)*x(2)*x(3)
end
is there any possible way to do it? (of course, not manually edit it)
Thanks
You can pass the vector x to another function, myfile2, then call myfile1 with the vector numbers, like that:
function y = myfile2(x)
y = myfile1(x(1),x(2),x(3))
end
So that a,b,c in the function myfile1 will be actually x(1), x(2), x(3).
I want to write a function that approximates integrals with the trapezoidal rule.
I first defined a function in one file:
function[y] = integrand(x)
y = x*exp(-x^2); %This will be integrand I want to approximate
end
Then I wrote my function that approximates definite integrals with lower bound a and upper bound b (also in another file):
function [result] = trapez(integrand,a,b,k)
sum = 0;
h = (b-a)/k; %split up the interval in equidistant spaces
for j = 1:k
x_j = a + j*h; %this are the points in the interval
sum = sum + ((x_j - x_(j-1))/2) * (integrand(x_(j-1)) + integrand(x_j));
end
result = sum
end
But when I want to call this function from the command window, using result = trapez(integrand,0,1,10) for example, I always get an error 'not enough input arguments'. I don't know what I'm doing wrong?
There are numerous issues with your code:
x_(j-1) is not defined, and is not really a valid Matlab syntax (assuming you want that to be a variable).
By calling trapez(integrand,0,1,10) you're actually calling integrand function with no input arguments. If you want to pass a handle, use #integrand instead. But in this case there's no need to pass it at all.
You should avoid variable names that coincide with Matlab functions, such as sum. This can easily lead to issues which are difficult to debug, if you also try to use sum as a function.
Here's a working version (note also a better code style):
function res = trapez(a, b, k)
res = 0;
h = (b-a)/k; % split up the interval in equidistant spaces
for j = 1:k
x_j1 = a + (j-1)*h;
x_j = a + j*h; % this are the points in the interval
res = res+ ((x_j - x_j1)/2) * (integrand(x_j1) + integrand(x_j));
end
end
function y = integrand(x)
y = x*exp(-x^2); % This will be integrand I want to approximate
end
And the way to call it is: result = trapez(0, 1, 10);
Your integrandfunction requires an input argument x, which you are not supplying in your command line function call
I have one file with the following code:
function fx=ff(x)
fx=x;
I have another file with the following code:
function g = LaplaceTransform(s,N)
g = ff(x)*exp(-s*x);
a=0;
b=1;
If=0;
h=(b-a)/N;
If=If+g(a)*h/2+g(b)*h/2;
for i=1:(N-1)
If=If+g(a+h*i)*h;
end;
If
Whenever I run the second file, I get the following error:
Undefined function or variable 'x'.
What I am trying to do is integrate the function g between 0 and 1 using trapezoidal approximations. However, I am unsure how to deal with x and that is clearly causing problems as can be seen with the error.
Any help would be great. Thanks.
Looks like what you're trying to do is create a function in the variable g. That is, you want the first line to mean,
"Let g(x) be a function that is calculated like this: ff(x)*exp(-s*x)",
rather than
"calculate the value of ff(x)*exp(-s*x) and put the result in g".
Solution
You can create a subfunction for this
function result = g(x)
result = ff(x) * exp(-s * x);
end
Or you can create an anonymous function
g = #(x) ff(x) * exp(-s * x);
Then you can use g(a), g(b), etc to calculate what you want.
You can also use the TRAPZ function to perform trapezoidal numerical integration. Here is an example:
%# parameters
a = 0; b = 1;
N = 100; s = 1;
f = #(x) x;
%# integration
X = linspace(a,b,N);
Y = f(X).*exp(-s*X);
If = trapz(X,Y) %# value returned: 0.26423
%# plot
area(X,Y, 'FaceColor',[.5 .8 .9], 'EdgeColor','b', 'LineWidth',2)
grid on, set(gca, 'Layer','top', 'XLim',[a-0.5 b+0.5])
title('$\int_0^1 f(x) e^{-sx} \,dx$', 'Interpreter','latex', 'FontSize',14)
The error message here is about as self-explanatory as it gets. You aren't defining a variable called x, so when you reference it on the first line of your function, MATLAB doesn't know what to use. You need to either define it in the function before referencing it, pass it into the function, or define it somewhere further up the stack so that it will be accessible when you call LaplaceTransform.
Since you're trying to numerically integrate with respect to x, I'm guessing you want x to take on values evenly spaced on your domain [0,1]. You could accomplish this using e.g.
x = linspace(a,b,N);
EDIT: There are a couple of other problems here: first, when you define g, you need to use .* instead of * to multiply the elements in the arrays (by default MATLAB interprets multiplication as matrix multiplication). Second, your calls g(a) and g(b) are treating g as a function instead of as an array of function values. This is something that takes some getting used to in MATLAB; instead of g(a), you really want the first element of the vector g, which is given by g(1). Similarly, instead of g(b), you want the last element of g, which is given by g(length(g)) or g(end). If this doesn't make sense, I'd suggest looking at a basic MATLAB tutorial to get a handle on how vectors and functions are used.