CumSum¶

Versioned name: CumSum-3

Category: Arithmetic unary

Short description: CumSum performs cumulative summation of the input elements along the given axis.

Detailed description: CumSum performs cumulative summation of the input elements along the axis specified by the second input. By default, the j-th output element is the inclusive sum of the first j elements in the given sequence, and the first element in the sequence is copied to the output as is. In the exclusive mode the j-th output element is the sum of the first j-1 elements and the first element in the output sequence is 0. To perform the summation in the opposite direction of the axis, set reverse attribute to true.

Attributes:

exclusive
- Description: If the attribute is set to true, then exclusive sums are returned, the j-th element is not included in the j-th sum. Otherwise, the inclusive sum of the first j elements for the j-th element is calculated.
- Range of values:
  - false - include the top element
  - true - do not include the top element
- Type: boolean
- Default value: false
- Required: no
reverse
- Description: If set to true will perform the sums in reverse direction.
- Range of values:
  - false - do not perform sums in reverse direction
  - true - perform sums in reverse direction
- Type: boolean
- Default value: false
- Required: no

Inputs

1: A tensor of type T and rank greater or equal to 1. Required.
2: Axis index along which the cumulative sum is performed. A scalar of type T_AXIS. Negative value means counting dimensions from the back. Default value is 0. Optional.

Outputs

1: Output tensor with cumulative sums of the input elements. A tensor of type T of the same shape as the first input.

Types

T: any numeric type.
T_AXIS: int64 or int32.

Examples

Example 1

<layer ... type="CumSum" exclusive="0" reverse="0">
    <input>
        <port id="0">     <!-- input value is: [1., 2., 3., 4., 5.] -->
            <dim>5</dim>
        </port>
        <port id="1"/>     <!-- axis value is: 0 -->
    </input>
    <output>
        <port id="2">     <!-- output value is: [1., 3., 6., 10., 15.] -->
            <dim>5</dim>
        </port>
    </output>
</layer>

Example 2

<layer ... type="CumSum" exclusive="1" reverse="0">
    <input>
        <port id="0">     <!-- input value is: [1., 2., 3., 4., 5.] -->
            <dim>5</dim>
        </port>
        <port id="1"/>     <!-- axis value is: 0 -->
    </input>
    <output>
        <port id="2">     <!-- output value is: [0., 1., 3., 6., 10.] -->
            <dim>5</dim>
        </port>
    </output>
</layer>

Example 3

<layer ... type="CumSum" exclusive="0" reverse="1">
    <input>
        <port id="0">     <!-- input value is: [1., 2., 3., 4., 5.] -->
            <dim>5</dim>
        </port>
        <port id="1"/>     <!-- axis value is: 0 -->
    </input>
    <output>
        <port id="2">     <!-- output value is: [15., 14., 12., 9., 5.] -->
            <dim>5</dim>
        </port>
    </output>
</layer>

Example 4

<layer ... type="CumSum" exclusive="1" reverse="1">
    <input>
        <port id="0">     < -- input value is: [1., 2., 3., 4., 5.] -->
            <dim>5</dim>
        </port>
        <port id="1"/>     < -- axis value is: 0 -->
    </input>
    <output>
        <port id="2">     < -- output value is: [14., 12., 9., 5., 0.] -->
            <dim>5</dim>
        </port>
    </output>
</layer>