# Tensor

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.

## Tensor Usage

### Create Tensor

```
>>> import numpy as np
>>> from singa import tensor
>>> tensor.from_numpy( np.asarray([[1, 0, 0], [0, 1, 0]], dtype=np.float32) )
[[1. 0. 0.]
[0. 1. 0.]]
```

### Convert to numpy

```
>>> a = np.asarray([[1, 0, 0], [0, 1, 0]], dtype=np.float32)
>>> tensor.from_numpy(a)
[[1. 0. 0.]
[0. 1. 0.]]
>>> tensor.to_numpy(tensor.from_numpy(a))
array([[1., 0., 0.],
[0., 1., 0.]], dtype=float32)
```

### Tensor Methods

```
>>> t = tensor.from_numpy(a)
>>> t.transpose([1,0])
[[1. 0.]
[0. 1.]
[0. 0.]]
```

`tensor`

transformation up to 6 dims

```
>>> a = tensor.random((2,3,4,5,6,7))
>>> a.shape
(2, 3, 4, 5, 6, 7)
>>> a.reshape((2,3,4,5,7,6)).transpose((3,2,1,0,4,5)).shape
(5, 4, 3, 2, 7, 6)
```

### Tensor Arithmetic Methods

`tensor`

is evaluated in real time.

```
>>> t + 1
[[2. 1. 1.]
[1. 2. 1.]]
>>> t / 5
[[0.2 0. 0. ]
[0. 0.2 0. ]]
```

`tensor`

broadcasting arithmetic:

```
>>> a
[[1. 2. 3.]
[4. 5. 6.]]
>>> b
[[1. 2. 3.]]
>>> a + b
[[2. 4. 6.]
[5. 7. 9.]]
>>> a * b
[[ 1. 4. 9.]
[ 4. 10. 18.]]
>>> a / b
[[1. 1. 1. ]
[4. 2.5 2. ]]
>>> a/=b # inplace operation
>>> a
[[1. 1. 1. ]
[4. 2.5 2. ]]
```

`tensor`

broadcasting on matrix multiplication (GEMM)

```
>>> from singa import tensor
>>> a = tensor.random((2,2,2,3))
>>> b = tensor.random((2,3,4))
>>> tensor.mult(a,b).shape
(2, 2, 2, 4)
```

### Tensor Functions

Functions in module `singa.tensor`

return new `tensor`

object after applying the
transformation defined in the function.

```
>>> tensor.log(t+1)
[[0.6931472 0. 0. ]
[0. 0.6931472 0. ]]
```

### Tensor on Different Devices

`tensor`

is created on host (CPU) by default; it can also be created on
different hardware devices by specifying the `device`

. A `tensor`

could be moved
between `device`

s via `to_device()`

function.

```
>>> from singa import device
>>> x = tensor.Tensor((2, 3), device.create_cuda_gpu())
>>> x.gaussian(1,1)
>>> x
[[1.531889 1.0128608 0.12691343]
[2.1674204 3.083676 2.7421203 ]]
>>> # move to host
>>> x.to_device(device.get_default_device())
```

### use Tensor to train MLP

```
"""
code snipet from examples/mlp/module.py
"""
label = get_label()
data = get_data()
dev = device.create_cuda_gpu_on(0)
sgd = opt.SGD(0.05)
# define tensor for input data and label
tx = tensor.Tensor((400, 2), dev, tensor.float32)
ty = tensor.Tensor((400,), dev, tensor.int32)
model = MLP(data_size=2, perceptron_size=3, num_classes=2)
# attached model to graph
model.set_optimizer(sgd)
model.compile([tx], is_train=True, use_graph=True, sequential=False)
model.train()
for i in range(1001):
tx.copy_from_numpy(data)
ty.copy_from_numpy(label)
out, loss = model(tx, ty, 'fp32', spars=None)
if i % 100 == 0:
print("training loss = ", tensor.to_numpy(loss)[0])
```

Output:

```
$ 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
```

## Tensor Implementation

The previous section shows the general usage of `Tensor`

, 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.

### Python Tensor

Python class `Tensor`

, defined in `python/singa/tensor.py`

, provides high level
tensor manipulations for implementing deep learning operations (via
autograd), as well as data management by end users.

It primarily works by simply wrapping around C++ tensor methods, both arithmetic
(e.g. `sum`

) and non arithmetic methods (e.g. `reshape`

). Some advanced
arithmetic operations are later introduced and implemented using pure Python
tensor API, e.g. `tensordot`

. Python Tensor APIs could be used to implement
complex neural network operations easily with the flexible methods available.

### C++ Tensor

C++ class `Tensor`

, defined in `include/singa/core/tensor.h`

, primarily manages
the memory that holds the data, and provides low level APIs for tensor
manipulation. Also, it provides various arithmetic methods (e.g. `matmul`

) by
wrapping different backends (CUDA, BLAS, cuBLAS, etc.).

#### Execution Context and Memory Block

Two important concepts or data structures for `Tensor`

are the execution context
`device`

, and the memory block `Block`

.

Each `Tensor`

is physically stored on and managed by a hardware device,
representing the execution context (CPU, GPU). Tensor math calculations are
executed on the device.

Tensor data in a `Block`

instance, defined in `include/singa/core/common.h`

.
`Block`

owns the underlying data, while tensors take ownership on the metadata
describing the tensor, like `shape`

, `strides`

.

#### Tensor Math Backends

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.

- 'tensor_math_cpp.h' implements operations using Cpp (with CBLAS) for CppCPU devices.
- 'tensor_math_cuda.h' implements operations using Cuda (with cuBLAS) for CudaGPU devices.
- 'tensor_math_opencl.h' implements operations using OpenCL for OpenclGPU devices.

### Exposing C++ APIs to Python

SWIG(http://www.swig.org/) 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 `python/singa/singa_wrap.py`

. The Python
modules (e.g., `tensor`

, `device`

and `autograd`

) imports this module to call
the C++ APIs for implementing the Python classes and functions.

```
import tensor
t = tensor.Tensor(shape=(2, 3))
```

For example, when a Python `Tensor`

instance is created as above, the `Tensor`

class implementation creates an instance of the `Tensor`

class defined in
`singa_wrap.py`

, which corresponds to the C++ `Tensor`

class. For clarity, the
`Tensor`

class in `singa_wrap.py`

is referred as `CTensor`

in `tensor.py`

.

```
# in tensor.py
from . import singa_wrap as singa
CTensor = singa.Tensor
```

### Create New Tensor Functions

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:

- Declare the new API to
`tensor.h`

- Generate code using the predefined macro in
`tensor.cc`

, refer to`GenUnaryTensorFn(Abs);`

as an example. - Declare the template method/function in
`tensor_math.h`

- Do the real implementation at least for CPU (
`tensor_math_cpp.h`

) and GPU(`tensor_math_cuda.h`

) - Expose the API via SWIG by adding it into
`src/api/core_tensor.i`

- Define the Python Tensor API in
`tensor.py`

by calling the automatically generated function in`singa_wrap.py`

- Write unit tests where appropriate

## Python API

*work in progress*

## CPP API

*work in progress*