Lua快速入门与Torch教程

Lua

最猛的版本还是在【2】里面,15 Min搞定Lua,因为Lua是一种脚本语言,用标准C语言编写并以源代码形式开放, 其设计目的是为了嵌入应用程序中,从而为应用程序提供灵活的扩展和定制功能。所以会Perl,Python,Shell的话应该很快上手。

变量和控制流

注释:
单行: –
多行:

--[[ --]]

num = 42 – 所有的数字都是double,整数有52bits来存储。
s = ‘first expression’
s2 = ”second expression of string”
muli_line_strings = [[ass
ssss]]
t = nil – 未定义的t;会有垃圾回收

while 循环:

while num < 50 do
    num = num + 1
end 

IF语句:

if num > 40 then
    print('Over 40')
elseif s~= 'hello' then 
    io.write('Not over 40\n')
else 
    thisIsGlobal = 5
    local line = io.read()
    print('Winter is coming,' .. line)
end 

Undefined Variable will be nil

foo = anUnknownVariable
aBoolValue = false

-- only nil and false are falsy
if not aBoolValue then
    print('twas false')
end 

karlSum = 0
for I = 1, 100 do
    karlSum = karlSum + i
end

fredSum = 0
for j = 100, 1, -1 do
    fredSum = fredSum + j
end

repeat 
    print('The way of the future')
    num = num - 1
until num == 0

函数表示

function fib(n)
    if n < 2 then
        return 1
    end
    return fib(n-2) + fib(n-1)
end 
-- closures and anonymous functions
function adder(x)
    return function(y) return x + y
end 
a1 = adder(9)
a2 = adder(36)
print(a1(16)) -- >25
print(a2(64)) --> 100

x, y, z = 1,2,3,4  -- 4 被扔掉
function bar(a,b,c)
    print(a,b,c)
    return 4,8,15,16,23,42
end
x,y = bar('zaphod')  -- print 'zaphod' nil nil
-- x = 4
-- y = 8

-- global function.
function f(x) 
    return x*x
end 
f = function (x) return x*x end  

-- local function
local function g(x) 
    return math.sin(x)
end 
local g;
g = function(x)
    return math.sin(x)
end

哈希表

t = {key1 = 'value1', key2 = false}
print(t.key1)
t.newkey = {}
t.key2 = nil -- remove key2 from the table.

u = {['@!#'] = 'qbert', [{}] = 1729, [6.28] = 'tau'}  
-- use any value as key
print(u[6.28])

a = u['@!#']
b = u[{}] -- b = nil since lookup fails.

function h(x) print(x.key1) end
h{key1 = 'Sonmi~451'}  -- Prints 'Sonmi~451'

for key, val in pairs(u) do -- table iteration
    print(key, val)
end 

print(_G['_G'] == _G) -- Print 'true'

v = {'value1', 'value2', 1.21, 'gigawatts'}
for i = 1, #v do
    print(v[i])
end

f1 = {a = 1, b = 2}  -- f1 = 0.5
f2 = {a = 2, b = 3}  -- fail: s = f1 + f2

metafraction = {}
function metafraction.__add(f1, f2)
  sum = {}
  sum.b = f1.b * f2.b
  sum.a = f1.a * f2.b + f2.a * f1.b
  return sum
end

setmetatable(f1, metafraction)
setmetatable(f2, metafraction)

s = f1 + f2  -- call __add(f1, f2) on f1's metatable 
defaultFavs = {animal = 'gru', food = 'donuts'}
myFavs = {food = 'piazza'}
setmetatable(myFavs, {__index = defaultFavs})
eatenBy = myFavs.animal

-- __add(a, b) for a + b -- __sub(a, b) for a - b -- __mul(a, b) for a * b -- __div(a, b) for a / b -- __mod(a, b) for a % b -- __pow(a, b) for a ^ b -- __unm(a) for -a -- __concat(a, b) for a .. b -- __len(a) for #a -- __eq(a, b) for a == b -- __lt(a, b) for a < b -- __le(a, b) for a <= b -- __index(a, b) <fn or a table> for a.b -- __newindex(a, b, c) for a.b = c -- __call(a, ...) for a(...)

像类一样的table和继承

Dog = {}
function Dog:new()
    newObj = {sound  =  'woof'}
    self.__index = self
    return setmetatable(newObj, self)
end

function Dog:makeSound()
    print('I say' .. self.sound)
end

mrDog = Dog:new()
mrDog:makeSound() -- 'Print I say woof' 
-- mrDog.makeSound(self)

-- 这里的Dog看起来像一个类,实际上是一个table,

继承:继承了所有的变量和函数

LoudDog = Dog:new()
function LoudDog:makeSound()
    s = self.sound .. ' '
    print(s .. s .. s)
end

seymour = LoudDog:new()
seymour:makeSound() -- 'woof woof woof'

-- 以下的子类和基类一样
function LoudDog:new()
    newObj = {}
    self.__index = self
    return setmetatable(newObj, self)
end

模块化

写一个文件叫做: mod.lua

local M = {}

local function sayMyName() 
    print('Hrunkner')
end

function M.sayHello()
    print('Why hello there')
    sayMyName()
end  

return M
-- 另外一个文件可以使用mod.lua

local mod = require('mod') -- 运行mod.lua

local mod = (function ()
    <contents of mod.lua>
end) () -- 可以使用mod.lua的非local function

mod.sayHello() -- 运行正常
mod.sayMyName()  -- 报错,因为这是一个local method

-- 假设在mod2.lua里面存在 "print('Hi!')"
local a = require('mode2')
local b = require('mode2') -- 第二次不执行,因为有缓存

dofile('mod2.lua')
dofile('mod2.lua') -- 可以运行第二遍

-- load是加载到内存中,但是没有执行
f = loadfile('mod2.lua')
g = loadstring('print(343)')
g()

还有一些标准库:
String library,【11】

> = string.byte("ABCDE")      -- no index, so the first character
65
> = string.byte("ABCDE",1)    -- indexes start at 1
65
> = string.byte("ABCDE",0)    -- we're not using C
> = string.byte("ABCDE",100)  -- index out of range, no value returned
> = string.byte("ABCDE",3,4)
67      68
> s = "ABCDE"
> = s:byte(3,4)               
> -- can apply directly to string variable 
67      68
> = string.char(65,66,67)
ABC
> = string.char()  -- empty string

Table Library 【12】:

table.concat(table [, sep [, i [, j]]])

> = table.concat({ 1, 2, "three", 4, "five" })
12three4five
> = table.concat({ 1, 2, "three", 4, "five" }, ", ")
1, 2, three, 4, five
> = table.concat({ 1, 2, "three", 4, "five" }, ", ", 2)
2, three, 4, five
> = table.concat({ 1, 2, "three", 4, "five" }, ", ", 2, 4)
2, three, 4

table.foreach(table, f)

> table.foreach({1,"two",3}, print) -- print the key-value pairs


1       1
2       two
3       3
> table.foreach({1,"two",3,"four"}, function(k,v) print(string.rep(v,k)) end)
1
twotwo
333
fourfourfourfour

table.sort(table [, comp])
> t = { 3,2,5,1,4 }
> table.sort(t)
> = table.concat(t, ", ")  -- display sorted values
1, 2, 3, 4, 5

table.insert(table, [pos,] value)
> t = { 1,3,"four" }
> table.insert(t, 2, "two")  -- insert "two" at position before element 2
> = table.concat(t, ", ")
1, two, 3, four

table.remove(table [, pos])
> t = { 1,"two",3,"four" }   -- create a table
> = # t                      -- find the size
4
> table.foreach(t, print)    -- have a look at the elements
1       1
2       two
3       3
4       four
> = table.remove(t,2)        -- remove element number 2 and display it
two
> table.foreach(t, print)    -- display the updated table contents
1       1
2       3
3       four
> = # t                      -- find the size
3

math library【13】:

math.abs
math.acos
math.asin
math.atan
math.ceil
math.cos
math.deg
math.exp
math.floor
math.fmod
math.huge
math.log
math.max
math.maxinteger
math.min
math.mininteger
math.modf
math.pi
math.rad
math.random
math.randomseed
math.sin
math.sqrt
math.tan
math.tointeger
math.type
math.ult

OS Library:

os.clock()  -- CPU time
os.date([format [, time]]) 
> = os.date("%d.%m.%Y")
06.10.2012

os.difftime(t2, t1)
> t1 = os.time()
> -- wait a little while then type....
> = os.difftime(os.time(), t1)
31
> = os.difftime(os.time(), t1)
38

os.execute([command])  -- 执行命令行上的命令
> = os.execute("echo hello")
hello
0
> = os.execute("mmmmm")  -- generate an error
'mmmmm' is not recognized as an internal or external command,
operable program or batch file.
1

os.exit([code]) -- 退出当前环境
> os.exit(0)   -- kill the Lua shell we are in and pass 0 back to parent shell

os.getenv(varname)  -- 获取系统变量
> = os.getenv("BANANA")
nil
> = os.getenv("USERNAME")
Nick

os.remove(filename)  -- 删除文件
> os.execute("echo hello > banana.txt")
> = os.remove("banana.txt")
true
> = os.remove("banana.txt")
nil     banana.txt: No such file or directory   2

os.rename(oldname, newname) -- 更改文件名字
> os.execute("echo hello > banana.txt")
> = os.rename("banana.txt", "apple.txt")
true
> = os.rename("banana.txt", "apple.txt")
nil     banana.txt: No such file or directory   2

os.setlocale(locale [, category]) 

os.tmpname () -- 生成一个可以用来做临时文件的名字
> = os.tmpname()  -- on windows
\s2js.
> = os.tmpname()  -- on debian
/tmp/lua_5xPi18

IO Library【14】:

file = io.open (filename [, mode])

io.close ([file]) -- f:close ()

io.flush ()

io.input ([file])

io.lines ([filename])

for line in io.lines(filename) do ... end

io.write (value1, ...)
-- io.output():write.

f:seek ([whence] [, offset])

Lua的安装:

curl -R -O http://www.lua.org/ftp/lua-5.3.0.tar.gz
tar zxf lua-5.3.0.tar.gz
cd lua-5.3.0
make macosx test
make install
-- 接着再命令行输入lua就可以运行

另外在Lua社区有一个reference,还算比较全,可以看看【9】,中文的手册【15】,另外有一份绝世高手秘籍,学习X在Y minutes以内【10】。

Torch

安装Torch(Mac):安装完以后比如安装rnn那就是:

luarocks install [packagename](rnn,dp)
git clone https://github.com/torch/distro.git ~/torch --recursive
cd ~/torch; bash install-deps;
./install.sh
source ~/.profile

没有source file的时候,参考【19】

然后学习Torch的时候,在命令行输入th:
这里写图片描述

退出的话输入两次ctrl c,或者输入:os.exit()

运行lua的文件的话: th file.lua 或者 th -h

另外,可以看官方的cheatsheet:【20】,还有Torch的教程可以看:【16】【17】【18】

这里我介绍Torch的基本的东西。

Tensor

Tensor就是n维矩阵,这个和TF一样。

首先是开辟数组和存储:

--- creation of a 4D-tensor 4x5x6x2
z = torch.Tensor(4,5,6,2)
--- for more dimensions, (here a 6D tensor) one can do:
s = torch.LongStorage(6)
s[1] = 4; s[2] = 5; s[3] = 6; s[4] = 2; s[5] = 7; s[6] = 3;
x = torch.Tensor(s)

--- 获取Tensor的维度和size
x:nDimension()
x:size()

-- 获取元素
x = torch.Tensor(7,7,7)
x[3][4][5]

-- 等同于:
x:storage()[x:storageOffset()
 +(3-1)*x:stride(1)+(4-1)*x:stride(2)+(5-1)*x:stride(3)] 

存储:

x = torch.Tensor(4,5)
s = x:storage()
for i=1,s:size() do -- fill up the Storage s[i] = i end > x -- s is interpreted by x as a 2D matrix 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 [torch.DoubleTensor of dimension 4x5] > x:stride() 5 1 -- element in the last dimension are contiguous! [torch.LongStorage of size 2] 根据数据类型不同,可以有: ByteTensor -- contains unsigned chars CharTensor -- contains signed chars ShortTensor -- contains shorts IntTensor -- contains ints LongTensor -- contains longs FloatTensor -- contains floats DoubleTensor -- contains doubles x = torch.Tensor(5):zero() 生成 0 > x:narrow(1, 2, 3):fill(1) -- narrow() returns a Tensor -- referencing the same Storage as x > x 0 1 1 1 0 [torch.Tensor of dimension 5] --- 拷贝Tensor y = torch.Tensor(x:size()):copy(x) y = x:clone() x = torch.Tensor(2,5):fill(3.14) > x 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 [torch.DoubleTensor of dimension 2x5] y = torch.Tensor(x) > y 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 3.1400 [torch.DoubleTensor of dimension 2x5] y:zero() > x -- elements of x are the same as y! 0 0 0 0 0 0 0 0 0 0 [torch.DoubleTensor of dimension 2x5] 所有的值赋予 1 x = torch.Tensor(torch.LongStorage({4}), torch.LongStorage({0})):zero() -- zeroes the tensor x[1] = 1 -- all elements point to the same address! > x 1 1 1 1 [torch.DoubleTensor of dimension 4] a = torch.LongStorage({1,2}) -- We have a torch.LongStorage containing the values 1 and 2 -- General case for TYPE ~= Long, e.g. for TYPE = Float: b = torch.FloatTensor(a) -- Creates a new torch.FloatTensor with 2 dimensions, the first of size 1 and the second of size 2 > b:size() 1 2 [torch.LongStorage of size 2] -- Special case of torch.LongTensor c = torch.LongTensor(a) -- Creates a new torch.LongTensor that uses a as storage and thus contains the values 1 and 2 > c 1 2 [torch.LongTensor of size 2] -- creates a storage with 10 elements s = torch.Storage(10):fill(1) -- we want to see it as a 2x5 tensor x = torch.Tensor(s, 1, torch.LongStorage{2,5}) > x 1 1 1 1 1 1 1 1 1 1 [torch.DoubleTensor of dimension 2x5] x:zero() > s -- the storage contents have been modified 0 0 0 0 0 0 0 0 0 0 [torch.DoubleStorage of size 10] i = 0 z = torch.Tensor(3,3) z:apply(function(x) i = i + 1 return i end) -- fill up the tensor > z 1 2 3 4 5 6 7 8 9 [torch.DoubleTensor of dimension 3x3] z:apply(math.sin) -- apply the sin function > z 0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794 0.6570 0.9894 0.4121 [torch.DoubleTensor of dimension 3x3] sum = 0 z:apply(function(x) sum = sum + x end) -- compute the sum of the elements > sum 1.9552094821074 > z:sum() -- it is indeed correct! 1.9552094821074

math function

这里的东西主要是和Matlab一样的接口,所以简单一些。

torch.log(x, x)
x:log()

> x = torch.rand(100, 100)
> k = torch.rand(10, 10)
> res1 = torch.conv2(x, k)   -- case 1

> res2 = torch.Tensor()
> torch.conv2(res2, x, k)     -- case 2

> res2:dist(res1)
0

case 2更好,因为不需要再进行内存分配。

把两个Tensor进行联合:
> torch.cat(torch.ones(3), torch.zeros(2))
 1
 1
 1
 0
 0
[torch.DoubleTensor of size 5]

> torch.cat(torch.ones(3, 2), torch.zeros(2, 2), 1)
 1  1
 1  1
 1  1
 0  0
 0  0
[torch.DoubleTensor of size 5x2]

> torch.cat(torch.ones(2, 2), torch.zeros(2, 2), 1)
 1  1
 1  1
 0  0
 0  0
[torch.DoubleTensor of size 4x2]

> torch.cat(torch.ones(2, 2), torch.zeros(2, 2), 2)
 1  1  0  0
 1  1  0  0
[torch.DoubleTensor of size 2x4]

> torch.cat(torch.cat(torch.ones(2, 2), torch.zeros(2, 2), 1), torch.rand(3, 2), 1)
 1.0000  1.0000
 1.0000  1.0000
 0.0000  0.0000
 0.0000  0.0000
 0.3227  0.0493
 0.9161  0.1086
 0.2206  0.7449
[torch.DoubleTensor of size 7x2]

> torch.cat({torch.ones(2, 2), torch.zeros(2, 2), torch.rand(3, 2)}, 1)
 1.0000  1.0000
 1.0000  1.0000
 0.0000  0.0000
 0.0000  0.0000
 0.3227  0.0493
 0.9161  0.1086
 0.2206  0.7449
[torch.DoubleTensor of size 7x2]

> torch.cat({torch.Tensor(), torch.rand(3, 2)}, 1)
 0.3227  0.0493
 0.9161  0.1086
 0.2206  0.7449
[torch.DoubleTensor of size 3x2]

返回对角线元素:
y = torch.diag(x, k)
y = torch.diag(x)

单位矩阵:
y = torch.eye(n, m)
y = torch.eye(n)

直方图:
y = torch.histc(x)
y = torch.histc(x, n)
y = torch.histc(x, n, min, max)

生成连续的数组:
y = torch.linspace(x1, x2)
y = torch.linspace(x1, x2, n)

生成log space:
y = torch.logspace(x1, x2)
y = torch.logspace(x1, x2, n)

y = torch.ones(m, n) returns a m × n Tensor filled with ones.

生成随机数:
y = torch.rand(m, n)

torch.range(2, 5)

element-wise的操作:基本上和matlab的接口一样
y = torch.abs(x) 
y = torch.sign(x)
y = torch.acos(x)
y = torch.asin(x)
x:asin() replaces all elements in-place with the arcsine of the elements of x.
y = torch.atan(x)

还有很多类似的操作。

Torch的CNN相关的内容

torch.conv2([res,] x, k, [, 'F' or 'V'])
-- F表示full convolution;V表示valid convolution

x = torch.rand(100, 100)
k = torch.rand(10, 10)
c = torch.conv2(x, k)
> c:size()
 91
 91
[torch.LongStorage of size 2]

c = torch.conv2(x, k, 'F')
> c:size()
 109
 109
[torch.LongStorage of size 2]

torch.xcorr2([res,] x, k, [, 'F' or 'V'])
-- 对输入增加了correlation的操作

torch.conv3([res,] x, k, [, 'F' or 'V'])

x = torch.rand(100, 100, 100)
k = torch.rand(10, 10, 10)
c = torch.conv3(x, k)
> c:size()
 91
 91
 91
[torch.LongStorage of size 3]

c = torch.conv3(x, k, 'F')
> c:size()
 109
 109
 109
[torch.LongStorage of size 3]

torch.xcorr3([res,] x, k, [, 'F' or 'V'])

逻辑操作:

torch.lt(a, b)
torch.le(a, b)
torch.gt(a, b)
torch.ge(a, b)
torch.eq(a, b)
torch.ne(a, b)
torch.all(a)
torch.any(a)

奇异值,SVD分解,线性系统

-- LU分解,解AX = B torch.gesv([resb, resa,] B, A) > a = torch.Tensor({{6.80, -2.11, 5.66, 5.97, 8.23}, {-6.05, -3.30, 5.36, -4.44, 1.08}, {-0.45, 2.58, -2.70, 0.27, 9.04}, {8.32, 2.71, 4.35, -7.17, 2.14}, {-9.67, -5.14, -7.26, 6.08, -6.87}}):t() > b = torch.Tensor({{4.02, 6.19, -8.22, -7.57, -3.03}, {-1.56, 4.00, -8.67, 1.75, 2.86}, {9.81, -4.09, -4.57, -8.61, 8.99}}):t() > b 4.0200 -1.5600 9.8100 6.1900 4.0000 -4.0900 -8.2200 -8.6700 -4.5700 -7.5700 1.7500 -8.6100 -3.0300 2.8600 8.9900 [torch.DoubleTensor of dimension 5x3] > a 6.8000 -6.0500 -0.4500 8.3200 -9.6700 -2.1100 -3.3000 2.5800 2.7100 -5.1400 5.6600 5.3600 -2.7000 4.3500 -7.2600 5.9700 -4.4400 0.2700 -7.1700 6.0800 8.2300 1.0800 9.0400 2.1400 -6.8700 [torch.DoubleTensor of dimension 5x5] > x = torch.gesv(b, a) > x -0.8007 -0.3896 0.9555 -0.6952 -0.5544 0.2207 0.5939 0.8422 1.9006 1.3217 -0.1038 5.3577 0.5658 0.1057 4.0406 [torch.DoubleTensor of dimension 5x3] > b:dist(a * x) 1.1682163181673e-14 -- torch.trtrs([resb, resa,] b, a [, 'U' or 'L'] [, 'N' or 'T'] [, 'N' or 'U']) X = torch.trtrs(B, A) -- returns the solution of AX = B where A is upper-triangular. -- orch.potrf([res,] A [, 'U' or 'L'] ) -- Cholesky Decomposition of 2D > A = torch.Tensor({ {1.2705, 0.9971, 0.4948, 0.1389, 0.2381}, {0.9971, 0.9966, 0.6752, 0.0686, 0.1196}, {0.4948, 0.6752, 1.1434, 0.0314, 0.0582}, {0.1389, 0.0686, 0.0314, 0.0270, 0.0526}, {0.2381, 0.1196, 0.0582, 0.0526, 0.3957}}) > chol = torch.potrf(A) > chol 1.1272 0.8846 0.4390 0.1232 0.2112 0.0000 0.4626 0.6200 -0.0874 -0.1453 0.0000 0.0000 0.7525 0.0419 0.0738 0.0000 0.0000 0.0000 0.0491 0.2199 0.0000 0.0000 0.0000 0.0000 0.5255 [torch.DoubleTensor of size 5x5] > torch.potrf(chol, A, 'L') > chol 1.1272 0.0000 0.0000 0.0000 0.0000 0.8846 0.4626 0.0000 0.0000 0.0000 0.4390 0.6200 0.7525 0.0000 0.0000 0.1232 -0.0874 0.0419 0.0491 0.0000 0.2112 -0.1453 0.0738 0.2199 0.5255 [torch.DoubleTensor of size 5x5] -- torch.eig([rese, resv,] a [, 'N' or 'V']) -- 奇异值分解 > a = torch.Tensor({{ 1.96, 0.00, 0.00, 0.00, 0.00}, {-6.49, 3.80, 0.00, 0.00, 0.00}, {-0.47, -6.39, 4.17, 0.00, 0.00}, {-7.20, 1.50, -1.51, 5.70, 0.00}, {-0.65, -6.34, 2.67, 1.80, -7.10}}):t() > a 1.9600 -6.4900 -0.4700 -7.2000 -0.6500 0.0000 3.8000 -6.3900 1.5000 -6.3400 0.0000 0.0000 4.1700 -1.5100 2.6700 0.0000 0.0000 0.0000 5.7000 1.8000 0.0000 0.0000 0.0000 0.0000 -7.1000 [torch.DoubleTensor of dimension 5x5] > b = a + torch.triu(a, 1):t() > b 1.9600 -6.4900 -0.4700 -7.2000 -0.6500 -6.4900 3.8000 -6.3900 1.5000 -6.3400 -0.4700 -6.3900 4.1700 -1.5100 2.6700 -7.2000 1.5000 -1.5100 5.7000 1.8000 -0.6500 -6.3400 2.6700 1.8000 -7.1000 [torch.DoubleTensor of dimension 5x5] > e = torch.eig(b) > e 16.0948 0.0000 -11.0656 0.0000 -6.2287 0.0000 0.8640 0.0000 8.8655 0.0000 [torch.DoubleTensor of dimension 5x2] > e, v = torch.eig(b, 'V') > e 16.0948 0.0000 -11.0656 0.0000 -6.2287 0.0000 0.8640 0.0000 8.8655 0.0000 [torch.DoubleTensor of dimension 5x2] > v -0.4896 0.2981 -0.6075 -0.4026 -0.3745 0.6053 0.5078 -0.2880 0.4066 -0.3572 -0.3991 0.0816 -0.3843 0.6600 0.5008 0.4564 0.0036 -0.4467 -0.4553 0.6204 -0.1622 0.8041 0.4480 -0.1725 0.3108 [torch.DoubleTensor of dimension 5x5] > v * torch.diag(e:select(2, 1))*v:t() 1.9600 -6.4900 -0.4700 -7.2000 -0.6500 -6.4900 3.8000 -6.3900 1.5000 -6.3400 -0.4700 -6.3900 4.1700 -1.5100 2.6700 -7.2000 1.5000 -1.5100 5.7000 1.8000 -0.6500 -6.3400 2.6700 1.8000 -7.1000 [torch.DoubleTensor of dimension 5x5] > b:dist(v * torch.diag(e:select(2, 1)) * v:t()) 3.5423944346685e-14 -- SVD分解 > a = torch.Tensor({{8.79, 6.11, -9.15, 9.57, -3.49, 9.84}, {9.93, 6.91, -7.93, 1.64, 4.02, 0.15}, {9.83, 5.04, 4.86, 8.83, 9.80, -8.99}, {5.45, -0.27, 4.85, 0.74, 10.00, -6.02}, {3.16, 7.98, 3.01, 5.80, 4.27, -5.31}}):t() > a 8.7900 9.9300 9.8300 5.4500 3.1600 6.1100 6.9100 5.0400 -0.2700 7.9800 -9.1500 -7.9300 4.8600 4.8500 3.0100 9.5700 1.6400 8.8300 0.7400 5.8000 -3.4900 4.0200 9.8000 10.0000 4.2700 9.8400 0.1500 -8.9900 -6.0200 -5.3100 > u, s, v = torch.svd(a) > u -0.5911 0.2632 0.3554 0.3143 0.2299 -0.3976 0.2438 -0.2224 -0.7535 -0.3636 -0.0335 -0.6003 -0.4508 0.2334 -0.3055 -0.4297 0.2362 -0.6859 0.3319 0.1649 -0.4697 -0.3509 0.3874 0.1587 -0.5183 0.2934 0.5763 -0.0209 0.3791 -0.6526 [torch.DoubleTensor of dimension 6x5] > s 27.4687 22.6432 8.5584 5.9857 2.0149 [torch.DoubleTensor of dimension 5] > v -0.2514 0.8148 -0.2606 0.3967 -0.2180 -0.3968 0.3587 0.7008 -0.4507 0.1402 -0.6922 -0.2489 -0.2208 0.2513 0.5891 -0.3662 -0.3686 0.3859 0.4342 -0.6265 -0.4076 -0.0980 -0.4933 -0.6227 -0.4396 [torch.DoubleTensor of dimension 5x5] > u * torch.diag(s) * v:t() 8.7900 9.9300 9.8300 5.4500 3.1600 6.1100 6.9100 5.0400 -0.2700 7.9800 -9.1500 -7.9300 4.8600 4.8500 3.0100 9.5700 1.6400 8.8300 0.7400 5.8000 -3.4900 4.0200 9.8000 10.0000 4.2700 9.8400 0.1500 -8.9900 -6.0200 -5.3100 [torch.DoubleTensor of dimension 6x5] > a:dist(u * torch.diag(s) * v:t()) 2.8923773593204e-14

rnn和nn不能共存的问题:class nn.SpatialGlimpse has been already assigned a parent class 【21】

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Ref Links:
【1】Lua官网:http://www.lua.org/start.html
【2】15 Min搞定Lua系列: http://tylerneylon.com/a/learn-lua/
【3】Lua菜鸟教程: http://www.runoob.com/lua/lua-tutorial.html
【4】Torch教程: https://www.cs.ox.ac.uk/people/nando.defreitas/machinelearning/
【5】更多参考资料: https://www.cs.ox.ac.uk/people/nando.defreitas/machinelearning/practicals/practical1.pdf
【6】Torch官网: http://torch.ch/docs/getting-started.html
【7】Torch 添加新的层: https://zhuanlan.zhihu.com/p/21550685
【8】小福利PyTorch: https://zhuanlan.zhihu.com/p/29779361
【9】Lua reference: http://lua-users.org/files/wiki_insecure/users/thomasl/luarefv51.pdf
【10】绝世高手秘籍: https://learnxinyminutes.com
【11】String Library:http://lua-users.org/wiki/StringLibraryTutorial
【12】Table Library: http://lua-users.org/wiki/TableLibraryTutorial
【13】Math Library: http://lua-users.org/wiki/MathLibraryTutorial
【14】IO Library: http://lua-users.org/wiki/IoLibraryTutorial
【15】Lua中文手册: http://www.runoob.com/manual/lua53doc/contents.html
【16】Torch Tensor的教程: https://github.com/torch/torch7/blob/master/doc/tensor.md
【17】Torch Math Function: https://github.com/torch/torch7/blob/master/doc/maths.md
【18】使用Torch实现的practice: https://github.com/oxford-cs-ml-2015/
【19】No Source File: http://www.voidcn.com/article/p-oeithnnf-bqk.html
【20】Torch Cheatsheet: https://github.com/torch/torch7/wiki/Cheatsheet
【21】rnn nn: https://github.com/Element-Research/dpnn/issues/95

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