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<p>Each Tensor instance is a multi-dimensional array allocated on a specific Device
instance. Tensor instances store variables and provide linear algebra operations
over different types of hardware devices without user awareness. Note that users
need to make sure the tensor operands are allocated on the same device except
copy functions.</p>
<h2><a class="anchor" aria-hidden="true" id="tensor-usage"></a><a href="#tensor-usage" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Usage</h2>
<h3><a class="anchor" aria-hidden="true" id="create-tensor"></a><a href="#create-tensor" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Create Tensor</h3>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span><span class="hljs-keyword">import</span> numpy <span class="hljs-keyword">as</span> np
<span class="hljs-meta">&gt;&gt;&gt; </span><span class="hljs-keyword">from</span> singa <span class="hljs-keyword">import</span> tensor
<span class="hljs-meta">&gt;&gt;&gt; </span>tensor.from_numpy( np.asarray([[<span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>], [<span class="hljs-number">0</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>]], dtype=np.float32) )
[[<span class="hljs-number">1.</span> <span class="hljs-number">0.</span> <span class="hljs-number">0.</span>]
 [<span class="hljs-number">0.</span> <span class="hljs-number">1.</span> <span class="hljs-number">0.</span>]]
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="convert-to-numpy"></a><a href="#convert-to-numpy" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Convert to numpy</h3>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>a = np.asarray([[<span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>], [<span class="hljs-number">0</span>, <span class="hljs-number">1</span>, <span class="hljs-number">0</span>]], dtype=np.float32)
<span class="hljs-meta">&gt;&gt;&gt; </span>tensor.from_numpy(a)
[[<span class="hljs-number">1.</span> <span class="hljs-number">0.</span> <span class="hljs-number">0.</span>]
 [<span class="hljs-number">0.</span> <span class="hljs-number">1.</span> <span class="hljs-number">0.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>tensor.to_numpy(tensor.from_numpy(a))
array([[<span class="hljs-number">1.</span>, <span class="hljs-number">0.</span>, <span class="hljs-number">0.</span>],
       [<span class="hljs-number">0.</span>, <span class="hljs-number">1.</span>, <span class="hljs-number">0.</span>]], dtype=float32)
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="tensor-methods"></a><a href="#tensor-methods" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Methods</h3>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>t = tensor.from_numpy(a)
<span class="hljs-meta">&gt;&gt;&gt; </span>t.transpose([<span class="hljs-number">1</span>,<span class="hljs-number">0</span>])
[[<span class="hljs-number">1.</span> <span class="hljs-number">0.</span>]
 [<span class="hljs-number">0.</span> <span class="hljs-number">1.</span>]
 [<span class="hljs-number">0.</span> <span class="hljs-number">0.</span>]]
</code></pre>
<p><code>tensor</code> transformation up to 6 dims</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>a = tensor.random((<span class="hljs-number">2</span>,<span class="hljs-number">3</span>,<span class="hljs-number">4</span>,<span class="hljs-number">5</span>,<span class="hljs-number">6</span>,<span class="hljs-number">7</span>))
<span class="hljs-meta">&gt;&gt;&gt; </span>a.shape
(<span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>)
<span class="hljs-meta">&gt;&gt;&gt; </span>a.reshape((<span class="hljs-number">2</span>,<span class="hljs-number">3</span>,<span class="hljs-number">4</span>,<span class="hljs-number">5</span>,<span class="hljs-number">7</span>,<span class="hljs-number">6</span>)).transpose((<span class="hljs-number">3</span>,<span class="hljs-number">2</span>,<span class="hljs-number">1</span>,<span class="hljs-number">0</span>,<span class="hljs-number">4</span>,<span class="hljs-number">5</span>)).shape
(<span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">2</span>, <span class="hljs-number">7</span>, <span class="hljs-number">6</span>)
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="tensor-arithmetic-methods"></a><a href="#tensor-arithmetic-methods" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Arithmetic Methods</h3>
<p><code>tensor</code> is evaluated in real time.</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>t + <span class="hljs-number">1</span>
[[<span class="hljs-number">2.</span> <span class="hljs-number">1.</span> <span class="hljs-number">1.</span>]
 [<span class="hljs-number">1.</span> <span class="hljs-number">2.</span> <span class="hljs-number">1.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>t / <span class="hljs-number">5</span>
[[<span class="hljs-number">0.2</span> <span class="hljs-number">0.</span>  <span class="hljs-number">0.</span> ]
 [<span class="hljs-number">0.</span>  <span class="hljs-number">0.2</span> <span class="hljs-number">0.</span> ]]
</code></pre>
<p><code>tensor</code> broadcasting arithmetic:</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>a
[[<span class="hljs-number">1.</span> <span class="hljs-number">2.</span> <span class="hljs-number">3.</span>]
 [<span class="hljs-number">4.</span> <span class="hljs-number">5.</span> <span class="hljs-number">6.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>b
[[<span class="hljs-number">1.</span> <span class="hljs-number">2.</span> <span class="hljs-number">3.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>a + b
[[<span class="hljs-number">2.</span> <span class="hljs-number">4.</span> <span class="hljs-number">6.</span>]
 [<span class="hljs-number">5.</span> <span class="hljs-number">7.</span> <span class="hljs-number">9.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>a * b
[[ <span class="hljs-number">1.</span>  <span class="hljs-number">4.</span>  <span class="hljs-number">9.</span>]
 [ <span class="hljs-number">4.</span> <span class="hljs-number">10.</span> <span class="hljs-number">18.</span>]]
<span class="hljs-meta">&gt;&gt;&gt; </span>a / b
[[<span class="hljs-number">1.</span>  <span class="hljs-number">1.</span>  <span class="hljs-number">1.</span> ]
 [<span class="hljs-number">4.</span>  <span class="hljs-number">2.5</span> <span class="hljs-number">2.</span> ]]
<span class="hljs-meta">&gt;&gt;&gt; </span>a/=b <span class="hljs-comment"># inplace operation</span>
<span class="hljs-meta">&gt;&gt;&gt; </span>a
[[<span class="hljs-number">1.</span>  <span class="hljs-number">1.</span>  <span class="hljs-number">1.</span> ]
 [<span class="hljs-number">4.</span>  <span class="hljs-number">2.5</span> <span class="hljs-number">2.</span> ]]
</code></pre>
<p><code>tensor</code> broadcasting on matrix multiplication (GEMM)</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span><span class="hljs-keyword">from</span> singa <span class="hljs-keyword">import</span> tensor
<span class="hljs-meta">&gt;&gt;&gt; </span>a = tensor.random((<span class="hljs-number">2</span>,<span class="hljs-number">2</span>,<span class="hljs-number">2</span>,<span class="hljs-number">3</span>))
<span class="hljs-meta">&gt;&gt;&gt; </span>b = tensor.random((<span class="hljs-number">2</span>,<span class="hljs-number">3</span>,<span class="hljs-number">4</span>))
<span class="hljs-meta">&gt;&gt;&gt; </span>tensor.mult(a,b).shape
(<span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">4</span>)
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="tensor-functions"></a><a href="#tensor-functions" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Functions</h3>
<p>Functions in module <code>singa.tensor</code> return new <code>tensor</code> object after applying the
transformation defined in the function.</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span>tensor.log(t+<span class="hljs-number">1</span>)
[[<span class="hljs-number">0.6931472</span> <span class="hljs-number">0.</span>        <span class="hljs-number">0.</span>       ]
 [<span class="hljs-number">0.</span>        <span class="hljs-number">0.6931472</span> <span class="hljs-number">0.</span>       ]]
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="tensor-on-different-devices"></a><a href="#tensor-on-different-devices" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor on Different Devices</h3>
<p><code>tensor</code> is created on host (CPU) by default; it can also be created on
different hardware devices by specifying the <code>device</code>. A <code>tensor</code> could be moved
between <code>device</code>s via <code>to_device()</code> function.</p>
<pre><code class="hljs css language-python"><span class="hljs-meta">&gt;&gt;&gt; </span><span class="hljs-keyword">from</span> singa <span class="hljs-keyword">import</span> device
<span class="hljs-meta">&gt;&gt;&gt; </span>x = tensor.Tensor((<span class="hljs-number">2</span>, <span class="hljs-number">3</span>), device.create_cuda_gpu())
<span class="hljs-meta">&gt;&gt;&gt; </span>x.gaussian(<span class="hljs-number">1</span>,<span class="hljs-number">1</span>)
<span class="hljs-meta">&gt;&gt;&gt; </span>x
[[<span class="hljs-number">1.531889</span>   <span class="hljs-number">1.0128608</span>  <span class="hljs-number">0.12691343</span>]
 [<span class="hljs-number">2.1674204</span>  <span class="hljs-number">3.083676</span>   <span class="hljs-number">2.7421203</span> ]]
<span class="hljs-meta">&gt;&gt;&gt; </span><span class="hljs-comment"># move to host</span>
<span class="hljs-meta">&gt;&gt;&gt; </span>x.to_device(device.get_default_device())
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="use-tensor-to-train-mlp"></a><a href="#use-tensor-to-train-mlp" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>use Tensor to train MLP</h3>
<pre><code class="hljs css language-python">
<span class="hljs-string">"""
  code snipet from examples/mlp/module.py
"""</span>

label = get_label()
data = get_data()

dev = device.create_cuda_gpu_on(<span class="hljs-number">0</span>)
sgd = opt.SGD(<span class="hljs-number">0.05</span>)

<span class="hljs-comment"># define tensor for input data and label</span>
tx = tensor.Tensor((<span class="hljs-number">400</span>, <span class="hljs-number">2</span>), dev, tensor.float32)
ty = tensor.Tensor((<span class="hljs-number">400</span>,), dev, tensor.int32)
model = MLP(data_size=<span class="hljs-number">2</span>, perceptron_size=<span class="hljs-number">3</span>, num_classes=<span class="hljs-number">2</span>)

<span class="hljs-comment"># attached model to graph</span>
model.set_optimizer(sgd)
model.compile([tx], is_train=<span class="hljs-literal">True</span>, use_graph=<span class="hljs-literal">True</span>, sequential=<span class="hljs-literal">False</span>)
model.train()

<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">1001</span>):
    tx.copy_from_numpy(data)
    ty.copy_from_numpy(label)
    out, loss = model(tx, ty, <span class="hljs-string">'fp32'</span>, spars=<span class="hljs-literal">None</span>)

    <span class="hljs-keyword">if</span> i % <span class="hljs-number">100</span> == <span class="hljs-number">0</span>:
        print(<span class="hljs-string">"training loss = "</span>, tensor.to_numpy(loss)[<span class="hljs-number">0</span>])
</code></pre>
<p>Output:</p>
<pre><code class="hljs css language-bash">$ python3 examples/mlp/module.py
training loss =  0.6158037
training loss =  0.52852553
training loss =  0.4571422
training loss =  0.37274635
training loss =  0.30146334
training loss =  0.24906921
training loss =  0.21128304
training loss =  0.18390492
training loss =  0.16362564
training loss =  0.148164
training loss =  0.13589878
</code></pre>
<h2><a class="anchor" aria-hidden="true" id="tensor-implementation"></a><a href="#tensor-implementation" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Implementation</h2>
<p>The previous section shows the general usage of <code>Tensor</code>, the implementation
under the hood will be covered below. First, the design of Python and C++
tensors will be introduced. Later part will talk about how the frontend (Python)
and backend (C++) are connected and how to extend them.</p>
<h3><a class="anchor" aria-hidden="true" id="python-tensor"></a><a href="#python-tensor" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Python Tensor</h3>
<p>Python class <code>Tensor</code>, defined in <code>python/singa/tensor.py</code>, provides high level
tensor manipulations for implementing deep learning operations (via
<a href="./autograd">autograd</a>), as well as data management by end users.</p>
<p>It primarily works by simply wrapping around C++ tensor methods, both arithmetic
(e.g. <code>sum</code>) and non arithmetic methods (e.g. <code>reshape</code>). Some advanced
arithmetic operations are later introduced and implemented using pure Python
tensor API, e.g. <code>tensordot</code>. Python Tensor APIs could be used to implement
complex neural network operations easily with the flexible methods available.</p>
<h3><a class="anchor" aria-hidden="true" id="c-tensor"></a><a href="#c-tensor" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>C++ Tensor</h3>
<p>C++ class <code>Tensor</code>, defined in <code>include/singa/core/tensor.h</code>, primarily manages
the memory that holds the data, and provides low level APIs for tensor
manipulation. Also, it provides various arithmetic methods (e.g. <code>matmul</code>) by
wrapping different backends (CUDA, BLAS, cuBLAS, etc.).</p>
<h4><a class="anchor" aria-hidden="true" id="execution-context-and-memory-block"></a><a href="#execution-context-and-memory-block" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Execution Context and Memory Block</h4>
<p>Two important concepts or data structures for <code>Tensor</code> are the execution context
<code>device</code>, and the memory block <code>Block</code>.</p>
<p>Each <code>Tensor</code> is physically stored on and managed by a hardware device,
representing the execution context (CPU, GPU). Tensor math calculations are
executed on the device.</p>
<p>Tensor data in a <code>Block</code> instance, defined in <code>include/singa/core/common.h</code>.
<code>Block</code> owns the underlying data, while tensors take ownership on the metadata
describing the tensor, like <code>shape</code>, <code>strides</code>.</p>
<h4><a class="anchor" aria-hidden="true" id="tensor-math-backends"></a><a href="#tensor-math-backends" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Tensor Math Backends</h4>
<p>To leverage on the efficient math libraries provided by different backend
hardware devices, SINGA has one set of implementations of Tensor functions for
each supported backend.</p>
<ul>
<li>'tensor_math_cpp.h' implements operations using Cpp (with CBLAS) for CppCPU
devices.</li>
<li>'tensor_math_cuda.h' implements operations using Cuda (with cuBLAS) for
CudaGPU devices.</li>
<li>'tensor_math_opencl.h' implements operations using OpenCL for OpenclGPU
devices.</li>
</ul>
<h3><a class="anchor" aria-hidden="true" id="exposing-c-apis-to-python"></a><a href="#exposing-c-apis-to-python" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Exposing C++ APIs to Python</h3>
<p>SWIG(<a href="http://www.swig.org/">http://www.swig.org/</a>) is a tool that can automatically convert C++ APIs
into Python APIs. SINGA uses SWIG to expose the C++ APIs to Python. Several
files are generated by SWIG, including <code>python/singa/singa_wrap.py</code>. The Python
modules (e.g., <code>tensor</code>, <code>device</code> and <code>autograd</code>) imports this module to call
the C++ APIs for implementing the Python classes and functions.</p>
<pre><code class="hljs css language-python"><span class="hljs-keyword">import</span> tensor

t = tensor.Tensor(shape=(<span class="hljs-number">2</span>, <span class="hljs-number">3</span>))
</code></pre>
<p>For example, when a Python <code>Tensor</code> instance is created as above, the <code>Tensor</code>
class implementation creates an instance of the <code>Tensor</code> class defined in
<code>singa_wrap.py</code>, which corresponds to the C++ <code>Tensor</code> class. For clarity, the
<code>Tensor</code> class in <code>singa_wrap.py</code> is referred as <code>CTensor</code> in <code>tensor.py</code>.</p>
<pre><code class="hljs css language-python"><span class="hljs-comment"># in tensor.py</span>
<span class="hljs-keyword">from</span> . <span class="hljs-keyword">import</span> singa_wrap <span class="hljs-keyword">as</span> singa

CTensor = singa.Tensor
</code></pre>
<h3><a class="anchor" aria-hidden="true" id="create-new-tensor-functions"></a><a href="#create-new-tensor-functions" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Create New Tensor Functions</h3>
<p>With the groundwork set by the previous description, extending tensor functions
could be done easily in a bottom up manner. For math operations, the steps are:</p>
<ul>
<li>Declare the new API to <code>tensor.h</code></li>
<li>Generate code using the predefined macro in <code>tensor.cc</code>, refer to
<code>GenUnaryTensorFn(Abs);</code> as an example.</li>
<li>Declare the template method/function in <code>tensor_math.h</code></li>
<li>Do the real implementation at least for CPU (<code>tensor_math_cpp.h</code>) and
GPU(<code>tensor_math_cuda.h</code>)</li>
<li>Expose the API via SWIG by adding it into <code>src/api/core_tensor.i</code></li>
<li>Define the Python Tensor API in <code>tensor.py</code> by calling the automatically
generated function in <code>singa_wrap.py</code></li>
<li>Write unit tests where appropriate</li>
</ul>
<h2><a class="anchor" aria-hidden="true" id="python-api"></a><a href="#python-api" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Python API</h2>
<p><em>work in progress</em></p>
<h2><a class="anchor" aria-hidden="true" id="cpp-api"></a><a href="#cpp-api" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>CPP API</h2>
<p><em>work in progress</em></p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated on 18/09/2020</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/next/device"><span class="arrow-prev">← </span><span>Device</span></a><a class="docs-next button" href="/docs/next/autograd"><span>Autograd</span><span class="arrow-next"> →</span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#tensor-usage">Tensor Usage</a><ul class="toc-headings"><li><a href="#create-tensor">Create Tensor</a></li><li><a href="#convert-to-numpy">Convert to numpy</a></li><li><a href="#tensor-methods">Tensor Methods</a></li><li><a href="#tensor-arithmetic-methods">Tensor Arithmetic Methods</a></li><li><a href="#tensor-functions">Tensor Functions</a></li><li><a href="#tensor-on-different-devices">Tensor on Different Devices</a></li><li><a href="#use-tensor-to-train-mlp">use Tensor to train MLP</a></li></ul></li><li><a href="#tensor-implementation">Tensor Implementation</a><ul class="toc-headings"><li><a href="#python-tensor">Python Tensor</a></li><li><a href="#c-tensor">C++ Tensor</a></li><li><a href="#exposing-c-apis-to-python">Exposing C++ APIs to Python</a></li><li><a href="#create-new-tensor-functions">Create New Tensor Functions</a></li></ul></li><li><a href="#python-api">Python API</a></li><li><a href="#cpp-api">CPP API</a></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><a href="/" class="nav-home"><img src="/img/singa-logo-square.png" alt="Apache SINGA" width="66" height="58"/></a><div><h5>Docs</h5><a href="/docs/installation">Getting Started</a><a href="/docs/device">Guides</a><a href="/en/https://apache-singa.readthedocs.io/en/latest/">API Reference</a><a href="/docs/examples">Examples</a><a href="/docs/download-singa">Development</a></div><div><h5>Community</h5><a href="/en/users.html">User Showcase</a><a href="/docs/history-singa">SINGA History</a><a href="/docs/team-list">SINGA Team</a><a href="/blog">SINGA News</a><a href="https://github.com/apache/singa">GitHub</a><div class="social"><a class="github-button" href="https://github.com/apache/singa" data-count-href="/apache/singa/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star this project on GitHub">apache/singa-doc</a></div><div class="social"><a href="https://twitter.com/ApacheSINGA" class="twitter-follow-button">Follow @ApacheSINGA</a></div></div><div><h5>Apache Software Foundation</h5><a href="https://apache.org/" target="_blank" rel="noreferrer noopener">Foundation</a><a href="http://www.apache.org/licenses/" target="_blank" rel="noreferrer noopener">License</a><a href="http://www.apache.org/foundation/sponsorship.html" target="_blank" rel="noreferrer noopener">Sponsorship</a><a href="http://www.apache.org/foundation/thanks.html" target="_blank" rel="noreferrer noopener">Thanks</a><a href="http://www.apache.org/events/current-event" target="_blank" rel="noreferrer noopener">Events</a><a href="http://www.apache.org/security/" target="_blank" rel="noreferrer noopener">Security</a></div></section><div style="width:100%;text-align:center"><a href="https://apache.org/" target="_blank" rel="noreferrer noopener" class="ApacheOpenSource"><img src="/img/asf_logo_wide.svg" alt="Apache Open Source"/></a><section class="copyright" style="max-width:60%;margin:0 auto">Copyright © 2021
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