I'm facing an issue with this simple Fibonacci number generator program:
function f = fibonr(n)
f(1) = 1;
f(2) = 1;
for i = 3:n
f(i) = f(i-1) + f(i-2);
end
end
If I want to display only the n-th number of the sequence, what adjustments should I make?
function f = fibonr(n)
f = zeros(n,1); %//initialise the output array
f(1,1) = 1;
f(2,1) = 1;
for ii = 3:n
f(ii,1) = f(ii-1,1) + f(ii-2,1);
end
%//create a string with text and variables
str = sprintf('The %d th number in the Fibonacci sequence is %d',n,f(ii,1));
disp(str) %//display your output.
end
first up: don't use i as a variable. Secondly, I switched to using column vectors, since MATLAB processes them faster, as well as I initialised the array, which is way faster (hence the shiny orange wiggles below your f(i)= line).
Call your function:
output = fibonr(10);
The 10 th number in the Fibonacci sequence is 55
If you use e.g. n=20 and still want the 10th argument just call output(10)
if you want the specified output right away you can use nargin. This code will give you all of the sequence if you call fibonr(n), or you can specify a vector to get the fibonacy numbers at said positions. If you are interested in both, your specified output and all the numbers, you can call the function with:
[output, fibnumbers] = fibonr(n,v);
function [output,f] = fibonr(n,v)
f(1) = 1;
f(2) = 1;
for i = 3:n
f(i) = f(i-1) + f(i-2);
end
if nargin() > 1
output = f(v);
else
output = f;
end
Related
I am trying to calculate on MatLab the Expectation for the function e^X where X ~ N(mu,sigma^2). In my example, mu = 0 and sigma = 1.
function [E] = expectedval(m,s)
%find E(e^x) with X~N(mu,sigma)
% mu = 0 , sigma = 1
X = normrnd(m,s);
f=exp(X);
mean(f)
So by the end I can run expectedval(0,1) to get my solution. The code runs with no issue, but I would like to compile a histogram to analyse the data with several runs. How may I collect this data with some sort of loop?
I'd appreciate any improvement ideas or suggestions!
Actually, your function just creates one random value for the given mean and variance... so there's actually no point in calculating a mean. On the top of that, the output E value is not assigned before the function finishes. The function can therefore be rewritten as follows:
function E = expectedval(m,s)
X = normrnd(m,s);
E = exp(X);
end
If you want to draw a sample from the normal distribution, and use the mean to compute the correct expected value, you can rewrite it as follows instead:
function E = expectedval(m,s,n)
X = normrnd(m,s,[n 1]);
f = exp(X);
E = mean(f);
end
And here is an example on how to run your function many times with different parameters, collecting the output on each iteration:
m = 0:4;
m_len = numel(m);
s = 1:0.25:2;
s_len = numel(s);
n = 100;
data = NaN(m_len*s_len,1);
data_off = 1;
for s = 1:s_len
for m = 1:m_len
data(data_off) = expectedval(m,s,n);
data_off = data_off + 1;
end
end
I'm trying to call a numerical integration function (namely one that uses the trapazoidal method) to compute a definite integral. However, I want to pass more than one value of 'n' to the following function,
function I = traprule(f, a, b, n)
if ~isa(f, 'function_handle')
error('Your first argument was not a function handle')
end
h = (b-a)./ n;
x = a:h:b;
S = 0;
for j = 2:n
S = S + f(x(j));
end
I = (h/2)*(f(a) + 2*S + f(b)); %computes indefinite integral
end
I'm using; f = #(x) 1/x, a = 1 and b = 2. I'm trying to pass n = 10.^(1:10) too, however, I get the following output for I when I do so,
I =
Columns 1 through 3
0.693771403175428 0.069377140317543 0.006937714031754
Columns 4 through 6
0.000693771403175 0.000069377140318 0.000006937714032
Columns 7 through 9
0.000000693771403 0.000000069377140 0.000000006937714
Column 10
0.000000000693771
Any ideas on how to get the function to take n = 10.^(1:10) so I get an output something like,
I = 0.693771403175428, 0.693153430481824, 0.693147243059937 ... and so on for increasing powers of 10?
In the script where you are calling this from, simply iterate over n
k = 3;
f = #(x)1./x;
a = 1; b = 2;
I = zeros(k,1);
for n = 1:k
I(n) = traprule(f, a, b, 10^n);
end
% output: I = 0.693771403175428
% 0.693153430481824
% 0.693147243059937
Then I will contain all of the outputs. Alternatively you can adapt your function to use the same logic to loop over the elements of n if it is passed
as a vector.
Note, you can improve the efficiency of your traprule code by removing the for loop:
% This loop operates on every element of x individually, and is inefficient
S = 0;
for j = 2:n
S = S + f(x(j));
end
% If you ensure you use element-wise equations like f=#(x)1./x instead of f=#(x)1/x
% Then you can use this alternative:
S = sum(f(x(2:n)));
I am trying to sum a function and then attempting to find the root of said function. That is, for example, take:
Consider that I have a matrix,X, and vector,t, of values: X(2*n+1,n+1), t(n+1)
for j = 1:n+1
sum = 0;
for i = 1:2*j+1
f = #(g)exp[-exp[X(i,j)+g]*(t(j+1)-t(j))];
sum = sum + f;
end
fzero(sum,0)
end
That is,
I want to evaluate at
j = 1
f = #(g)exp[-exp[X(1,1)+g]*(t(j+1)-t(j))]
fzero(f,0)
j = 2
f = #(g)exp[-exp[X(1,2)+g]*(t(j+1)-t(j))] + exp[-exp[X(2,2)+g]*(t(j+1)-t(j))] + exp[-exp[X(3,2)+g]*(t(j+1)-t(j))]
fzero(f,0)
j = 3
etc...
However, I have no idea how to actually implement this in practice.
Any help is appreciated!
PS - I do not have the symbolic toolbox in Matlab.
I suggest making use of matlab's array operations:
zerovec = zeros(1,n+1); %preallocate
for k = 1:n+1
f = #(y) sum(exp(-exp(X(1:2*k+1,k)+y)*(t(k+1)-t(k))));
zerovec(k) = fzero(f,0);
end
However, note that the sum of exponentials will never be zero, unless the exponent is complex. Which fzero will never find, so the question is a bit of a moot point.
Another solution is to write a function:
function [ sum ] = func(j,g,t,X)
sum = 0;
for i = 0:2*j
f = exp(-exp(X(i+1,j+1)+g)*(t(j+3)-t(j+2)));
sum = sum + f;
end
end
Then loop your solver
for j=0:n
fun = #(g)func(j,g,t,X);
fzero(fun,0)
end
I wrote a function that displays the Fibonacci sequence up to the nth term. The code runs fine, but I want to make two changes and am not sure how to do so.
Here is my code:
function [ F ] = get_fib( k )
F(1) = 1;
F(2) = 1;
i = 3;
while k >= i;
F(i) = F(i-1) + F(i-2);
i = i + 1;
end
end
The first problem is that the code does not accept 0 as an input. I tried changing the function to:
function [ F ] = get_fib( k )
F(0) = 0;
F(1) = 1;
F(2) = 1;
i = 3;
while k >= i;
F(i) = F(i-1) + F(i-2);
i = i + 1;
end
end
But the following error appears:
Attempted to access F(0); index must be a positive integer or logical.
Error in get_fib (line 2)
F(0) = 0;
I would also like the code to display the last term in the sequence, rather than the entire sequence.
I changed the function to:
function [ F ] = get_fib( k );
F(1) = 1;
F(2) = 1;
i = 3;
while k >= i;
F(i) = F(i-1) + F(i-2);
i = i + 1;
end
term = F(k)
end
but the sequence it still being assigned to ans.
How can I make my function accept 0 as an argument and only display the last term of the sequence?
First let's get your function to output just the last item in the sequence. You're setting term like this:
term = F(k);
Which is good (notice I added the ; at the end, though). But the return value from your function is F. You need to change it to term.
function [ term ] = get_fib( k )
%// ^^^^- change this ^-- semicolon not necessary here
Now, to handle an input of 0, you can add a special check for zero:
function [ term ] = get_fib( k )
if k == 0
term = [];
return;
end
while k >= i
%// ^-- semicolon not needed here, either
<the rest of your code>
The semicolons after the function header and the while statement don't hurt anything, they just represent empty statements. But they might be misleading, so it's best to remove them.
The semicolon after the assignment to term prevents the ans = ... line from printing out to the console.
To address your first problem, F(0) is not a valid call. This is because MATLAB indexing starts from 1. In other words, the first element of a matrix is index 1. There is no 0th index of a matrix in MATLAB. See here for why MATLAB indexing starts from 1. What I would recommend to address this is to shift your output array by one index.
Thus, your code for the function should be:
function [ F ] = get_fib( k )
k = k + 1
F(1) = 0; % 0th Fibonacci term
F(2) = 1; % 1st Fibonacci term
F(3) = 1; % 2nd Fibonacci term
i = 4;
while k >= i
F(i) = F(i-1) + F(i-2);
i = i + 1;
end
term = F(k)
end
To address your second problem, it would depend on what you want. Do you (1) want the last term in the sequence to be returned when you call term = get_fib(k)or (2) want the last term of the sequence to be displayed and the entire sequence to be returned?
To achieve (1), fix the top line of your code to function term = F(k). To achieve (2), call the function with F = get_fib(some_number), as #rayryeng stated.
Since others already pointed out how to fix your code, I'd like to show you one approach to calculate the nth Fibonacci number without relying on the F(n-1) and F(n-2) terms calculation.
It involves the golden ratio, and you can read more about its relationship to the Fibonacci sequence here.
function [ F ] = get_fib( n )
% Changed your input variable from k to n (standard notation)
Phi = (1+sqrt(5))/2; % Golden ratio value
F = round((Phi^n - ((-1)^n)/(Phi^n))/sqrt(5)); %nth fibonacci number
end
Since you are only interested in the last value of the sequence, it could speed up the calculation for large values of n.
Note i have rounded the output (F) to avoid floating point arithmetic errors.
Hi i have the following 3 functions that are in different m. files in the same folder:
The first two functions (sum and mult) are for summing and multiplying elements respectively:
function sum = sum_elements()
a = 1;
sum = 0;
for i = 1:5
sum = sum + a;
end
return
function mult = mult_elements()
b = 2;
mult = 1;
for i = 1:5
mult = mult * b;
end
return
In the third function i want to use structures for perform summing and multiplying tasks and storing them in a variable "calc":
function calc_sum_mult(a,b,sum,mult)
I = 5;
for i = 1:I
calc(i).sum = sum_elements()
calc(i).mult = mult_elements()
end
But when i run the 3rd function i get and error " not enough input argument"
Any help???
Change calc(i).sum = sum() to calc(i).sum = sum_elements(), and calc(i).mult = mult() to calc(i).mult = mult_elements(). Functions are called by its name, not by the name of the output argument used in its definition.
In your code as it stands, sum is a Matlab bulitin function that can't be called without input elements. That's why you get the error.