CODEWITHSUNDEEP
matlabvector
Ravonrip
Ravonrip

Reputation: 614

How to create a polynomial that accepts vectors?

I have a problem with creating a polynomial function of arbitrary length in Matlab, that would work, when used with a vector as an argument.

I have to do an algorithm, that includes and returns a value of a polynomial. Bellow is my code:

n = 4 % For simplicity, could be arbitrary positive integer
f = @(x) x.^[0:n] %Coefficients are 1 (for this example), if not, would be multiplied with vector of them
p = @(x) sum(f(x))  %My polynomial

>> p(5)
ans =
781

This goes as planed. But because I need a plot, I need my polynomial to be able to receive vectors of values and return them. But when I do this, an error pops up. Example:

>>p([1 2 3 4])
Error using  .^ 
Matrix dimensions must agree.

Error in @(x)x.^[0:n]

Error in @(x)sum(f(x))

What I want it to return is a vector of length 4 with values of my polynomial [p(1) p(2) p(3) p(4)] I got around this by creating a values vector with a for loop, but am just wondering, is it possible to change my code, so this would work?

Upvotes: 2

Views: 81

Answers (1)

m7913d
m7913d

Reputation: 11072

The problem can be easily fixed using a row and a column vector, instead of two row vectors:

p([1 2 3 4]')

and explicitly defining the dimension along which you want to take the summation:

p = @(x) sum(f(x), 2)

Explanation

Note that .^ is an element wise operation. p([1 2 3 4 5]) works, because both row vectors have the same size, but doesn't return the desired result, i.e. it calculates 1^0 + 2^1 + 3^2 + 4^3 + 5^4 = 701.

Matlab automatically expands (in pseudo matlab code)

[1  .^ [0 1 2 3 4]
 2
 3
 4]

to

[1 1 1 1   .^ [0 1 2 3 4
 2 2 2 2       0 1 2 3 4
 3 3 3 3       0 1 2 3 4
 4 4 4 4]      0 1 2 3 4]

Backward compatibility (2006-2016a)

The definition of f should be changed because matlab does not support automatic arithmetic expansion yet.

f = @(x) bsxfun(@power, x, 0:n);

Backward compatibility (1996-2005)

bsxfun didn't exist yet, so one should resort to repmat.

Upvotes: 2

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