Topic: Describing Submatrices
Due: 11:59pm Tuesday, 6 November 2012

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Submatrices in MATLAB

MATLAB colon syntax

MATLAB allows submatrices to be specified by using a syntax with colons to describe ranges on the respective rows and columns. As an example, If matrix A in MATLAB has contents:

 5 15  3  8 44 15
20  2 14  3  1 22
40 12  7 30 24 35

20 14  1
40  7 24

General MATLAB submatrix

In fact, MATLAB is really more general as it allows you to describe a set of relevant rows (respectively, columns) using any one-dimensional matrix. That is, for the above matrix, the syntax A([2 1 2], [1 4 3 1]) produces the result following result

20  3 14 20
 5  8  3  5
20  3 14 20

C++ variation

Our goal is to provide some similar functionality for our C++ matrices. However, there are several factors to consider.

• How to conveniently create row matrices with contents that follow a typical range pattern
• How to use any one-dimensional matrix as a parameter to describe the set of rows (or columns) of a matrix that should be included in a submatrix.

A range function

To resolve the first question, we can define a new range function that produces a row-matrix having contents that follow a typical range pattern. We have already noted the difference in conventions between MATLAB's use of indices starting with 1, versus the C++ convention of indices starting with 0. When describing range, a similar question of convention arises. MATLAB chooses to use a syntax such as 4:7 to express the inclusive range of values 4, 5, 6, 7. There is a strong history in C++ of expressing ranges that are half-open intervals, whereby a range is described using parameters range(start, stop) such that the range begins with index start and goes up to but not including index stop. Thus we might have the syntax range(4,7) designate the set of indices 4, 5, 6 (but not 7).

To describe a range with a non-unit stride, we can provide a three-parameter version of this function with signature range(start, stride, stop). For example, range(1, 2, 5) could return a matrix with contents 1 3 (note well that the stop value is not included).

For convenience, we technically allow a one-parameter form, range(start) that includes only that start value.

However, for the current assignment, we will ignore several related variants that are legal in MATLAB and could eventually be incorporated in our C++ version.

• We will not consider negative strides (e.g., 7:-1:3)


• We will not have an analog for more general MATLAB colon syntax in which you can omit the first or last parameter and have it default respectively to the first or last extent (e.g., A(:, 3:4) to get all of columns 3 and 4.)

Describing Submatricies (your task!)

Your task is to modify the matrix.h code to support the new functionality of allowing one-dimensional matrices to be used to generate a submatrix. In particular, you must provide an appropriate implementation for the matrix class method having signature

  matrix operator()(matrix rows, matrix cols) const

Exceptions

You are also expected to properly throw an out_of_range exception anytime this function is called with a range that includes any illegal index for the given matrix. For example, on the original 3-by-6 matrix given above, the evaluation of A(range(2,5), range(1,3)) should be illegal because range(2,5) designates the set of indices 2, 3, and 4 for the choice of rows, but there is no such thing as row 3 or 4 in such a matrix.

Files we are providing

We are continuing with the development of the same matrix.h code that you have been working with, but our version does not have your solutions to the most recent assignments. However, our version has the new definition for the range class within the matrix.h file, so you will need to either switch to our matrix.h file or port that range definition to your own most recent version of matrix.h

If working on turing, change directories into a desired subdirectory of your home folder if desired, and to execute the following command verbatim

  cp -R /Public/goldwasser/146/asgn06 .

The driver test.cpp that we are providing has some code that should more easily allow you to run your matrix through a battery of tests. There are two different segments during the execution of that test program:

• First, it allows for a convenient way to execute a series of submatrix comptuations using the new range function to select the choice of rows and columns. In particular, starting with line 105 of that file, you will find some code that reads:

      testcase tests[] = {
        {  "range(3)",       range(3,3),    "range(2,7)",         range(2,7)       },
        {  "range(3,5)",     range(3,5),    "range(2,3,10)",      range(2,3,10)    },
        {  "range(3,5)",     range(3,5),    "range(2,3,100)",     range(2,3,100)   },
      };
  

  involve ranges. In particular, You should not concern yourself with the rest of the surrounding code (although I'm happy to explain it to those who are interested). What is important is that you can added additional lines using a similar format, where you specify the range of rows and range of columns. In particular, note that the first and second columns match except that the first is a string and the second is not. This describes a range of rows. Similarly, the third and fourth columns are used to describe a range of columns. The rest of the code is designed so that it will attempt to compute and output the appopriate submatrix for each line of this test set.


• After executing all of those predefined tests, the script then queries the user to enter additional tests based on arbitrary collections of rows in columns. This will allow you to test cases that are not standard increments computed by the range function.

Submitting your project

Your revised matrix.h file should be submitted electronically (details on the submission process).