From 7bbe3e29f0e8475710e7d8a2ac92f5ed9b782256 Mon Sep 17 00:00:00 2001
From: Patrice Matz <ofjokg@gmail.com>
Date: Tue, 16 Jan 2018 22:24:13 +0100
Subject: [PATCH] - added 5.4.2 (optim.) and started 4.1.2 (lin. interpol.)

---
 Mex/a411.cpp | 109 +++++++++++++++++++++++++++++++++++++++++++++++++++
 Mex/a411.m   |  18 +++++++++
 Mex/a412.cpp | 109 +++++++++++++++++++++++++++++++++++++++++++++++++++
 Mex/a542.cpp |  60 ++++++++++++++++++++++++++++
 4 files changed, 296 insertions(+)
 create mode 100644 Mex/a411.cpp
 create mode 100644 Mex/a411.m
 create mode 100644 Mex/a412.cpp
 create mode 100644 Mex/a542.cpp

diff --git a/Mex/a411.cpp b/Mex/a411.cpp
new file mode 100644
index 0000000..b85eb34
--- /dev/null
+++ b/Mex/a411.cpp
@@ -0,0 +1,109 @@
+#include "mex.h" 
+#include "matrix.h"
+#include "stdlib.h"
+#include "math.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, 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;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];
+	}
+
+	
+	
+	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
+	}
+	
+	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");
+	
+	
+	for (int i = 0; i <= variables; i++ ){
+		free(GA[i]);
+	}
+	
+	free(GA);
+	free(x);
+  
+return;
+}
\ No newline at end of file
diff --git a/Mex/a411.m b/Mex/a411.m
new file mode 100644
index 0000000..3d064a8
--- /dev/null
+++ b/Mex/a411.m
@@ -0,0 +1,18 @@
+% function accepts 1 double and 1 double matrix (#of_variables, [row1;row2])
+% each row1 contains #of_variables+1 elements
+% returns solution vector
+% outputs the function
+% bsp.:
+%			6x^2+12x=30
+%			3x^2+ 3x= 9
+%		a21(2,[6,12,30;3,3,9]);
+%			2*x^1+1				<-function
+%
+%				OR
+%
+%			6x^2+12x=30
+%			3x^2+ 3x= 9
+%		[a1,a2]=a21(2,[6,12,30;3,3,9])
+%			2*x^1+1				<-function
+%			a1 = 1				<-factors of x^...
+%			a2 = 2
\ No newline at end of file
diff --git a/Mex/a412.cpp b/Mex/a412.cpp
new file mode 100644
index 0000000..b85eb34
--- /dev/null
+++ b/Mex/a412.cpp
@@ -0,0 +1,109 @@
+#include "mex.h" 
+#include "matrix.h"
+#include "stdlib.h"
+#include "math.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, 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;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];
+	}
+
+	
+	
+	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
+	}
+	
+	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");
+	
+	
+	for (int i = 0; i <= variables; i++ ){
+		free(GA[i]);
+	}
+	
+	free(GA);
+	free(x);
+  
+return;
+}
\ No newline at end of file
diff --git a/Mex/a542.cpp b/Mex/a542.cpp
new file mode 100644
index 0000000..8e4405a
--- /dev/null
+++ b/Mex/a542.cpp
@@ -0,0 +1,60 @@
+#include "mex.h" 
+#include "matrix.h"
+#include "stdlib.h"
+#include "math.h"
+double g_von_theta(long double x, long double y)
+{
+	return -(x*x + y*y);
+}
+
+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),
+	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
+	{
+		if (xTOy == 1)
+		{
+			xnew = x;
+			ynew = y;
+			if (zinitial / 2 == z)				//appropriate criteria?
+			{
+				iAThalf = i;
+				ynew = y + increments;
+			}
+			else
+				xnew = x + increments;
+		}
+		else
+		{
+			xnew = x;
+			ynew = y + increments;
+		}
+
+		znew = g_von_theta(xnew, ynew);
+		zold = z;
+		if(znew > z)
+		{
+			z = znew;
+			x = xnew;
+			y = ynew;
+		}
+		else
+			if (xTOy == 1)
+				xTOy = 2;		
+	}
+	
+	// Output
+	plhs[0] = mxCreateDoubleScalar(x);
+	plhs[1] = mxCreateDoubleScalar(y);
+	plhs[2] = mxCreateDoubleScalar(z);
+	plhs[3] = mxCreateDoubleScalar(i);
+return;
+}
\ No newline at end of file