Matrices

Matrices in AUXLAB follow the same general style as vectors, with row-wise storage and matrix-aware indexing rules.

Arithmetic With Scalars And Matrices

A scalar can be added to every element of a matrix.

AUX> [3 4; 4 1] + 10
ans =
13 14
14 11

To add one matrix to another, both must have the same row count. The operation then becomes a vector operation for each row.

Matrix addition example 1

AUX> [1 2; 3 4]+[.1 .2; .3 .4]
ans =
1.1 2.2
3.3 4.4

Two operands may have different column counts, in which case the operation follows the vector rules row by row.

Matrix addition example 2

AUX> (1:6).matrix(2)+[1 6; 10 10]
ans =
2 8 3
14 15 6

If one operand is a column vector, it is applied row-wise.

Matrix addition example 3

AUX> (1:12).matrix(3)+[10 -6 0]'
ans =
11 12 13 14
-1 0 1 2
9 10 11 12

Matrix Indexing

Indexing a matrix takes two values, row and column indices, separated by a comma.
The colon operator can represent consecutive numbers, and a vector can also be used as an index.

Matrix indexing example

AUX> a(1,2) = 8;
AUX> a
a = 1 8 3
0 1 -1

If a matrix is indexed with only one value, it uses serialized indexing.
AUXLAB stores matrix data row-wise.
In the older help example, the serialized order is shown below.

Serialized matrix indexing

The indexing keyword end refers to row count, column count, or total element count depending on where it appears.

a(end,1) // end means 2
a(1,end) // end means 3
a(end)   // end means 6

Replacement Rules

Replacement of matrix elements follows the same general principles as vector indexing.
If the right-hand side is a scalar, that scalar can be applied over the targeted matrix region.
If the right-hand side is a column vector, its values can be applied row by row.

AUX> a(1,end) = [7 6]   // Invalid! LHS is 2x1, RHS is 1x2
AUX> a(1,end) = [7 6]'  // There you go!

If the target elements are not described by simple row/column indexing, serialized indexing can be used.

AUX> a([2 4]) = rand(2) // rand(2) generates a 2-element vector of random numbers
AUX> a
a =
1 0.2736 3
0.8461 1 -1

Compound Assignment And Conditional Indexing

Compound operators and conditional indexing can be combined for concise matrix manipulations.

AUX> x=rand(100).matrix(10);
AUX> x((1:end)%2==0,:) *= 10;
AUX> x(:,[2 5 7]) *= -1;
AUX> x*=100; x=x.round; x/=100 // to round up to third decimal place

Current source basis:

matrices.html