Little matrix DSL for Red
Features:
- binary ops:
['+ | '- | '* | '/ | '% | '** | '>> | '<< | '>>> | 'and | 'or | 'xor | 'div | 'x | 'augment] - unary-matrix ops
transpose,rotate n,swap rows x1 x2,determinant,trace,identity,rref(reduced row eschelon form),invert divturns args to floatsxis standard matrix multiplication op*is Hadamard multiplication opXis Kronecker's multiplication opaugmentappends a matrix with same number of rows- ops with scalar args
- order of ops as usual
- parens to change priority
- set-words to catch states
do %matrix.red
>> matrix [2x3 [1 2 3 4 5 6]]
== [
1 2 3
4 5 6
]
;### Prettify ###
>> matrix [m: 2x3 [1 2 3 444 55 666]]
== [
1 2 3
444 55 666
]
>> m/pretty
┌ ┐
│ 1 2 3 │
│ 444 55 666 │
└ ┘
;### Unary ops ###
; a) Transpose
>> matrix [transpose 2x3 [1 2 3 4 5 6]]
== [
1 4
2 5
3 6
]
; b) Rotate (clockwise [1 | 2 | 3] or counter-clockwise [-3 | -2 | -1])
>> matrix [rotate 1 2x3[1 2 3 4 5 6]]
== [
4 1
5 2
6 3
]
>> matrix [rotate 2 2x3[1 2 3 4 5 6]]
== [
6 5 4
3 2 1
]
>> matrix [rotate 3 2x3[1 2 3 4 5 6]]
== [
3 6
2 5
1 4
]
>> matrix [rotate -1 2x3[1 2 3 4 5 6]]
== [
3 6
2 5
1 4
]
;### Hadamard-like ops (preserving dims) ###
matrix [2x3 [1 2 3 4 5 6] + 2x3 [2 3 4 5 6 7]]
== [
3 5 7
9 11 13
]
matrix [2x3 [1 2 3 4 5 6] * 2x3 [2 3 4 5 6 7]]
== [
2 6 12
20 30 42
]
;Any binary op from ['+ | '- | '* | '/ | '% | '** | '>> | '<< | '>>> | 'and | 'or | 'xor | 'div]
;### Standard product ###
matrix [2x3 [1 2 3 4 5 6] x 3x2 [2 3 4 5 6 7]]
== [
28 34
64 79
]
;### Kronecker product ###
matrix [2x3 [1 2 3 4 5 6] X 3x2 [2 3 4 5 6 7]]
== [
2 3 4 6 6 9
4 5 8 10 12 15
6 7 12 14 18 21
8 12 10 15 12 ...
;### Augmenting ###
>> matrix [m: 2x2[1 2 3 4] n: m augment 2x1[3 5]]
== [
1 2 3
3 4 5
]
;### Reduced row eschelon form (continued from last example)
>> matrix [o: rref n]
== [
1.0 0.0 -1.0
0.0 1.0 2.0
]
>> ((1 * -1) + (2 * 2)) = 3
== true
>> ((3 * -1) + (4 * 2)) = 5
== true
a: first m/split-col 3
b: second o/split-col 3
matrix [a x b]
== [
3.0
5.0
]
;### Boolean logic ###
matrix [2x2 [1 0 1 1] and 2x2 [0 1 1 0]]
== [
0 0
1 0
]
;### Scalar args ### NB! This doesn't work as intended after last update!
matrix [3x3 [1 2 3 2 4 5 3 6 2] * 2 - 5]
== [
-3 -1 1
-1 3 5
1 7 -1
]
;### Prepared data ###
>> data1: [1 2 3 4 5 6]
== [1 2 3 4 5 6]
>> matrix [2x3 data1]
== [
1 2 3
4 5 6
]
>> matrix [2x3 data1 x 3x3 [1 2 2 1 3 1 2 2 3]]
== [
9 14 13
21 35 31
]
>> data2: object [rows: 3 cols: 2 data: [1 2 3 3 2 1]]
== make object! [
rows: 3
cols: 2
data: [1 2 3 3 2 1]
]
>> matrix [2x3 data1 x data2]
== [
13 11
31 29
]
;### Catching state ###
>> matrix [m: 3x3[1 2 3 4 5 6 7 8 9]]
== [
1 2 3
4 5 6
7 8 9
]
>> probe m ; This has changed! More funcs.
make object! [
rows: 3
cols: 3
data: [1 2 3 4 5 6 7 8 9]
get-col: func [col][extract at data col cols]
get-row: func [row][copy/part at data row - 1 * cols + 1 cols]
get-idx: func [row col][pick data row - 1 * cols + col]
to-float: func [][forall data [data/1: system/words/to-float data/1]]
swap-dim: func [][c: cols cols: rows rows: c]
]
;### Pair entries ###
matrix [2x2[1x1 1x2 2x1 2x2] x 2x2[1x2 2x1 3x2 2x3]]
== [
4x6 4x7
8x6 8x7
]
;### Date entries ###
matrix [2x2[1-2-2017 1-3-2018 1-4-2017 31-5-2017] + 2x2[2 1 3 3]]
== [
3-Feb-2017 2-Mar-2018
4-Apr-2017 3-Jun-2017
]
;### Different entries ###
>> matrix [2x2[1.2.3.4 1-3-2018 12:05 1%] + 2x2[2 1 60 3%]]
== [
3.4.5.6 2-Mar-2018
12:06:00 4%
]
>> date: 2017-3-25
>> matrix [2x2[1.2.0.4 1-3-2018 12:05 1%] + 2x2[191.166.1.46 date/day 55 * 60 3%]]
== [
192.168.1.50 26-Mar-2018
13:00:00 4%
]
;### Determinant ###
>> matrix [determinant 2x2[1 2 3 4]]
== -2
;### Trace ###
>> matrix [trace 2x2[1 2 3 4]]
== 5
;### Identity ###
; a) Symmetric
>> matrix [identity 3x3[1 2 3 4 5 6 7 8 9]]
== [
1 0 0
0 1 0
0 0 1
]
; b) Asymmetric
>> matrix [identity 'l 2x3[1 2 3 4 5 6]]
== [
1 0
0 1
]
>> matrix [identity 'r 2x3[1 2 3 4 5 6]]
== [
1 0 0
0 1 0
0 0 1
]
;### Reduced row eschelon form ###
>> matrix [rref 2x3[2 1 3 5 2 4]]
== [
1.0 0.0 -2.0
0.0 1.0 7.0
]
;### Invert ###
>> matrix [m: 2x2[1 2 3 4] n: invert m]
== [
-2.0 1.0
1.5 -0.5
]
>> matrix [x: m x n]
== [
1.0 0.0
0.0 1.0
]
>> matrix [m: 3x3[2 3 4 5 2 3 4 2 1] n: invert m]
== [
-0.1904761904761904 0.2380952380952381 0.04761904761904758
0.3333...
>> matrix [x: m x n]
== [
1.0 0.0 0.0
2.220446049250313e-16 1.0 -2.220446049250313e-16
...
>> x/pretty
┌ ┐
│ 1.0 0.0 0.0 │
│ 2.220446049250313e-16 1.0 -2.220446049250313e-16 │
│ 0.0 0.0 1.0 │
└ ┘
>> 0.000000000000001 > 2.220446049250313e-16
== true
;### Filling ###
>> matrix [x: 3x3[0]]
== [
0 0 0
0 0 0
0 0 0
]
;### Sub-matrix addition ###
>> x/sub/put 1x1 2x2[1]
== [0 0 0 0]
>> x/show
== [
1 1 0
1 1 0
0 0 0
]
;### Row rotation (poitive - right, negative - left) ###
>> x/rotate-row 1 1
...
>> x/show
== [
0 1 1
1 1 0
0 0 0
]
;### Column rotation (positive - down, negative - up) ###
>> x/rotate-col 2 -1
...
>> x/show
== [
0 1 1
1 0 0
0 1 0
]
; Also multi-column rotation
>> x/rotate-col [2 3] 1
...
>> x/show
== [
0 1 0
1 1 1
0 0 0
]
; m/pretty/tight/box removes spaces from between columns and can produce eg such maze:
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└─────────────────────────────────────────┘