Cumulative Product

Cumulative product of channel, column, or row elements

• 

Libraries:
DSP System Toolbox / Math Functions / Math Operations

Description

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

Ports

Input

In — Input signal

vector | matrix

Specify the input signal as a vector or a matrix.

This port is unnamed until you set the Reset port parameter to any value other than None.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | 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^® numeric 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.

For more information on this port, see Resetting Running Product.

Dependencies

This port is unnamed until you set the Reset port parameter to any value other than None.

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

Output

Out — Cumulative product

vector | matrix

Cumulative product of the signal, returned as a vector or a matrix.

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

Parameters

Main Tab

Multiply input along — Dimension to multiply input along

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

Specify the dimension along which to compute the cumulative product. You can set this parameter to one of these options:

• Channels (running product)

• Columns

• Rows

For more information, see the following sections:

• Computing Running Product Along Channels of Input

• Multiplying Along Columns

• Multiplying Along Rows

Input processing — Input processing

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

Specify how the block should process the input when computing the running product along the channels of the input. You can set this parameter to one of the following 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.

For more information, see Computing Running Product Along Channels of Input.

Dependencies

To enable this parameter, set the Multiply input along parameter to Channels (running product).

Reset port — Reset type

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

Specify the reset event that causes the block to reset the product along channels. You can set this parameter to one of these options:

• None

• Rising edge

• Falling edge

• Either edge

• Non-zero sample

For more information on these options, see Resetting Running Product.

Dependencies

To enable this parameter, set the Multiply input along parameter to Channels (running product).

Data Types Tab

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, and 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 on integer overflow

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.

Intermediate product — Intermediate product

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

Specify the intermediate product data type. As shown in Fixed-Point Data Types, the output of the multiplier is cast to the intermediate product data type before the next element of the input is multiplied into it. You can set it to:

• A rule that inherits a data type, for example, Inherit: Same as input

• An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Product output — Product output

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

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:

• A rule that inherits a data type, for example, Inherit: Same as input

• An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Accumulator — Accumulator

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

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example, Inherit: Same as input

• A rule that inherits a data type, for example, Inherit: Same as product output

• An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Output — Output

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

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set it to:

• A rule that inherits a data type, for example, Inherit: Same as input

• A rule that inherits a data type, for example, Inherit: Same as product output

• An expression that evaluates to a valid data type, for example, fixdt([],16,0)

If both inputs are unsigned, all data types including the output data type is unsigned. If one of the inputs is signed, internal and output data types are signed.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Data Types of Signals (Simulink) for more information.

Output Minimum — Minimum

[] (default)

Specify the minimum value that the block must output. The default value is [] (unspecified). Simulink uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Output Maximum — Maximum

[] (default)

Specify the maximum value that the block must output. The default value is [] (unspecified). Simulink uses this 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 Running Product Along Channels of Input

When you set the Multiply input along parameter to Channels (running product), the block computes the cumulative product of the elements in each input channel. The running product of the current input takes into account the running product 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 product along each column of the current input. When you set the Input processing parameter to Elements as channels (sample based), the block computes a running product for each element of the input across time. See the following sections for more information.

Computing Running Product for Each Column of 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 these 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 element-wise product 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

$$y_{1,j}\left(t\right)=u_{1,j}\left(t\right)\cdot y_{M,j}\left(t-T_f\right).$$

Computing Running Product for Each Element of 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 element-wise product 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

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

For convenience, the block treats length-M unoriented vector inputs as M-by-1 column vectors when multiplying along channels. In such cases, the output is a length-M unoriented vector.

Resetting Running Product

When you are computing the running product, you can configure the block to reset the running product 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 input to the Rst port can be of the Boolean data type.

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 (see figure)

    

• 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 (see figure)

    

• Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge (as described above)

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

Note

When you run simulations in 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).

Multiplying Along Columns

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

The equivalent MATLAB^® code is

y = cumprod(u).

The output has the same size, dimension, data type, and complexity as the input. The mth output row is the element-wise product 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

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

When multiplying along columns, the block treats length-M unoriented vector inputs as M-by-1 column vectors.

Multiplying Along Rows

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

The equivalent MATLAB code is

y = cumprod(u,2).

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

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

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

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

Fixed-Point Data Types

This diagram shows the data types used within the Cumulative Product block for fixed-point signals.

The output of the multiplier is in the product output data type when at least one of the inputs to the multiplier is real. When both of the inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types. You can set the accumulator, product output, intermediate product, 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