From 9a2d6028b4c415715bb50b4befe4b70da0db7b6c Mon Sep 17 00:00:00 2001
From: Patrice Matz <ofjokg@gmail.com>
Date: Thu, 18 Jan 2018 15:22:20 +0100
Subject: [PATCH] - fixed a4.1.1, a4.1.2 and a542 now handels inputs

---
 Mex/a411.cpp | 103 +++++++++++++++++--------------------
 Mex/a412.cpp | 142 ++++++++++++++++++++-------------------------------
 Mex/a542.cpp |  34 ++++++++----
 Mex/a542.m   |  11 ++++
 4 files changed, 135 insertions(+), 155 deletions(-)
 create mode 100644 Mex/a542.m

diff --git a/Mex/a411.cpp b/Mex/a411.cpp
index b85eb34..404858b 100644
--- a/Mex/a411.cpp
+++ b/Mex/a411.cpp
@@ -7,103 +7,94 @@ void mexFunction(int nlhs, mxArray *plhs[], 			// Output variables
 				 int nrhs, const mxArray *prhs[]) 		// Input variables 
 {
 	int variables = *mxGetPr(prhs[0]);
+	double inc = *mxGetPr(prhs[1]);
 	
 	double* x = (double *)mxCalloc(variables, sizeof(double));					//create solution array
 	
-	double* xx = (double *)mxCalloc(variables, sizeof(double));
-	double* yy = (double *)mxCalloc(variables, sizeof(double));
+	double* x_in = (double *)mxCalloc(variables, sizeof(double));				//input x
+	double* y = (double *)mxCalloc(variables, sizeof(double));					//input y
 	
-	double** GA = (double **)mxCalloc(variables+1, sizeof(double*));				//create Gauss Array (GA)
+	double** GA = (double **)mxCalloc(variables+1, sizeof(double*));			//create Gauss Array (GA)
 	for (int i = 0; i <= variables; i++){
 		GA[i] = (double *)mxCalloc(variables+1, sizeof(double));
 	}
 	
 	for(int i=0;i<variables;i++){
-		xx[i]=mxGetPr(prhs[1])[i];
+		x_in[i]=mxGetPr(prhs[2])[i];
 	}
 	for(int i=0;i<variables;i++){
-		yy[i]=mxGetPr(prhs[2])[i];
+		y[i]=mxGetPr(prhs[3])[i];
 	}
 	
-	for(int i=0;i<variables;i++){
+	for(int i=0;i<variables;i++){											//fill GA with the polynoms
 		for(int j=0; j<variables;j++){
-			GA[i][j] = pow(xx[i],j);
+			GA[i][j] = pow(x_in[i],j);
 		}
 	}
-	for(int i=0;i<variables;i++){
-		GA[i][variables] = yy[i];
+	for(int i=0;i<variables;i++){											
+		GA[i][variables] = y[i];
 	}
 
+	double len = (x_in[variables-1]-x_in[0])/inc +1;
 	
+	double* xx = (double *)mxCalloc(len, sizeof(double));					//return array with x values
+	double* yy = (double *)mxCalloc(len, sizeof(double));					//return array with interpolated y values
 	
-	int i, j, k;
-	for (i = 0; i<variables; i++)						//Pivotisation
-		for (k = i + 1; k<variables; k++)
+	double temp=x_in[0];
+	for(int i=0;temp <= x_in[variables-1]+inc;i++){							//generate return array with x values
+		xx[i]=temp;
+		temp += inc;
+	}
+
+// Gauß
+	for (int i = 0; i<variables; i++)					//Pivotisation
+		for (int k = i + 1; k<variables; k++)
 			if (abs(GA[i][i])<abs(GA[k][i]))
-				for (j = 0; j <= variables; j++)
+				for (int 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++)
+	for (int i = 0; i<variables - 1; i++)				//gauss elimination
+		for (int k = i + 1; k<variables; k++)
 		{
 			long double t = GA[k][i] / GA[i][i];
-			for (j = 0; j <= variables; j++)
+			for (int 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
+	for (int 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++)
+		for (int 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
 	}
-	
-	nlhs = variables;
-	for(int j=0; j < variables; j++){
-		plhs[j]=mxCreateDoubleScalar(x[j]);
-		
-	}
-	for(int l=0;l<variables;l++){
-		char temp;
-		
-		if(x[variables-1-l] != 0)
-		{
-			if(l!=0){
-			mexPrintf("+");
-			}
-			if(x[variables-1-l] < 0 ){
-				mexPrintf("-");
-				x[variables-l] *= -1;
-			}
-			temp=(char)(48+x[variables-1-l]);
-			mexPrintf("%c",temp);
-			
-			if(variables-1-l != 0){
-				mexPrintf("*");
-				mexPrintf("x");
-				mexPrintf("^");
-				temp=(char)(48+variables-1-l);
-				mexPrintf("%c",temp);
-			}
-			
+
+//polyval: filling yy with the interpolated values
+
+	for (int i = 0; i < len; i++){
+		double tmp = 0;
+		for (int j = 0; j < variables; j++){
+			tmp += pow(xx[i], j) * x[j];
 		}
-		
+		yy[i]=tmp;
 	}
-	mexPrintf("\n");
+
+//return values
+	nlhs = 2;
 	
+	plhs[0] = mxCreateDoubleMatrix(1, len, mxREAL);
+    memcpy(mxGetPr(plhs[0]), xx, len*sizeof(double));	
 	
-	for (int i = 0; i <= variables; i++ ){
-		free(GA[i]);
-	}
-	
-	free(GA);
-	free(x);
-  
+	plhs[1] = mxCreateDoubleMatrix(1, len, mxREAL);
+    memcpy(mxGetPr(plhs[1]), yy, len*sizeof(double));
+
+//free memory 
+
+// causes errors
 return;
 }
\ No newline at end of file
diff --git a/Mex/a412.cpp b/Mex/a412.cpp
index b85eb34..ba520c8 100644
--- a/Mex/a412.cpp
+++ b/Mex/a412.cpp
@@ -7,103 +7,69 @@ void mexFunction(int nlhs, mxArray *plhs[], 			// Output variables
 				 int nrhs, const mxArray *prhs[]) 		// Input variables 
 {
 	int variables = *mxGetPr(prhs[0]);
+	variables++;
+	double inc = *mxGetPr(prhs[1]);
+
+		
+	double* x = (double *)mxCalloc(variables, sizeof(double));
+	double* y = (double *)mxCalloc(variables, sizeof(double));
 	
-	double* x = (double *)mxCalloc(variables, sizeof(double));					//create solution array
-	
-	double* xx = (double *)mxCalloc(variables, sizeof(double));
-	double* yy = (double *)mxCalloc(variables, sizeof(double));
-	
-	double** GA = (double **)mxCalloc(variables+1, sizeof(double*));				//create Gauss Array (GA)
-	for (int i = 0; i <= variables; i++){
-		GA[i] = (double *)mxCalloc(variables+1, sizeof(double));
+	for(int i=0;i<variables-1;i++){
+		x[i]=mxGetPr(prhs[2])[i];
 	}
-	
-	for(int i=0;i<variables;i++){
-		xx[i]=mxGetPr(prhs[1])[i];
-	}
-	for(int i=0;i<variables;i++){
-		yy[i]=mxGetPr(prhs[2])[i];
-	}
-	
-	for(int i=0;i<variables;i++){
-		for(int j=0; j<variables;j++){
-			GA[i][j] = pow(xx[i],j);
-		}
-	}
-	for(int i=0;i<variables;i++){
-		GA[i][variables] = yy[i];
+	x[variables-1]=x[variables-2];
+	x[variables-1]+=inc;
+
+	for(int i=0;i<variables-1;i++){
+		y[i]=mxGetPr(prhs[3])[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;
-				}
+	y[variables-1]=y[variables-2];
 
-	for (i = 0; i<variables - 1; i++)					//gauss elimination
-		for (k = i + 1; k<variables; k++)
+	
+	double len = (x[variables-1]-x[0])/inc +1;
+	
+	double* xx = (double *)mxCalloc(len, sizeof(double));
+	double* yy = (double *)mxCalloc(len, sizeof(double));
+	
+	double temp=x[0];
+	for(int i=0;temp <= x[variables-1]+inc;i++){
+		xx[i]=temp;
+		temp += inc;
+	}
+	
+	
+//Code von Marvin Lehmann start
+	unsigned int savepoint = 0;
+
+	// Zwischen jeweils 2 Punkten
+	for (unsigned int i = 0; i < variables-1; i++)
+	{
+		// Für alle Zwischenwerte (xx) y interpolieren (yy)
+		for (unsigned int j = savepoint; j < len; j++)
 		{
-			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
+			if (xx[j] >= x[i] && xx[j] <= x[i + 1])
+			{
+				// Interpolationsformel
+				yy[j] = ((y[i + 1] - y[i]) / (x[i + 1] - x[i])) * (xx[j] - x[i]) + y[i];
+			}
+			else if (xx[j] > x[i + 1])
+			{
+				savepoint = j;
+				break;
+			}
 		}
+	}
+//Code von Marvin Lehmann ende
 
-	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
-	}
+	nlhs = 2;
 	
-	nlhs = variables;
-	for(int j=0; j < variables; j++){
-		plhs[j]=mxCreateDoubleScalar(x[j]);
-		
-	}
-	for(int l=0;l<variables;l++){
-		char temp;
-		
-		if(x[variables-1-l] != 0)
-		{
-			if(l!=0){
-			mexPrintf("+");
-			}
-			if(x[variables-1-l] < 0 ){
-				mexPrintf("-");
-				x[variables-l] *= -1;
-			}
-			temp=(char)(48+x[variables-1-l]);
-			mexPrintf("%c",temp);
-			
-			if(variables-1-l != 0){
-				mexPrintf("*");
-				mexPrintf("x");
-				mexPrintf("^");
-				temp=(char)(48+variables-1-l);
-				mexPrintf("%c",temp);
-			}
-			
-		}
-		
-	}
-	mexPrintf("\n");
+	plhs[0] = mxCreateDoubleMatrix(1, len, mxREAL);
+    memcpy(mxGetPr(plhs[0]), xx, len*sizeof(double));	
 	
-	
-	for (int i = 0; i <= variables; i++ ){
-		free(GA[i]);
-	}
-	
-	free(GA);
-	free(x);
-  
+	plhs[1] = mxCreateDoubleMatrix(1, len, mxREAL);
+    memcpy(mxGetPr(plhs[1]), yy, len*sizeof(double));
+
+
 return;
 }
\ No newline at end of file
diff --git a/Mex/a542.cpp b/Mex/a542.cpp
index 8e4405a..310fab6 100644
--- a/Mex/a542.cpp
+++ b/Mex/a542.cpp
@@ -2,29 +2,41 @@
 #include "matrix.h"
 #include "stdlib.h"
 #include "math.h"
-double g_von_theta(long double x, long double y)
+double g_von_theta(long double x, long double y, char * func_Name)
 {
-	return -(x*x + y*y);
+																		//-(x*x + y*y);
+	mxArray *func_Inputs[2];
+	mxArray *func_Outputs[1];
+	func_Inputs[0] = mxCreateDoubleScalar(x); 			
+	func_Inputs[1] = mxCreateDoubleScalar(y);
+	mexCallMATLAB(1, func_Outputs , 2 , func_Inputs , func_Name);		  
+	return *mxGetPr(func_Outputs[0]);
+
 }
 
 void mexFunction(int nlhs, mxArray *plhs[], 			// Output variables 
 				 int nrhs, const mxArray *prhs[]) 		// Input variables 
 {
-	double x = -2, y = -2, 
-	xnew, ynew,
-	increments = 0.1,
-	z = g_von_theta(x, y),
+	char *func_Name;
+	func_Name = mxArrayToString(prhs[0]);
+														//x = -2, y = -2
+	double x = *mxGetPr(prhs[1]);
+	double y = *mxGetPr(prhs[2]);
+	double increments = *mxGetPr(prhs[3]);
+
+	double	xnew, ynew,
+	z = g_von_theta(x, y, func_Name),
 	znew = 0, zold = 1,
 	zinitial = z;
 	int xTOy = 1, iAThalf = 1000; 				//iAThalf: max iterations/2
-int i;
-	for( i = 0 ; i <= 2 * iAThalf + 1; ++i) // add. exit crit. needed
+
+	for(int i = 0 ; i <= 2 * iAThalf + 1; ++i) 	// add. exit crit. needed
 	{
 		if (xTOy == 1)
 		{
 			xnew = x;
 			ynew = y;
-			if (zinitial / 2 == z)				//appropriate criteria?
+			if (zinitial / 2 == z)				
 			{
 				iAThalf = i;
 				ynew = y + increments;
@@ -38,7 +50,7 @@ int i;
 			ynew = y + increments;
 		}
 
-		znew = g_von_theta(xnew, ynew);
+		znew = g_von_theta(xnew, ynew, func_Name);
 		zold = z;
 		if(znew > z)
 		{
@@ -55,6 +67,6 @@ int i;
 	plhs[0] = mxCreateDoubleScalar(x);
 	plhs[1] = mxCreateDoubleScalar(y);
 	plhs[2] = mxCreateDoubleScalar(z);
-	plhs[3] = mxCreateDoubleScalar(i);
+
 return;
 }
\ No newline at end of file
diff --git a/Mex/a542.m b/Mex/a542.m
new file mode 100644
index 0000000..2cd07a7
--- /dev/null
+++ b/Mex/a542.m
@@ -0,0 +1,11 @@
+%function accepts 1 string, 2 double and increments
+%		a542("func_name", x, y, inc)
+% function returns lowest found return of passed function
+%
+%exp.:
+%		function z=func(x,y)
+%		z=-(x*x + y*y);
+%		end
+%
+%		a542("func",-2,-2, 0.1)
+%		ans=6.3838e-016
\ No newline at end of file