pytorch的矩阵操作分类
<h2 id="pytorch-的矩阵操作">PyTorch 的矩阵操作</h2><p>注意：</p>
<ol>
<li>无论是torch.f()还是tensor.f()，都是返回新的Tensor，不会修改原始的tensor</li>
</ol>
<h3 id="单个tensor">单个tensor</h3>
<h4 id="初始化">初始化</h4>
<ul>
<li>
<p><code>empty</code></p>
<p>用于创建一个未初始化的张量，其值是<strong>随机的</strong></p>
<p>与<code>torch.randn</code>的区别在于，<code>torch.randn</code>是从正态分布中采样的</p>
<pre><code class="language-python3">torch.empty(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, pin_memory=False, memory_format=torch.contiguous_format) → Tensor
torch.empty((2,3), dtype=torch.int64)
tensor([[ 9.4064e+13,2.8000e+01,9.3493e+13],
[ 7.5751e+18,7.1428e+18,7.5955e+18]])
</code></pre>
</li>
<li>
<p><code>zeros</code></p>
<pre><code class="language-python3">torch.zeros(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False)
torch.zeros(2, 3)
tensor([[ 0.,0.,0.],
[ 0.,0.,0.]])
</code></pre>
</li>
<li>
<p><code>randn</code></p>
<p><span class="math inline">\(out_i \sim \mathcal{N}(0, 1)\)</span>，满足正态分布</p>
<pre><code class="language-python3">torch.randn(*size, *, generator=None, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, pin_memory=False)
torch.randn(2, 3)
tensor([[ 1.5954,2.8929, -1.0923],
[ 1.1719, -0.4709, -0.1996]])
</code></pre>
</li>
<li>
<p><code>randint</code></p>
<p>生成制定范围[low, high) 和形状size的tensor</p>
<pre><code class="language-python">torch.randint(low=0, high, size, \*, generator=None, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor
torch.randint(3, 10, (2, 2))
tensor([,
])
</code></pre>
</li>
<li>
<p><code>arange</code></p>
<p>和<code>list(range())</code>的原理相同</p>
<pre><code class="language-python3">torch.arange(start=0, end, step=1, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor
torch.arange(5)
tensor([ 0,1,2,3,4])
torch.arange(1, 4)
tensor([ 1,2,3])
torch.arange(1, 2.5, 0.5)
tensor([ 1.0000,1.5000,2.0000])
</code></pre>
</li>
<li>
<p><code>range(deprecated)</code></p>
<p>类似于<code>list(range())</code>的用法,但是，torch.range的返回的最后一个元素是可以为end的</p>
<pre><code class="language-python">torch.range(start=0, end, step=1, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False)
# 0.5 指的是每步的大小
torch.range(1, 4, 0.5)
tensor([ 1.0000,1.5000,2.0000,2.5000,3.0000,3.5000,4.0000])
</code></pre>
</li>
<li>
<p><code>linspace</code></p>
<p>不同于<code>torch.range</code>，这里的step指的是有多少步，根据步数，计算每步的大小</p>
<p><strong>torch.linspace的第一个元素一定是start，最后一个元素一定是end</strong></p>
<pre><code class="language-python">torch.linspace(start, end, steps, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False)
torch.linspace(start=-10, end=10, steps=5)
tensor([-10.,-5., 0., 5.,10.])
torch.linspace(start=-10, end=10, steps=1)
tensor([-10.]
</code></pre>
</li>
<li>
<p><code>eye</code></p>
<p>返回<strong>对角线</strong>矩阵</p>
<pre><code class="language-python">torch.eye(n, m=None, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor
torch.eye(3)
tensor([[ 1.,0.,0.],
[ 0.,1.,0.],
[ 0.,0.,1.]])
</code></pre>
</li>
<li>
<p><code>full</code></p>
<p>把一个数字扩展到指定的形状上，是ones zeros的一般化</p>
<p><code>torch.full((2,3), 0.0) = torch.zeros((2,3))</code></p>
<p><code>torch.full((2,3), 1.0) = torch.ones((2,3))</code></p>
<pre><code class="language-python">torch.full(size, fill_value, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) → Tensor
torch.full((2, 3), 3.141592)
tensor([[ 3.1416,3.1416,3.1416],
[ 3.1416,3.1416,3.1416]])
</code></pre>
</li>
<li>
<p><code>zeros_like</code></p>
<p>返回于input tensor形状相同的元素全是0的tensor</p>
<pre><code class="language-python3">torch.zeros_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) → Tensor
input = torch.empty(2, 3)
torch.zeros_like(input)
tensor([[ 0.,0.,0.],
[ 0.,0.,0.]])
</code></pre>
</li>
</ul>
<h4 id="改变形状">改变形状</h4>
<ul>
<li>
<p><code>premute</code></p>
<p>改变维度的顺序</p>
<pre><code class="language-python">torch.permute(input, dims) -> Tensor
x = torch.randn(2, 3, 5)
x.size()
torch.Size()
torch.permute(x, (2, 0, 1)).size()
torch.Size()
</code></pre>
</li>
<li>
<p><code>reshape</code></p>
<p>改变tensor的形状，但是元素的数量和值不改变</p>
<pre><code class="language-python">torch.reshape(input, shape) → Tensor
a = torch.arange(4.)
torch.reshape(a, (2, 2))
tensor([[ 0.,1.],
[ 2.,3.]])
b = torch.tensor([, ])
torch.reshape(b, (-1,))
tensor([ 0,1,2,3])
</code></pre>
</li>
<li>
<p><code>transpose</code></p>
<p>将两个指定维度的位置进行替换</p>
<p><code>torch.permute(x, (0,2,1)) = torch.transpose(x, 1, 2)</code></p>
<pre><code class="language-python">torch.transpose(input, dim0, dim1) -> Tensor
x = torch.randn(2, 3)
tensor([[ 1.0028, -0.9893,0.5809],
[-0.1669,0.7299,0.4942]])
torch.transpose(x, 0, 1)
tensor([[ 1.0028, -0.1669],
[-0.9893,0.7299],
[ 0.5809,0.4942]])
</code></pre>
</li>
<li>
<p><code>view</code></p>
<p><code>tensor.view</code> 创建的张量 <code>tensor_view</code> 是原始张量 <code>tensor</code> 的一个视图（view），而不是一个新的张量。因此，<strong><code>tensor_view</code> 不会单独存储梯度信息</strong>。梯度信息会直接存储在原始张量 <code>tensor</code> 中。</p>
<p><em>Tensor.view而不是torch.view</em></p>
<pre><code class="language-python">Tensor.view(*shape) → Tensor
x = torch.randn(4, 4)
x.size()
torch.Size()
y = x.view(16)
y.size()
torch.Size()
z = x.view(-1, 8)# the size -1 is inferred from other dimensions
z.size()
torch.Size()
</code></pre>
<p>b_view 只是b的一个不同形状的视图，后续使用b_view导致的属性的修改还是保存在b中</p>
<pre><code class="language-python">a = torch.randn(1,6)
b = torch.randn(3,2,requires_grad=True)
b_view = b.view(6,1)
loss = a@b_view
loss.backward()
b_view.grad
空
b.grad
tensor([[-0.3020, -1.4392],
[ 0.7194,0.1363],
[-1.3413, -0.2453]])
</code></pre>
<p>此外，只有在内存中连续存储的tensor才可以使用view，否则使用reshape，reshape和view的性质一致</p>
<p>其中，tensor的转置会导致tensor是不连续的</p>
<pre><code class="language-python">tensor = torch.randn(2,3)
>>> # 转置张量，使其变为非连续
>>> tensor_transposed = tensor.transpose(0, 1)
>>> print("Transposed tensor:")
Transposed tensor:
>>> print(tensor_transposed)
tensor([[ 2.2194, -0.6988],
[ 0.5496,0.2167],
[-0.2635, -2.5029]])
>>> print("Is the transposed tensor contiguous?", tensor_transposed.is_contiguous())
Is the transposed tensor contiguous? False
</code></pre>
</li>
<li>
<p><code>squeeze</code></p>
<p>把大小是1的维度 remove掉</p>
<p>When <code>dim</code> is given, a squeeze operation is done only in the given dimension(s). If input is of shape: (A×1×B)(<em>A</em>×1×<em>B</em>), <code>squeeze(input, 0)</code> leaves the tensor unchanged, but <code>squeeze(input, 1)</code> will squeeze the tensor to the shape (A×B)(<em>A</em>×<em>B</em>).</p>
<pre><code class="language-python">torch.squeeze(input: Tensor, dim: Optional]]) → Tensor
x = torch.zeros(2, 1, 2, 1, 2)
x.size()
torch.Size()
y = torch.squeeze(x)
y.size()
torch.Size()
y = torch.squeeze(x, 0)
y.size()
torch.Size()
y = torch.squeeze(x, 1)
y.size()
torch.Size()
y = torch.squeeze(x, (1, 2, 3))
torch.Size()
</code></pre>
</li>
<li>
<p><code>unsqueeze</code></p>
<p>添加维度</p>
<pre><code class="language-python">x = torch.randn(4)
torch.unsqueeze(x, 0).size()
torch.Size(1,4)
torch.unsqueeze(x, 1).size()
torch.Size(4,1)
</code></pre>
</li>
<li>
<p><code>size</code></p>
<p><code>t.size() = t.shape</code>. <code>tuple(t.size())</code>返回一个维度的元组</p>
</li>
</ul>
<h4 id="索引">索引</h4>
<p>待更新。。。</p>
<h3 id="多个tensor之间">多个tensor之间</h3>
<ul>
<li>
<p><code>matmul</code></p>
<pre><code class="language-python">torch.matmul(input, other, *, out=None) → Tensor
# vector x vector
tensor1 = torch.randn(3)
tensor2 = torch.randn(3)
torch.matmul(tensor1, tensor2).size()
# matrix x vector
tensor1 = torch.randn(3, 4)
tensor2 = torch.randn(4)
torch.matmul(tensor1, tensor2).size()
# batched matrix x broadcasted vector
tensor1 = torch.randn(10, 3, 4)
tensor2 = torch.randn(4)
torch.matmul(tensor1, tensor2).size()
# batched matrix x batched matrix
tensor1 = torch.randn(10, 3, 4)
tensor2 = torch.randn(10, 4, 5)
torch.matmul(tensor1, tensor2).size()
# batched matrix x broadcasted matrix
tensor1 = torch.randn(10, 3, 4)
tensor2 = torch.randn(4, 5)
torch.matmul(tensor1, tensor2).size()
</code></pre>
<p><code>torch.mm</code> 仅能支持两个2D矩阵tensor的乘法</p>
</li>
<li>
<p><code>stack</code></p>
<p>堆叠，从而产生一个新的维度</p>
<pre><code class="language-python">torch.stack(tensors, dim=0, *, out=None) → Tensor
x = torch.randn(2,3)
c = torch.stack((x,x), dim=0)
# c.size() = torch.Size(2,2,3)
</code></pre>
</li>
<li>
<p><code>cat</code></p>
<p>在一个维度上进行拼接</p>
<pre><code class="language-python">torch.stack(tensors, dim=0, *, out=None) → Tensor
x = torch.randn(2,3)
c = torch.cat((x,x), dim=0)
# c.size() = torch.Size(4, 3)
c = torch.cat((x,x), dim=1)
# c.size() = torch.Size(2, 6)
</code></pre>
</li>
<li>
<p><code>split</code></p>
<p>根据指定维度，切分成指定大小的tuple(tensor)</p>
<pre><code class="language-python">torch.split(tensor, split_size_or_sections, dim=0)
a = torch.arange(10).reshape(5, 2)
tensor([,
,
,
,
])
torch.split(a, 2)
(tensor([,
]),
tensor([,
]),
tensor([]))
torch.split(a, )
(tensor([]),
tensor([,
,
,
]))
</code></pre>
</li>
</ul>
<p>参考：pytorch 官网API</p><br><br>
来源：https://www.cnblogs.com/qlhh/p/19142823
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