-added mex files for 1.2, 1.3 and 2.1

Mex/a11.cpp

@@ -0,0 +1,35 @@
+#include "mex.h" 
+#include "matrix.h"
+
+
+void mexFunction(int nlhs, mxArray *plhs[], 		/* Output variables */
+				 int nrhs, const mxArray *prhs[]) 	/* Input variables */
+{
+
+if (nrhs != 3 || ! mxIsNumeric (prhs[0]))
+    mexErrMsgTxt ("ARG1 must be a 3 dimensional matrix");
+
+if( mxGetNumberOfElements(prhs[0]) != mxGetNumberOfElements(prhs[1]) ||
+	mxGetNumberOfElements(prhs[0]) != mxGetNumberOfElements(prhs[2]))
+	{
+	mexErrMsgTxt ("arrays need to be of same size!");
+	}
+	
+	double *heights, *d, *densities;
+	heights =  mxGetPr (prhs[0]);
+	d =  mxGetPr (prhs[1]);
+	densities =  mxGetPr (prhs[2]);
+
+	double mass = 0;
+	for (int i = mxGetNumberOfElements(prhs[0]); i--;)
+	{
+		mass = mass + ((heights[i] / 10) * (d[i] / 20)*(d[i] / 20) * 3.14159265359 * densities[i]);
+	}	
+	
+//return value
+	plhs[0] = mxCreateDoubleScalar(mass);
+
+
+
+return;
+}

Mex/a11.m

@@ -0,0 +1,3 @@
+%function accepts 3 double arrays (heights, radii, densities)
+%passed arrays have to be of same size
+%function returns a double value

Mex/a12.cpp

@@ -0,0 +1,34 @@
+#include "mex.h" 
+#include "matrix.h"
+
+void mexFunction(int nlhs, mxArray *plhs[], 		/* Output variables */
+				 int nrhs, const mxArray *prhs[]) 	/* Input variables */
+{
+
+if (nrhs != 4 || ! mxIsNumeric (prhs[0]))
+    mexErrMsgTxt ("ARG1 must be a 4 dimensional matrix");
+
+if( mxGetNumberOfElements(prhs[0]) != mxGetNumberOfElements(prhs[1]) ||
+	mxGetNumberOfElements(prhs[0]) != mxGetNumberOfElements(prhs[2]) ||
+	mxGetNumberOfElements(prhs[0]) != mxGetNumberOfElements(prhs[3]))
+	{
+	mexErrMsgTxt ("arrays need to be of same size!");
+	}
+	
+	double *heights, *d, *densities, *resistances;
+	heights =  mxGetPr (prhs[0]);
+	d =  mxGetPr (prhs[1]);
+	densities =  mxGetPr (prhs[2]);
+	resistances = mxGetPr(prhs[3]);
+
+	double resistance = 0;
+	for (int i = mxGetNumberOfElements(prhs[0]); i--;)
+	{
+		resistance = resistance + ((heights[i] / 1000) * resistances[i]) / ((d[i] / 20)*(d[i] / 20) * 3.14159265359);
+	}
+
+//return value
+	plhs[0] = mxCreateDoubleScalar(resistance);
+
+return;
+}

Mex/a12.m

@@ -0,0 +1,3 @@
+%function accepts 4 double arrays (heights, radii, densities, resistances)
+%passed arrays have to be of same size
+%function returns a double value

Mex/a21.cpp

@@ -0,0 +1,62 @@
+#include "mex.h" 
+#include "matrix.h"
+#include "stdlib.h"
+
+void mexFunction(int nlhs, mxArray *plhs[], 			// Output variables 
+				 int nrhs, const mxArray *prhs[]) 		// Input variables 
+{
+	int variables = *mxGetPr(prhs[0]);
+	
+	double* x = (double *)mxCalloc(variables+1, sizeof(double));					//create solution array
+	
+	double** GA = (double **)mxCalloc(variables+1, sizeof(double*));				//create Gauss Array (GA)
+	for (int i = 0; i <= variables+1; i++){
+		GA[i] = (double *)mxCalloc(variables+1, sizeof(double));
+	}
+	
+	for(int i = 0; i < variables*(variables+1); i++){							//copy input array into GA								
+		GA[i%variables][i/variables] = mxGetPr(prhs[1])[i];	
+	}
+	
+	
+	int i, j, k;
+	for (i = 0; i<variables; i++)						//Pivotisation
+		for (k = i + 1; k<variables; k++)
+			if (abs(GA[i][i])<abs(GA[k][i]))
+				for (j = 0; j <= variables; j++)
+				{
+					long double temp = GA[i][j];
+					GA[i][j] = GA[k][j];
+					GA[k][j] = temp;
+				}
+
+	for (i = 0; i<variables - 1; i++)					//gauss elimination
+		for (k = i + 1; k<variables; k++)
+		{
+			long double t = GA[k][i] / GA[i][i];
+			for (j = 0; j <= variables; j++)
+				GA[k][j] = GA[k][j] - t*GA[i][j];		//make the elements below the pivot elements equal to zero or elimnate the variables
+		}
+
+	for (i = variables - 1; i >= 0; i--)                //back-substitution
+	{													//x is an array whose values correspond to the values of x,y,z..
+		x[i] = GA[i][variables];						//make the variable to be calculated equal to the rhs of the last equation
+		for (j = i + 1; j<variables; j++)
+			if (j != i)									//then subtract all the lhs values except the coefficient of the variable whose value is being calculated
+				x[i] = x[i] - GA[i][j] * x[j];
+		x[i] = x[i] / GA[i][i];							//now finally divide the rhs by the coefficient of the variable to be calculated
+	}
+	
+	for(int j=0; j < variables; j++){
+		plhs[j]=mxCreateDoubleScalar(x[j]);
+		
+	}
+	for (int i = 0; i <= variables; i++ ){
+		free(GA[i]);
+	}
+	
+	free(GA);
+	free(x);
+  
+return;
+}

Mex/a21.m

@@ -0,0 +1,9 @@
+%function accepts 1 double and 1 double matrix (#of_variables, [row1;row2])
+%each row1 contains #of_variables+1 elements
+%returns solution vector
+%bsp.:
+%			6x+12y=30
+%			3x+ 3y= 9
+%		[a1,a2]=a21(2,[6,12,30;3,3,9])
+%			a1 = 1
+%			a2 = 2