# Keras-Like API 

## 1. Introduction
[DLlib](dllib.md) provides __Keras-like API__ based on [__Keras 1.2.2__](https://faroit.github.io/keras-docs/1.2.2/) for distributed deep learning on Apache Spark. Users can easily use the Keras-like API to create a neural network model, and train, evaluate or tune it in a distributed fashion on Spark.

To define a model in Scala using the Keras-like API, one just needs to import the following packages:

```scala
import com.intel.analytics.bigdl.dllib.keras.layers._
import com.intel.analytics.bigdl.dllib.keras.models._
import com.intel.analytics.bigdl.dllib.utils.Shape
```

One of the highlighted features with regard to the new API is __shape inference__. Users only need to specify the input shape (a `Shape` object __excluding__ batch dimension, for example, `inputShape=Shape(3, 4)` for 3D input) for the first layer of a model and for the remaining layers, the input dimension will be automatically inferred.

---
## 2. LeNet Example
Here we use the Keras-like API to define a LeNet CNN model and train it on the MNIST dataset:

```scala
import com.intel.analytics.bigdl.numeric.NumericFloat
import com.intel.analytics.bigdl.dllib.keras.layers._
import com.intel.analytics.bigdl.dllib.keras.models._
import com.intel.analytics.bigdl.dllib.utils.Shape

val model = Sequential()
model.add(Reshape(Array(1, 28, 28), inputShape = Shape(28, 28, 1)))
model.add(Convolution2D(6, 5, 5, activation = "tanh").setName("conv1_5x5"))
model.add(MaxPooling2D())
model.add(Convolution2D(12, 5, 5, activation = "tanh").setName("conv2_5x5"))
model.add(MaxPooling2D())
model.add(Flatten())
model.add(Dense(100, activation = "tanh").setName("fc1"))
model.add(Dense(10, activation = "softmax").setName("fc2"))

model.getInputShape().toSingle().toArray // Array(-1, 28, 28, 1)
model.getOutputShape().toSingle().toArray // Array(-1, 10)
```
---
## 3. Shape
Input and output shapes of a model in the Keras-like API are described by the `Shape` object in Scala, which can be classified into `SingleShape` and `MultiShape`.

`SingleShape` is just a list of Int indicating shape dimensions while `MultiShape` is essentially a list of `Shape`.

Example code to create a shape:
```scala
// create a SingleShape
val shape1 = Shape(3, 4)
// create a MultiShape consisting of two SingleShape
val shape2 = Shape(List(Shape(1, 2, 3), Shape(4, 5, 6)))
```
You can use method `toSingle()` to cast a `Shape` to a `SingleShape`. Similarly, use `toMulti()` to cast a `Shape` to a `MultiShape`.

---
## 4. Define a model
You can define a model either using [Sequential API](#sequential-api) or [Functional API](#functional-api). Remember to specify the input shape for the first layer.

After creating a model, you can call the following __methods__:

```scala
getInputShape()
```
```scala
getOutputShape()
```
* Return the input or output shape of a model, which is a [`Shape`](#2-shape) object. For `SingleShape`, the first entry is `-1` representing the batch dimension. For a model with multiple inputs or outputs, it will return a `MultiShape`.

```scala
setName(name)
```
* Set the name of the model.

---
## 5. Sequential API
The model is described as a linear stack of layers in the Sequential API. Layers can be added into the `Sequential` container one by one and the order of the layers in the model will be the same as the insertion order.

To create a sequential container:
```scala
Sequential()
```

Example code to create a sequential model:
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.{Dense, Activation}
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape

val model = Sequential[Float]()
model.add(Dense[Float](32, inputShape = Shape(128)))
model.add(Activation[Float]("relu"))
```

---
## 6. Functional API
The model is described as a graph in the Functional API. It is more convenient than the Sequential API when defining some complex model (for example, a model with multiple outputs).

To create an input node:
```scala
Input(inputShape = null, name = null)
```
Parameters:

* `inputShape`: A [`Shape`](#shape) object indicating the shape of the input node, not including batch.
* `name`: String to set the name of the input node. If not specified, its name will by default to be a generated string.

To create a graph container:
```scala
Model(input, output)
```
Parameters:

* `input`: An input node or an array of input nodes.
* `output`: An output node or an array of output nodes.

To merge a list of input __nodes__ (__NOT__ layers), following some merge mode in the Functional API:
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Merge.merge

merge(inputs, mode = "sum", concatAxis = -1) // This will return an output NODE.
```

Parameters:

* `inputs`: A list of node instances. Must be more than one node.
* `mode`: Merge mode. String, must be one of: 'sum', 'mul', 'concat', 'ave', 'cos', 'dot', 'max'. Default is 'sum'.
* `concatAxis`: Int, axis to use when concatenating nodes. Only specify this when merge mode is 'concat'. Default is -1, meaning the last axis of the input.

Example code to create a graph model:
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.{Dense, Input}
import com.intel.analytics.bigdl.dllib.keras.layers.Merge.merge
import com.intel.analytics.bigdl.dllib.keras.models.Model
import com.intel.analytics.bigdl.dllib.utils.Shape

// instantiate input nodes
val input1 = Input[Float](inputShape = Shape(8))
val input2 = Input[Float](inputShape = Shape(6))
// call inputs() with an input node and get an output node
val dense1 = Dense[Float](10).inputs(input1)
val dense2 = Dense[Float](10).inputs(input2)
// merge two nodes following some merge mode
val output = merge(inputs = List(dense1, dense2), mode = "sum")
// create a graph container
val model = Model[Float](Array(input1, input2), output)
```

---
## 7. Core Layers
This section describes all the available layers in the Keras-like API. 

To set the name of a specific layer, you call the method `setName(name)` of that layer.

### 7.1 Masking
Use a mask value to skip timesteps for a sequence.

**Scala:**
```scala
Masking(maskValue = 0.0, inputShape = null)
```
**Python:**
```python
Masking(mask_value=0.0, input_shape=None, name=None)
```

**Parameters:**

* `maskValue`: Mask value. For each timestep in the input (the second dimension), if all the values in the input at that timestep are equal to 'maskValue', then the timestep will be masked (skipped) in all downstream layers.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Masking
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Masking[Float](inputShape = Shape(3)))
val input = Tensor[Float](2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
1.4539868       1.5623108       -1.4101523
0.77073747      -0.18994702     2.2574463
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
1.4539868       1.5623108       -1.4101523
0.77073747      -0.18994702     2.2574463
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```

**Python example:**
```python
import numpy as np
from bigdl.nn.keras.topology import Sequential
from bigdl.nn.keras.layer import Masking

model = Sequential()
model.add(Masking(input_shape=(3, )))
input = np.random.random([2, 3])
output = model.forward(input)
```
Input is:
```python
[[0.31542103 0.20640659 0.22282763]
 [0.99352167 0.90135718 0.24504717]]
```
Output is
```python
[[0.31542102 0.2064066  0.22282763]
 [0.9935217  0.9013572  0.24504717]]
```

---
### 7.2 SparseDense
SparseDense is the sparse version of layer Dense. SparseDense has two different from Dense:
firstly, SparseDense's input Tensor is a SparseTensor. Secondly, SparseDense doesn't backward
gradient to next layer in the backpropagation by default, as the gradInput of SparseDense is
useless and very big in most cases.

But, considering model like Wide&Deep, we provide backwardStart and backwardLength to backward
part of the gradient to next layer.

The most common input is 2D.

**Scala:**
```scala
SparseDense(outputDim, init = "glorot_uniform", activation = null, wRegularizer = null, bRegularizer = null, backwardStart = -1, backwardLength = -1, initWeight = null, initBias = null, initGradWeight = null, initGradBias = null, bias = true, inputShape = null)
```
**Python:**
```python
SparseDense(output_dim, init="glorot_uniform", activation=None, W_regularizer=None, b_regularizer=None, backward_start=-1, backward_length=-1, init_weight=None, init_bias=None, init_grad_weight=None, init_grad_bias=None, bias=True, input_shape=None, name=None)
```

**Parameters:**

* `outputDim`: The size of the output dimension.
* `init`: String representation of the initialization method for the weights of the layer. Default is 'glorot_uniform'.
* `activation`: String representation of the activation function to use. Default is null.
* `wRegularizer`: An instance of [Regularizer], applied to the input weights matrices. Default is null.
* `bRegularizer`: An instance of [Regularizer], applied to the bias. Default is null.
* `bias`: Whether to include a bias (i.e. make the layer affine rather than linear). Default is true.
* `backwardStart`: Backward start index, counting from 1.
* `backwardLength`: Backward length.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a `Shape` object. For Python API, it should be a shape tuple. Batch dimension should be excluded.
* `name`: String to set the name of the layer. If not specified, its name will by default to be a generated string.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.SparseDense
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val layer = SparseDense[Float](outputDim = 5, inputShape = Shape(2, 4))
layer.build(Shape(-1, 2, 4))
val input = Tensor[Float](Array(2, 4)).rand()
input.setValue(1, 1, 1f)
input.setValue(2, 3, 3f)
val sparseInput = Tensor.sparse(input)
val output = layer.forward(sparseInput)
```
Input is:
```scala
input: 
(0, 0) : 1.0
(0, 1) : 0.2992794
(0, 2) : 0.11227019
(0, 3) : 0.722947
(1, 0) : 0.6147614
(1, 1) : 0.4288646
(1, 2) : 3.0
(1, 3) : 0.7749917
[com.intel.analytics.bigdl.tensor.SparseTensor of size 2x4]
```
Output is:
```scala
output: 
0.053516	0.33429605	0.22587383	-0.8998945	0.24308181	
0.76745665	-1.614114	0.5381658	-2.2226436	-0.15573677	
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x5]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential
from bigdl.dllib.utils.common import JTensor

model = Sequential()
model.add(SparseDense(output_dim=2, input_shape=(3, 4)))
input = JTensor.sparse(
    a_ndarray=np.array([1, 3, 2, 4]),
    i_ndarray = np.array([[0, 0, 1, 2],
             [0, 3, 2, 1]]),
    shape = np.array([3, 4])
)
output = model.forward(input)
```
Input is:
```python
JTensor: storage: [1. 3. 2. 4.], shape: [3 4] ,indices [[0 0 1 2]
 [0 3 2 1]], float
```
Output is
```python
[[ 1.57136     2.29596   ]
 [ 0.5791738  -1.6598101 ]
 [ 2.331141   -0.84687066]]
 ```

### 7.3 SoftShrink
Applies the soft shrinkage function element-wise to the input.

When you use this layer as the first layer of a model, you need to provide
the argument inputShape (a Single Shape, does not include the batch dimension).

Remark: This layer is from Torch and wrapped in Keras style.


**Scala:**
```scala
SoftShrink(value = 0.5, inputShape = null)
```
**Python:**
```python
SoftShrink(value = 0.5, input_shape=None, name=None)
```

**Parameters:**

* `value`: value The threshold value. Default is 0.5.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a `Shape` object. For Python API, it should be a shape tuple. Batch dimension should be excluded.
* `name`: String to set the name of the layer. If not specified, its name will by default to be a generated string.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.SoftShrink
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(SoftShrink[Float](0.6, inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-0.36938807	0.023556225	-1.1655436	-0.34449077
0.9444338	-0.086538695	-1.0425501	1.364976
-1.2563878	-0.1842559	0.43428117	1.0756494

(1,2,.,.) =
-0.19888283	1.251872	0.114836805	-0.6208773
0.0051822234	-0.8998633	0.06937465	-0.3929931
-0.1058129	0.6945743	-0.40083578	-0.6252444

(2,1,.,.) =
-0.9899709	-0.77926594	-0.15497442	-0.15031165
-0.6028622	0.86623466	-2.1543107	0.41970536
-0.8215522	0.3014275	-0.32184362	0.14445356

(2,2,.,.) =
0.74701905	0.10044397	-0.40519297	0.03822808
0.30726334	0.27862388	1.731753	0.032177072
-1.3476961	-0.2294767	0.99794704	0.7398458

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.0	0.0	-0.56554353	0.0
0.34443378	0.0	-0.44255006	0.764976
-0.6563878	0.0	0.0	0.47564936

(1,2,.,.) =
0.0	0.6518719	0.0	-0.020877302
0.0	-0.29986328	0.0	0.0
0.0	0.09457427	0.0	-0.025244355

(2,1,.,.) =
-0.3899709	-0.17926592	0.0	0.0
-0.0028621554	0.26623464	-1.5543107	0.0
-0.2215522	0.0	0.0	0.0

(2,2,.,.) =
0.14701903	0.0	0.0	0.0
0.0	0.0	1.131753	0.0
-0.74769604	0.0	0.397947	0.13984579

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(SoftShrink(0.6, input_shape=(2, 3, 4)))
input = np.random.random([2, 2, 3, 4])
output = model.forward(input)
```
Input is:
```python
array([[[[ 0.43421006,  0.28394451,  0.15221226,  0.47268966],
         [ 0.22426224,  0.24855662,  0.790498  ,  0.67767582],
         [ 0.14879562,  0.56077882,  0.61470262,  0.94875862]],

        [[ 0.72404932,  0.89780875,  0.08456734,  0.01303937],
         [ 0.25023568,  0.45392504,  0.587254  ,  0.51164461],
         [ 0.12277567,  0.05571182,  0.17076456,  0.71660884]]],


       [[[ 0.06369975,  0.85395557,  0.35752425,  0.606633  ],
         [ 0.67640252,  0.86861737,  0.18040722,  0.55467108],
         [ 0.24102058,  0.37580645,  0.81601612,  0.56513788]],

        [[ 0.8461435 ,  0.65668365,  0.17969807,  0.51602926],
         [ 0.86191073,  0.34245714,  0.62795207,  0.36706125],
         [ 0.80344028,  0.81056003,  0.80959083,  0.15366483]]]])
```
Output is
```python
array([[[[ 0.        ,  0.        ,  0.        ,  0.        ],
         [ 0.        ,  0.        ,  0.19049799,  0.07767582],
         [ 0.        ,  0.        ,  0.01470262,  0.34875858]],

        [[ 0.12404931,  0.29780871,  0.        ,  0.        ],
         [ 0.        ,  0.        ,  0.        ,  0.        ],
         [ 0.        ,  0.        ,  0.        ,  0.1166088 ]]],


       [[[ 0.        ,  0.25395554,  0.        ,  0.00663298],
         [ 0.07640249,  0.26861733,  0.        ,  0.        ],
         [ 0.        ,  0.        ,  0.21601611,  0.        ]],

        [[ 0.24614346,  0.05668366,  0.        ,  0.        ],
         [ 0.26191074,  0.        ,  0.02795208,  0.        ],
         [ 0.20344025,  0.21056002,  0.20959079,  0.        ]]]], dtype=float32)

 ```

---
### 7.4 Reshape
Reshapes an output to a certain shape.

Supports shape inference by allowing one -1 in the target shape. For example, if input shape is (2, 3, 4), target shape is (3, -1), then output shape will be (3, 8).

**Scala:**
```scala
Reshape(targetShape, inputShape = null)
```
**Python:**
```python
Reshape(target_shape, input_shape=None, name=None)
```

**Parameters:**

* `targetShape`: The target shape that you desire to have. Batch dimension should be excluded.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Reshape
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Reshape(Array(3, 8), inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-1.7092276	-1.3941092	-0.6348466	0.71309644
0.3605411	0.025597548	0.4287048	-0.548675
0.4623341	-2.3912702	0.22030865	-0.058272455

(1,2,.,.) =
-1.5049093	-1.8828062	0.8230564	-0.020209199
-0.3415721	1.1219939	1.1089007	-0.74697906
-1.503861	-1.616539	0.048006497	1.1613717

(2,1,.,.) =
0.21216023	1.0107462	0.8586909	-0.05644316
-0.31436008	1.6892323	-0.9961186	-0.08169463
0.3559391	0.010261055	-0.70408463	-1.2480727

(2,2,.,.) =
1.7663039	0.07122444	0.073556066	-0.7847014
0.17604464	-0.99110585	-1.0302067	-0.39024687
-0.0260166	-0.43142694	0.28443158	0.72679126

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-1.7092276	-1.3941092	-0.6348466	0.71309644	    0.3605411	0.025597548	0.4287048	-0.548675
0.4623341	-2.3912702	0.22030865	-0.058272455	-1.5049093	-1.8828062	0.8230564	-0.020209199
-0.3415721	1.1219939	1.1089007	-0.74697906	    -1.503861	-1.616539	0.048006497	1.1613717

(2,.,.) =
0.21216023	1.0107462	0.8586909	-0.05644316	    -0.31436008	1.6892323	-0.9961186	-0.08169463
0.3559391	0.010261055	-0.70408463	-1.2480727	    1.7663039	0.07122444	0.073556066	-0.7847014
0.17604464	-0.99110585	-1.0302067	-0.39024687	    -0.0260166	-0.43142694	0.28443158	0.72679126

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3x8]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential


model = Sequential()
model.add(Reshape(target_shape=(3, 8), input_shape=(2, 3, 4)))
input = np.random.random([2, 2, 3, 4])
output = model.forward(input)
```
Input is:
```python
[[[[0.39260304 0.10383185 0.87490319 0.89167328]
   [0.61649117 0.43285247 0.86851582 0.97743004]
   [0.90018969 0.04303951 0.74263493 0.14208656]]
  [[0.66193405 0.93432157 0.76160537 0.70437459]
   [0.99953431 0.23016734 0.42293405 0.66078049]
   [0.03357645 0.9695145  0.30111138 0.67109948]]]

 [[[0.39640201 0.92930203 0.86027666 0.13958544]
   [0.34584767 0.14743425 0.93804016 0.38053062]
   [0.55068792 0.77375329 0.84161166 0.48131356]]
  [[0.90116368 0.53253689 0.03332962 0.58278686]
   [0.34935685 0.32599554 0.97641892 0.57696434]
   [0.53974677 0.90682861 0.20027319 0.05962118]]]]
```
Output is
```python
[[[0.39260304 0.10383185 0.8749032  0.89167327 0.6164912  0.43285248 0.86851585 0.97743005]
  [0.9001897  0.04303951 0.74263495 0.14208655 0.661934   0.9343216  0.7616054  0.7043746 ]
  [0.9995343  0.23016734 0.42293406 0.6607805  0.03357645 0.9695145  0.30111137 0.6710995 ]]

 [[0.396402   0.92930204 0.86027664 0.13958544 0.34584767 0.14743425 0.93804014 0.38053063]
  [0.5506879  0.7737533  0.8416117  0.48131356 0.9011637  0.53253686 0.03332962 0.58278686]
  [0.34935686 0.32599553 0.9764189  0.5769643  0.53974676 0.9068286  0.20027319 0.05962119]]]
```

---
### 7.5 Merge
Used to merge a list of inputs into a single output, following some merge mode.

Merge must have at least two input layers.

**Scala:**
```scala
Merge(layers = null, mode = "sum", concatAxis = -1, inputShape = null)
```
**Python:**
```python
Merge(layers=None, mode="sum", concat_axis=-1, input_shape=None, name=None)
```

**Parameters:**

* `layers`: A list of layer instances. Must be more than one layer.
* `mode`: Merge mode. String, must be one of: 'sum', 'mul', 'concat', 'ave', 'cos', 'dot', 'max'. Default is 'sum'.
* `concatAxis`: Integer, axis to use when concatenating layers. Only specify this when merge mode is 'concat'. Default is -1, meaning the last axis of the input.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`MultiShape`](../keras-api-scala/#shape) object. For Python API, it should be a list of shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.InputLayer
import com.intel.analytics.bigdl.dllib.keras.layers.Merge
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.utils.{Shape, T}
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
val l1 = InputLayer[Float](inputShape = Shape(2, 3))
val l2 = InputLayer[Float](inputShape = Shape(2, 3))
val layer = Merge[Float](layers = List(l1, l2), mode = "sum")
model.add(layer)
val input1 = Tensor[Float](2, 2, 3).rand(0, 1)
val input2 = Tensor[Float](2, 2, 3).rand(0, 1)
val input = T(1 -> input1, 2 -> input2)
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.utils.Table =
 {
	2: (1,.,.) =
	   0.87815475	0.15025006	0.34412447
	   0.07909282	0.008027249	0.111715704

	   (2,.,.) =
	   0.52245367	0.2547527	0.35857987
	   0.7718501	0.26783863	0.8642062

	   [com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
	1: (1,.,.) =
	   0.5377018	0.28364193	0.3424284
	   0.0075349305	0.9018168	0.9435114

	   (2,.,.) =
	   0.09112563	0.88585275	0.3100201
	   0.7910178	0.57497376	0.39764535

	   [com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
 }
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
1.4158566	0.433892	0.6865529
0.08662775	0.90984404	1.0552272

(2,.,.) =
0.6135793	1.1406054	0.66859996
1.5628679	0.8428124	1.2618515

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
l1 = InputLayer(input_shape=(3, 4))
l2 = InputLayer(input_shape=(3, 4))
model.add(Merge(layers=[l1, l2], mode='sum'))
input = [np.random.random([2, 3, 4]), np.random.random([2, 3, 4])]
output = model.forward(input)
```
Input is:
```python
[[[[0.28764351, 0.0236015 , 0.78927442, 0.52646492],
   [0.63922826, 0.45101604, 0.4555552 , 0.70105653],
   [0.75790798, 0.78551523, 0.00686686, 0.61290369]],

  [[0.00430865, 0.3303661 , 0.59915782, 0.90362298],
   [0.26230717, 0.99383052, 0.50630521, 0.99119486],
   [0.56138318, 0.68165639, 0.10644523, 0.51860127]]],

 [[[0.84365767, 0.8854741 , 0.84183673, 0.96322321],
   [0.49354248, 0.97936826, 0.2266097 , 0.88083622],
   [0.11011776, 0.65762034, 0.17446099, 0.76658969]],

  [[0.58266689, 0.86322199, 0.87122999, 0.19031255],
   [0.42275118, 0.76379413, 0.21355413, 0.81132937],
   [0.97294728, 0.68601731, 0.39871792, 0.63172344]]]]
```
Output is
```python
[[[1.1313012  0.90907556 1.6311111  1.4896882 ]
  [1.1327708  1.4303843  0.6821649  1.5818927 ]
  [0.8680257  1.4431355  0.18132785 1.3794935 ]]

 [[0.5869755  1.1935881  1.4703878  1.0939355 ]
  [0.68505836 1.7576246  0.71985936 1.8025242 ]
  [1.5343305  1.3676738  0.50516313 1.1503248 ]]]
```

---
### 7.6 MaxoutDense
A dense maxout layer that takes the element-wise maximum of linear layers.

This allows the layer to learn a convex, piecewise linear activation function over the inputs.

The input of this layer should be 2D.

**Scala:**
```scala
MaxoutDense(outputDim, nbFeature = 4, wRegularizer = null, bRegularizer = null, bias = true, inputShape = null)
```
**Python:**
```python
MaxoutDense(output_dim, nb_feature=4, W_regularizer=None, b_regularizer=None, bias=True, input_dim=None, input_shape=None, name=None)
```

**Parameters:**

* `outputDim`: The size of output dimension.
* `nbFeature`: Number of Dense layers to use internally. Integer. Default is 4.
* `wRegularizer`: An instance of [Regularizer](https://bigdl-project.github.io/master/#APIGuide/Regularizers/), (eg. L1 or L2 regularization), applied to the input weights matrices. Default is null.
* `bRegularizer`: An instance of [Regularizer](https://bigdl-project.github.io/master/#APIGuide/Regularizers/), applied to the bias. Default is null.
* `bias`: Whether to include a bias (i.e. make the layer affine rather than linear). Default is true.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.MaxoutDense
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(MaxoutDense(2, inputShape = Shape(3)))
val input = Tensor[Float](2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
-1.3550005	-1.1668127	-1.2882779
0.83600295	-1.94683	1.323666
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
0.71675766	1.2987505
0.9871184	0.6634239
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(MaxoutDense(2, input_shape=(3, )))
input = np.random.random([2, 3])
output = model.forward(input)
```
Input is:
```python
[[0.15996114 0.8391686  0.81922903]
 [0.52929427 0.35061754 0.88167693]]
```
Output is
```python
[[0.4479192  0.4842512]
 [0.16833156 0.521764 ]]
```

---
### 7.7 Squeeze
Delete the singleton dimension(s). The batch dimension needs to be unchanged.

For example, if input has size (2, 1, 3, 4, 1):

Squeeze(1) will give output size (2, 3, 4, 1),

Squeeze() will give output size (2, 3, 4)

**Scala:**
```scala
Squeeze(dims = null, inputShape = null)
```
**Python:**
```python
Squeeze(dim=None, input_shape=None, name=None)
```

**Parameters:**

* `dims`: The dimension(s) to squeeze. 0-based index. Cannot squeeze the batch dimension. The selected dimensions must be singleton, i.e. having size 1. Default is null, and in this case all the non-batch singleton dimensions will be deleted.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Squeeze
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Squeeze[Float](1, inputShape = Shape(1, 1, 32)))
val input = Tensor[Float](1, 1, 1, 32).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
0.5521966       -1.2199087      0.365958        1.3845297       0.115254946     -0.20352958     2.4912808       0.987046        -0.2115477      3.0530396      -1.0043625      1.4688021       -1.2412603      -0.25383064     0.49164283      -0.40329486     0.26323202      0.7979045       0.025444122   0.47221214       1.3995043       0.48498031      -0.86961967     -0.058370713    -0.85965866     -1.2727696      0.45570874      0.73393697      0.2567143      1.4261572       -0.37773672     -0.7339463

[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x1x1x32]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
0.5521966       -1.2199087      0.365958        1.3845297       0.115254946     -0.20352958     2.4912808       0.987046        -0.2115477      3.0530396      -1.0043625      1.4688021       -1.2412603      -0.25383064     0.49164283      -0.40329486     0.26323202      0.7979045       0.025444122   0.47221214       1.3995043       0.48498031      -0.86961967     -0.058370713    -0.85965866     -1.2727696      0.45570874      0.73393697      0.2567143      1.4261572       -0.37773672     -0.7339463

[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x1x32]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Squeeze(1, input_shape=(1, 1, 32)))
input = np.random.random([1, 1, 1, 32])
output = model.forward(input)
```
Input is:
```python
[[[[0.20585343, 0.47011701, 0.14553177, 0.93915599, 0.57234281,
    0.91631229, 0.32244256, 0.94243351, 0.86595631, 0.73916763,
    0.35898731, 0.65208275, 0.07935983, 0.89313423, 0.68601269,
    0.48919672, 0.28406399, 0.20962799, 0.88071757, 0.45501821,
    0.60931183, 0.46709718, 0.14218838, 0.42517758, 0.9149958 ,
    0.0843243 , 0.27302307, 0.75281922, 0.3688931 , 0.86913729,
    0.89774196, 0.77838838]]]]
```
Output is
```python
[[[0.20585343, 0.470117  , 0.14553176, 0.939156  , 0.5723428 ,
   0.9163123 , 0.32244256, 0.94243354, 0.8659563 , 0.73916763,
   0.3589873 , 0.65208274, 0.07935983, 0.89313424, 0.6860127 ,
   0.48919672, 0.284064  , 0.20962799, 0.8807176 , 0.45501822,
   0.6093118 , 0.46709716, 0.14218839, 0.42517757, 0.9149958 ,
   0.0843243 , 0.27302307, 0.75281924, 0.36889312, 0.8691373 ,
   0.897742  , 0.7783884 ]]]
```

---
### 7.8 BinaryThreshold
Threshold the input.

If an input element is smaller than the threshold value, it will be replaced by 0; otherwise, it will be replaced by 1.

**Scala:**
```scala
BinaryThreshold(value = 1e-6, inputShape = null)
```
**Python:**
```python
BinaryThreshold(value=1e-6, input_shape=None, name=None)
```

**Parameters:**

* `value`: The threshold value to compare with. Default is 1e-6.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.BinaryThreshold
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(BinaryThreshold[Float](inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-1.1907398      -0.18995096     -2.0344417      -1.3789974
-1.8801064      -0.74757665     -0.4339697      0.0058485097
0.7012256       -0.6363152      2.0156987       -0.5512639

(1,2,.,.) =
-0.5251603      0.082127444     0.29550993      1.6357868
-1.3828015      -0.11842779     0.3316966       -0.14360528
0.21216457      -0.117370956    -0.12934707     -0.35854268

(2,1,.,.) =
-0.9071151      -2.8566089      -0.4796377      -0.915065
-0.8439908      -0.25404388     -0.39926198     -0.15191565
-1.0496653      -0.403675       -1.3591816      0.5311797

(2,2,.,.) =
0.53509855      -0.08892822     1.2196561       -0.62759316
-0.47476718     -0.43337926     -0.10406987     1.4035174
-1.7120812      1.1328355       0.9219375       1.3813454

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.0     0.0     0.0     0.0
0.0     0.0     0.0     1.0
1.0     0.0     1.0     0.0

(1,2,.,.) =
0.0     1.0     1.0     1.0
0.0     0.0     1.0     0.0
1.0     0.0     0.0     0.0

(2,1,.,.) =
0.0     0.0     0.0     0.0
0.0     0.0     0.0     0.0
0.0     0.0     0.0     1.0

(2,2,.,.) =
1.0     0.0     1.0     0.0
0.0     0.0     0.0     1.0
0.0     1.0     1.0     1.0

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(BinaryThreshold(input_shape=(2, 3, 4)))
input = np.random.random([2, 2, 3, 4])
output = model.forward(input)
```
Input is:
```python
array([[[[0.30421481, 0.47800487, 0.54249411, 0.90109767],
         [0.72650405, 0.53096719, 0.66346109, 0.0589329 ],
         [0.12994731, 0.92181174, 0.43129874, 0.97306968]],

        [[0.3031087 , 0.20339982, 0.69034712, 0.40191   ],
         [0.57517034, 0.30159448, 0.4801747 , 0.75175084],
         [0.8599362 , 0.93523811, 0.34768628, 0.10840162]]],


       [[[0.46102959, 0.33029002, 0.69340103, 0.32885719],
         [0.84405147, 0.03421879, 0.68242578, 0.03560338],
         [0.12244515, 0.3610654 , 0.01312785, 0.84485178]],

        [[0.73472287, 0.75707757, 0.77070527, 0.40863145],
         [0.01137898, 0.82896826, 0.1498069 , 0.22309423],
         [0.92737483, 0.36217222, 0.06679799, 0.33304362]]]])
```
Output is
```python
array([[[[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]],

        [[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]]],


       [[[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]],

        [[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]]]], dtype=float32)
```

---
### 7.9 Sqrt
Applies an element-wise square root operation to the input.

**Scala:**
```scala
Sqrt(inputShape = null)
```
**Python:**
```python
Sqrt(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Sqrt
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Sqrt[Float](inputShape = Shape(3)))
val input = Tensor[Float](2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
0.6950394       0.5234307       1.7375475
0.25833175      0.02685826      -0.6046901
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
0.8336902       0.7234851       1.3181607
0.50826347      0.16388491      NaN
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Sqrt(input_shape=(3, )))
input = np.random.random([2, 3])
output = model.forward(input)
```
Input is:
```python
[[0.2484558 , 0.65280218, 0.35286984],
 [0.19616094, 0.30966802, 0.82148169]]
```
Output is
```python
[[0.4984534 , 0.80796176, 0.5940285 ],
 [0.4429006 , 0.55647826, 0.9063563 ]]
```

---
### 7.10 Mul
Multiply a single scalar factor to the incoming data

**Scala:**
```scala
Mul(inputShape = null)
```
**Python:**
```python
Mul(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.
* `name`: String to set the name of the layer. If not specified, its name will by default to be a generated string.


**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Mul
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Mul[Float](inputShape = Shape(3, 4)))
val input = Tensor[Float](2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
-1.2316265  -2.008802 -1.3908259  -0.61135375
-0.48992255 0.1786112 0.18872596  0.49621895
-0.6931602  -0.919745 -0.09019699 -0.41218707

(2,.,.) =
-0.3135355  -0.4385771  -0.3317269  1.0412029
-0.8859662  0.17758773  -0.73779273 -0.4445366
0.3921595 1.6923207 0.014470488 0.4044164

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-0.59036994 -0.9629025  -0.6666808  -0.29304734
-0.2348403  0.0856158 0.09046422  0.23785843
-0.33226058 -0.44087213 -0.043235175  -0.19757845

(2,.,.) =
-0.15029064 -0.21022828 -0.15901053 0.49909195
-0.42468053 0.0851252 -0.3536548  -0.21308492
0.18797839  0.81119984  0.006936308 0.19385365

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Mul(input_shape=(3, 4)))
input = np.random.random([2, 3, 4])
output = model.forward(input)
```
Input is:
```python
array([[[ 0.22607292,  0.59806062,  0.19428923,  0.22928606],
        [ 0.13804536,  0.1615547 ,  0.52824658,  0.52794904],
        [ 0.4049169 ,  0.94109084,  0.58158453,  0.78368633]],

       [[ 0.86233305,  0.47995805,  0.80430949,  0.9931171 ],
        [ 0.35179631,  0.33615276,  0.87756877,  0.73560288],
        [ 0.29775703,  0.11404466,  0.77695536,  0.97580018]]])
```
Output is
```python
array([[[-0.22486402, -0.59486258, -0.1932503 , -0.22805998],
        [-0.13730718, -0.1606908 , -0.52542186, -0.52512592],
        [-0.40275168, -0.93605846, -0.57847458, -0.77949566]],

       [[-0.85772187, -0.47739154, -0.80000854, -0.9878065 ],
        [-0.34991512, -0.33435524, -0.87287611, -0.73166931],
        [-0.29616481, -0.11343482, -0.77280068, -0.97058219]]], dtype=float32)
```

---
### 7.11 MulConstant
Multiply the input by a (non-learnable) scalar constant.

**Scala:**
```scala
MulConstant(constant, inputShape = null)
```
**Python:**
```python
MulConstant(constant, input_shape=None, name=None)
```

**Parameters:**

* `constant`: The scalar constant to be multiplied.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.MulConstant
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(MulConstant[Float](2.2, inputShape = Shape(3, 4)))
val input = Tensor[Float](2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
-0.16873977     1.0812985       1.0942211       -0.67091423
1.0086882       0.5915831       0.26184535      -1.361431
1.5616825       -0.037591368    1.2794676       1.0692137

(2,.,.) =
0.29868057      -0.23266982     -0.7679556      -2.209848
-0.13954644     -0.1368473      -0.54510623     1.8397199
-0.58691734     -0.56410027     -1.5567777      0.050648995

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-0.3712275      2.3788567       2.4072864       -1.4760114
2.219114        1.3014828       0.57605976      -2.9951482
3.4357016       -0.08270101     2.8148286       2.3522704

(2,.,.) =
0.6570973       -0.5118736      -1.6895024      -4.8616657
-0.3070022      -0.30106407     -1.1992338      4.047384
-1.2912182      -1.2410206      -3.424911       0.11142779

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import *
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(MulConstant(2.2, input_shape=(3, 4)))
input = np.random.random([2, 3, 4])
output = model.forward(input)
```
Input is:
```python
[[[0.39874191, 0.66634984, 0.23907766, 0.31587494],
  [0.78842014, 0.93057835, 0.80739529, 0.71541279],
  [0.2231424 , 0.3372844 , 0.94678072, 0.52928034]],

 [[0.60142458, 0.41221671, 0.00890549, 0.32069845],
  [0.51122554, 0.76280426, 0.87579418, 0.17182832],
  [0.54133184, 0.19814384, 0.92529327, 0.5616615 ]]]
```
Output is
```python
[[[0.8772322 , 1.4659697 , 0.5259709 , 0.6949249 ],
  [1.7345244 , 2.0472724 , 1.7762697 , 1.5739082 ],
  [0.4909133 , 0.7420257 , 2.0829177 , 1.1644168 ]],

 [[1.3231341 , 0.9068768 , 0.01959208, 0.7055366 ],
  [1.1246961 , 1.6781695 , 1.9267472 , 0.37802234],
  [1.19093   , 0.43591645, 2.0356452 , 1.2356553 ]]]
```

---
### 7.12 Scale
Scale is the combination of CMul and CAdd.

Computes the element-wise product of the input and weight, with the shape of the weight "expand" to match the shape of the input.

Similarly, perform an expanded bias and perform an element-wise add.

**Scala:**
```scala
Scale(size, inputShape = null)
```
**Python:**
```python
Scale(size, input_shape=None, name=None)
```

**Parameters:**

* `size`: Size of the weight and bias.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Scale
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
var array = Array(1, 2)
model.add(Scale[Float](array, inputShape = Shape(3)))
val input = Tensor[Float](2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
-0.006399727    -0.06412822     -0.2334789
0.31029955      1.6557469       1.9614618
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
0.09936619      0.57585865      0.20324506
0.38537437      -0.8598822      -1.0186496
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import Scale
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Scale((2, 1), input_shape=(3, )))
input = np.random.random([2, 3])
output = model.forward(input)
```
Input is:
```python
[[0.7242994 , 0.77888884, 0.71470432],
 [0.03058471, 0.00602764, 0.57513629]]
```
Output is
```python
[[1.0946966 , 1.1255064 , 1.0892813 ],
 [0.58151895, 0.5909191 , 0.37307182]]
```

---
### 7.13 Log
Applies a log transformation to the input.

**Scala:**
```scala
Log(inputShape = null)
```
**Python:**
```python
Log(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Log
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Log[Float](inputShape = Shape(2, 4, 4)))
val input = Tensor[Float](1, 2, 4, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
0.38405678      -0.5502389      -0.383079       -0.988537
-0.6294056      -0.7838047      0.8747865       -1.0659786
-2.2445498      -0.5488076      -0.42898977     0.6916364
1.6542299       -0.9966279      -0.38244298     1.6954672

(1,2,.,.) =
0.43478605      -0.6678534      1.9530942       -0.5209587
0.12899925      0.20572199      2.0359943       0.55223215
0.65247816      0.8792108       -0.38860792     0.48663738
-1.0084358      0.31141177      0.69208467      0.48385203

[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x2x4x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
-0.95696485     NaN     NaN     NaN
NaN     NaN     -0.13377543     NaN
NaN     NaN     NaN     -0.36869493
0.5033356       NaN     NaN     0.5279584

(1,2,.,.) =
-0.83290124     NaN     0.6694149       NaN
-2.0479486      -1.5812296      0.7109843       -0.5937868
-0.4269776      -0.12873057     NaN     -0.720236
NaN     -1.1666392      -0.36804697     -0.72597617

[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x2x4x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import Log
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Log(input_shape=(2, 4, 4)))
input = np.random.random([1, 2, 4, 4])
output = model.forward(input)
```
Input is:
```python
[[[[0.90127539, 0.9861594 , 0.04722941, 0.63719453],
   [0.46529477, 0.81511804, 0.24435558, 0.45003562],
   [0.15170845, 0.35157662, 0.0925214 , 0.63852947],
   [0.27817508, 0.42572846, 0.44363004, 0.03536394]],

  [[0.65027784, 0.00429838, 0.07434429, 0.18653305],
   [0.19659183, 0.66647529, 0.77821197, 0.65894478],
   [0.28212032, 0.52307663, 0.09589939, 0.71547588],
   [0.84344158, 0.25291738, 0.52145649, 0.82982377]]]]
```
Output is
```python
[[[[-0.10394441, -0.01393729, -3.0527387 , -0.45068032],
   [-0.76508415, -0.20442237, -1.4091308 , -0.79842854],
   [-1.8857948 , -1.0453277 , -2.3803153 , -0.44858742],
   [-1.2795045 , -0.85395354, -0.8127643 , -3.3420627 ]],

  [[-0.43035555, -5.4495163 , -2.5990484 , -1.6791469 ],
   [-1.6266255 , -0.4057522 , -0.25075635, -0.41711554],
   [-1.2654216 , -0.64802724, -2.3444557 , -0.33480743],
   [-0.1702646 , -1.3746924 , -0.6511295 , -0.1865419 ]]]]
```

---
### 7.14 Identity
Identity just return the input to output.

It's useful in same parallel container to get an origin input.

**Scala:**
```scala
Identity(inputShape = null)
```
**Python:**
```python
Identity(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.Identity
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Identity[Float](inputShape = Shape(4, 4)))
val input = Tensor[Float](3, 4, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
1.9601166       -0.86010313     0.0023731247    -0.81219757
1.1469674       -1.5375912      -1.5348053      -0.34829113
-1.236773       -0.7183283      -0.89256984     0.8605067
0.7937664       0.52992857      -1.6157389      0.36134166

(2,.,.) =
-0.44434744     -0.23848957     -0.01632014     -0.58109635
-0.19856784     -2.3421717      -0.5868049      -0.76775354
0.80254126      1.78778 -1.1835604      1.4489703
0.8731402       0.8906672       0.2800079       -0.6715317

(3,.,.) =
1.4093032       2.358169        -1.4620789      1.1904576
-0.18263042     -0.31869793     2.01061 1.2159953
-0.5801479      1.2949371       -0.7510707      -1.0707517
0.30815956      -1.161963       -0.26964024     -0.4759499

[com.intel.analytics.bigdl.tensor.DenseTensor of size 3x4x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
1.9601166       -0.86010313     0.0023731247    -0.81219757
1.1469674       -1.5375912      -1.5348053      -0.34829113
-1.236773       -0.7183283      -0.89256984     0.8605067
0.7937664       0.52992857      -1.6157389      0.36134166

(2,.,.) =
-0.44434744     -0.23848957     -0.01632014     -0.58109635
-0.19856784     -2.3421717      -0.5868049      -0.76775354
0.80254126      1.78778 -1.1835604      1.4489703
0.8731402       0.8906672       0.2800079       -0.6715317

(3,.,.) =
1.4093032       2.358169        -1.4620789      1.1904576
-0.18263042     -0.31869793     2.01061 1.2159953
-0.5801479      1.2949371       -0.7510707      -1.0707517
0.30815956      -1.161963       -0.26964024     -0.4759499

[com.intel.analytics.bigdl.tensor.DenseTensor of size 3x4x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import Identity
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Identity(input_shape=(4, 4)))
input = np.random.random([3, 4, 4])
output = model.forward(input)
```
Input is:
```python
[[[0.36751123, 0.92287101, 0.73894405, 0.33699379],
  [0.69405782, 0.9653215 , 0.2617223 , 0.68205229],
  [0.71455325, 0.99419333, 0.90886495, 0.10232991],
  [0.1644055 , 0.30013138, 0.98921154, 0.26803146]],

  [[0.35898357, 0.72067882, 0.13236563, 0.71935521],
   [0.30865626, 0.71098844, 0.86718946, 0.12531168],
   [0.84916882, 0.84221518, 0.52186664, 0.87239729],
   [0.50637899, 0.10890469, 0.86832705, 0.93581179]],

  [[0.19640105, 0.09341008, 0.12043328, 0.09261859],
   [0.66019486, 0.07251262, 0.80929761, 0.39094486],
   [0.63027391, 0.39537796, 0.55578905, 0.53933265],
   [0.13885559, 0.56695373, 0.17036027, 0.4577097 ]]]
```
Output is
```python
[[[0.36751124, 0.922871  , 0.73894405, 0.33699378],
  [0.6940578 , 0.9653215 , 0.2617223 , 0.6820523 ],
  [0.71455324, 0.9941933 , 0.908865  , 0.10232991],
  [0.1644055 , 0.30013138, 0.98921156, 0.26803148]],

 [[0.35898358, 0.7206788 , 0.13236563, 0.7193552 ],
  [0.30865628, 0.71098846, 0.86718947, 0.12531169],
  [0.84916884, 0.8422152 , 0.5218666 , 0.8723973 ],
  [0.506379  , 0.10890469, 0.868327  , 0.9358118 ]],

 [[0.19640104, 0.09341008, 0.12043328, 0.09261858],
  [0.6601949 , 0.07251262, 0.8092976 , 0.39094487],
  [0.63027394, 0.39537796, 0.55578905, 0.5393326 ],
  [0.13885559, 0.5669537 , 0.17036027, 0.4577097 ]]]
```

---
### 7.15 Select
Select an index of the input in the given dim and return the subset part.

The batch dimension needs to be unchanged.

For example, if input is:

[[1, 2, 3], 
 [4, 5, 6]]

Select(1, 1) will give output [2 5]

Select(1, -1) will give output [3 6]

**Scala:**
```scala
Select(dim, index, inputShape = null)
```
**Python:**
```python
Select(dim, index, input_shape=None, name=None)
```

**Parameters:**

* `dim`: The dimension to select. 0-based index. Cannot select the batch dimension. -1 means the last dimension of the input.
* `index`: The index of the dimension to be selected. 0-based index. -1 means the last dimension of the input.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Select
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Select[Float](1, 2, inputShape = Shape(3, 1, 3)))
val input = Tensor[Float](1, 3, 1, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-0.67646945     -0.5485965      -0.11103154
(1,2,.,.) =
-0.13488655     0.43843046      -0.04482145
(1,3,.,.) =
-0.18094881     0.19431554      -1.7624844
[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x3x1x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-0.18094881     0.19431554      -1.7624844
[com.intel.analytics.bigdl.tensor.DenseTensor of size 1x1x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import Select
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(Select(1, 2, input_shape=(3, 1, 3)))
input = np.random.random([1, 3, 1, 3])
output = model.forward(input)
```
Input is:
```python
array([[[[0.53306099, 0.95147881, 0.15222129]],
        [[0.89604861, 0.90160974, 0.5230576 ]],
        [[0.70779386, 0.14438568, 0.37601195]]]])
```
Output is:
```python
array([[[0.7077939 , 0.14438568, 0.37601194]]], dtype=float32)
```

---
### 7.16 Dense
A densely-connected NN layer.

The most common input is 2D.

**Scala:**
```scala
Dense(outputDim, init = "glorot_uniform", activation = null, wRegularizer = null, bRegularizer = null, bias = true, inputShape = null)
```
**Python:**
```python
Dense(output_dim, init="glorot_uniform", activation=None, W_regularizer=None, b_regularizer=None, bias=True, input_dim=None, input_shape=None, name=None)
```

**Parameters:**

* `outputDim`: The size of the output dimension.
* `init`: Initialization method for the weights of the layer. Default is Xavier.You can also pass in corresponding string representations such as 'glorot_uniform' or 'normal', etc. for simple init methods in the factory method.
* `activation`: Activation function to use. Default is null.You can also pass in corresponding string representations such as 'relu'or 'sigmoid', etc. for simple activations in the factory method.
* `wRegularizer`: An instance of [Regularizer](https://bigdl-project.github.io/master/#APIGuide/Regularizers/), applied to the input weights matrices. Default is null.
* `bRegularizer`: An instance of [Regularizer](https://bigdl-project.github.io/master/#APIGuide/Regularizers/), applied to the bias. Default is null.
* `bias`: Whether to include a bias (i.e. make the layer affine rather than linear). Default is true.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Dense
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Dense[Float](5, activation = "relu", inputShape = Shape(4)))
val input = Tensor[Float](2, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
1.4289935       -1.7659454      -0.08306135     -1.0153456
1.0191492       0.37392816      1.3076705       -0.19495767
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
0.5421522       0.49008092      0.0     0.0     0.0
0.07940009      0.0     0.12953377      0.0     0.0
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x5]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import Dense
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(Dense(5, activation="relu", input_shape=(4, )))
input = np.random.random([2, 4])
output = model.forward(input)
```
Input is:
```python
array([[0.64593485, 0.67393322, 0.72505368, 0.04654095],
       [0.19430753, 0.47800889, 0.00743648, 0.6412403 ]])
```
Output is
```python
array([[0.        , 0.        , 1.2698183 , 0.        , 0.10656227],
       [0.        , 0.        , 0.6236721 , 0.00299606, 0.29664695]],
      dtype=float32)
```

---
### 7.17 Negative
Computes the negative value of each element of the input.

**Scala:**
```scala
Negative(inputShape = null)
```
**Python:**
```python
Negative(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Negative
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Negative[Float](inputShape = Shape(2, 3)))
val input = Tensor[Float](2, 2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
1.031705        -0.5723963      1.998631
-0.32908052     2.4069138       -2.4111257
(2,.,.) =
0.5355049       -1.4404331      -0.38116863
-0.45641592     -1.1485358      0.94766915
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-1.031705       0.5723963       -1.998631
0.32908052      -2.4069138      2.4111257
(2,.,.) =
-0.5355049      1.4404331       0.38116863
0.45641592      1.1485358       -0.94766915
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import Negative
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(Negative(input_shape=(2, 3)))
input = np.random.random([2, 2, 3])
output = model.forward(input)
```
Input is:
```python
array([[[0.39261261, 0.03164615, 0.32179116],
        [0.11969367, 0.61610712, 0.42573733]],
       [[0.36794656, 0.90912174, 0.540356  ],
        [0.42667627, 0.04154093, 0.84692964]]])
```
Output is
```python
array([[[-0.3926126 , -0.03164615, -0.32179114],
        [-0.11969367, -0.6161071 , -0.42573732]],
       [[-0.36794657, -0.90912175, -0.540356  ],
        [-0.42667627, -0.04154094, -0.84692967]]], dtype=float32)
```

---
### 7.18 CAdd
This layer has a bias with given size.

The bias will be added element-wise to the input.

If the element number of the bias matches the input, a simple element-wise addition will be done.

Or the bias will be expanded to the same size of the input.

The expand means repeat on unmatched singleton dimension (if some unmatched dimension isn't a singleton dimension, an error will be raised).

**Scala:**
```scala
CAdd(size, bRegularizer = null, inputShape = null)
```
**Python:**
```python
CAdd(size, b_regularizer=None, input_shape=None, name=None)
```

**Parameters:**

* `size`: the size of the bias
* `bRegularizer`: An instance of [Regularizer](https://bigdl-project.github.io/master/#APIGuide/Regularizers/), applied to the bias. Default is null.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.CAdd
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(CAdd[Float](Array(2, 3), inputShape = Shape(2, 3)))
val input = Tensor[Float](2, 2, 3).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
0.2183351       0.32434112      0.89350265
0.3348259       0.78677046      0.24054797
(2,.,.) =
0.9945844       0.72363794      0.7737936
0.05522544      0.3517818       0.7417069
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
0.1358028       0.6956667       1.0837181
0.6767027       0.7955346       0.5063505
(2,.,.) =
0.9120521       1.0949634       0.96400905
0.3971022       0.36054593      1.0075095
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import CAdd
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(CAdd([2, 1], input_shape=(2, 3)))
input = np.random.rand(2, 2, 3)
output = model.forward(input)
```
Input is:
```python
array([[[0.4122004 , 0.73289359, 0.11500016],
        [0.26974491, 0.32166632, 0.91408442]],
       [[0.66824327, 0.80271314, 0.75981145],
        [0.39271431, 0.07312566, 0.4966805 ]]])
```
Output is
```python
array([[[ 0.06560206,  0.38629526, -0.23159817],
        [ 0.44287407,  0.4947955 ,  1.0872136 ]],
       [[ 0.32164496,  0.45611483,  0.41321313],
        [ 0.56584346,  0.24625483,  0.6698097 ]]], dtype=float32)
```

---
### 7.19 RepeatVector
Repeats the input n times.

The input of this layer should be 2D, i.e. (num_samples, features).
The output of thi layer should be 3D, i.e. (num_samples, n, features).

**Scala:**
```scala
RepeatVector(n, inputShape = null)
```
**Python:**
```python
RepeatVector(n, input_shape=None, name=None)
```

**Parameters:**

* `n`: Repetition factor. Integer.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.
* `name`: String to set the name of the layer. If not specified, its name will by default to be a generated string.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.RepeatVector
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(RepeatVector[Float](4, inputShape = Shape(3)))
val input = Tensor[Float](2, 3).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
-0.31839952 -0.3495366  0.542486
-0.54981124 -0.8428188  0.8225184
[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
-0.31839952 -0.3495366  0.542486
-0.31839952 -0.3495366  0.542486
-0.31839952 -0.3495366  0.542486
-0.31839952 -0.3495366  0.542486

(2,.,.) =
-0.54981124 -0.8428188  0.8225184
-0.54981124 -0.8428188  0.8225184
-0.54981124 -0.8428188  0.8225184
-0.54981124 -0.8428188  0.8225184

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x4x3]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.layers import RepeatVector
from bigdl.dllib.keras.models import Sequential

model = Sequential()
model.add(RepeatVector(4, input_shape=(3, )))
input = np.random.random([2, 3])
output = model.forward(input)
```
Input is:
```python
array([[ 0.90715922,  0.54594769,  0.53952404],
       [ 0.08989831,  0.07265549,  0.45830114]])
```
Output is
```python
array([[[ 0.90715921,  0.54594767,  0.53952402],
        [ 0.90715921,  0.54594767,  0.53952402],
        [ 0.90715921,  0.54594767,  0.53952402],
        [ 0.90715921,  0.54594767,  0.53952402]],

       [[ 0.08989831,  0.07265549,  0.45830116],
        [ 0.08989831,  0.07265549,  0.45830116],
        [ 0.08989831,  0.07265549,  0.45830116],
        [ 0.08989831,  0.07265549,  0.45830116]]], dtype=float32)
```
---
### 7.20 GaussianSampler
Takes {mean, log_variance} as input and samples from the Gaussian distribution.

**Scala:**
```scala
GaussianSampler(inputShape = null)
```
**Python:**
```python
GaussianSampler(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`MultiShape`](../keras-api-scala/#shape) object that consists of two identical Single Shape. For Python API, it should be a list of two identical shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.GaussianSampler
import com.intel.analytics.bigdl.utils.{Shape, MultiShape, T}
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
val shape1 = Shape(2, 3)
val shape2 = Shape(2, 3)
model.add(GaussianSampler[Float](inputShape = MultiShape(List(shape1,shape2))))
val input1 = Tensor[Float](2, 2, 3).rand(0, 1)
val input2 = Tensor[Float](2, 2, 3).rand(0, 1)
val input = T(1 -> input1, 2 -> input2)
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.utils.Table =
 {
        2: (1,.,.) =
           0.9996127    0.8964211       0.7424038
           0.40628982   0.37035564      0.20108517

           (2,.,.) =
           0.6974727    0.60202897      0.1535999
           0.012422224  0.5993025       0.96206

           [com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
        1: (1,.,.) =
           0.21060324   0.576583        0.21633287
           0.1484059    0.2730577       0.25317845

           (2,.,.) =
           0.58513683   0.58095694      0.18811373
           0.7029449    0.41235915      0.44636542

           [com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
 }
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
1.5258198       1.9536011       -1.8591263
-1.0618867      -0.751225       0.35412917

(2,.,.) =
1.3334517       -0.60312974     0.7324476
0.09502721      0.8094909       0.44807082

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.models import Sequential
from bigdl.dllib.keras.layers import GaussianSampler

model = Sequential()
model.add(GaussianSampler(input_shape=[(3,),(3,)]))
input1 = np.random.random([2, 3])
input2 = np.random.random([2, 3])
input = [input1, input2]
output = model.forward(input)
```
Input is:
```python
[[[0.79941342, 0.87462822, 0.9516901 ],
  [0.20111287, 0.54634077, 0.83614511]], 
  
 [[0.31886989, 0.22829382, 0.84355419],
  [0.51186641, 0.28043938, 0.29440057]]]
```
Output is
```python
[[ 0.71405387  2.2944303  -0.41778684]
 [ 0.84234     2.3337283  -0.18952972]]
```

---
### 7.21 Exp
Applies element-wise exp to the input.

When you use this layer as the first layer of a model, you need to provide the argument inputShape (a Single Shape, does not include the batch dimension).

**Scala:**
```scala
Exp(inputShape = null)
```
**Python:**
```python
Exp(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`MultiShape`](../keras-api-scala/#shape) object that consists of two identical Single Shape. For Python API, it should be a list of two identical shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Exp
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Exp[Float](inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-1.5841372      -0.13795324     -2.144475       0.09272669
1.055668        -1.2310301      1.2145554       -0.6073714
0.9296467       0.2923885       1.3364213       0.1652137

(1,2,.,.) =
0.2099718       -0.3856573      -0.92586        -0.5317779
0.6618383       -0.9677452      -1.5014665      -0.35464883
2.045924        -0.317644       -1.812726       0.95438373

(2,1,.,.) =
-0.4536791      -0.34785584     1.6424289       -0.07981159
-0.8022624      -0.4211059      0.3461831       1.9598864
-0.84695745     -0.6115283      0.7729755       2.3077402

(2,2,.,.) =
-0.08438411     -0.908458       0.6688936       -0.7292123
-0.26337254     0.55425745      -0.14925817     -0.010179609
-0.62562865     -1.0517743      -0.23839666     -1.144982

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.20512469      0.8711394       0.11712951      1.0971619
2.8738942       0.29199165      3.3687959       0.544781
2.533614        1.3396233       3.8054006       1.1796452

(1,2,.,.) =
1.2336433       0.6800035       0.39619055      0.5875594
1.9383523       0.37993878      0.22280318      0.7014197
7.7363033       0.7278619       0.16320862      2.5970695

(2,1,.,.) =
0.63528657      0.70620066      5.167706        0.92329025
0.44831353      0.6563206       1.4136615       7.0985208
0.42871734      0.5425211       2.1662023       10.051684

(2,2,.,.) =
0.9190782       0.4031454       1.9520763       0.48228875
0.76845556      1.740648        0.8613467       0.98987204
0.53492504      0.34931743      0.7878901       0.31822965

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.models import Sequential
from bigdl.dllib.keras.layers import Exp

model = Sequential()
model.add(Exp(input_shape=(2, 3, 4)))
input = np.random.random([2, 2, 3, 4])
output = model.forward(input)
```
Input is:
```python
[[[[0.93104587 0.94000338 0.84870765 0.98645553]
   [0.83708846 0.33375541 0.50119834 0.24879265]
   [0.51966475 0.84514791 0.15496452 0.61538968]]

  [[0.57250337 0.42520832 0.94850757 0.54317573]
   [0.64228691 0.9904079  0.01008592 0.51365217]
   [0.78640595 0.7717037  0.51277595 0.24245034]]]


 [[[0.82184752 0.92537331 0.20632728 0.47539445]
   [0.44604637 0.1507692  0.5437313  0.2074501 ]
   [0.93661363 0.93962609 0.29230559 0.74850958]]

  [[0.11659768 0.76177132 0.33194573 0.20695088]
   [0.49636212 0.85987328 0.49767861 0.96774006]
   [0.67669121 0.15542122 0.69981032 0.3349874 ]]]]
```
Output is
```python
[[[[2.5371614 2.5599902 2.3366253 2.6817122]
   [2.3096325 1.3962016 1.6506982 1.2824761]
   [1.6814638 2.3283222 1.1676165 1.8503776]]

  [[1.7726992 1.5299091 2.5818534 1.721465 ]
   [1.9008229 2.6923325 1.010137  1.6713842]
   [2.1954916 2.163449  1.6699204 1.2743679]]]


 [[[2.2746985 2.52281   1.2291554 1.6086487]
   [1.5621239 1.1627283 1.7224218 1.2305363]
   [2.551327  2.5590243 1.3395122 2.1138473]]

  [[1.1236672 2.1420672 1.3936772 1.2299222]
   [1.6427343 2.3628614 1.6448984 2.6319895]
   [1.9673574 1.16815   2.0133708 1.3979228]]]]
```

---
### 7.22 Square
Applies an element-wise square operation to the input.

When you use this layer as the first layer of a model, you need to provide the argument inputShape (a Single Shape, does not include the batch dimension).

**Scala:**
```scala
Square(inputShape = null)
```
**Python:**
```python
Square(input_shape=None, name=None)
```

**Parameters:**

* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`MultiShape`](../keras-api-scala/#shape) object that consists of two identical Single Shape. For Python API, it should be a list of two identical shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Square
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Square[Float](inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).randn()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
-0.108013034    1.8879265       1.2232096       -1.5076439
1.4895755       -0.37966672     -0.34892964     0.15224025
-0.9296686      -1.1523775      0.14153497      -0.26954007

(1,2,.,.) =
-1.0875931      2.190617        -0.6903083      1.0039362
-0.1275677      -1.1096588      0.37359753      -0.17367937
0.23349741      0.14639114      -0.2330162      0.5343827

(2,1,.,.) =
0.3222191       0.21463287      -1.0157064      -0.22627507
1.1714277       0.43371263      1.069315        0.5122436
0.1958086       -1.4601041      2.5394423       -0.470833

(2,2,.,.) =
-0.38708544     -0.951611       -0.37234613     0.26813275
1.9477026       0.32779223      -1.2308712      -2.2376378
0.19652915      0.3304719       -1.7674786      -0.86961496

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.011666816     3.5642662       1.4962418       2.2729902
2.218835        0.14414681      0.1217519       0.023177093
0.86428374      1.3279738       0.020032147     0.07265185

(1,2,.,.) =
1.1828587       4.7988033       0.47652552      1.0078878
0.016273517     1.2313428       0.13957511      0.030164523
0.05452104      0.021430366     0.054296546     0.28556487

(2,1,.,.) =
0.10382515      0.046067268     1.0316595       0.05120041
1.3722429       0.18810664      1.1434345       0.26239353
0.038341008     2.131904        6.448767        0.22168371

(2,2,.,.) =
0.14983514      0.9055635       0.13864164      0.07189517
3.7935455       0.10744774      1.5150439       5.007023
0.038623706     0.109211676     3.1239805       0.7562302

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```

**Python example:**
```python
import numpy as np
from bigdl.dllib.keras.models import Sequential
from bigdl.dllib.keras.layers import Square

model = Sequential()
model.add(Square(input_shape=(2, 3, 4)))
input = np.random.random([2, 2, 3, 4])
output = model.forward(input)
```
Input is:
```python
[[[[0.8708819  0.2698243  0.55854849 0.71699472]
   [0.66647234 0.72310216 0.8082119  0.66566951]
   [0.6714764  0.61394108 0.35063125 0.60473593]]

  [[0.37993365 0.64222557 0.96762005 0.18931697]
   [0.00529722 0.99133455 0.09786619 0.28988077]
   [0.60052911 0.83712995 0.59847519 0.54361243]]]


 [[[0.32832672 0.83316023 0.41272485 0.01963383]
   [0.89593955 0.73433713 0.67529323 0.69711912]
   [0.81251711 0.56755577 0.31958151 0.09795917]]

  [[0.46465895 0.22818875 0.31505317 0.41912166]
   [0.87865447 0.3799063  0.091204   0.68144165]
   [0.88274284 0.70479132 0.32074672 0.71771481]]]]
```
Output is
```python
[[[[7.5843531e-01 7.2805151e-02 3.1197643e-01 5.1408142e-01]
   [4.4418535e-01 5.2287674e-01 6.5320653e-01 4.4311589e-01]
   [4.5088059e-01 3.7692365e-01 1.2294226e-01 3.6570552e-01]]

  [[1.4434958e-01 4.1245368e-01 9.3628860e-01 3.5840917e-02]
   [2.8060573e-05 9.8274422e-01 9.5777912e-03 8.4030852e-02]
   [3.6063525e-01 7.0078653e-01 3.5817260e-01 2.9551446e-01]]]


 [[[1.0779844e-01 6.9415593e-01 1.7034180e-01 3.8548734e-04]
   [8.0270761e-01 5.3925103e-01 4.5602092e-01 4.8597506e-01]
   [6.6018403e-01 3.2211956e-01 1.0213234e-01 9.5959986e-03]]

  [[2.1590793e-01 5.2070107e-02 9.9258497e-02 1.7566296e-01]
   [7.7203369e-01 1.4432879e-01 8.3181690e-03 4.6436274e-01]
   [7.7923489e-01 4.9673077e-01 1.0287846e-01 5.1511449e-01]]]]
```

---
### 7.23 Power
Applies an element-wise power operation with scale and shift to the input.

f(x) = (shift + scale * x)^power^

```scala
Power(power, scale = 1, shift = 0, inputShape = null)
```
**Python:**
```python
Power(power, scale=1, shift=0, input_shape=None, name=None)
```

**Parameters:**

* `power`: The exponent
* `scale`: The scale parameter. Default is 1.
* `shift`: The shift parameter. Default is 0.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Power
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Power[Float](2, inputShape = Shape(2, 3)))
val input = Tensor[Float](2, 2, 3).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
0.24691099      0.7588585       0.5785183
0.10356348      0.2252714       0.3129436

(2,.,.) =
0.6277785       0.75136995      0.044648796
0.46396527      0.9793776       0.92727077

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
0.060965035     0.5758662       0.3346834
0.010725395     0.050747205     0.0979337

(2,.,.) =
0.39410582      0.5645568       0.001993515
0.21526377      0.95918053      0.8598311

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import Power
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(Power(2, input_shape=(2, 3)))
input = np.random.rand(2, 2, 3)
output = model.forward(input)
```
Input is:
```python
array([[[0.5300817 , 0.18128031, 0.19534253],
        [0.28380639, 0.78365165, 0.6893    ]],

       [[0.05574091, 0.400077  , 0.77051193],
        [0.033559  , 0.61051396, 0.13970227]]])
```
Output is
```python
array([[[0.2809866 , 0.03286255, 0.03815871],
        [0.08054607, 0.61410993, 0.4751345 ]],

       [[0.00310705, 0.16006161, 0.5936886 ],
        [0.00112621, 0.37272733, 0.01951673]]], dtype=float32)
```

---
### 7.24 AddConstant
Add a (non-learnable) scalar constant to the input.

```scala
AddConstant(constant, inputShape = null)
```
**Python:**
```python
AddConstant(constant, input_shape=None, name=None)
```

**Parameters:**

* `constant`: The scalar constant to be added.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.AddConstant
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(AddConstant[Float](1, inputShape = Shape(2, 3)))
val input = Tensor[Float](2, 2, 3).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,.,.) =
0.5658301       0.3508225       0.4012322
0.1941942       0.18934165      0.6909284

(2,.,.) =
0.5985211       0.5485885       0.778548
0.16745302      0.10363362      0.92185616

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,.,.) =
1.5658301       1.3508224       1.4012322
1.1941942       1.1893417       1.6909285

(2,.,.) =
1.5985211       1.5485885       1.778548
1.167453        1.1036336       1.9218562

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import AddConstant
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(AddConstant(1, input_shape=(2, 3)))
input = np.random.rand(2, 2, 3)
output = model.forward(input)
```
Input is:
```python
array([[[0.71730919, 0.07752598, 0.10448237],
        [0.52319608, 0.38668494, 0.19588814]],

       [[0.15496092, 0.48405899, 0.41441248],
        [0.13792111, 0.7523953 , 0.55991187]]])
```
Output is
```python
array([[[1.7173092, 1.077526 , 1.1044824],
        [1.5231961, 1.3866849, 1.1958882]],

       [[1.1549609, 1.484059 , 1.4144125],
        [1.1379211, 1.7523953, 1.5599118]]], dtype=float32)
```

---
### 7.25 Narrow
Narrow the input with the number of dimensions not being reduced.

The batch dimension needs to be unchanged.

For example, if input is:

[[1 2 3],
 [4 5 6]]

Narrow(1, 1, 2) will give output

[[2 3],
 [5 6]]

Narrow(1, 2, -1) will give output

[3,
 6]

```scala
Narrow(dim, offset, length = 1, inputShape = null)
```
**Python:**
```python
Narrow(dim, offset, length=1, input_shape=None, name=None)
```

**Parameters:**

* `dim`: The dimension to narrow. 0-based index. Cannot narrow the batch dimension. 
         -1 means the last dimension of the input.
* `offset`: Non-negative integer. The start index on the given dimension. 0-based index.
* `length`: The length to narrow. Default is 1.
            Can use a negative length such as -1 in the case where input size is unknown.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Narrow
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Narrow[Float](1, 1, inputShape = Shape(2, 3, 4)))
val input = Tensor[Float](2, 2, 3, 4).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
0.13770224      0.63719153      0.7776689       0.46612367
0.9026256       0.11982094      0.8282868       0.05095969
0.889799        0.6386537       0.35438475      0.298043

(1,2,.,.) =
0.5029727       0.20103335      0.20150806      0.06437344
0.2255908       0.5388977       0.59737855      0.5210477
0.4055072       0.11848069      0.7118382       0.9796308

(2,1,.,.) =
0.63957494      0.1921936       0.7749439       0.19744827
0.91683346      0.16140814      0.9753973       0.8161283
0.8481694       0.8802563       0.1233245       0.5732614

(2,2,.,.) =
0.275001        0.35905758      0.15939762      0.09233412
0.16610192      0.032060683     0.37298614      0.48936844
0.031097537     0.82767457      0.10246291      0.9951448

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x3x4]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.5029727       0.20103335      0.20150806      0.06437344
0.2255908       0.5388977       0.59737855      0.5210477
0.4055072       0.11848069      0.7118382       0.9796308

(2,1,.,.) =
0.275001        0.35905758      0.15939762      0.09233412
0.16610192      0.032060683     0.37298614      0.48936844
0.031097537     0.82767457      0.10246291      0.9951448

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x1x3x4]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import Narrow
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(Narrow(1, 1, input_shape=(2, 3, 4)))
input = np.random.rand(2, 2, 3, 4)
output = model.forward(input)
```
Input is:
```python
array([[[[0.74305305, 0.33925069, 0.31289333, 0.43703923],
         [0.28316902, 0.3004414 , 0.40298034, 0.37476436],
         [0.18825825, 0.38979411, 0.32963262, 0.37783457]],

        [[0.14824117, 0.43532988, 0.57077087, 0.91535978],
         [0.46375725, 0.90511296, 0.18859044, 0.92820822],
         [0.13675737, 0.48270908, 0.04260755, 0.97255687]]],
       [[[0.4836805 , 0.45262542, 0.7233705 , 0.63486529],
         [0.07472717, 0.5715716 , 0.57029986, 0.26475783],
         [0.56757079, 0.27602746, 0.45799196, 0.74420842]],

        [[0.89048761, 0.08280716, 0.99030481, 0.35956427],
         [0.70802689, 0.14425212, 0.08320864, 0.82271697],
         [0.6915224 , 0.70490768, 0.41218963, 0.37024863]]]])
```
Output is
```python
array([[[[0.14824118, 0.43532988, 0.57077086, 0.9153598 ],
         [0.46375725, 0.905113  , 0.18859044, 0.92820823],
         [0.13675737, 0.48270908, 0.04260755, 0.9725569 ]]],

       [[[0.8904876 , 0.08280716, 0.9903048 , 0.35956427],
         [0.7080269 , 0.14425212, 0.08320864, 0.82271695],
         [0.6915224 , 0.70490766, 0.41218963, 0.37024862]]]],
      dtype=float32)
```

---
### 7.26 Permute
Permutes the dimensions of the input according to a given pattern.

Useful for connecting RNNs and convnets together.

```scala
Permute(dims, inputShape = null)
```
**Python:**
```python
Permute(dims, input_shape=None, name=None)
```

**Parameters:**

* `dims`: Int array. Permutation pattern, does not include the batch dimension.
          Indexing starts at 1.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.Permute
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential[Float]()
model.add(Permute[Float](Array(2, 1, 3), inputShape = Shape(2, 2, 3)))
val input = Tensor[Float](2, 2, 2, 3).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
0.8451549       0.06361471      0.7324815
0.31086245      0.21210302      0.35112163

(1,2,.,.) =
0.61466074      0.50173014      0.8759959
0.19090249      0.671227        0.73089105
(2,1,.,.) =
0.47867084      0.9341955       0.063592255
0.24063066      0.502274        0.9114748
(2,2,.,.) =
0.93335986      0.25173688      0.88615775
0.5394321       0.330763        0.89036304

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x2x3]
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.8451549       0.06361471      0.7324815
0.61466074      0.50173014      0.8759959

(1,2,.,.) =
0.31086245      0.21210302      0.35112163
0.19090249      0.671227        0.73089105
(2,1,.,.) =
0.47867084      0.9341955       0.063592255
0.93335986      0.25173688      0.88615775
(2,2,.,.) =
0.24063066      0.502274        0.9114748
0.5394321       0.330763        0.89036304

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import Permute
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(Permute((2, 1, 3), input_shape=(2, 2, 3)))
input = np.random.rand(2, 2, 2, 3)
output = model.forward(input)
```
Input is:
```python
array([[[[0.14016896, 0.7275626 , 0.79087092],
         [0.57259566, 0.97387138, 0.70001999]],

        [[0.9232002 , 0.07644555, 0.24705828],
         [0.17257354, 0.93951155, 0.46183983]]],
       [[[0.79432476, 0.64299062, 0.33959594],
         [0.58608318, 0.338014  , 0.92602687]],

        [[0.32638575, 0.69032582, 0.25168083],
         [0.46813027, 0.95118373, 0.13145026]]]])
```
Output is
```python
array([[[[0.14016896, 0.7275626 , 0.7908709 ],
         [0.9232002 , 0.07644555, 0.24705827]],

        [[0.57259566, 0.97387135, 0.70002   ],
         [0.17257354, 0.93951154, 0.46183982]]],
       [[[0.79432476, 0.64299065, 0.33959594],
         [0.32638577, 0.6903258 , 0.25168082]],
        [[0.5860832 , 0.338014  , 0.9260269 ],
         [0.46813026, 0.95118374, 0.13145027]]]], dtype=float32)
```
---
### 7.27 ResizeBilinear
Resize the input image with bilinear interpolation. The input image must be a float tensor with NHWC or NCHW layout.

```scala
ResizeBilinear(outputHeight, outputWidth, alignCorners = false, dimOrdering = "th", inputShape = null)
```
**Python:**
```python
ResizeBilinear(output_height, output_width, align_corner=False, dim_ordering="th", input_shape=(2, 3, 5, 7), name=None)
```

**Parameters:**

* `outputHeight`: output height
* `outputWidth`: output width
* `alignCorners`: align corner or not
* `dimOrdering`: Format of input data. Either DataFormat.NCHW (dimOrdering='th') or DataFormat.NHWC (dimOrdering='tf'). Default is NCHW.
* `inputShape`: Only need to specify this argument when you use this layer as the first layer of a model. For Scala API, it should be a [`Shape`](../keras-api-scala/#shape) object. For Python API, it should be a shape tuple. Batch dimension should be excluded.

**Scala example:**
```scala
import com.intel.analytics.bigdl.dllib.keras.models.Sequential
import com.intel.analytics.bigdl.dllib.keras.layers.ResizeBilinear
import com.intel.analytics.bigdl.dllib.utils.Shape
import com.intel.analytics.bigdl.tensor.Tensor

val model = Sequential()
model.add(ResizeBilinear[Float](2, 3, inputShape = Shape(2, 3, 5)))
val input = Tensor[Float](2, 2, 3, 5).rand()
val output = model.forward(input)
```
Input is:
```scala
input: com.intel.analytics.bigdl.tensor.Tensor[Float] =
(1,1,.,.) =
0.6991891       0.007127314     0.73871046      0.95916307      0.9433856
0.41275907      0.37573513      0.99193203      0.06930728      0.5922364
0.024281504     0.2592453       0.3898136       0.6635241       0.85888565

(1,2,.,.) =
0.38028112      0.43709648      0.62538666      0.8468501       0.6445014
0.45252413      0.48801896      0.59471387      0.013207023     0.3567462
0.85187584      0.49279585      0.7973665       0.81287366      0.07852263

(2,1,.,.) =
0.1452374       0.6140467       0.36384684      0.066476084     0.96101314
0.54862195      0.66091377      0.86857307      0.6844842       0.7368217
0.25342992      0.71737933      0.12789607      0.21691357      0.7543404

(2,2,.,.) =
0.79176855      0.1204049       0.58971256      0.115073755     0.10459962
0.5225398       0.742363        0.7612815       0.9881919       0.13359445
0.9026869       0.13972941      0.92064524      0.9435532       0.5502235

[com.intel.analytics.bigdl.tensor.DenseTensor of...
```
Output is:
```scala
output: com.intel.analytics.bigdl.nn.abstractnn.Activity =
(1,1,.,.) =
0.6991891       0.4948494       0.9539039
0.21852028      0.5664119       0.48613077

(1,2,.,.) =
0.38028112      0.56262326      0.7794005
0.6522  0.6274959       0.34790504

(2,1,.,.) =
0.1452374       0.4472468       0.36465502
0.40102595      0.5618719       0.54899293

(2,2,.,.) =
0.79176855      0.43327665      0.111582376
0.71261334      0.70765764      0.75788474

[com.intel.analytics.bigdl.tensor.DenseTensor of size 2x2x2x3]
```

**Python example:**
```python
from bigdl.dllib.keras.layers import ResizeBilinear
from bigdl.dllib.keras.models import Sequential
import numpy as np

model = Sequential()
model.add(ResizeBilinear(2, 3, input_shape=(2, 3, 5, 5)))
input = np.random.rand(2, 2, 3, 5, 5)
output = model.forward(input)
```
Input is:
```python
array([[[[0.43790358, 0.41882914, 0.71929122, 0.19673119, 0.36950189],
         [0.38808651, 0.34287751, 0.34076998, 0.02581254, 0.42406155],
         [0.84648848, 0.18411068, 0.97545126, 0.5468195 , 0.32136674]],

        [[0.32965599, 0.06883324, 0.17350748, 0.01181338, 0.59180775],
         [0.24667588, 0.36422516, 0.59648387, 0.48699443, 0.32323264],
         [0.67661373, 0.58779956, 0.55286771, 0.59629101, 0.69727522]]],


       [[[0.09462238, 0.35658325, 0.6787812 , 0.78676645, 0.99019452],
         [0.81501527, 0.13348641, 0.71749101, 0.40543351, 0.3959018 ],
         [0.608378  , 0.10531177, 0.78000335, 0.51679768, 0.65067605]],

        [[0.12074634, 0.92682843, 0.52227042, 0.98856558, 0.28105255],
         [0.78411841, 0.19625097, 0.83108171, 0.03777509, 0.15700493],
         [0.95528158, 0.94003855, 0.61092905, 0.68651048, 0.57563719]]]])
```
Output is
```python
array([[[[0.43790358, 0.61913717, 0.2543214 ],
         [0.6172875 , 0.52657175, 0.3151154 ]],

        [[0.329656  , 0.13861606, 0.20514478],
         [0.46164483, 0.541788  , 0.5311798 ]]],


       [[[0.09462238, 0.57138187, 0.8545758 ],
         [0.7116966 , 0.5389645 , 0.48184   ]],

        [[0.12074634, 0.6571231 , 0.752728  ],
         [0.86969995, 0.6700518 , 0.36353552]]]], dtype=float32)
```
---
## 8. Persistence
This section describes how to save and load the Keras-like API.

### 8.1 save
To save a Keras model, you call the method `saveModel(path)`.

**Scala:**
```scala
import com.intel.analytics.bigdl.dllib.keras.layers.{Dense, Activation}
import com.intel.analytics.bigdl.dllib.keras.models.Sequential

val model = Sequential[Float]()
model.add(Dense[Float](32, inputShape = Shape(128)))
model.add(Activation[Float]("relu"))
model.saveModel("/tmp/seq.model")
```
**Python:**
```python
import bigdl.dllib.keras.Sequential
from bigdl.dllib.keras.layer import Dense

model = Sequential()
model.add(Dense(input_shape=(32, )))
model.saveModel("/tmp/seq.model")
```

### 8.2 load
To load a saved Keras model, you call the method `load_model(path)`.

**Scala:**
```scala
import com.intel.analytics.bigdl.dllib.keras.Models

val model = Models.loadModel[Float]("/tmp/seq.model")
```

**Python:**
```python
from bigdl.dllib.keras.models
model = load_model("/tmp/seq.model")
```
