Data Processing with ODMath

Basic Arithmetic

For example, define two matrices A and B.

\[\begin{split}A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \ , B = \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}\end{split}\]

If we used the expression string ‘2 * A + B’ we would get the following.

\[\begin{split}2 \times A + B = \begin{bmatrix} 4 & 8 \\ 12 & 16 \end{bmatrix}\end{split}\]

You can also use brackets to change the order of operations.

\[\begin{split}2 \times (A + B) = \begin{bmatrix} 6 & 12 \\ 18 & 24 \end{bmatrix}\end{split}\]

Division can also be performed using ‘B / A’.

\[\begin{split}B / A = \begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix}\end{split}\]

Multiplication ‘A * B’ would result in:

\[\begin{split}A \times B = \begin{bmatrix} 2 & 8 \\ 18 & 32 \end{bmatrix}\end{split}\]

Powers ‘A ^ B’ would result in:

\[\begin{split}A ^ B &= \begin{bmatrix} 1 & 16 \\ 729 & 65536 \end{bmatrix}\end{split}\]

Vectors

Vectors can also be used in arithmetic. In the following we define C as a Vertical matrix, and D is a Horizontal matrix. If a matrix is loaded from a data source it will not have a directionality and must be given one before being used with matrices.

\[\begin{split}C = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \ , D = \begin{bmatrix} 1 \\ 3 \end{bmatrix}\end{split}\]

The following is the difference between the basic arithmetic with vertical and horizontal vectors applied to A:

Functions

There are a number of built-in functions to help facilitate more complicated calculations. A function call is structured as ‘functionName(parameter1,parameter2,…,parameter)’. In the table below we can see a quick reference of all of the functions, their input types, and output times.

Function Name	Parameter Type	Output Type
Tranpose	Matrix	Matrix
Tranpose	Vector	Vector
SumRows	Vector	Vector (Vertical)
SumColumns	Matrix	Vector (Horizontal)
AsHorizontal	Vector	Vector (Horizontal)
AsVertical	Vector	Vector (Vertical)