Task Description

Lets say that we want to multiply matrix A with the dimension m by k by a matrix B with the dimension k by n$.$ To obtain the product, say matrix C$,$ we compute dot products for each row of A and each column of B; i$.$e$.,$ to compute a specific element cij of the matrix C$,$ we compute a dot product of row ai from the matrix A and the column bj from the matrix B$.$

LaTeX

The application should accept input in the following format:

the first line contains three numbers that specify the sizes of the matrices; for example, m$,$ k$,$ and n$,$ followed by

m lines of k numbers that represent matrix A$,$ and in turn followed by

k lines of n numbers that represent matrix B$.$

The program should assume the validity of m$,$ k$,$ and n $($i$.$e$.,$ that the matrices A and B can be legally multiplied$).$

The tests should verify that any number of pairs of matrices can be multiplied concurrently.

Sample input for concurrent multiplication of two pairs of matrices:

in$.$txt

$323$

$14$

$25$

$36$

$876$

$543$

$425$

$15$

$26$

$37$

$48$

$98765$

$43210$

The program should output the content of both input matrices followed by their product as shown here:

Sample output for concurrent multiplication of two pairs of matrices:

MATRIX A$1$

$14$

$25$

$36$

MATRIX B$1$

$876$

$543$

MATRIX A$1$ x B$1$

$282318$

$413427$

$544536$

MATRIX A$2$

$42$

$51$

$52$

$63$

MATRIX B$2$

$74898$

$76543$

MATRIX A$2$ x B$2$

$4228424438$

$4226454943$

$4932505346$

$6342636657$

Implementation

Recall that we have several choices to passing information to the threads:

global variables

or a struct.

Global variables will not work since this will prevent the program from multiplying multiple pairs of matrices concurrently. In general, we stay away from global variables when using threads, though there are cases where it makes sense. For this lab, you must not use global variables to pass information.

In your implementation, you must use m$*$n single unique threads to compute the values of every element cij of the product matrix. Therefore, you must pass a pointer to the following structure:

struct matrixCell

$\{$

int i;

int j;

int k;

int $**$a;

int $**$b;

int $**$c;

$\}$;

as a parameter to pthread$\_$create$().$

The integer i is the index of the row in the matrix A$,$

j is the index of the column in the matrix B$,$

and k indicates the number of elements in the row and

the number of elements in the column.

The pointers will point to matrices A$,$ B$,$ and C that will be placed in dynamically allocated space in the function allocatAndLoadMatrices$().$ The pointer $**$a points to the matrix A$,**$b to B$,$ and $**$c to C$.$ The function takes pointers to these pointers $($i$.$e$.,$ pointers to two$-$dimensional arrays$)$ as parameters $($hence $***$a$,***$b$,$ and $***$c$).$ You must allocate space for all rows and all columns in every of the arrays, so they can hold the corresponding matrices. The function loadMatrix$()$ is an auxiliary function that focuses on loading one matrix at a time.

You MUST NOT use thread$\_$join$()$ after the creation of each thread, since that would cause sequential execution of the threads, and there would be no concurrency whatsoever. However, you must wait for the threads to complete in another place before printing the result, since if you do not, then the product matrix C will be only partially calculated as the program may exit before all threads manage to complete their execution.

Note, this means that you must create both sets of multiplication threads $($one for each pair of input$)$ before calling pthread$\_$join$().$

The archive matrixMult.zip contains starting code for your implementation. Implement all missing parts as indicated in the comments

You must submit the following:

the signed source code,

the CMakeLists.txt file with which you built your application,

and multiple scripts of robust tests that confirm that your program is capable of multiplying any a number of matrix pairs concurrently.

in$.$txt file:

$323$

$14$

$25$

$36$

$876$

$543$

$425$

$15$

$26$

$37$

$48$

$98765$

$43210$

CMakeLists.txt:

project$($matrixMult C$)$

set$($CMAKE$\_$C$\_$STANDARD $17)$

set$($CMAKE$\_$C$\_$FLAGS $"$$$\{$CMAKE$\_$C$\_$FLAGS$\}-$D$\_$FILE$\_$OFFSET$\_$BITS$=64")$

set$($CMAKE$\_$C$\_$FLAGS$\_$DEBUG $"$$$\{$CMAKE$\_$C$\_$FLAGS$\_$DEBUG$\}-$Wall $--$pedantic $-$g $-$O$0-$D$\_$DEBUG"$)$

set$($CMAKE$\_$MODULE$\_$PATH $"$$$\{$CMAKE$\_$CURRENT$\_$SOURCE$\_$DIR$\}/$CMake$"$ $$\{$CMAKE$\_$MODULE$\_$PATH$\})$

set$($CMAKE$\_$EXPORT$\_$COMPILE$\_$COMMANDS $1)$

set$($SOURCE$\_$FILES matrixMult.c$)$

add$\_$executable$($matrixMult $$\{$SOURCE$\_$FILES$\})$

find$\_$package$($Threads$)$

target$\_$link$\_$libraries$($matrixMult $$\{$CMAKE$\_$THREAD$\_$LIBS$\_$INIT$\})$

matrixMult.c:

#include "matrixMult.h$"$

int

main$($int argc, char$**$ argv$)$

$\{$

$//$ Input file should be passed to the program: $./$matrixMult in$.$txt

if $($freopen$($argv$[1],"$r$",$ stdin$)==0)\{$

oops$("$Cannot open the input file.

$",-1)$;

$\}$

$//$ two pairs of matrices

int$**$ a$1,**$ b$1,**$ c$1$;

int$**$ a$2,**$ b$2,**$ c$2$;

$//$ dimensions of the matices m x k and k x n

int m$1,$ k$1,$ n$1$;

int m$2,$ k$2,$ n$2$;

allocateAndLoadMatrices$($&a$1,$ &b$1,$ &c$1,$ &m$1,$ &k$1,$ &n$1)$;

allocateAndLoadMatrices$($&a$2,$ &b$2,$ &c$2,$ &m$2,$ &k$2,$ &n$2)$;

$//$