Pytorch-----(3A)基本的统计

一、问题

　　　　进行基本的张量统计如均值、中位数、众数等；进行基本的统计有助于应用概率分布和统计推断。Ｔorch功能与Ｎumpy类似，但是Ｔorch函数支持GPU加速。以下是创建基本统计量的函数；

二、如何实现

　　　　１Ｄ张量统计均值很简单，但是计算２Ｄ张量的统计量需要额外的参数，因为在这些计算中需要指定维度。

#计算均值
torch.mean(torch.tensor([10., 10., 13., 10., 34.,
45., 65., 67., 87., 89., 87., 34.]))
tensor(45.9167)

# 计算行和列的统计量

d = torch.randn(4, 5)
d
tensor([[-1.6406, 0.9295, 1.2907, 0.2612, 0.9711], [ 0.3551, 0.8562, -0.3635, -0.1552, -1.2282], [ 1.2445, 1.1750, -0.2217, -2.0901, -1.2658], [-1.8761, -0.6066, 0.7470, 0.4811, 0.6234]])

torch.mean(d,dim=0)　＃　０维表示平行纵轴方向，即按列统计
tensor([-0.4793, 0.5885, 0.3631, -0.3757, -0.2249])
torch.mean(d,dim=1)
tensor([ 0.3624, -0.1071, -0.2316, -0.1262])　＃　１维表示平行纵轴方向，即按行统计

中位数、众数和标准差类似：

#计算列中位数
torch.median(d,dim=0)
＃结果：
torch.return_types.median( values=tensor([-1.6406, 0.8562, -0.2217, -0.1552, -1.2282]), indices=tensor([0, 1, 2, 1, 1]))

＃计算行中位数
torch.median(d,dim=1)
torch.return_types.median( values=tensor([ 0.9295, -0.1552, -0.2217, 0.4811]), indices=tensor([1, 3, 2, 3]))

# 计算众数
torch.mode(d)
torch.return_types.mode( values=tensor([-1.6406, -1.2282, -2.0901, -1.8761]), indices=tensor([0, 4, 3, 0]))

torch.mode(d,dim=0)
torch.return_types.mode( values=tensor([-1.8761, -0.6066, -0.3635, -2.0901, -1.2658]), indices=tensor([3, 3, 1, 2, 2]))

torch.mode(d,dim=1)
torch.return_types.mode( values=tensor([-1.6406, -1.2282, -2.0901, -1.8761]), indices=tensor([0, 4, 3, 0]))
＃由上可见计算mode 不指定dim时，默认是dim=１

        标准差反映了偏离中心度量的程度，指示着数据或变量的一致性，它表明数据中是否有较大的波动或异常。

#compute the standard deviation

torch.std(d)
tensor(1.0944)

torch.std(d,dim=0)
tensor([1.5240, 0.8083, 0.7911, 1.1730, 1.1889])

torch.std(d,dim=1)
tensor([1.1807, 0.7852, 1.4732, 1.1165])

#计算方差
torch.var(d)
tensor(1.1978)
torch.var(d,dim=0)
tensor([2.3224, 0.6534, 0.6259, 1.3758, 1.4134])
torch.var(d,dim=1)
tensor([1.3940, 0.6166, 2.1703, 1.2466])

# 计算最小、最大值
torch.min(d)
tensor(-2.0901)
torch.min(d,dim=0)
torch.return_types.min( values=tensor([-1.8761, -0.6066, -0.3635, -2.0901, -1.2658]), indices=tensor([3, 3, 1, 2, 2]))
torch.min(d,dim=1)
torch.return_types.min( values=tensor([-1.6406, -1.2282, -2.0901, -1.8761]), indices=tensor([0, 4, 3, 0]))

# 张量排序　默认是１维的；
torch.sort(d)
torch.return_types.sort( values=tensor([[-1.6406, 0.2612, 0.9295, 0.9711, 1.2907], [-1.2282, -0.3635, -0.1552, 0.3551, 0.8562], [-2.0901, -1.2658, -0.2217, 1.1750, 1.2445], [-1.8761, -0.6066, 0.4811, 0.6234, 0.7470]]), indices=tensor([[0, 3, 1, 4, 2], [4, 2, 3, 0, 1], [3, 4, 2, 1, 0], [0, 1, 3, 4, 2]]))

torch.sort(d,dim=0)
torch.return_types.sort( values=tensor([[-1.8761, -0.6066, -0.3635, -2.0901, -1.2658], [-1.6406, 0.8562, -0.2217, -0.1552, -1.2282], [ 0.3551, 0.9295, 0.7470, 0.2612, 0.6234], [ 1.2445, 1.1750, 1.2907, 0.4811,0.9711]]), indices=tensor([[3, 3, 1, 2, 2], [0, 1, 2, 1, 1], [1, 0, 3, 0, 3], [2, 2, 0, 3, 0]]))

torch.sort(d,dim=0,descending=True)　＃降序排列
torch.return_types.sort( values=tensor([[ 1.2445, 1.1750, 1.2907, 0.4811, 0.9711], [ 0.3551, 0.9295, 0.7470, 0.2612, 0.6234], [-1.6406, 0.8562, -0.2217, -0.1552, -1.2282], [-1.8761, -0.6066, -0.3635, -2.0901, -1.2658]]), indices=tensor([[2, 2, 0, 3, 0], [1, 0, 3, 0, 3], [0, 1, 2, 1, 1], [3, 3, 1, 2, 2]]))

torch.sort(d,dim=1,descending=True)
torch.return_types.sort( values=tensor([[ 1.2907, 0.9711, 0.9295, 0.2612, -1.6406], [ 0.8562, 0.3551, -0.1552, -0.3635, -1.2282], [ 1.2445, 1.1750, -0.2217, -1.2658, -2.0901], [ 0.7470, 0.6234, 0.4811, -0.6066, -1.8761]]), indices=tensor([[2, 4, 1, 3, 0], [1, 0, 3, 2, 4], [0, 1, 2, 4, 3], [2, 4, 3, 1, 0]]))

from torch.autograd import Variable
Variable(torch.ones(2,2),requires_grad=True)
tensor([[1., 1.], [1., 1.]], requires_grad=True)

a, b = 12,23
x1 = Variable(torch.randn(a,b),requires_grad=True)
x2 = Variable(torch.randn(a,b),requires_grad=True)
x3 =Variable(torch.randn(a,b),requires_grad=True)

c = x1 * x2　　
d = a + x3
e = torch.sum(d)

e.backward()

print(e)

tensor(3278.1235, grad_fn=<SumBackward0>)