Topic: Using Ranges to Describe Submatrices
Due: 11:59pm Tuesday, 12 October 2010

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Introduction

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

C++ variation

Our goal is to provide some similar functionality for our C++ matrices. However, there are several factors to consider. The first is that it is impossible for us to mimic the : syntax directly. That is a core syntax supported by MATLAB for matrices, but it is not a core syntax of C++ and we cannot make it so for our class. Instead, we decided to define a new class range so that a range instance describes an appropriate set of indices.

The second issue was how to appropriately use indices in describe a range for C++. 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

Our range class

During lecture, we developed an implementation of a simple range class. It supports two different versions of a constructor, range(start, stop) and range(start, stride, stop). A complete definition for that class is given within the matrix.h file that we are providing for this assignment.

Unsupported variants:

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.)


• We will not allow you to mix the use of a range for one dimension and an integer for the other, for example, A(3, range(2,4)). Instead, such a submatrix must be specified using a range object, even if trivial, as in A(range(3,4), range(2,4)).

Your task

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

  matrix operator()(range rows, range 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

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 involve ranges. In particular, starting with line 104 of that file, you will find some code that reads:

    testcase tests[] = {
      {  "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)   },
    };

Submitting your project