964 lines
17 KiB
Plaintext
964 lines
17 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Python Numpy Review\n",
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"\n",
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"主要复习numpy\n",
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"\n",
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"tutor: `chongjiujin # gmail.com`\n",
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"\n",
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"```\n",
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"if you have any question in python or pytorch:\n",
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"\n",
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" print(add personal weichat:flypython)\n",
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" ```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# List Slicing\n",
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"\n",
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"List elements can be accessed in convenient ways.\n",
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"\n",
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"Basic format: some_list[start_index:end_index]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[0, 1, 2, 3, 4, 5, 6]"
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||
]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"numbers = [0, 1, 2, 3, 4, 5, 6]\n",
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"numbers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[0, 1, 2]"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"numbers[0:3]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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||
"metadata": {},
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||
"outputs": [
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{
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||
"data": {
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"text/plain": [
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"[0, 1, 2, 3]"
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]
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},
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"execution_count": 4,
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||
"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"numbers[:4]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[5, 6]"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"numbers[5:]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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||
"metadata": {},
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||
"outputs": [
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||
{
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||
"data": {
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||
"text/plain": [
|
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"[0, 1, 2, 3, 4, 5, 6]"
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]
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},
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"execution_count": 7,
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||
"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"numbers[:]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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||
"data": {
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||
"text/plain": [
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"6"
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]
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},
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||
"execution_count": 9,
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||
"metadata": {},
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"output_type": "execute_result"
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||
}
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],
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"source": [
|
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"# Negative index wraps around\n",
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"numbers[-1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[4, 5, 6]"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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||
],
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"source": [
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"numbers[-3:]"
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||
]
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},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 14,
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||
"metadata": {
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||
"scrolled": true
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||
},
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||
"outputs": [
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||
{
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"data": {
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"text/plain": [
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"[]"
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||
]
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||
},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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||
],
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"source": [
|
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"# Can mix and match\n",
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"numbers[1:-10]"
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]
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},
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{
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"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"# Numpy python矩阵计算库\n",
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"\n",
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"\n",
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||
"Optimized library for matrix and vector computation.\n",
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"\n",
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||
"用于矩阵和向量\n",
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"\n",
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||
"\n",
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||
"\n",
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"Makes use of C/C++ subroutines and memory-efficient data structures.\n",
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||
"\n",
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||
"底层是C/C++编译的，效率更高\n",
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||
"\n",
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||
"(Lots of computation can be efficiently represented as vectors.)\n",
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"\n",
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"**Main data type: `np.ndarray`**\n",
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"\n",
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"This is the data type that you will use to represent matrix/vector computations.\n",
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"这个数据结构是用来放矩阵/向量的\n",
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"\n",
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"Note: constructor function is `np.array()`\n",
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"\n",
|
||
" `np.array()`初始化函数\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np#导入库"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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||
"metadata": {},
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||
"outputs": [
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||
{
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||
"data": {
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"text/plain": [
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"(3,)"
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]
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},
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"execution_count": 18,
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"metadata": {},
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||
"output_type": "execute_result"
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||
}
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],
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"source": [
|
||
"x = np.array([1,2,3])#一维向量\n",
|
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"x\n",
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"x.shape"
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]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 20,
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||
"metadata": {},
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||
"outputs": [
|
||
{
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||
"data": {
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||
"text/plain": [
|
||
"(2, 3)"
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||
]
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||
},
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||
"execution_count": 20,
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||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
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||
],
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"source": [
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||
"y = np.array([[3,4,5],[6,7,8]])#二维矩阵\n",
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||
"y.shape"
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]
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},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 21,
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||
"metadata": {},
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||
"outputs": [
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||
{
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||
"data": {
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||
"text/plain": [
|
||
"(3, 1)"
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||
]
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||
},
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||
"execution_count": 21,
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||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
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||
"y = np.array([[1],[2],[3]])#每个框是增加一个维度\n",
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||
"y.shape"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# np.ndarray Operations 操作函数\n",
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"\n",
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"Reductions: `np.max`, `np.min`, `np.argmax`, `np.sum`, `np.mean`, …\n",
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"\n",
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||
"Always reduces along an axis! (Or will reduce along all axes if not specified.)\n",
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||
"\n",
|
||
"(You can think of this as “collapsing” this axis into the function’s output.)"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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"execution_count": 22,
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||
"metadata": {},
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||
"outputs": [
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||
{
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||
"data": {
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||
"text/plain": [
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"3"
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||
]
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||
},
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||
"execution_count": 22,
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||
"metadata": {},
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"output_type": "execute_result"
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||
}
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||
],
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"source": [
|
||
"x = np.array([1,2,3])#一维向量\n",
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||
"x.max()#np.max(x)\n",
|
||
"#x.min()\n",
|
||
"#x.sum()\n",
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||
"#x.mean()\n"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 25,
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||
"metadata": {
|
||
"scrolled": true
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||
},
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||
"outputs": [
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||
{
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||
"data": {
|
||
"text/plain": [
|
||
"array([[5],\n",
|
||
" [8]])"
|
||
]
|
||
},
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||
"execution_count": 25,
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||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
|
||
"y = np.array([[3,4,5],[6,7,8]])#按维度取最大值\n",
|
||
"#np.max(y,axis = 1)\n",
|
||
"np.max(y, axis = 1, keepdims = True)\n",
|
||
"#https://docs.scipy.org/doc/numpy/reference/generated/numpy.amax.html#numpy.amax"
|
||
]
|
||
},
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||
{
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||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 基本矩阵运算\n",
|
||
"\n",
|
||
"\n",
|
||
"`np.dot`矩阵点乘\n",
|
||
"$$ np.dot(v,w)=v^T w $$\n",
|
||
"https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html?highlight=dot#numpy.dot\n",
|
||
"\n",
|
||
"`np.multiply` 在 np.array 中重载为元素乘法，在 np.matrix 中重载为矩阵乘法\n",
|
||
"\n",
|
||
"https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html\n",
|
||
"\n",
|
||
"\n",
|
||
"我们这里只讨论一维向量"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
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||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"14"
|
||
]
|
||
},
|
||
"execution_count": 26,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
|
||
],
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||
"source": [
|
||
"#np.dot点乘\n",
|
||
"\n",
|
||
"x=np.array([1,2,3])#一维向量\n",
|
||
"y=np.array([1,2,3])#一维向量\n",
|
||
"np.dot(x,y)\n",
|
||
"#"
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||
]
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||
},
|
||
{
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||
"cell_type": "code",
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||
"execution_count": 27,
|
||
"metadata": {
|
||
"scrolled": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"14"
|
||
]
|
||
},
|
||
"execution_count": 27,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"sum(x.T*y)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([1, 4, 9])"
|
||
]
|
||
},
|
||
"execution_count": 28,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x=np.array([1,2,3])#一维向量\n",
|
||
"np.multiply(x,x)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Indexing 索引"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([3])"
|
||
]
|
||
},
|
||
"execution_count": 29,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"#基本同list\n",
|
||
"x = np.array([1,2,3])#一维向量\n",
|
||
"x[x > 2]\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([3, 2, 1])"
|
||
]
|
||
},
|
||
"execution_count": 30,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"index=[2,1,0]#按索引排序\n",
|
||
"x[index]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 矩阵遍历\n",
|
||
"\n",
|
||
"有时候需要遍历矩阵里所有的向量"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[3 4 5]\n",
|
||
" [6 7 8]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"y = np.array([[3,4,5],[6,7,8]])#二维矩阵\n",
|
||
"print(y)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"metadata": {
|
||
"scrolled": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[3 4 5]\n",
|
||
"-----\n",
|
||
"[6 7 8]\n",
|
||
"-----\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"#默认按第1维度遍历\n",
|
||
"for y1 in y:\n",
|
||
" print(y1)\n",
|
||
" print(\"-----\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 33,
|
||
"metadata": {
|
||
"scrolled": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"2 3\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"#按指定维度遍历\n",
|
||
"d1,d2= y.shape\n",
|
||
"print(d1,d2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 34,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"0 [3 6]\n",
|
||
"1 [4 7]\n",
|
||
"2 [5 8]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"for d in range(d2):\n",
|
||
" print(d,y[:,d])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Efficient Numpy Code\n",
|
||
"尽量用Numpy的特性提升效率"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 36,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"x = np.array([[3,4,5],[6,7,8]])#二维矩阵\n",
|
||
"y = np.array([[1,2,3],[9,0,10]])#二维矩阵"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 37,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 9, 16, 25],\n",
|
||
" [36, 49, 64]])"
|
||
]
|
||
},
|
||
"execution_count": 37,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"for i in range(x.shape[0]):\n",
|
||
" for j in range(x.shape[1]):\n",
|
||
" x[i,j] **= 2\n",
|
||
"x"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 38,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 81, 256, 625],\n",
|
||
" [1296, 2401, 4096]])"
|
||
]
|
||
},
|
||
"execution_count": 38,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x **= 2\n",
|
||
"x"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 全0 和全 1 矩阵"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 40,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([1.30950800e+06, 1.82888704e+08])"
|
||
]
|
||
},
|
||
"execution_count": 40,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"z=np.zeros((2,))\n",
|
||
"for i in range(x.shape[0]):\n",
|
||
" x1=x[i]\n",
|
||
" y1=y[i]\n",
|
||
" z[i]=np.dot(x1,y1)\n",
|
||
"z"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 41,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1., 1., 1.],\n",
|
||
" [1., 1., 1.]])"
|
||
]
|
||
},
|
||
"execution_count": 41,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"z=np.ones((2,3))\n",
|
||
"z"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 矩阵和常数计算以及 Broadcasting广播"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 42,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(3, 3)"
|
||
]
|
||
},
|
||
"execution_count": 42,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x = np.array([[3,4,5],[6,7,8],[1,2,3]])#二维矩阵\n",
|
||
"x.shape"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 43,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 5, 6, 7],\n",
|
||
" [ 8, 9, 10],\n",
|
||
" [ 3, 4, 5]])"
|
||
]
|
||
},
|
||
"execution_count": 43,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x+2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 44,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 6, 8, 10],\n",
|
||
" [12, 14, 16],\n",
|
||
" [ 2, 4, 6]])"
|
||
]
|
||
},
|
||
"execution_count": 44,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x*2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 52,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(3, 1)"
|
||
]
|
||
},
|
||
"execution_count": 52,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"y=np.array([[2],[4],[8]])\n",
|
||
"y.shape"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 46,
|
||
"metadata": {
|
||
"scrolled": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 5, 6, 7],\n",
|
||
" [10, 11, 12],\n",
|
||
" [ 9, 10, 11]])"
|
||
]
|
||
},
|
||
"execution_count": 46,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x+y"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 矩阵变换"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(1, 3)"
|
||
]
|
||
},
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"z=np.array([[2, 4, 8]])\n",
|
||
"z.shape"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 50,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(3, 1)"
|
||
]
|
||
},
|
||
"execution_count": 50,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"z=y.reshape(-1,1)\n",
|
||
"z.shape"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 53,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(1, 3)"
|
||
]
|
||
},
|
||
"execution_count": 53,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"z=y.T\n",
|
||
"z.shape"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 54,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 6, 16, 40],\n",
|
||
" [12, 28, 64],\n",
|
||
" [ 2, 8, 24]])"
|
||
]
|
||
},
|
||
"execution_count": 54,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x*z"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 思考题\n",
|
||
"y=np.array([[2],[4],[8]])\n",
|
||
"\n",
|
||
"(y + y.T)是什么\n",
|
||
"\n",
|
||
"\n",
|
||
"# 如果对操作有不确定，开一个jupyter notebook，测试后使用"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.7.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|