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GA: UA-34467841-15
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自己的 NumPy 自己做！從零開始打造多維陣列 - 張安邦
===
<blockquote>
近年來多維陣列的應用越來越廣泛。從機器學習到資料分析甚至到科學運算都可以看到多維陣列的身影。但是它背後的原理都像是黑魔法一樣；broadcasting、view、transpose、reshape 的機制摸也摸不著。但是它其實沒有那麼難！？40 分鐘帶你走玩一遭可以回家自幹 ：3

## 先備知識
能理解中階C++語法(模板、STL)熟悉陣列使用者
</blockquote>

###### tags: `SITCON 2020 共筆` `SITCON 2020` `2020` `共筆` `難。` `R2`

{%hackmd dTfmj-h3QvSA0myqavKbxg %}

> 請從這裡開始

# whoami
張安邦/marty1885

## phosh
- Linux 手機的UI
- GTK + Wayland

## 起源
Hierarchical Temporal Memory
一個基於於生物學的 AI 模型

## Etaler
講者開發的，歡迎打星星
高興能HTM實作
支援 CPU+GPU
Python Binding
社群內三大實作之一
用張量表達資料
> tensor
Working on DL support!

## Hierarchical Temporal Memory

- 通常用作序列預測/異常偵測

## 起源

- 我需要一個同時支援OpenCL與CPU的張量
- 但是怎麼找都是 404 或 402
- 只好鼓起勇氣自己寫惹
- 架構上接近xtensor和ArrayFile

## ROOT
- 自帶C++直譯器
- https://root.cern/

## TOC
1. Vector and matrix
2. Shape, stride and view
3. Broadcasting

## Vector and matrix
### Array

int arr1[4] = {0,1,2,3};
int arr2[4] = {0,1,2,3};
int res[4];
for (int i = 0; i < 4; i++) {
    res[i] = arr1[i] + arr2[i];
}
// 好麻煩
// 還有資安問題

// use template & operation overloading
template <typename T>
struct tensor
{
    tensor() = 
    tensor(size_t size)
        :storage()
        ,size_(size)
        {}
    size_t size()

};

### Matrix

- 一維->多維
- shape 改成不只兩個 element

## Shape, stride and view

Access element from a tensor
How to reshape the tensor

tensor<int> &
{{1,2},
{3,4}}
a.data()[1] (int) 2

- overload operator "[]"
- operator[] only allows 1 param

T & operator[](shape coord){
    return somehow_get_value(coord);
}

<!-- - -->

如何用 2D index 的方式存取？
- 1D: coord[0]
- 2D: cood[1] + shape[0] * cood[0]
- nD: coord[n-1] + $\sum_{i=0}^{n-2}$(coord[i] * $\prod_{j=0}^{i}$(shape[j]))
- $\prod$ 裡面是 stride

T & operator[](){

}

用 array[{1,2}] 來存取元素
Numpy則是： array[1,2]

## How views work?

int num[3][4] = {
    {1,2,3,4}
    {5,6,7,8}
    {9,}
}

Now instead of evaulating shape[j] every time
- we **pre-compute** ...

Take 1D `tensor<int>` for example
shape

Too complex for a talk
Talk to me later
Special views!

Transpose

| 2 | 4 | -1 |
| --- | --- | --- |
| -10 | 5 | 11 |
| 18 | -7 | 6 |

| 2 | -10 | 18 |
| --- | --- | --- |
| 4 | 5 | -7 |
| -1 | 11 | 6 |

- reverse the stride!
reshape
- you literally just recompute the stride

- easy and simple

## Broadcasting
- Numpy's killer feature
- Mat[$3*3*3$] 可和 Mat[$3*1*3$]做相加
- operating
### Limitations on shape
-
- Dimension either
### why?
- $3*3$ matrix is a $1*1*1*1*1*3*3$

### Observation
- Dimaensions of 1 does not effect strides

#### Ex:Turning a scalar into matrix