08.Linear_Interpolation_Profiled.c

/***********************************
Purpose : Interpolation Error
Authors : Kirtan Patel(AE19B038)
Date    : 10/09/2020
Input   : File Path, Downsampling Constant
Output  : The Squared Error for the Input Downsampling Constant
*************************************/

/*
argc : saves the number of arguements input by the user in the command line
argv : saves the arguements input by the user in the command line
fptr : pointer to access the Data file
size : stores the size of the array required to store the data from the file
x_true[],y_true[] : stores the original data accessed in the file
y_interpolated[] : stores the interpolated data
index : stores the index value of data being accessed
skip_line : counter to check if the line is to be skipped or not
line_count : stores the row number of the data being accessed
ch :  stores the character being accessed
extra : reference to an already allocated object of type char*, 
        whose value is set by the function to the next character in str after the numerical value. 
current_number[] : stores the number being accessed in the file
DownSampled_Point_count : stores the number of points after Downsampling
Ds_c : (Downsampling Constant) stores the value of the Downsampling Constant accepted from user
ip_func[i][0] : Stores the value of slope of ith linear interpolated function
ip_func[i][1] : Stores the value of constant of ith linear interpolated function
e_squared : stores the value of squared error
*/

/*********Usage : Compile using 'gcc Linear_Interpolation.c -lm -o epsilon'*************/
/*****Usage : enter "./epsilon ~filepath~ ~Downsampling Constant~"  to get the columnwise Mean and Standard Deviation*****/


//Header files and initial declarations
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <math.h>

double* x_true;
double* y_true;
double* y_interpolated;
int size;
int Ds_c;
int DownSampled_Point_count=0;

int e2()
{
    //CODE TO FIND EPSILON SQUARED
	double e_squared=0.0;

	for(int i=0;i<size;i++)
		e_squared = e_squared + (y_true[i]-y_interpolated[i])*(y_true[i]-y_interpolated[i]);
	//Downsampling by Ds_c , the error is e_squared
	printf("%d	%le \n",Ds_c,e_squared);

    return 0;
    
}

int Downsample()
{	
    //CODE TO DOWNSAMPLE THE DATA

	if(Ds_c>=size)          //checking if the Downsampling is possible
	{	printf("Cannot Downsample so much\n");   //printing error message
  		exit(1);
  	}

	y_interpolated = (double*) calloc(size,sizeof(double));

	for(int i=0;i<size;i++)
    { 
		if(i%(Ds_c)==0)	//initializing downsampled points to original value
		{	DownSampled_Point_count++;
			y_interpolated[i]=y_true[i];
		}
		if(i%(Ds_c)!=0)	//initializing non-downsampled points to zero
			y_interpolated[i]=0.0;
	}

	if((size-1)%Ds_c!=0)	//if last point is not included, explicitly include it in the downsampled dataset
	{	y_interpolated[(size-1)]=y_true[(size-1)];
		DownSampled_Point_count++;
	}

    return 0;

}

int Interpolate()
{
	
//CODE TO FIND PIECEWISE INTERPOLATING FUNCTION

	double ip_func[DownSampled_Point_count-1][2];
	if((size-1)%Ds_c==0)	//if last point is present in downsampled data
	{
		for(int i=0;i<DownSampled_Point_count-1;i++) //Defining coefficients of piecewise Function.
		{	ip_func[i][0]=(y_true[(i+1)*Ds_c]-y_true[i*Ds_c])/(x_true[(i+1)*Ds_c]-x_true[i*Ds_c]);	//slope m
			ip_func[i][1]=y_true[i*Ds_c]-(x_true[i*Ds_c]*(ip_func[i][0]));	//constant c
		}	
	}

	if((size-1)%Ds_c!=0)	//if last point is not present in downsampled data
	{
		for(int i=0;i<DownSampled_Point_count-1;i++) //To find out the coefficients of Linear Interpolated Function.
		{
			if((i+1)*Ds_c<size)
			{	ip_func[i][0]=(y_true[(i+1)*Ds_c]-y_true[i*Ds_c])/(x_true[(i+1)*Ds_c]-x_true[i*Ds_c]);	//slope m
				ip_func[i][1]=y_true[i*Ds_c]-(x_true[i*Ds_c]*(ip_func[i][0]));	//constant c
			}
			if((i+1)*Ds_c>(size-1))
			{	ip_func[i][0]=(y_true[size-1]-y_true[i*Ds_c])/(x_true[size-1]-x_true[i*Ds_c]);	//slope m
				ip_func[i][1]=y_true[i*Ds_c]-(x_true[i*Ds_c]*(ip_func[i][0]));	//constant c
			}
		}
	}	

	//CODE TO FIND Y_INTERPOLATED

	for(int i=0;i<size;i++)
    {
		if(i%(Ds_c)!=0)
		{	int f_num=floor(i/Ds_c);	//decide which function number to use for interpolation
			y_interpolated[i]=((ip_func[f_num][0])*(x_true[i]))+ip_func[f_num][1];	//find the interpolated value
		}
	}

    return 0;

}

int Print_Elements()
{
    for(int i=0;i<size;i++)
		printf("%le	%le     %le\n",x_true[i],y_true[i],y_interpolated[i]);
    return 0;    
}

int main(int argc,char *argv[])  //taking filepath arguement NOTE:Code works even for oversized Data file i.e if columns > 2
{	

	/***CODE TO READ THE DATA FROM THE FILE AND SAVE IT IN AN ARRAY***/

	FILE* fptr;
	fptr=fopen(argv[1],"r");   //opening file 
	if(fptr==NULL)          //checking if file exist or filepath is correct
	{
 		printf("FILE NOT VALID");   //printing error message
  		exit(1);
  	}

    size = 1;
    x_true = (double*)malloc(size*sizeof(double));
    y_true = (double*)malloc(size*sizeof(double));
    
	int skip_line=0,index=0,line_count=0;   //initializing variables
	char ch,*extra;
	char current_number[100];

	while((ch=fgetc(fptr))!=EOF)  //accessing the file character by character
	{
		if(ch=='#')              //checking if row starts with #
			skip_line=1;         //skip line if it starts with #

		if(skip_line==0)
		{
			if(isalpha(ch)||isdigit(ch)||ch=='-'||ch=='.')   //checking if char is a part of the field
					strncat(current_number,&ch,1);	         //if yes adding it to current number
			else 
			{   double new_digits = strtod(current_number,&extra);      //if field data ends, converting it to double
				if(index==0)
                    x_true[line_count]=new_digits;                      //adding number to Array of x_true
				if(index==1)
                    y_true[line_count]=new_digits;		     //adding square of number to sum of squares of corresponding column
				index++;                                         // switching to next column
				current_number[0]='\0';						     //Resetting the number to be added to zero
			}
		}

		if(ch=='\n')        //checking for next line
		{   size++;
			line_count++;      //counter to count the lines
			skip_line=0;	   //reseting the counter to check if line starts with #
			index=0;		   //reseting index to zero
            //x_true = (double*)malloc(size*sizeof(double));
            //y_true = (double*)malloc(size*sizeof(double));
            x_true=(double*)realloc(x_true,(size)*sizeof(double));
            y_true=(double*)realloc(y_true,(size)*sizeof(double)); 
		}
	}

	size=size-1;	//correcting the size after it is incremented one extra time in the last
    
    x_true=(double*)realloc(x_true,(size)*sizeof(double));	//optimizing space by discarding excess memory
    y_true=(double*)realloc(y_true,(size)*sizeof(double)); 

	Ds_c = atoi(argv[2]);  //Take Dsc=DownSampling_Constant from the user

    Downsample();
    Interpolate();
    e2();

    //Print_Elements();

	//freeing the pointers
	fclose(fptr);

	free(x_true);	
    free(y_true);
    free(y_interpolated);

	
	return 0;
}