A Sample of Smalltalk Code...

The following is a sample listing of methods running a small application. We simply want to show the Smalltalk syntax and calling procedures.

rows: anArrayOrVector
^self new initializeRows: anArrayOrVector

accumulate: aMatrix
| n |
n := 0.
self rowsCollect: [ :each | n := n + 1. each accumulate: ( aMatrix rowAt: n)]

addWithMatrix: aMatrix class: aMatrixClass
| n |
n := 0.
^aMatrixClass rows: ( self rowsCollect: [ :each | n := n + 1. each + ( aMatrix rowAt: n)])

initializeRows: anArrayOrVector
rows := anArrayOrVector asVector collect: [ :each | each asVector].

columnsDo: aBlock
| n |
n := 0.
^rows last do: [ :each | n := n + 1. aBlock value: ( self columnAt: n)]

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A vector is akin to an instance of the Smalltalk class Array, for which mathematical operations have been defined. Thus, a vector in Smalltalk can be implemented directly as a subclass of the class Array.

All operations can be assigned to the corresponding natural operators. The multiplication, however, can involve several type of operands:

The screens on the next page show the implementation of operations between matrices.

The Workspace Window is a notepad window that can be used as a place to write, evaluate, and store fragments of Smalltalk code. The Transcript is actually a global variable that points to a text window. The Transcript can be used for displaying system messages, test results, and errors.

Our implementation of matrix operations follow:

The above code was executed using Smalltalk's development environment. The Transcript screen was used to display output. Results are shown below:

Various operators...

With this setup, it is possible to execute multiple operations using vectors and matrices. The following could easily be implemented just by setting the code up in Workspace and executing as shown before. For example:

Given:
| u v w a b c |
u := #(123) asVector.
v := #(3 4 5) asVector
a := KmpMatrix rows: #( (1 0 1) (-1 –2 3))
b := KmpMatrix rows: #( (1 2 3) (-2 1 7) (5 6 7)).

Can easily be calculated:
w := 4 * u + (3 * v).
c := a * b. (as shown in implementation)
v := a * u.
w := c transpose * v.
w := v * c.

As well as any other combination using complex vectors and matrices.

Other Applications