We continue our discussion on Conjugate Gradient method. We review the non-linear conjugate gradient method. CG can be used not only to find the minimum point of a quadratic form but to  minimize any continuous function where the gradient can be computed. CG for the non-linear forms have the following challenges:
1) the recursive formula for residual cannot be calculated.
2) the step size alpha is difficult to calculate although we still use a linear expression using alpha to compute the next step but a function of it and we try to minimize  it.
3) and the Gram-Schmidt constants have many choices
We set the residual to be the negative of the gradient. The search directions are computed by the Gram-Schmidt conjugation of the residuals as with linear CG.
To overcome 1 we set the residual to be the negative of the gradient.
To overcome 2 we minimize the function
To overcome 3 we use one of two different techniques to choose the constants

Int GetDistinctMax (int [] A)

{

if (A == null) return 0;

return A.DistinctMax ();

}