From 8dce83172bdb260e5b004821a01598fe72f1bd3a Mon Sep 17 00:00:00 2001
From: mtzikara <tzitzima.ee@gmail.com>
Date: Sun, 16 Sep 2018 18:19:00 +0200
Subject: [PATCH] Add files via upload

---
 serial_v2/Makefile                       |  37 ++
 serial_v2/pagerank.out                   | Bin 0 -> 18669 bytes
 serial_v2/pagerank_output                |   1 +
 serial_v2/serial_gs_pagerank.c           |  33 ++
 serial_v2/serial_gs_pagerank.o           | Bin 0 -> 2824 bytes
 serial_v2/serial_gs_pagerank_functions.c | 437 +++++++++++++++++++++++
 serial_v2/serial_gs_pagerank_functions.h |  86 +++++
 serial_v2/serial_gs_pagerank_functions.o | Bin 0 -> 12784 bytes
 8 files changed, 594 insertions(+)
 create mode 100644 serial_v2/Makefile
 create mode 100644 serial_v2/pagerank.out
 create mode 100644 serial_v2/pagerank_output
 create mode 100644 serial_v2/serial_gs_pagerank.c
 create mode 100644 serial_v2/serial_gs_pagerank.o
 create mode 100644 serial_v2/serial_gs_pagerank_functions.c
 create mode 100644 serial_v2/serial_gs_pagerank_functions.h
 create mode 100644 serial_v2/serial_gs_pagerank_functions.o

diff --git a/serial_v2/Makefile b/serial_v2/Makefile
new file mode 100644
index 0000000..a038971
--- /dev/null
+++ b/serial_v2/Makefile
@@ -0,0 +1,37 @@
+SHELL := /bin/bash
+
+# ============================================
+# COMMANDS
+
+CC = gcc
+RM = rm -f
+CFLAGS_DEBUG=-O0 -g -I.
+CFLAGS=-std=gnu99 -O3 -I.
+OBJ=serial_gs_pagerank.o serial_gs_pagerank_functions.o
+DEPS=serial_gs_pagerank_functions.h
+
+# ==========================================
+# TARGETS
+
+EXECUTABLES = pagerank.out
+
+.PHONY: all clean
+
+all: $(EXECUTABLES)
+
+# ==========================================
+# DEPENDENCIES (HEADERS)
+
+%.o: %.c $(DEPS)
+	$(CC) -c -o $@ $< $(CFLAGS)
+
+.PRECIOUS: $(EXECUTABLES) $(OBJ)
+
+# ==========================================
+# EXECUTABLE (MAIN)
+
+$(EXECUTABLES): $(OBJ)
+	$(CC) -o $@ $^ $(CFLAGS)
+
+clean:
+	$(RM) *.o *~ $(EXECUTABLES)
diff --git a/serial_v2/pagerank.out b/serial_v2/pagerank.out
new file mode 100644
index 0000000000000000000000000000000000000000..713bdcb3602545b7145e875f064edfd432b59126
GIT binary patch
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diff --git a/serial_v2/pagerank_output b/serial_v2/pagerank_output
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diff --git a/serial_v2/serial_gs_pagerank.c b/serial_v2/serial_gs_pagerank.c
new file mode 100644
index 0000000..041d784
--- /dev/null
+++ b/serial_v2/serial_gs_pagerank.c
@@ -0,0 +1,33 @@
+#include <sys/time.h>
+
+#include "serial_gs_pagerank_functions.h"
+
+struct timeval startwtime, endwtime;
+double seq_time;
+
+int main(int argc, char **argv) {
+	int **directedWebGraph;
+	int **transitionMatrix;
+	double *pagerankVector;
+	Parameters parameters;
+
+	parseArguments(argc, argv, &parameters);
+
+	initialize(&directedWebGraph, &transitionMatrix, &pagerankVector, &parameters);
+
+	// Starts wall-clock timer
+	gettimeofday (&startwtime, NULL);
+
+	int iterations = pagerank(&transitionMatrix, &pagerankVector, parameters);
+	if (parameters.verbose) {
+		printf("\n----- Results -----\
+			\nTotal iterations = %d\n", iterations);
+	}
+
+	// Stops wall-clock timer
+	gettimeofday (&endwtime, NULL);
+	double seq_time = (double)((endwtime.tv_usec - startwtime.tv_usec)/1.0e6 +
+		endwtime.tv_sec - startwtime.tv_sec);
+	printf("%s wall clock time = %f\n","Pagerank (Gauss-Seidel method), serial implementation",
+		seq_time);
+}
diff --git a/serial_v2/serial_gs_pagerank.o b/serial_v2/serial_gs_pagerank.o
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diff --git a/serial_v2/serial_gs_pagerank_functions.c b/serial_v2/serial_gs_pagerank_functions.c
new file mode 100644
index 0000000..ca7ba9a
--- /dev/null
+++ b/serial_v2/serial_gs_pagerank_functions.c
@@ -0,0 +1,437 @@
+#include "serial_gs_pagerank_functions.h"
+
+const char *ARGUMENT_CONVERGENCE_TOLERANCE = "-c";
+const char *ARGUMENT_MAX_ITERATIONS = "-m";
+const char *ARGUMENT_DAMPING_FACTOR = "-a";
+const char *ARGUMENT_VERBAL_OUTPUT = "-v";
+const char *ARGUMENT_OUTPUT_HISTORY = "-h";
+const char *ARGUMENT_OUTPUT_FILENAME = "-o";
+
+const int NUMERICAL_BASE = 10;
+char *DEFAULT_OUTPUT_FILENAME = "pagerank_output";
+
+// ==================== PAGERANK ====================
+
+int pagerank(int ***transitionMatrix, double **pagerankVector, Parameters parameters) {
+	int iterations = 0;
+	double delta,
+	*vectorDifference = (double *) malloc(parameters.numberOfPages * sizeof(double)),
+	*previousPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double)),
+	*convergedPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double)),
+	**linksFromConvergedPages = (double **) malloc(parameters.numberOfPages * sizeof(double *)),
+	*linksFromConvergedPagesPagerankVector = (double *) malloc(parameters.numberOfPages * sizeof(double));
+	bool *converganceMatrix = (bool *) malloc(parameters.numberOfPages * sizeof(bool));
+
+	for (int i=0; i<parameters.numberOfPages; ++i) {
+		convergedPagerankVector[i] = 0;
+		converganceMatrix[i] = false;
+		linksFromConvergedPagesPagerankVector[i] = 0;
+
+		linksFromConvergedPages[i] = (double *) malloc(parameters.numberOfPages * sizeof(double));
+		for (int j=0; j<parameters.numberOfPages; ++j) {
+			linksFromConvergedPages[i][j] = 0;
+		}
+	}
+
+	if (parameters.verbose) {
+		printf("\n----- Starting iterations -----\n");
+	}
+
+	do {
+		memcpy(previousPagerankVector, *pagerankVector, parameters.numberOfPages * sizeof(double));
+
+		matrixVectorMultiplication(*transitionMatrix, previousPagerankVector,
+			linksFromConvergedPagesPagerankVector, convergedPagerankVector,
+			pagerankVector, parameters.numberOfPages, parameters.dampingFactor);
+
+		if (parameters.history) {
+			savePagerankToFile(parameters.outputFilename, iterations != 0,
+				*pagerankVector, parameters.numberOfPages);
+		}
+
+		for (int i=0; i<parameters.numberOfPages; ++i) {
+			vectorDifference[i] = (*pagerankVector)[i] - previousPagerankVector[i];
+		}
+		delta = vectorNorm(vectorDifference, parameters.numberOfPages);
+
+		if (!iterations % 10) {
+			for (int i=0; i<parameters.numberOfPages; ++i) {
+				double temp = fabs((*pagerankVector)[i] - previousPagerankVector[i]) / fabs(previousPagerankVector[i]);
+				if (temp < parameters.convergenceCriterion){
+					converganceMatrix[i] = true;
+					convergedPagerankVector[i] = (*pagerankVector)[i];
+				}
+			}
+
+			for (int i=0; i<parameters.numberOfPages; ++i) {
+				if (converganceMatrix[i] == true) {
+					for (int j=0; j<parameters.numberOfPages; ++j){
+						if (converganceMatrix[j] == false){
+							linksFromConvergedPages[i][j] = (*transitionMatrix)[i][j];
+						}
+						// Zeros out CN and CC sub-matrices
+						(*transitionMatrix)[i][j] = 0;
+						// Zeros out NC sub-matrix
+						(*transitionMatrix)[j][i] = 0;
+					}
+
+					double sum = 0;
+					for (int j=0; j<parameters.numberOfPages; ++j) {
+						sum += linksFromConvergedPages[i][j] * (*pagerankVector)[j];
+					}
+					linksFromConvergedPagesPagerankVector[i] = sum;
+				}
+			}
+		}
+
+		++iterations;
+		printf("Iteration %d: delta = %f\n", iterations, delta);
+	} while (delta > parameters.convergenceCriterion &&
+		(parameters.maxIterations == 0 || iterations < parameters.maxIterations));
+
+	if (!parameters.history) {
+		savePagerankToFile(parameters.outputFilename, false, *pagerankVector,
+			parameters.numberOfPages);
+	}
+
+	return iterations;
+}
+
+// ==================== INITIALIZATION ====================
+
+/*
+ * initialize allocates required memory for arrays, reads the web graph from the
+ * from the file and creates the initial transition probability distribution
+ * matrix.
+*/
+void initialize(int ***directedWebGraph, int ***transitionMatrix,
+	double **pagerankVector, Parameters *parameters) {
+
+	// Reads web graph from file
+	if ((*parameters).verbose) {
+		printf("----- Reading graph from file -----\n");
+	}
+	readGraphFromFile(directedWebGraph, parameters);
+
+	// Outputs the algorithm parameters to the console
+	if ((*parameters).verbose) {
+		printf("\n----- Running with parameters -----\
+			\nNumber of pages: %d", (*parameters).numberOfPages);
+		if (!(*parameters).maxIterations) {
+			printf("\nMaximum number of iterations: inf");
+		} else {
+			printf("\nMaximum number of iterations: %d", (*parameters).maxIterations);
+		}
+		printf("\nConvergence criterion: %f\
+			\nDamping factor: %f\
+			\nGraph filename: %s\n", (*parameters).convergenceCriterion,
+			(*parameters).dampingFactor, (*parameters).graphFilename);
+	}
+
+	// Allocates memory for the pagerank vector
+	(*pagerankVector) = (double *) malloc((*parameters).numberOfPages * sizeof(double));
+	double webUniformProbability = 1. / (*parameters).numberOfPages;
+	for (int i=0; i<(*parameters).numberOfPages; ++i) {
+		(*pagerankVector)[i] = webUniformProbability;
+	}
+
+	// Generates the initial transition matrix (matrix P).
+	generateNormalizedTransitionMatrix(transitionMatrix, *directedWebGraph, *parameters);
+	// Transposes the transition matrix (P^T).
+	transposeMatrix(transitionMatrix, (*parameters).numberOfPages, (*parameters).numberOfPages);
+}
+
+/*
+ * generateNormalizedTransitionMatrix generates the normalized transition matrix
+ * from the graph data (matrix P').
+*/
+void generateNormalizedTransitionMatrix(int ***transitionMatrix,
+	int **directedWebGraph, Parameters parameters) {
+	// Allocates memory for the transitionMatrix rows
+	(*transitionMatrix) = (int **) malloc(parameters.numberOfPages * sizeof(int *));
+
+	for (int i=0; i<parameters.numberOfPages; ++i) {
+		// Allocates memory for this row's columns
+		(*transitionMatrix)[i] = (int *) malloc(parameters.numberOfPages * sizeof(int));
+		/*
+		// Calculates the outdegree of this page
+		int pageOutdegree = 0;
+		for (int j=0; j<parameters.numberOfPages; ++j) {
+			pageOutdegree += directedWebGraph[i][j];
+		}
+
+		// Populates this row of the transition matrix
+		if (pageOutdegree != 0) {
+			// Calculates the uniform probability once.
+			double pageUniformProbability = 1. / pageOutdegree;
+
+			for (int j=0; j<parameters.numberOfPages; ++j) {
+				if (directedWebGraph[i][j] == 1){
+					(*transitionMatrix)[i][j] = pageUniformProbability;
+				} else {
+					(*transitionMatrix)[i][j] = 0;
+				}
+			}
+		} else {
+			for (int j=0; j<parameters.numberOfPages; ++j) {
+				(*transitionMatrix)[i][j] = 0;
+			}
+		}
+		*/
+		
+	}
+	for (int i=0; i<parameters.numberOfPages; ++i){
+		for (int j=0; i<parameters.numberOfPages; ++i){
+			(*transitionMatrix)[i][j] = directedWebGraph[i][j];
+		}
+	}
+}
+
+// ==================== MATH UTILS ====================
+
+/*
+ * matrixVectorMultiplication calculates the product of the multiplication
+ * between a matrix and the a vector in a cheap way.
+*/
+void matrixVectorMultiplication(int **transitionMatrix, double *previousPagerankVector,
+	double *linksFromConvergedPagesPagerankVector, double *convergedPagerankVector,
+	double **pagerankVector, int vectorSize, double dampingFactor) {
+	double webUniformProbability = 1. / vectorSize;
+
+	for (int i=0; i<vectorSize; ++i) {
+		double sum1 = 0;
+		double sum2 = 0;
+
+		for (int j=0; j<i; ++j) {
+			sum1 += transitionMatrix[i][j] * previousPagerankVector[j];
+		}
+		for (int j=i; j<vectorSize; ++j) {
+			sum2 += transitionMatrix[i][j] * (*pagerankVector)[j];
+		}
+		(*pagerankVector)[i] = dampingFactor * sum1+dampingFactor * sum2+(1-dampingFactor);
+	}
+
+	//double normDifference = vectorNorm(previousPagerankVector, vectorSize) -
+	//vectorNorm(*pagerankVector, vectorSize);
+
+	for (int i=0; i<vectorSize; ++i) {
+		//(*pagerankVector)[i] += normDifference * webUniformProbability +
+		//linksFromConvergedPagesPagerankVector[i] + convergedPagerankVector[i];
+		(*pagerankVector)[i] += linksFromConvergedPagesPagerankVector[i] + convergedPagerankVector[i];
+	}
+}
+
+/*
+ * vectorNorm calculates the first norm of a vector.
+*/
+double vectorNorm(double *vector, int vectorSize) {
+	double norm = 0.;
+
+	for (int i=0; i<vectorSize; ++i) {
+		norm += fabs(vector[i]);
+	}
+
+	return norm;
+}
+
+/*
+ * transposeMatrix transposes the matrix passed (by reference) in the arguments.
+*/
+void transposeMatrix(int ***matrix, int rows, int columns) {
+	// Transposes the matrix
+	// Rows become columns and vice versa
+
+	int **tempArray = (int **) malloc(columns * sizeof(int *));
+	for (int i=0; i<columns; ++i) {
+		tempArray[i] = malloc(rows * sizeof(int));
+
+		for (int j=0; j<rows; ++j) {
+			tempArray[i][j] = (*matrix)[j][i];
+		}
+	}
+
+	// TODO free memory
+
+	//double **pointerToFreeMemoryLater = *matrix;
+	*matrix = tempArray;
+	/*for (int i=0; i<rows; ++i) {
+		free(pointerToFreeMemoryLater[i]);
+	}
+	free(pointerToFreeMemoryLater);*/
+}
+
+// ==================== PROGRAM INPUT AND OUTPUT UTILS ====================
+
+/*
+ * parseArguments parses the command line arguments given by the user.
+*/
+void parseArguments(int argumentCount, char **argumentVector, Parameters *parameters) {
+	if (argumentCount < 2 || argumentCount > 10) {
+		validUsage(argumentVector[0]);
+	}
+
+	(*parameters).numberOfPages = 0;
+	(*parameters).maxIterations = 0;
+	(*parameters).convergenceCriterion = 1;
+	(*parameters).dampingFactor = 0.85;
+	(*parameters).verbose = false;
+	(*parameters).history = false;
+	(*parameters).outputFilename = DEFAULT_OUTPUT_FILENAME;
+
+	char *endPointer;
+	int argumentIndex = 1;
+
+	while (argumentIndex < argumentCount) {
+		if (!strcmp(argumentVector[argumentIndex], ARGUMENT_CONVERGENCE_TOLERANCE)) {
+			argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]);
+
+			double convergenceInput = strtod(argumentVector[argumentIndex], &endPointer);
+			if (convergenceInput == 0) {
+				printf("Invalid convergence argument\n");
+				exit(EXIT_FAILURE);
+			}
+			(*parameters).convergenceCriterion = convergenceInput;
+		} else if (!strcmp(argumentVector[argumentIndex], ARGUMENT_MAX_ITERATIONS)) {
+			argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]);
+
+			size_t iterationsInput = strtol(argumentVector[argumentIndex], &endPointer, NUMERICAL_BASE);
+			if (iterationsInput == 0 && endPointer) {
+				printf("Invalid iterations argument\n");
+				exit(EXIT_FAILURE);
+			}
+			(*parameters).maxIterations = iterationsInput;
+		} else if (!strcmp(argumentVector[argumentIndex], ARGUMENT_DAMPING_FACTOR)) {
+			argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]);
+
+			double alphaInput = strtod(argumentVector[argumentIndex], &endPointer);
+			if ((alphaInput == 0 || alphaInput > 1) && endPointer) {
+				printf("Invalid alpha argument\n");
+				exit(EXIT_FAILURE);
+			}
+			(*parameters).dampingFactor = alphaInput;
+		} else if (!strcmp(argumentVector[argumentIndex], ARGUMENT_VERBAL_OUTPUT)) {
+			(*parameters).verbose = true;
+		} else if (!strcmp(argumentVector[argumentIndex], ARGUMENT_OUTPUT_HISTORY)) {
+			(*parameters).history = true;
+		} else if (!strcmp(argumentVector[argumentIndex], ARGUMENT_OUTPUT_FILENAME)) {
+			argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]);
+
+			if (fopen(argumentVector[argumentIndex], "w") == NULL) {
+				printf("Invalid output filename. Reverting to default.\n");
+				continue;
+			}
+			(*parameters).outputFilename = argumentVector[argumentIndex];
+		} else if (argumentIndex == argumentCount - 1) {
+			(*parameters).graphFilename = argumentVector[argumentIndex];
+		} else {
+			validUsage(argumentVector[0]);
+			exit(EXIT_FAILURE);
+		}
+		++argumentIndex;
+	}
+}
+
+/*
+ * readGraphFromFile loads the file supplied in the command line arguments to an
+ * array (directedWebGraph) that represents the graph.
+*/
+void readGraphFromFile(int ***directedWebGraph, Parameters *parameters) {
+	FILE *graphFile;
+
+	// Opens the file for reading
+	graphFile = fopen((*parameters).graphFilename, "r+");
+	if (!graphFile) {
+		printf("Error opening file \n");
+		exit(EXIT_FAILURE);
+	}
+
+	// Reads the dimensions of the (square) array from the file
+	int readChar, numberOfLines=0;
+	while((readChar = fgetc(graphFile))) {
+		// Breaks if end of file
+		if (readChar == EOF) break;
+		// Otherwise, if the character is a break line, adds one to the count of lines
+		if (readChar == '\n') {
+			++numberOfLines;
+		}
+	}
+
+	if ((*parameters).verbose) {
+		printf("Line count of file is %d \n", numberOfLines + 1);
+	}
+
+	// Each line of the file represents one page of the graph
+	(*parameters).numberOfPages = numberOfLines + 1;
+	rewind(graphFile);
+
+	// Allocates memory and loads values into directedWebGraph (matrix A)
+	// Allocates memory for the rows
+	(*directedWebGraph) = (int **) malloc((*parameters).numberOfPages * sizeof(int *));
+
+	for (int i=0; i<(*parameters).numberOfPages; ++i) {
+		// Allocates memory for the columns of this row
+		(*directedWebGraph)[i] = (int *) malloc((*parameters).numberOfPages * sizeof(int));
+		// Reads values from the file
+		for (int j=0; j<(*parameters).numberOfPages; ++j) {
+			if (!fscanf(graphFile, "%d ", &(*directedWebGraph)[i][j])) {
+				break;
+			}
+		}
+	}
+
+	fclose(graphFile);
+}
+
+/*
+ * validUsage outputs a message to the console that informs the user of the
+ * correct (valid) way to use the program.
+*/
+void validUsage(char *programName) {
+	printf("%s [-c convergence_criterion] [-m max_iterations] [-a alpha] [-v] [-h] [-o output_filename] <graph_file>\
+		\n-c convergence_criterion\
+		\n\tthe convergence tolerance criterion\
+		\n-m max_iterations\
+		\n\tmaximum number of iterations to perform\
+		\n-a alpha\
+		\n\tthe damping factor\
+		\n-v enable verbal output\
+		\n-h enable history output to file\
+		\n-o output_filename\
+		\n\tfilename and path for the output\
+		\n", programName);
+	exit(EXIT_FAILURE);
+}
+
+/*
+ * checkIncrement is a helper function for parseArguments function.
+*/
+int checkIncrement(int previousIndex, int maxIndex, char *programName) {
+	if (previousIndex == maxIndex) {
+		validUsage(programName);
+		exit(EXIT_FAILURE);
+	}
+	return ++previousIndex;
+}
+
+void savePagerankToFile(char *filename, bool append, double *pagerankVector,
+	int vectorSize) {
+	FILE *outputFile;
+
+	if (append) {
+		outputFile = fopen(filename, "a");
+	} else {
+		outputFile = fopen(filename, "w");
+	}
+
+	if (outputFile == NULL) {
+		printf("Error while opening the output file.\n");
+		return;
+	}
+
+	for (int i=0; i<vectorSize; ++i) {
+		fprintf(outputFile, "%f ", pagerankVector[i]);
+	}
+	fprintf(outputFile, "\n");
+
+	fclose(outputFile);
+}
\ No newline at end of file
diff --git a/serial_v2/serial_gs_pagerank_functions.h b/serial_v2/serial_gs_pagerank_functions.h
new file mode 100644
index 0000000..9003381
--- /dev/null
+++ b/serial_v2/serial_gs_pagerank_functions.h
@@ -0,0 +1,86 @@
+#ifndef SERIAL_GS_PAGERANK_FUNCTIONS_H	/* Include guard */
+#define SERIAL_GS_PAGERANK_FUNCTIONS_H
+
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+/*
+ * Constant strings that store the command line options available.
+*/
+extern const char *ARGUMENT_CONVERGENCE_TOLERANCE;
+extern const char *ARGUMENT_MAX_ITERATIONS;
+extern const char *ARGUMENT_DAMPING_FACTOR;
+extern const char *ARGUMENT_VERBAL_OUTPUT;
+extern const char *ARGUMENT_OUTPUT_HISTORY;
+extern const char *ARGUMENT_OUTPUT_FILENAME;
+
+// This is the numerical base used when parsing the numerical command line
+// arguments.
+extern const int NUMERICAL_BASE;
+// Default filename used for the output.
+extern char *DEFAULT_OUTPUT_FILENAME;
+
+// Declares a data structure to conveniently hold the algorithm's parameters.
+typedef struct parameters {
+	int numberOfPages, maxIterations;
+	double convergenceCriterion, dampingFactor;
+	bool verbose, history;
+	char *outputFilename, *graphFilename;
+} Parameters;
+
+// Function validUsage outputs the correct way to use the program with command
+// line arguments.
+void validUsage(char *programName);
+
+// Function checkIncrement is a helper function used in parseArguments (see
+// bellow).
+int checkIncrement(int previousIndex, int maxIndex, char *programName);
+
+// Function parseArguments parses command line arguments.
+void parseArguments(int argumentCount, char **argumentVector, Parameters *parameters);
+
+// Function readGraphFromFile loads adjacency matrix, that represents the web
+// graph, stored in the file provided in the command line arguments to the array
+// directedWebGraph.
+void readGraphFromFile(int ***directedWebGraph, Parameters *parameters);
+
+// Function savePagerankToFile appends or overwrites the pagerank vector
+// "pagerankVector" to the file with the filename supplied in the arguments 
+void savePagerankToFile(char *filename, bool append, double *pagerankVector,
+	int vectorSize);
+
+// Function generateNormalizedTransitionMatrix generates the normalized
+// transition matrix from the web graph data.
+void generateNormalizedTransitionMatrix(int ***transitionMatrix,
+	int **directedWebGraph, Parameters parameters);
+
+// Function transposeMatrix transposes a matrix.
+void transposeMatrix(int ***matrix, int rows, int columns);
+
+// Function initialize allocates required memory for arrays, reads the dataset
+// from the file and creates the transition probability distribution matrix.
+void initialize(
+	int ***directedWebGraph, /*This is matrix G (web graph)*/
+	int ***transitionMatrix, /*This is matrix A (transition probability distribution matrix)*/
+	double **pagerankVector, /*This is the resulting pagerank vector*/
+	Parameters *parameters
+	);
+
+// Function vectorNorm calculates the first norm of a vector.
+double vectorNorm(double *vector, int vectorSize);
+
+// Function matrixVectorMultiplication calculates the product of the
+// multiplication between a matrix and the a vector.
+void matrixVectorMultiplication(int **transitionMatrix, double *previousPagerankVector,
+			double *linksFromConvergedPagesPagerankVector, double *convergedPagerankVector,
+			double **pagerankVector, int vectorSize, double dampingFactor);
+
+// Function pagerank iteratively calculates the pagerank of each page until
+// either the convergence criterion is met or the maximum number of iterations
+// is reached.
+int pagerank(int ***transitionMatrix, double **pagerankVector, Parameters parameters);
+
+#endif	// SERIAL_GS_PAGERANK_FUNCTIONS_H
\ No newline at end of file
diff --git a/serial_v2/serial_gs_pagerank_functions.o b/serial_v2/serial_gs_pagerank_functions.o
new file mode 100644
index 0000000000000000000000000000000000000000..7c9075b2557dc51ee7089430fb823c26f0d079e6
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