Cumulative product of channel, column, or row elements
Math Functions / Math Operations
dspmathops
The Cumulative Product block computes the cumulative product along the specified dimension of the input or across time (running product).
The input can be a vector or matrix. The output always has the same dimensions, rate, data type, and complexity as the input.
The Cumulative Product block accepts vector or matrix inputs containing real or complex values.
The optional reset port, Rst
, accepts scalar
values, which can be any builtin 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.
The output always has the same dimensions, rate, data type, and complexity as the data signal 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:
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 elementwise 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 MbyN matrix input, u, the output, y, is an MbyN matrix whose first row has elements
$${y}_{1,j}\left(t\right)={u}_{1,j}\left(t\right)\cdot {y}_{M,j}\left(t{T}_{f}\right)$$
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 the following characteristics:
The first output is the same as the first input.
Each subsequent output is the elementwise 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 MbyN matrix input, u, the output, y, is an MbyN matrix with the elements
$${y}_{i,j}(t)={u}_{i,j}(t)\cdot {y}_{i,j}(t{T}_{s})\text{\hspace{0.17em}}\text{\hspace{0.17em}}\begin{array}{c}1\le i\le M\\ 1\le j\le N\end{array}$$
For convenience, the block treats lengthM unoriented vector inputs as Mby1 column vectors when multiplying along channels. In such cases, the output is a lengthM unoriented vector.
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 samplebased processing, the block initializes the current output to the values of the current input. If a reset event occurs while the block is performing framebased 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 the following 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 the following figure)
Either edge
— Triggers
a reset operation when the Rst
input is a Rising
edge
or Falling edge
(as
described above)
Nonzero sample
—
Triggers a reset operation at each sample time that the Rst
input
is not zero
Note:
When you run simulations in Simulink 
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.
y = cumprod(u) % Equivalent MATLAB code
The output has the same size, dimension, data type, and complexity as the input. The mth output row is the elementwise product of the first m input rows.
Given an MbyN input, u, the output, y, is an MbyN matrix whose jth column has elements
$${y}_{i,j}={\displaystyle \prod _{k=1}^{i}{u}_{k,j}}\text{}1\le i\le M$$
When multiplying along columns, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
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.
y = cumprod(u,2) % Equivalent MATLAB code
The output has the same size, dimension, and data type as the input. The nth output column is the elementwise product of the first n input columns.
Given an MbyN matrix input, u, the output, y, is an MbyN matrix whose ith row has elements
$${y}_{i,j}={\displaystyle \prod _{k=1}^{j}{u}_{i,k}}\text{}1\le j\le N$$
When you multiply along rows, the block treats lengthN unoriented vector inputs as 1byN row vectors.
The following diagram shows the data types used within the Cumulative Product block for fixedpoint 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 as discussed in Dialog Box.
The Main pane of the Cumulative Product block dialog appears as follows.
Specify the dimension along which to compute the cumulative
product. You can choose to multiply along Channels (running
product)
, Columns
, or Rows
.
For more information, see the following sections:
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)
—
When you select this option, the block treats each column of the input
as a separate channel.
Elements as channels (sample based)
—
When you select this option, the block treats each element of the
input as a separate channel.
This parameter is available only when you set the Multiply
input along parameter to Channels (running
product)
.
Determines the reset event that causes the block to reset the
product 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. This parameter appears only when you set
the Multiply input along parameter to Channels
(running product)
. For more information, see Resetting the Running Product.
The Data Types pane of the Cumulative Product block dialog appears as follows.
Note: Floatingpoint 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. 
Select the rounding mode for fixedpoint operations.
Select the overflow mode for fixedpoint operations.
Specify the intermediate product data type. As shown in FixedPoint 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 data type parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the product output data type. See FixedPoint 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 data type parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the accumulator data type. See FixedPoint 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
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 data type parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the output data type. See FixedPoint 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
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 Output data type parameter.
See Control Signal Data Types (Simulink) for more information.
Specify the minimum value that the block should output. The
default value is []
(unspecified). Simulink software
uses this value to perform:
Simulation range checking (see Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
Specify the maximum value that the block should output. The
default value is []
(unspecified). Simulink software
uses this value to perform:
Simulation range checking (see Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Input and Output Ports  Supported Data Types 

Data input port, 

Reset input port,  All builtin Simulink data types:

Output port 

Cumulative Sum  DSP System Toolbox 
Matrix Product  DSP System Toolbox 
cumprod  MATLAB 