Torch 是一个以机器学习为核心的科学计算框架。由于采用了高效的脚本语言LuaJIT，同时提供了一个灵活的交互计算环境，因此，Torch 特别适合用来开发机器学习相关任务。此外Torch对C/CUDA支持非常好，因此也能很好的胜任大规模的计算任务，如深度学习的训练。
关键的特征：
$ th
______ __ | Torch7
/_ __/__ ________/ / | Scientific computing for Lua.
/ / / _ \/ __/ __/ _ \ |
/_/ \___/_/ \__/_//_/ | https://github.com/torch
| http://torch.ch
In [1]:
-- 构造一个5x5的随机矩阵
N = 5
A = torch.rand(N, N)
print(A)
Out[1]:
以下代码输出对称矩阵 $$ A = A * A^T $$
In [2]:
A = A*A:t()
print(A)
Out[2]:
下面代码实现计算：矩阵乘向量，即列向量的线性组合。
$$ B = A * v $$
In [3]:
v = torch.rand(5,1)
B = A*v
print("v=")
print(v)
print("B=")
print(B)
Out[3]:
计算反矩阵：
$$ C = A^{-1} $$
In [4]:
C = torch.inverse(A)
print(C)
print(C*A)
Out[4]:
In [1]:
require('image')
itorch.image(image.lena())
In [6]:
require ('nn')
-- 利用神经网络构造一个随机的3x3x3滤波器，对RGB图像进行进行滤波操作
m=nn.SpatialConvolution(3,1,3,3)
n=m:forward(image.lena())
itorch.image(n)
In [7]:
Plot = require 'itorch.Plot'
x1 = torch.randn(40):mul(100)
y1 = torch.randn(40):mul(100)
x2 = torch.randn(40):mul(100)
y2 = torch.randn(40):mul(100)
x3 = torch.randn(40):mul(200)
y3 = torch.randn(40):mul(200)
plot = Plot():circle(x1, y1, 'red', 'hi'):circle(x2, y2, 'blue', 'bye'):draw()
plot:circle(x3,y3,'green', 'yolo'):redraw()
plot:title('Scatter Plot Demo'):redraw()
plot:xaxis('length'):yaxis('width'):redraw()
plot:legend(true)
plot:redraw()
Torch支持多种数值计算优化算法，包括SGD, Adagrad, Conjugate-Gradient, LBFGS, RProp等等。
This package contains several optimization routines for Torch. Each optimization algorithm is based on the same interface:
x*, {f}, ... = optim.method(func, x, state)where:
func: a user-defined closure that respects this API: f, df/dx = func(x)x: the current parameter vector (a 1D torch.Tensor)state: a table of parameters, and state variables, dependent upon the algorithmx*: the new parameter vector that minimizes f, x* = argmin_x f(x){f}: a table of all f values, in the order they've been evaluated (for some simple algorithms, like SGD, #f == 1)这里设计一个一维的线性回归，即直线拟合的例子。
In [8]:
-- 构造训练样本
N = 32
x = {}
y = {}
for i=1, N do
x[i] = (math.random() - 0.5) * 20
y[i] = 0.7*x[i] + 5.0 + (math.random()-0.5)
end
Plot = require 'itorch.Plot'
local plot = Plot()
plot:circle(x,y,'black', 'yolo'):draw()
plot:title('直线拟合'):redraw()
In [9]:
require('optim')
-- 纪录输出日志
batchLog = {}
batchLog.value = {}
batchLog.seq = {}
parameter = torch.Tensor(2)
parameter[1] = 0
parameter[2] = 0
-- 首先构造 func(x)
function batchFunc(inParameter)
local sum = 0.0
local deltaP = torch.Tensor(2)
deltaP[1] = 0.0
deltaP[2] = 0.0
for i=1,#x do
sum = sum + math.pow(inParameter[1] * x[i] + inParameter[2] - y[i],2)
deltaP[1] = deltaP[1] + (inParameter[1] * x[i] + inParameter[2] - y[i]) * x[i]
deltaP[2] = deltaP[2] + (inParameter[1] * x[i] + inParameter[2] - y[i])
end
sum = 0.5 * sum / #x
deltaP = deltaP / #x
batchLog.value[#batchLog.value+1] = sum
batchLog.seq[#batchLog.seq+1] = #batchLog.seq+1
return sum , deltaP
end
local state = {
learningRate = 1.0e-2,
}
for i = 1,500 do
optim.sgd(batchFunc, parameter ,state)
end
local plot = Plot()
plot:line(batchLog.seq, batchLog.value,'black', 'yolo'):draw()
plot:title('BGD'):redraw()
In [13]:
-- 绘制拟合出来的直线
drawResultLine = function()
local resultValue = {}
local resultSeq = {}
for i=-10,10,0.1 do
resultSeq[#resultSeq+1] = i
resultValue[#resultValue+1] = i*parameter[1] + parameter[2]
end
local plot = Plot()
plot:circle(x,y,'red', 'yolo'):draw()
plot:line(resultSeq, resultValue,'black', 'yolo'):redraw()
plot:title('直线拟合'):redraw()
end
drawResultLine()
由上面的曲线可以看出，设置learningRate非常重要，下面演示一下SGD算法。
In [12]:
require('optim')
-- 纪录输出日志
sgdLog = {}
sgdLog.value = {}
sgdLog.seq = {}
parameter[1] = 0
parameter[2] = 0
local sgdNumber = 0
-- 首先构造 func(x)
function sgdFunc(inParameter)
local sum = 0.0
local deltaP = torch.Tensor(2)
sgdNumber = (sgdNumber + 1) % #x
local i = sgdNumber + 1
sum = 0.5 * math.pow(inParameter[1] * x[i] + inParameter[2] - y[i],2)
deltaP[1] = (inParameter[1] * x[i] + inParameter[2] - y[i]) * x[i]
deltaP[2] = (inParameter[1] * x[i] + inParameter[2] - y[i])
sgdLog.value[#sgdLog.value+1] = sum
sgdLog.seq[#sgdLog.seq+1] = #sgdLog.seq+1
return sum , deltaP
end
local state = {
learningRate = 1.0e-2,
}
for i = 1,200 do
optim.sgd(sgdFunc, parameter ,state)
end
local plot = Plot()
plot:line(sgdLog.seq, sgdLog.value,'black', 'yolo'):draw()
plot:title('SGD'):redraw()
drawResultLine()