Question

suppose that there is given following matlab code

function dp = derp(p)
n = length(p) - 1;
p = p(:)';
dp = p(1:n).*(n:-1:1);
k = find(dp ~= 0);
if ~isempty(k)
dp = dp(k(1):end);
else
dp = 0;
end

as i know from the book,from where i have taken this code,it is explained just that it calculates derivative of function,of polynomials,but in case of i would like to write it in c++,how to rewrite it?please explain me ideas of this code,i just need to fully understand even in matlab what does it do,for a few moment let’s forget c++ and pay attention to main ideas of code,please guys help me,i know actualy ,mathematicaly how derivative is calculated,i need understanding in code

Answer 1

The polynomial is represented as a list of coeficients.

make sure p is a row vector.

p = p(:)';

multiply each element by it’s index

dp = p(1:n).*(n:-1:1);

remove any zero items from the front of the list

k = find(dp ~= 0);
if ~isempty(k)
   dp = dp(k(1):end);
else
   dp = 0;
end

in C you would write it probably like this:

void derivative(const double *poly, int polysize, double *dervpoly)
{
    for (int i=0 ; i<polysize-1 ; i++)
        dervpoly[i] = poly[i]*(polysize-i-1);
}

Where the caller is responsible for allocating an array of size polysize-1 for dervpoly.

The polynomial is:

poly[0]*x^(polysize-1) + poly[1]*x^(polysize-2) + .. + poly[polysize-2]*x + poly[polysize-1]

Note that it may be more convenient to store the coefficients in reverse order.