#coding exercise
Bool memcmp (char* src, char* dest, size_t n)
{
If ( !src || !dest || n <= 0) return false;
While (n)
{
If (*dest != *src) return false;
Dest++;
Src++;
n--;
}
Return true;
}

We will continue our discussion on steepest descent method and conjugate directions. The steepest descent method often finds itself taking steps in the same direction. It would have been better if the steps were taken right the first time. How do we correct this ? We take two orthogonal search directions and take steps with just the right length along these directions such that after a certain number of steps we are done. This is what we will discuss in conjugate direction method.

As an example, we can use the co-ordinate axes as search directions. The first step leads to the correct x-coordinate and the second step is the vertical step to reach the center. For each step we choose a point such that it is a step length in the direction di. We use the fact that ei is orthogonal to di, so that we should never step in the direction of di again. Using this we want to determine the step length but we have a catch-22 situation. We don't know the step length without knowing ei and if we knew ei, we wouldn't have to compute at all.  To overcome this, we don't use search directions but instead use A-orthogonal or conjugate directions To picture these conjugate directions we imagine ellipsis that can be expanded or stretched on a bubble to form concentric circles. Our new requirement is that ei+1 is A-orthogonal to di. The benefit of this new orthogonality condition is that it equivalent to finding the minimum point along the search direction di as in the steepest descent. We can prove this by setting the directional derivative to zero. but we look at finding the step length when the search directions are A-orthogonal. The step length can now be calculated just the same way we derived that for the steepest descent and we see that it is expressed in terms of the residual. In fact, if the search vector were the residual, this step length would be the same as in the steepest descent.
While the method of orthogonal directions works only when we know the final destination, the conjugate directions method works in n-iterations. The method of conjugate directions converges in n-steps. The first step is taken along some direction d(0). The minimum point x is chosen by some constraint that e(1) must be A-orthogonal to d(0) The initial error can be expressed as a sum of A-orthogonal components. Each step of the conjugate directions eliminates one of these components.