From 1cd1940dd72d0d7ce26e3985b023a1ab2df75596 Mon Sep 17 00:00:00 2001
From: Shifa <121536886+ShifatJahanShifa@users.noreply.github.com>
Date: Sat, 1 Apr 2023 15:01:39 +0600
Subject: [PATCH] for 3X3 matrix using Gauss Elimination

---
 leastSquareFit.c | 134 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 134 insertions(+)
 create mode 100644 leastSquareFit.c

diff --git a/leastSquareFit.c b/leastSquareFit.c
new file mode 100644
index 0000000..4fbcf63
--- /dev/null
+++ b/leastSquareFit.c
@@ -0,0 +1,134 @@
+Question: Find the Quadratic polynomial that is the least square fit to the following data: 
+
+  x | 0 | 1 | 2 | 3
+----------------------
+f(x)| 1 | 0 | 1 | 2    
+    
+ and f(x)=C1+C2*x+C3*x^2
+ 
+//**i solved the problem using Gauss elimination process
+
+                                                  
+                                                  solution 
+ -----------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+#include<stdio.h>
+#include<stdlib.h>
+
+int main()
+{
+	double x[4]={0,1,2,3},b[4][1]={1,0,1,2};
+	double a[4][3],at[3][4],A[3][3],B[3][1],mat[3][4]; 
+	
+	for(int i=0;i<4;i++)
+	{
+		a[i][0]=1;
+		a[i][1]=x[i];
+		a[i][2]=x[i]*x[i];
+		//a[i][3]=x[i]*x[i]*x[i];
+	}
+	
+	
+	/** making transpose matrix **/ 
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<4;j++) 
+		{
+			at[i][j]=a[j][i]; 
+		} 
+	} 
+	
+	
+	/* multilication of transpose matrix X matrix */
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<4;j++) 
+		{
+			A[i][j]=0;
+		} 
+	} 
+	
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<3;j++) 
+		{
+			for(int k=0;k<4;k++)
+			{
+				A[i][j]+=(at[i][k]*a[k][j]); 
+			}
+		} 
+	} 
+	
+	
+	/* updating B */
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<1;j++) 
+		{
+			B[i][j]=0;
+		} 
+	} 
+	
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<1;j++) 
+		{
+			for(int k=0;k<4;k++)
+			{
+				B[i][j]+=(at[i][k]*b[k][j]); 
+			}
+		} 
+	} 
+	
+	
+	/** using gauss elimination process to find the least square fitted values **/
+	for(int i=0;i<3;i++)
+	{
+		for(int j=0;j<3;j++) 
+		{
+			mat[i][j]=A[i][j];
+		} 
+		mat[i][3]=B[i][0];
+	}
+	
+	
+	/** upper triangular matrix **/
+	for(int j=0;j<3;j++)
+	{
+		for(int i=j+1;i<3;i++) 
+		{
+			int m=mat[j][j];
+			int n=mat[i][j]; 
+			
+			for(int k=0;k<=3;k++) 
+			{
+				mat[i][k]=(m*mat[i][k])-(n*mat[j][k]);
+			} 
+		} 
+	}
+	
+	
+	/** back substitution **/ 
+	double ans[3];
+	ans[3-1]=(mat[3-1][3]/mat[3-1][3-1]);
+	
+	for(int j=3-2;j>-1;j--)
+	{
+		double sum=0;
+		for(int i=j+1;i<3;i++) 
+		{
+			sum+=(mat[j][i]*ans[i]); 
+			//printf("sum %9.3lf\n",sum);
+		} 
+		
+		ans[j]=(mat[j][3]-sum)/(mat[j][j]);
+	}
+	
+	
+	/** answer **/
+	for(int i=0;i<3;i++) 
+	{
+		printf("c%d = %9.3lf\n",i+1,ans[i]);
+	}
+}
+