File: lsm.h
#include<matrix.h>
typedef struct readings {
float *x;
float *y;
int len;
}Readings;
typedef struct lsm_line {
float *x;
float *y;
float *x2;
float *xy;
float X , Y , XY , X2;
float *newy;
float Dev;
int len;
}LsmLine;
Readings* lsm_new_Readings(int n);
LsmLine* lsm_new_LsmLine(Readings *Read);
int lsm_del_Readings(Readings *anchor);
int lsm_Read_farray(float *array,int len);
int lsm_Print_farray(float *array,int len);
int lsm_Calc_LsmLine(LsmLine* line);
int lsm_Print_LsmLine(LsmLine* line);
File : lsm.c
#include "lsm.h"
Readings* lsm_new_Readings(int len)
{
Readings *newRead = (Readings*)malloc(sizeof(Readings));
newRead->x = (float*)malloc(sizeof(float)*len);
newRead->y = (float*)malloc(sizeof(float)*len);
newRead->len = len;
return newRead;
}
LsmLine* lsm_new_LsmLine(Readings *read)
{
LsmLine *newLine = (LsmLine*)malloc(sizeof(LsmLine));
int len = read->len;
newLine->x = (float*)malloc(sizeof(float)*len);
newLine->y = (float*)malloc(sizeof(float)*len);
newLine->xy = (float*)malloc(sizeof(float)*len);
newLine->x2= (float*)malloc(sizeof(float)*len);
newLine->newy= (float*)malloc(sizeof(float)*len);
newLine->len = len;
newLine->X = 0;
newLine->Y = 0;
newLine->XY = 0;
newLine->X2 = 0;
newLine->Dev=0;
int i;
newLine->len = read->len;
for(i = 0;i<newLine->len;i++){
newLine->x[i]=read->x[i];
newLine->y[i]=read->y[i];
newLine->xy[i]=read->x[i]*read->y[i];
newLine->x2[i]=read->x[i]*read->x[i];
newLine->X += newLine->x[i];
newLine->Y += newLine->y[i];
newLine->XY += newLine->xy[i];
newLine->X2 += newLine->x2[i];
}
return newLine;
}
int lsm_Calc_LsmLine(LsmLine *Line)
{
int i;
Matrix *lhs = matrix_new_Matrix(2,2);
Matrix *rhs = matrix_new_Matrix(2,1);
Assuming Eqn is y=ax+b
lhs->mat[0][0] = Line->X;
lhs->mat[0][1] = Line->len;
lhs->mat[1][0] = Line->X2;
lhs->mat[1][2] = Line->X;
rhs->mat[0][0]=Line->Y;
rhs->mat[1][0]=Line->XY;
MatrixEqn *Eqn = matrix_new_MatrixEqn(lhs,rhs);
matrix_Solve_Det(Eqn);
float a = Eqn->Soln->mat[0][0];
float b = Eqn->Soln->mat[1][0] ;
for(i=0;i<Line->len;i++){
Line->newy[i] = a*Line->x[i]+b;
Line->Dev += (Line->y[i]-Line->newy[i])*(Line->y[i]-Line->newy[i]);
}
}
int lsm_Print_LsmLine(LsmLine* line)
{
printf("\nS.No\tX\t\tY\t\tX2\t\tXY\t\tNewY\n");
int i;
for (i=0;i<line->len;i++){
printf("\n%d",i+1);
printf("\t%0.3f",line->x[i]);
printf("\t\t%0.3f",line->y[i]);
printf("\t\t%0.3f",line->x2[i]);
printf("\t%0.3f",line->xy[i]);
printf("\t\t%0.3f",line->newy[i]);
}
printf("\n\nTotal");
printf("\t%0.3f",line->X);
printf("\t\t%0.3f",line->Y);
printf("\t\t%0.3f",line->X2);
printf("\t%0.3f",line->XY);
printf("\n\n%0.3f = %0.3fa + %db ",line->Y,line->X,line->len);
printf("\n%0.3f = %0.3fa + %0.3fb ",line->XY,line->X2,line->X);
printf("\n\nDeviation = %0.3f",line->Dev);
return 0;
}
void lsm_Read_farray(float *array,int len)
{
int i=0;
for(i=0;i<len;i++){
scanf("%f",&array[i]);
}
return 0;
}
lsm_Print_farray(float *array,int len)
{
int i=0;
for(i=0;i<len;i++){
printf("%0.3f",array[i]);
}
return 0;
}
Sample program to test.
#include<stdio.h>
#include"lsm.h"
int main()
{
printf("\n\n\t\t\tLEAST SQUARE METHOD FOR BEST LINE");
int n,choice;
printf("\n\nEnter the number of readings\t:");
scanf("%d",&n);
Readings *read = lsm_new_Readings(n);
printf("\nEnter the type of Variation of X:");
printf("\n\t1.Constant Steps of X");
printf("\n\t2.Variable Steps of X\n");
printf("\nEnter the Choice\t:");
scanf("%d",&choice);
switch(choice){
case 1: printf("\nEnter First : Step : Last of X\t:") ;
float first , step , last;
scanf("%f %f %f",&first,&step,&last);
int i;
float value;
for( i=0,value=first;value<=last; value +=step,i++){
read->x[i] = value;
}
break;
case 2: printf("\nEnter X\t:\n");
lsm_Read_farray(read->x,n);
break;
default: printf("\nWrong Option Restart the program!!!");
break;
}
printf("\nEnter Y\t:\n");
lsm_Read_farray(read->y,n);
LsmLine *line = lsm_new_LsmLine(read);
lsm_Calc_LsmLine(line);
lsm_Print_LsmLine(line);
return 0;
}
We can extend these project to various curves, and choose the curve which has least summation of error 'S', since all set of points will not be as above.
