ReduceL1¶

Versioned name : ReduceL1-4

Category : Reduction

Short description : ReduceL1 operation performs the reduction with finding the L1 norm (sum of absolute values) on a given input data along dimensions specified by axes input.

Detailed Description

ReduceL1 operation performs the reduction with finding the L1 norm (sum of absolute values) on a given input data along dimensions specified by axes input. Each element in the output is calculated as follows:

output[i0, i1, ..., iN] = L1[j0, ..., jN](x[j0, ..., jN]))

where indices i0, …, iN run through all valid indices for input data, and finding the L1 norm L1[j0, ..., jN] has jk = ik for those dimensions k that are not in the set of indices specified by axes input.

Particular cases:

If axes is an empty list, ReduceL1 corresponds to the identity operation.
If axes contains all dimensions of input data, a single reduction value is calculated for the entire input tensor.

Attributes

keep_dims
- Description : If set to true, it holds axes that are used for the reduction. For each such axis, the output dimension is equal to 1.
- Range of values : true or false
- Type : boolean
- Default value : false
- Required : no

Inputs

1 : data - A tensor of type T and arbitrary shape. Required.
2 : axes - Axis indices of data input tensor, along which the reduction is performed. A scalar or 1D tensor of unique elements and type T_IND. The range of elements is [-r, r-1], where r is the rank of data input tensor. Required.

Outputs

1 : The result of ReduceL1 function applied to data input tensor. A tensor of type T and shape[i] = shapeOf(data)[i] for all i dimensions not in axes input tensor. For dimensions in axes, shape[i] == 1 if keep_dims == true; otherwise, the i -th dimension is removed from the output.

Types

T : any supported numeric type.
T_IND : any supported integer type.

Examples

<layer id="1" type="ReduceL1" ...>
    <data keep_dims="true" />
    <input>
        <port id="0">
            <dim>6</dim>
            <dim>12</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
        <port id="1">
            <dim>2</dim>         <!-- value is [2, 3] that means independent reduction in each channel and batch -->
        </port>
    </input>
    <output>
        <port id="2">
            <dim>6</dim>
            <dim>12</dim>
            <dim>1</dim>
            <dim>1</dim>
        </port>
    </output>
</layer>

<layer id="1" type="ReduceL1" ...>
    <data keep_dims="false" />
    <input>
        <port id="0">
            <dim>6</dim>
            <dim>12</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
        <port id="1">
            <dim>2</dim>         <!-- value is [2, 3] that means independent reduction in each channel and batch -->
        </port>
    </input>
    <output>
        <port id="2">
            <dim>6</dim>
            <dim>12</dim>
        </port>
    </output>
</layer>

<layer id="1" type="ReduceL1" ...>
    <data keep_dims="false" />
    <input>
        <port id="0">
            <dim>6</dim>
            <dim>12</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
        <port id="1">
            <dim>1</dim>         <!-- value is [1] that means independent reduction in each channel and spatial dimensions -->
        </port>
    </input>
    <output>
        <port id="2">
            <dim>6</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
    </output>
</layer>

<layer id="1" type="ReduceL1" ...>
    <data keep_dims="false" />
    <input>
        <port id="0">
            <dim>6</dim>
            <dim>12</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
        <port id="1">
            <dim>1</dim>         <!-- value is [-2] that means independent reduction in each channel, batch and second spatial dimension -->
        </port>
    </input>
    <output>
        <port id="2">
            <dim>6</dim>
            <dim>12</dim>
            <dim>24</dim>
        </port>
    </output>
</layer>