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#-------------------------------------------------------------
#
# THIS SCRIPT SOLVES CUBIC SPLINE INTERPOLATION
#
# INPUT PARAMETERS:
# --------------------------------------------------------------------------------------------
# NAME  TYPE           DEFAULT   MEANING
# --------------------------------------------------------------------------------------------
# X      Matrix[Double]  ---       1-column matrix of x values knots. It is assumed that x values are
#                                  monotonically increasing and there is no duplicates points in X
# Y      Matrix[Double]  ---       1-column matrix of corresponding y values knots
# inp_x  Double          ---       the given input x, for which the cspline will find predicted y
# mode   String          "DS"      Specifies the method for cspline (DS - Direct Solve, CG - Conjugate Gradient)
# tol    Double          -1.0      Tolerance (epsilon); conjugate graduent procedure terminates early if
#                                  L2 norm of the beta-residual is less than tolerance * its initial norm
# maxi   Integer         -1        Maximum number of conjugate gradient iterations, 0 = no maximum
# --------------------------------------------------------------------------------------------
# OUTPUT: 
# pred_Y Matrix[Double] ---      Predicted value
# K      Matrix[Double] ---      Matrix of k parameters
#

#Algorithms: It implement the https://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline
#it usages natural spline with q1''(x0) == qn''(xn) == 0.0


m_cspline = function(Matrix[Double] X, Matrix[Double] Y, Double inp_x, 
String mode = "DS", Double tol = -1.0, Integer maxi = -1)
  return (Matrix[Double] pred_Y, Matrix[Double] K)
{
  if( mode == "CG" & maxi != -1 & tol != -1.0)
  {
    [pred_Y, K] = csplineCG(X=X, Y=Y, inp_x=inp_x, tol=tol, maxi=maxi);
  }
  else 
  {    
    [pred_Y, K] = csplineDS(X=X, Y=Y, inp_x=inp_x);
  }
}
