Neural Networks with Geoffrey Hinton

Octave Notes

• Octave Language Reference
• configured pycharm for using the octave/matlab textmate syntax highlighting bundle
  • considered this plugin from 2013 but decided against it
  • pycharm instructions
  • matlab.tmbundle
• wikibooks: printf

Matrices - Basic

• from A Programmer's Guide to Octave

% row vector
A=[1,2,3]

% column vector - think of semicolons as newlines
A=[1;2;3]

% matrix multiplication
A=[1,2,3;4,5,6]
B=[7,8;9,10;11,12]
A*B

% scalar multiplication
C=10
C*A

% element by element multiplication-put a dot before the operator.
% For example
A.*B
% performs an element-by-element multiplication of the two matrices 
% and not a matrix multiplication i.e. a_{ij}*b_{ij}.

% single quote to "complex transpose" a matrix
% following is a column matrix:
A=[1,2,3]'

You can use the inverse function to find the inverse of any square non-singular matrix. For example
A=[1,2;3,4]
B=inverse[A]
A*B
displays the identity matrix.

The expression  x\y is the left division of y by x and is equivalent to
inverse(x)*y
The advantage of using this notation is that the inverse isn't actually used in the calculation.

The expression x/y is the right division of x by y and it is equivalent to
x*inverse(y)
Again the inverse matrix is never computed and generalized inverses are used if necessary

A(1,2)
is the value in row 1 column 2. You can remember this because that's 
how they are addressed in math: 2x3 matrix means two rows of three columns.

You can assign a new value to a single element e.g.
A(1,2)=3

A vector of indexes just picks out the combined set of elements that 
each index would pick out. For example:
A([1,2],1)
picks out A(1,1) and A(2,1) and the result is a column vector because 
you have specified part of a column of the original matrix.

• Vector Index to a matrix:

  A vector of indexes just picks out the combined set of elements that each index would pick out. For example, A([1,2],1) picks out A(1,1) and A(2,1) and the result is a column vector because you have specified part of a column of the original matrix.

• Range Index to a matrix:

  In general a range is specified as start:increment:end and if you leave out the increment it is assumed to be 1 and the range is start:end. The increment can be negative.

Arithmetic Ops https://www.gnu.org/software/octave/doc/v4.0.1/Arithmetic-Ops.html

• x ./ y: "Element-by-element right division"

  • You cannot use / to divide two matrices element-wise, since /
    and \ are reserved for left and right matrix "division". Instead, you
    must use the ./ function:
    octave:6> x = [1, 2, 3]; y = [5, 6, 2]; y./x
       5.00000   3.00000   0.66667
    octave:7> 1 ./ x
       1.00000   0.50000   0.33333