## Description

This assignment asks you to write bash shell scripts to compute matrix operations. The

purpose is to get you familiar with the Unix shell, shell programming, Unix utilities,

standard input, output, and error, pipelines, process ids, exit values, and signals (at a

basic level).

What you’re going to submit is your script, called simply “matrix”.

## Overview

In this assignment, you will write a bash shell script that calculates basic matrix

operations using input from either a file or stdin. The input will be whole number values

separated by tabs into a rectangular matrix. Your script should be able to print the

dimensions of a matrix, transpose a matrix, calculate the mean vector of a matrix, add

two matrices, and multiply two matrices.

You will be using bash builtins and Unix utilities to complete the assignment. Some

commands to read up on are while, cat, read, expr, cut, head, tail, wc, and

sort.

Your script must be called simply “matrix”. The general format of the matrix command

is:

matrix OPERATION [ARGUMENT]…

Refer to man(1) for an explanation of the conventional notation regarding command

syntax, to understand the line above. Note that many terminals render italic font style as

an underline:

matrix OPERATION [ARGUMENT]…

## Specifications

Your program must perform the following operations: dims, transpose, mean, add, and

multiply. Usage is as follows:

matrix dims [MATRIX]

matrix transpose [MATRIX]

matrix mean [MATRIX]

matrix add MATRIX_LEFT MATRIX_RIGHT

matrix multiply MATRIX_LEFT MATRIX_RIGHT

The dims, transpose, and mean operations should either perform their respective

operations on the file named MATRIX, or on a matrix provided via stdin. The add and

multiply operations do not need to process input via stdin.

● dims should print the dimensions of the matrix as the number of rows,

followed by a space, then the number of columns.

● transpose should reflect the elements of the matrix along the main diagonal.

Thus, an MxN matrix will become an NxM matrix and the values along the

main diagonal will remain unchanged.

● mean should take an MxN matrix and return an 1xN row vector, where the

first element is the mean of column one, the second element is the mean of

column two, and so on.

● add should take two MxN matrices and add them together element-wise to

produce an MxN matrix. add should return an error if the matrices do not

have the same dimensions.

● multiply should take an MxN and NxP matrix and produce an MxP matrix.

Note that, unlike addition, matrix multiplication is not commutative. That is

A*B != B*A.

Here is a brief example of what the output should look like.

$ cat m1

1 2 3 4

5 6 7 8

$ cat m2

1 2

3 4

5 6

7 8

$ ./matrix dims m1

2 4

$ cat m2 | ./matrix dims

4 2

$ ./matrix add m1 m1

2 4 6 8

10 12 14 16

$ ./matrix add m2 m2

2 4

6 8

10 12

14 16

$ ./matrix mean m1

3 4 5 6

$ ./matrix transpose m1

1 5

2 6

3 7

4 8

$ ./matrix multiply m1 m2

50 60

114 140

You must check for the right number and format of arguments to matrix. This means

that, for example, you must check that a given input file is readable, before attempting

to read it. You are not required to test if the input file itself is valid. In other words, the

behavior of matrix is undefined when the matrix input is not a valid matrix. for the

purposes of this assignment, a valid matrix is a tab-delimited table containing at least

one element, where each element is a signed integer, every entry is defined, and the

table is rectangular.

The following are examples of invalid matrices and will not be tested against your code,

and may not be output by your program:

● An empty matrix.

● A matrix where the final entry on a row is followed by a tab character.

● A matrix with empty lines.

● A matrix with any element that is blank or not an integer.

Here is a valid matrix file, m1:

$ cat m1

8 5 6

3 2 2

1 6 7

5 0 7

2 2 4

$ cat -A m1 # The ‘-A’ flag shows tabs as ‘^I’ and newlines as ‘$’.

This is a good way to check correctness.

8^I5^I6$

3^I2^I2$

1^I6^I7$

5^I0^I7$

2^I2^I4$

$

If the inputs are valid — your program should output only to stdout, and nothing to stderr.

The return value should be 0.

If the inputs are invalid — your program should output only to stderr, and nothing to

stdout. The return value should be any number except 0. The error message you print is

up to you; you will receive points as long as you print something to stderr and return a

non-zero value.

Your program will be tested with matrices up to dimension 100 x 100.

Though optional, I do recommend that you use temporary files; arrays are not

recommended. For this assignment, anytemporary files you use should be put in the

current working directory. (A more standard place for temporary files is in /tmp but don’t

do that for this assignment; it makes grading easier if they are in the current directory.)

Be sure any temporary file you create uses the process id as part of its name, so that

there will not be conflicts if the program is running more than once. Be sure you remove

any temporary files when your program is done. You should also use the trap command

to catch interrupt, hangup, and terminate signals to remove the temporary files if the

program is terminated unexpectedly.

All values and results are and must be integers. You may use the expr command to do

your calculations, or any other bash shell scripting method, such as ((expr)). Do not

use any other languages other than bash shell scripting: this means that, among others,

awk, sed, tcl, bc, perl, & the python languages and tools are off-limits for this

assignment.

Note that expr only works with whole numbers. When you calculate the

average you must round to the nearest integer, where half values round away from 0

(i.e. 7.5 rounds up to 8, but -7.5 rounds down to -8). This is the most common form of

rounding. When doing truncating integer division (as bash does), this formula works to

divide two numbers and end up with the proper rounding:

(a + (b/2)*( (a>0)*2-1 )) / b

You can learn more about rounding methods here:

Rounding – Wikipedia (Links to an external site.)Links to an external site.

## Grading With a Script

To make it easy to see how you’re doing, you can download the actual grading script

here:

p1gradingscript

This script is very close to the one that will be used to assign your script a grade. To use

the script, just place it in the same directory as your matrix script and run it like this:

$ ./p1gradingscript

When we run your script for grading, we will do this to put your results into a file we can

examine more easily:

$ ./p1gradingscript > grading_result.username

To compare yours to a perfect solution, you can download here a completely correct run

of my script that shows what you should get if everything is working correctly:

p1perfectoutput

The p1gradingscript itself is a good resource for seeing how some of the more complex

shell scripting commands work, too.

## Summary

Your script must support the following operations:

● matrix dims [MATRIX]

○ Prints error message to stderr, nothing to stdout

and return value != 0 if:

■ Argument count is greater than 1 (e.g.

`matrix dims m1 m2`).

■ Argument count is 1 but the file named by

argument 1 is not readable (e.g. `matrix

dims no_such_file`).

○ Otherwise, prints “ROWS COLS” (Space separated!) to

stdout, nothing to stderr, and returns 0.

● matrix transpose [MATRIX]

○ Prints error message to stderr, nothing to stdout

and return value != 0 if:

■ Argument count is greater than 1 (e.g.

`matrix transpose m1 m2`).

■ Argument count is 1 but the file named by

argument 1 is not readable (e.g. `matrix

transpose no_such_file`).

○ Otherwise, prints the transpose of the input, in a

valid matrix format to stdout, nothing to stderr,

and returns 0.

● matrix mean [MATRIX]

○ Prints error message to stderr, nothing to stdout

and return value != 0 if:

■ Argument count is greater than 1 (e.g.

`matrix mean m1 m2`).

■ Argument count is 1 but the file named by

argument 1 is not readable (e.g. `matrix

mean no_such_file`).

○ Otherwise, prints a row vector mean of the input

matrix, in a valid matrix format to stdout, nothing

to stderr, and returns 0. All values must round to

the nearest integer, with ***.5 values rounded away

from zero.

● matrix add MATRIX_LEFT MATRIX_RIGHT

○ Prints error message to stderr, nothing to stdout

and return value != 0 if:

■ Argument count does not equal 2 (e.g.

`matrix add m1 m2 m3` or `matrix add m1`).

■ Argument count is 2 but the file named by

either argument is not readable (e.g.

`matrix add m1 no_such_file`).

■ The dimensions of the input matrices do not

allow them to be added together following

the rules of matrix addition.

○ Otherwise, prints the sum of both matricies, in a

valid matrix format to stdout, nothing to stderr,

and returns 0.

● matrix multiply MATRIX_LEFT MATRIX_RIGHT

○ Prints error message to stderr, nothing to stdout

and return value != 0 if:

■ Argument count does not equal 2 (e.g.

`matrix multiply m1 m2 m3` or `matrix

multiply m1`).

■ Argument count is 2 but the file named by

either argument is not readable (e.g.

`matrix multiply m1 no_such_file`).

■ The dimensions of the input matrices do not

allow them to be multiplied together

following the rules of matrix

multiplication.

○ Otherwise, prints the product of both matricies,

with the first argument as the left matrix and the

second argumentas the right matrix, in a valid

matrix format to stdout, nothing to stderr, and

returns 0. (`matrix multiply A B` should return A*B,

not B*A)

`

An invalid command must result in an error message to stderr, nothing to stdout, and a

return value != 0.