Advanced Data Structures

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Sparse Matrix

A matrix representing connections between nodes in a graph can have many zeros.

For example, a matrix can have 81 elements where only 26 are non zero. You can save space by only representing the non-zero values.

• Standard reresentation: all elements are explicitly represented in memory
• Sparse representation: locations (row, col) and their values are stored.

Generating sparse matrix sparse() converts regular matrices to sparse matrices. full() is the oppposite. speye() generates a sparse identity matrix sprand() generates a sparserandom matrix.

Add elements using S(3, 7) = -5

Interrogating sparse matrixes nnz: number of non-zero elements nonzeros: a column of the non-zero elements spones: replace all non-zero elements with ones spalloc: allocate space for a sparse matrix issparse: true if the matrix is sparse spfun: apply function to non-zero elments spy: graphically represent sparsity

Cell Array

Arrays of data strctures.

• Data structures are represented by placing braces {} around a MATLAB array object. They can encapsulate other MATLAB arrays of various types and lengths.

Usage

• () parentheses to reference the data structure itself: cells(1,1) ={[1,2,3]}
• {} braces to access the array in the data strcture: cells{1,2} = 'hello there'
• Preallocate a cell array by using the cell function: mycell = cell(3,3)
• Or, use braces to construct a cell array: thiscell = {[1 2;3 4], 'bird'; [34 21], eye95)+i.*ones(5)}
• Extend by using indexing: thiscell{3,2} = 'More!'
• Gaps are filled with the empty array.

View

• Type the name of the cell array to display a description of the data structure i each element. Or, use celldisp(thiscell) function to view full conetents.
• cellplot(thiscell) generates a graphical representation.

Access Access data inside cell arrays by indexing the structure then the element: thiscell{2,1}(2).

Update Delete rows or columns by setting them equal to the empty matrix: thiscell(2,:)=[]

As Strings

Strings are difficult to store in arrays because each row must have the same number of columns. Use cell arrays to get around this problem

stringlist = ['hi'; 'byebye'] % illegal
stringlist= ['hi    '; 'byebye']
stringcell = {'hi'; 'byebye'}

Convert between the two representations with

stringlist = char(stringcell)
stringcell = cellstr(stringlist)

As Function Arguments

A variable number of function input/output arguments can done using a dummy argument,varagin. Place it last on the listof input arguments. nargin can determine the total number of input arguments.

function doit(str1, varagin)
	for n = 1:nargin-1
		disp([str '' varagin{n}]);
	end

For output, use varargout last in the list of output arguments. nargout determines the tortal number of output arguments requested by the user.

function varargout = timestable(num)
	for n:1nargout
		varargout{n} = [num2str(num `x` num2str(n) '=' num2str(num*n)];
	end

Structures

Structures are another way of putting together unlike data. Each element in a structure is called a field.

• A structure is like a record in a database.
• E.g., a student may have a name, id, and gpa.

Creation Construct an array of structures by adding a subscript:

strudent.name = 
student.name = 'Robin'
student.id = 2343465
student.gpa = 3.2

student(2).name = 'Maid'
student(2).id = 386748
student(2).gpa = 3.90
student(2).exams = [100 69 80]

• Whenever a new field is added to an element, it is added to all elements. Unfilled elements contain the empty array.

Allocate a structure or array of structures with

student(2) = struct('name', 'Maid', 'id', 98473245, 'gpa', 2.9);
student[50] = ('name', [], 'id', [], 'gpa', [], 'exams', []);

Updating Remove a field with rmfield(studnet, 'id')

setfiled() function can be used to add data to a structure

student = setfield(student, {1}, 'exams', [78 98 88]);

Dynamic field names also work:

studnet(1).('exams') = [87 94 88];

Accessing Reference data within an element using multiple subscripting: studnet(2).exams(2) = 99;

Extract all the data from a single field using bracket notation: gpalist = [student.gpa]

getfield() function extracts data from a structure

agpa = getfield(student, {2}, 'gpa');
anexam = getfield(student, {2}, 'exams', {3});

Dynamic field names:

agpa = studnet(2).('gpa');
studnet(1).('exams') = [78 98 88];

Nested Fields in structures can be other structures.

student(1).class(1).num = '520.123';
student(1).class(1).name = 'Computational Modelling for ECE';
class(1).roster = {'Robin Hood', 'Maid Marion', 'Friar Tuck'}

Function Handles

Contains information used in referencing a function. Once such a handle is created, it can be used to execute the function at any time, even if it is a nested function or subfunction.

• Note: if the function has no input parameters, it must still be followed by empty parentheses.
• Each handle has its own independent workspaces that remains in existence as long as the handle does.

Creation

hand = @functionname;
hand = str2func('functionname');