Cumulative Sum

Cumulative sum of channel, column, or row elements

• 

Libraries:
DSP System Toolbox / Math Functions / Math Operations

Description

The Cumulative Sum block computes the cumulative sum along the specified dimension of the input or across time (running sum).

Ports

Input

In — Input signal

vector | matrix

Input, specified as a vector or as matrix inputs containing real or complex values.

This port is unnamed until you select a non-None value for the Reset port parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point
Complex Number Support: Yes

Rst — Reset port

scalar

The optional reset port, Rst, accepts scalar values, which can be any built-in Simulink^® data type including boolean. The rate of the input to the Rst port must be the same or slower than that of the input data signal. The sample time of the input to the Rst port must be a positive integer multiple of the input sample time.

This port is unnamed until you select a non-None value for the Reset port parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean

Output

Out — Cumulative sum

vector | matrix

Cumulative sum of input, specified as a vector or a matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Parameters

Main

Sum input along — Dimension to sum along

Channels (running sum) (default) | Columns | Rows

Specify the dimension along which to compute the cumulative summations. You can choose to sum along Channels (running sum), Columns, or Rows. For more information, see these sections:

• Computing the Running Sum Along Channels of the Input

• Summing Along Columns

• Summing Along Rows

Input processing — Method to process the input

Columns as channels (frame based) (default) | Elements as channels (sample based)

Specify how the block processes the input when computing the running sum along the channels of the input. You can set this parameter to one of these options:

• Columns as channels (frame based) — The block treats each column of the input as a separate channel.

• Elements as channels (sample based) — The block treats each element of the input as a separate channel.

Dependencies

This parameter is available only when you set the Sum input along parameter to Channels (running sum).

Reset port — Reset type

None (default) | Rising edge | Falling edge | Either edge | Non-zero sample

Determines the reset event that causes the block to reset the sum along channels. The rate of the input to the Rst port must be the same or slower than that of the input data signal. The sample time of the input to the Rst port must be a positive integer multiple of the input sample time. For more information, see Resetting the Running Sum.

Dependencies

This parameter is available only when you set the Sum input along parameter to Channels (running sum).

Data Types

Note

Floating-point inheritance takes precedence over the data type settings defined on this pane. When inputs are floating point, the block ignores these settings. All internal data types are floating point.

Rounding mode — Rounding mode

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Specify the rounding mode for fixed-point operations as one of the following:

• Floor

• Ceiling

• Convergent

• Nearest

• Round

• Simplest

• Zero

For more details, see rounding mode.

Saturate on integer overflow — Saturate for fixed-point operation

off (default) | on

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Accumulator — Data type of accumulator

Inherit: Same as first input (default) | fixdt([],16,0)

Accumulator specifies the data type of the output of an accumulation operation in the Cumulative Sum block. For illustrations on how to use the accumulator data type in this block, see Fixed-Point Data Types.

• Inherit: Same as input — The block specifies the accumulator data type to be the same as the input data type.

• fixdt([],16,0) — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Accumulator data type by using the Data Type Assistant. Click the Show data type assistant button.

For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Output — Data type of output

Inherit: Same as accumulator (default) | Inherit: Same as input | fixdt([],16,0)

Output specifies the data type of the output of the Cumulative Sum block. For more information on the output data type, see Fixed-Point Data Types.

• Inherit: Same as input — The block specifies the output data type to be the same as the input data type.

• Inherit: Same as accumulator — The block specifies the output data type to be the same as the accumulator data type.

• fixdt([],16,0) — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Output data type by using the Data Type Assistant. Click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

Output Minimum — Minimum value the block can output

[] (default) | scalar

Specify the minimum value the block can output. Simulink software uses this minimum value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Output Maximum — Maximum value block can output

[] (default) | scalar

Specify the maximum value the block can output. Simulink software uses this maximum value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

Data Types	double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

More About

Computing the Running Sum Along Channels of the Input

When you set the Sum input along parameter to Channels (running sum), the block computes the cumulative sum of the elements in each input channel. The running sum of the current input takes into account the running sum of all previous inputs. In this mode, you must also specify a value for the Input processing parameter.

When you set the Input processing parameter to:

• Columns as channels (frame based) –– The block computes the running sum along each column of the current input.

• Elements as channels (sample based) –– The block computes a running sum for each element of the input across time.

Computing the Running Sum for Each Column of the Input

When you set the Input processing parameter to Columns as channels (frame based), the block treats each input column as an independent channel. As the following figure and equation illustrate, the output has the following characteristics:

• The first row of the first output is the same as the first row of the first input.

• The first row of each subsequent output is the sum of the first row of the current input (time t), and the last row of the previous output (time t - T_f, where T_f is the frame period).

• The output has the same size, dimension, data type, and complexity as the input.

Given an M-by-N matrix input, u, the output, y, is an M-by-N matrix whose first row has elements

$$y_{1,j}(t)=u_1{,}_j(t)+y_{M,j}(t-T_f)$$

Computing the Running Sum for Each Element of the Input

When you set the Input processing parameter to Elements as channels (sample based), the block treats each element of the input matrix as an independent channel. As the following figure and equation illustrate, the output has these characteristics:

• The first output is the same as the first input.

• Each subsequent output is the sum of the current input (time t) and the previous output (time t - T_s, where T_s is the sample period).

• The output has the same size, dimension, data type, and complexity as the input.

Given an M-by-N matrix input, u, the output, y, is an M-by-N matrix with the elements

$$y_{i,j}(t)=u_{i,j}(t)+y_{i,j}(t-T_s)\begin{array}{c}1\le i\le M\\ 1\le j\le N\end{array}$$

Resetting the Running Sum

When you are computing the running sum, you can configure the block to reset the running sum whenever it detects a reset event at the optional Rst port. The rate of the input to the Rst port must be the same or slower than that of the input data signal. The sample time of the input to the Rst port must be a positive integer multiple of the input sample time. The reset sample time must be a positive integer multiple of the input sample time. The input to the Rst port can be boolean.

If a reset event occurs while the block is performing sample-based processing, the block initializes the current output to the values of the current input. If a reset event occurs while the block is performing frame-based processing, the block initializes the first row of the current output to the values in the first row of the current input.

The Reset port parameter specifies the reset event, which can be one of the following:

• None disables the Rst port.

• Rising edge — Triggers a reset operation when the Rst input does one of the following:

  • Rises from a negative value to a positive value or zero

  • Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero

    

• Falling edge — Triggers a reset operation when the Rst input does one of the following:

  • Falls from a positive value to a negative value or zero

  • Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero

    

• Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge

• Non-zero sample — Triggers a reset operation at each sample time that the Rst input is not zero

Note

When you run simulations in the Simulink MultiTasking mode, reset signals have a one-sample latency. When the block detects a reset event, a one-sample delay occurs at the reset port rate before the block applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

Summing Along Columns

When you set the Sum input along parameter to Columns, the block computes the cumulative sum of each column of the input. In this mode, the current cumulative sum is independent of the cumulative sums of previous inputs.

y = cumsum(u) % Equivalent MATLAB code 

The output has the same size, dimension, data type, and complexity as the input. The mth output row is the sum of the first m input rows.

Given an M-by-N input, u, the output, y, is an M-by-N matrix whose jth column has elements

$$y_{i,j}={\displaystyle \sum _{k=1}^j{u}_{k,j}}1\le i\le M$$

The block treats length-M unoriented vector inputs as M-by-1 column vectors when summing along columns.

Summing Along Rows

When you set the Sum input along parameter to Rows, the block computes the cumulative sum of the row elements. In this mode, the current cumulative sum is independent of the cumulative sums of previous inputs.

y = cumsum(u,2)						% Equivalent MATLAB code 

The output has the same size, dimension, and data type as the input. The nth output column is the sum of the first n input columns.

Given an M-by-N input, u, the output, y, is an M-by-N matrix whose ith row has elements

$$y_{i,j}={\displaystyle \sum _{k=1}^j{u}_{i,k}}1\le j\le N$$

When you sum along rows, the block treats length-N unoriented vector inputs as 1-by-N row vectors.

Fixed-Point Data Types

The following diagram shows the data types used within the Cumulative Sum block for fixed-point signals.

You can set the accumulator and output data types in the block dialog box.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a