How to compute a polynomial derivative?

Question

I am trying to write a function for calculating the derivative of a polynomial function. degr is the degree of the polynomial, arr is the array that contains the coefficients of the polynomial. I want to calculate the derivative at point t.

Below is my attempt, but it always returns 0. I do not understand what is wrong.

float derv(int degr,int arr[],float t)
{
  int i,n;
  float sum=0;
  float arr2[degr+1];

  for (i=0;i<degr+1;i++) {
    arr[i]=(arr[i]*(i+1)); 
  } 
  degr=degr-1;
  for (i=0;i<degr+1;i++)
  {
     arr2[i] = (pow(t,degr-i)*arr[i]);
  }

  for(n=0;n<degr+1;n++)
  {
    sum = sum + arr2[n];
  } 
  return sum;
}

Also, have you tried adding print statements (or using a debugger) to inspect the values of intermediate values? — Oliver Charlesworth, Jul 11 '12 at 20:27
yes actually this is just function part of my program.But rest of program working good.But from this function sum returns as Zero — allstar, Jul 11 '12 at 20:32
A couple of rules - name variables by the thing you save into them (not `arr2`!), don't initialize them long before you use them for the first time (`sum = 0`). Then your code will be readable and you will probably see the error immediately. — Sulthan, Jul 11 '12 at 20:55

jxh · Answer 1 · 2012-07-11T21:28:10.040

Let's make some assumptions. If the polynomial looks like this:

         degr
        .---
p(x) =   >     arr[i] * pow(x, i)
        `---
         i=0

Then, the derivative would be obtained by:

           degr
d         .---
-- p(x) =  >    i * arr[i] * pow(x, i-1)
dx        `---
           i=1

You should be able to compute this with a loop similar to Horner's method.

For your program, you are processing it in several loops, which is unnecessary. But, your first loop is trying to recompute the coefficients. The first coefficient is a constant, so it should be recomputed to zero when the derivative is applied. Instead, you are multiplying by (i+1). Just multiply by i instead.

In your second loop, you understand that the degree has been reduced, but since the first term is 0, you do not have to decrement the degr variable. You should start the loop from index 1. Within the body of the for loop itself, the pow computation should raise to the i-1 power.

In your sum calculation loop, also start from index 1.

You should be able to see how the changes I suggested to you came straight from the formula I provided above.

Note, since you modify the array that represents the polynomial, you cannot call the function again to compute the derivative for a different value. You can fix this by modifying the first loop so that the coefficients get stored in arr2 instead, and then changing the second loop so that you are obtaining the coefficients from arr2. Now, you can declare your input array to be constant in your derv function.

The code with my suggested changes looks like:

float derv(int degr,const int arr[],float t)
{
  int i,n;
  float sum=0;
  float arr2[degr+1];

  for (i=0;i<degr+1;i++) {
    arr2[i]=(arr[i]*i);
  }
  for (i=1;i<degr+1;i++)
  {
     arr2[i] = (pow(t,i-1)*arr2[i]);
  }

  for(n=1;n<degr+1;n++)
  {
    sum = sum + arr2[n];
  }
  return sum;
}

@OliCharlesworth: The OP does not seem to know what the formula for the derivative is, because it is being computed incorrectly. Regards — jxh, Jul 11 '12 at 20:58
I imagine the OP knows the maths behind evaluating a polynomial derivative (the code wouldn't look *almost* correct if they didn't). But the question is what is wrong with the code? — Oliver Charlesworth, Jul 11 '12 at 21:00
@OliCharlesworth: Updated the answer with specific fixes to the code. Regards — jxh, Jul 11 '12 at 21:06

How to compute a polynomial derivative?

1 Answers1