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Lua快速入门与Torch教程

2017-12-31 10:10 761 查看

Lua

变量和控制流

函数表示

哈希表

像类一样的table和继承
模块化

Torch

Tensor

math function

Torch的CNN相关的内容

奇异值SVD分解线性系统

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：

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】

转载请注明出处： http://blog.csdn.net/c602273091/article/details/78940781

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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