- added 6.1.2 (mid_differentiation)

Mex/a612.cpp

@@ -0,0 +1,51 @@
+#include "mex.h" 
+#include "matrix.h"
+#include "stdlib.h"
+
+
+
+void mexFunction(int nlhs, mxArray *plhs[], 			// Output  
+				 int nrhs, const mxArray *prhs[]) 		// Input  
+{
+	
+	int num_data_points = *mxGetPr(prhs[0]);
+	
+	double* x = (double *)mxCalloc(num_data_points, sizeof(double));
+	double* y = (double *)mxCalloc(num_data_points, sizeof(double));
+	double* temp = (double *)mxCalloc(num_data_points, sizeof(double));
+	
+	for(int j=0; j < num_data_points; j++)
+	{
+		x[j] = mxGetPr(prhs[1])[j];
+		y[j] = mxGetPr(prhs[2])[j];
+	}
+	
+//Mid-diff
+	int i = 0;
+
+	temp[i] = (y[i+1] - y[i]) / (x[i+1] - x[i]);
+	i++;
+	temp[i] = (y[i+1] - y[i]) / (x[i+1] - x[i]);
+	temp[i]  += (y[i+1] - y[i-1]) / (x[i+1] - x[i-1]);
+	temp[i]  /= 2;
+
+	for (; i < num_data_points - 2; ++i)
+	{
+		temp[i] = (y[i+1] - y[i-1] ) / (x[i+1] - x[i-1]);
+	}
+
+	temp[i] += (y[i] - y[i-1]) / (x[i] - x[i-1]);
+	temp[i] /= 2;
+	i++;
+	temp[i] = (y[i] - y[i-1]) / (x[i] - x[i-1]);
+
+// Output
+	nlhs = num_data_points;
+	for(int j=0; j < num_data_points; j++){
+		plhs[j]=mxCreateDoubleScalar(temp[j]);
+	}
+	
+
+		 
+ return;
+}

Mex/a612.m

@@ -0,0 +1,14 @@
+% function accepts 1 double and 2 vectors of double 
+%		a611(#num_of_points, vector_a, vector_b)
+% number of datapoints in both vectors must be equal, 
+% or else the result will not be correct
+%
+%exp.:
+%	a=[0, 5, 10, 15, 20 ]
+%	b=[1, 0.8811, 0.7366, 0.5430, 0.1698]
+%	[a1,a2,a3,a4,a5]=a611(5,a,b)
+%	a1 = -0.023780
+%	a2 = -0.026340
+%	a3 = -0.033810
+%	a4 = -0.019360
+%	a5 = -0.074640