Product of Elements
Copy or invert one scalar input, or collapse one nonscalar input
Libraries:
Simulink /
Math Operations
HDL Coder /
HDL Floating Point Operations
HDL Coder /
Math Operations
Description
The Product of Elements block inputs one scalar, vector, or matrix. You can use the block to:
Copy a scalar input unchanged
Invert a scalar input (divide 1 by it)
Collapse a vector or matrix to a scalar by multiplying together all elements or taking successive inverses of the elements
Collapse a matrix to a vector using one of these options:
Multiply together the elements of each row or column
Take successive inverses of the elements of each row or column
The Product of Elements block is functionally a Product block that has two preset parameter values:
Multiplication:
Elementwise(.*)
Number of inputs:
*
Setting nondefault values for either of those parameters can change a Product of Elements block to be functionally equivalent to a Product block or a Divide block.
Examples
ElementWise Multiplication and Division Using the Product of Elements Block
This example shows how to use the Product of Elements block to perform elementwise multiplication and division of inputs.
Complex Division Using the Product of Elements Block
This example shows how to perform elementwise complex division using the Product of Elements block.
The top Product of Elements block collapses the matrix input to a scalar by taking successive inverses of the four elements:
y = ((((1/2+i)/3)/4i)/5)
The bottom Product of Elements block collapses the matrix input to a vector by taking successive inverses along the second dimension:
y(1) = ((1/2+i)/3)
y(2) = ((1/4i)/5)
Ports
Input
Port_1 — First input to multiply or divide
scalar  vector  matrix  ND array
First input to multiply or divide, provided as a scalar, vector, matrix, or ND array.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Port_N — Nth input to multiply or divide
scalar  vector  matrix  ND array
Nth input to multiply or divide, provided as a scalar, vector, matrix, or ND array.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
X — Input signal to multiply
scalar  vector  matrix  ND array
Input signal to be multiplied with other inputs.
Dependencies
To enable one or more X ports, specify one or
more *
characters for the Number of
inputs parameter.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
÷ — Input signal to divide or invert
scalar  vector  matrix  ND array
Input signal for division or inversion operations.
Dependencies
To enable one or more ÷ ports, specify one or
more /
characters for the Number of
inputs parameter.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Output
Port_1 — Output computed by multiplying, dividing, or inverting inputs
scalar  vector  matrix  ND array
Output computed by multiplying, dividing, or inverting inputs.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Parameters
Main
Number of inputs — Control number of inputs and type of operation
*
(default)  positive integer scalar  *
or /
for each input
port
Control two properties of the block:
The number of input ports on the block
Whether each input is multiplied or divided into the output
When you specify:
1
or*
or/
The block has one input port. In elementwise mode, the block processes the input as described for the Product of Elements block. In matrix mode, if the parameter value is
1
or*
, the block outputs the input value. If the value is/
, the input must be a square matrix (including a scalar as a degenerate case) and the block outputs the matrix inverse. See ElementWise Mode and Matrix Mode for more information.Integer value > 1
The block has the number of inputs given by the integer value. The inputs are multiplied together in elementwise mode or matrix mode, as specified by the Multiplication parameter. See ElementWise Mode and Matrix Mode for more information.
Unquoted string of two or more
*
and/
charactersThe block has the number of inputs given by the length of the character vector. Each input that corresponds to a
*
character is multiplied into the output. Each input that corresponds to a/
character is divided into the output. The operations occur in elementwise mode or matrix mode, as specified by the Multiplication parameter. See ElementWise Mode and Matrix Mode for more information.
Programmatic Use
Block Parameter:
Inputs 
Type: character vector 
Values:
'2'  '*'  '**'  '*/'  '*/*' 
... 
Default:
'*' 
Multiplication — Elementwise (.*) or Matrix (*) multiplication
Elementwise(.*)
(default)  Matrix(*)
Specify whether the block performs Elementwise(.*)
or
Matrix(*)
multiplication.
Programmatic Use
Block Parameter:
Multiplication 
Type: character vector 
Values:
'Elementwise(.*)'  'Matrix(*)' 
Default:
'Elementwise(.*)' 
Apply over — How to apply function along specified dimensions
All dimensions
(default)  Specified dimension
Specify how to apply the function along specified dimensions.
All dimensions
— Apply function for all input values for all dimensions.For example, in this model, Multiplication is set to
Elementwise(.*)
, and Apply over is set toAll dimensions
. The block returns the product of all values from all dimensions.When you select
All dimensions
and select the configuration parameter Use algorithms optimized for rowmajor array layout, Simulink^{®} enables rowmajor algorithms for simulation. To generate rowmajor code, set configuration parameter Array layout (Simulink Coder) toRowmajor
, and select Use algorithms optimized for rowmajor array layout. The columnmajor and rowmajor algorithms differ only in the multiplication order. In some cases, due to operation function order on the same data set, you might experience minor numeric differences in the outputs of columnmajor and rowmajor algorithms.Specified dimensions
— Apply function for all input values for specified dimension.
Dependencies
To enable this parameter, set Number of
inputs to *
and
Multiplication to Elementwise
(.*)
.
Programmatic Use
Block Parameter:
CollapseMode 
Type: character vector 
Values:
'All dimensions'  'Specified
dimension' 
Default:
'All dimensions' 
Dimension — Dimension along which to multiply
1
(default)  positive integer
Specify the dimension along which to multiply, as a
positive integer. For example, for a 2D matrix, 1
applies the function to each column, and 2
applies
the function to each row.
For example, in this model,
Multiplication is set to
Elementwise(.*)
,
Apply over is set to
Specified dimension
,
and Dimension is set to
2
. The block returns the
product of all values from each row.
Dependencies
To enable this parameter:
Set Number of inputs to
*
Set Multiplication to
Elementwise (.*)
Set Apply over to
Specified dimension
Programmatic Use
Block
Parameter:
CollapseDim 
Type: character vector 
Values:
'1'  '2'  ... 
Default:
'1' 
Sample time (1 for inherited) — Interval between samples
1
(default)  scalar  vector
Specify the time interval between samples. To inherit the sample time, set this
parameter to 1
. For more information, see Specify Sample Time.
Dependencies
This parameter is visible only if you set it to a value other than
1
. To learn more, see Blocks for Which Sample Time Is Not Recommended.
Programmatic Use
Block Parameter:
SampleTime 
Type: string scalar or character vector 
Default:
"1" 
Signal Attributes
Require all inputs to have the same data type — Require that all inputs have the same data type
off
(default)  on
Specify if input signals must all have the same data type. If you enable this parameter, then an error occurs during simulation if the input signal types are different.
Programmatic Use
Block Parameter:
InputSameDT 
Type: character vector 
Values:
'off'  'on' 
Default:
'off' 
Output minimum — Minimum output value for range checking
[]
(default)  scalar
Lower value of the output range that Simulink checks.
Simulink uses the minimum to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (see Specify Signal Ranges and Enable Simulation Range Checking).
Automatic scaling of fixedpoint data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, see Optimize using the specified minimum and maximum values (Embedded Coder).
Note
Output minimum does not saturate or clip the actual output signal. Use the Saturation block instead.
Programmatic Use
Block Parameter:
OutMin 
Type: character vector 
Values: '[ ]' 
scalar 
Default: '[ ]' 
Output maximum — Maximum output value for range checking
[]
(default)  scalar
Upper value of the output range that Simulink checks.
Simulink uses the maximum value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (see Specify Signal Ranges and Enable Simulation Range Checking).
Automatic scaling of fixedpoint data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, see Optimize using the specified minimum and maximum values (Embedded Coder).
Note
Output maximum does not saturate or clip the actual output signal. Use the Saturation block instead.
Programmatic Use
Block Parameter:
OutMax 
Type: character vector 
Values: '[ ]' 
scalar 
Default: '[ ]' 
Output data type — Specify the output data type
Inherit: Inherit via internal
rule
(default)  Inherit: Inherit via back propagation
 Inherit: Same as first input
 double
 single
 int8
 uint8
 int16
 uint16
 int32
 uint32
 int64
 uint64
 fixdt(1,16)
 fixdt(1,16,0)
 fixdt(1,16,2^0,0)
 <data type expression>
Choose the data type for the output. The type can be inherited, specified
directly, or expressed as a data type object such as
Simulink.NumericType
. For more information, see
Control Data Types of Signals.
When you select an inherited option, the block behaves as follows:
Inherit: Inherit via internal rule
— Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. For example, if the block multiplies an input of typeint8
by a gain ofint16
andASIC/FPGA
is specified as the targeted hardware type, the output data type issfix24
. IfUnspecified (assume 32bit Generic)
, in other words, a generic 32bit microprocessor, is specified as the target hardware, the output data type isint32
. If none of the word lengths provided by the target microprocessor can accommodate the output range, Simulink software displays an error in the Diagnostic Viewer.It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn’t meet your specific needs for numerical accuracy or performance, use one of the following options:
Specify the output data type explicitly.
Use the simple choice of
Inherit: Same as input
.Explicitly specify a default data type such as
fixdt(1,32,16)
and then use the FixedPoint Tool to propose data types for your model. For more information, seefxptdlg
(FixedPoint Designer).To specify your own inheritance rule, use
Inherit: Inherit via back propagation
and then use a Data Type Propagation block. Examples of how to use this block are available in the Signal Attributes library Data Type Propagation Examples block.
Inherit: Inherit via back propagation
— Use data type of the driving block.Inherit: Same as first input
— Use data type of first input signal.
Dependencies
When input is a floatingpoint data type smaller than single
precision, the Inherit: Inherit via internal
rule
output data type depends on the setting
of the Inherit floatingpoint output type smaller than single precision configuration parameter. Data types are smaller than single
precision when the number of bits needed to encode the data type is
less than the 32 bits needed to encode the singleprecision data
type. For example, half
and
int16
are smaller than single
precision.
Programmatic Use
Block Parameter:
OutDataTypeStr 
Type: character vector 
Values: 'Inherit:
Inherit via internal rule 
'Inherit: Same as first input' 
'Inherit: Inherit via back
propagation'  'double'
 'single'  'int8' 
'uint8' 
'int16' 
'uint16' 
'int32' 
'uint32' 
'int64' 
'uint64' 
'fixdt(1,16)' 
'fixdt(1,16,0)' 
'fixdt(1,16,2^0,0)' 
'<data type
expression>' 
Default: 'Inherit:
Inherit via internal rule' 
Lock output data type setting against changes by the fixedpoint tools — Option to prevent fixedpoint tools from overriding Output data type
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the Output data type you specify on the block. For more information, see Use Lock Output Data Type Setting (FixedPoint Designer).
Programmatic Use
Block Parameter:
LockScale 
Type: character vector 
Values:
'off'  'on' 
Default:
'off' 
Integer rounding mode — Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Select the rounding mode for fixedpoint operations. You can select:
Ceiling
Rounds positive and negative numbers toward positive infinity. Equivalent to the MATLAB^{®}
ceil
function.Convergent
Rounds number to the nearest representable value. If a tie occurs, rounds to the nearest even integer. Equivalent to the FixedPoint Designer™
convergent
function.Floor
Rounds positive and negative numbers toward negative infinity. Equivalent to the MATLAB
floor
function.Nearest
Rounds number to the nearest representable value. If a tie occurs, rounds toward positive infinity. Equivalent to the FixedPoint Designer
nearest
function.Round
Rounds number to the nearest representable value. If a tie occurs, rounds positive numbers toward positive infinity and rounds negative numbers toward negative infinity. Equivalent to the FixedPoint Designer
round
function.Simplest
Chooses between rounding toward floor and rounding toward zero to generate rounding code that is as efficient as possible.
Zero
Rounds number toward zero. Equivalent to the MATLAB
fix
function.
For more information, see Rounding (FixedPoint Designer).
Block parameters always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB rounding function into the mask field.
Programmatic Use
Block Parameter:
RndMeth 
Type: character vector 
Values:
'Ceiling'  'Convergent'  'Floor'  'Nearest'  'Round'  'Simplest' 
'Zero' 
Default:
'Floor' 
Saturate on integer overflow — Method of overflow action
off
(default)  on
Specify whether overflows saturate or wrap.
Action  Rationale  Impact on Overflows  Example 

Select this check box ( 
Your model has possible overflow, and you want explicit saturation protection in the generated code. 
Overflows saturate to either the minimum or maximum value that the data type can represent. 
The maximum value that the 
Do not select this check box ( 
You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles outofrange signals. For more information, see Troubleshoot Signal Range Errors. 
Overflows wrap to the appropriate value that is representable by the data type. 
The maximum value that the 
When you select this check box, saturation applies to every internal operation on the block, not just the output, or result. Usually, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.
Programmatic Use
Block Parameter: SaturateOnIntegerOverflow 
Type: character vector 
Values:
'off'  'on' 
Default: 'off' 
Mode — Select data type mode
Inherit
(default)  Built in
 Fixed Point
Select the category of data to specify.
Inherit
— Inheritance rules for data types. SelectingInherit
enables a second menu/text box to the right where you can select the inheritance mode.Built in
— Builtin data types. SelectingBuilt in
enables a second menu/text box to the right where you can select a builtin data type.Fixed point
— Fixedpoint data types. SelectingFixed point
enables additional parameters that you can use to specify a fixedpoint data type.Expression
— Expressions that evaluate to data types. SelectingExpression
enables a second menu/text box to the right, where you can enter the expression.
For more information, see Specify Data Types Using Data Type Assistant.
Dependencies
To enable this parameter, click the Show data type assistant button.
Data type override — Specify data type override mode for this signal
Inherit
 Off
Select the data type override mode for this signal.
When you select
Inherit
, Simulink inherits the data type override setting from its context, that is, from the block,Simulink.Signal
object or Stateflow^{®} chart in Simulink that is using the signal.When you select
Off
, Simulink ignores the data type override setting of its context and uses the fixedpoint data type specified for the signal.
For more information, see Specify Data Types Using Data Type Assistant in the Simulink documentation.
Dependencies
To enable this parameter, set Mode to Built
in
or Fixed point
.
Tips
The ability to turn off data type override for an individual data type provides greater control over the data types in your model when you apply data type override. For example, you can use this option to ensure that data types meet the requirements of downstream blocks regardless of the data type override setting.
Signedness — Specify signed or unsigned
Signed
(default)  Unsigned
Specify whether the fixedpoint data is signed or unsigned. Signed data can represent positive and negative values, but unsigned data represents positive values only.
Signed
, specifies the fixedpoint data as signed.Unsigned
, specifies the fixedpoint data as unsigned.
For more information, see Specify Data Types Using Data Type Assistant.
Dependencies
To enable this parameter, set the Mode to Fixed
point
.
Word length — Bit size of the word that holds the quantized integer
16
(default)  integer from 0 to 32
Specify the bit size of the word that holds the quantized integer. For more information, see Specifying a FixedPoint Data Type.
Dependencies
To enable this parameter, set Mode to
Fixed point
.
Fraction length — Specify fraction length for fixedpoint data type
0
(default)  scalar integer
Specify fraction length for fixedpoint data type as a positive or negative integer. For more information, see Specifying a FixedPoint Data Type.
Dependencies
To enable this parameter, set Scaling to
Binary point
.
Scaling — Method for scaling fixedpoint data
Best precision
(default)  Binary point
 Slope and bias
Specify the method for scaling your fixedpoint data to avoid overflow conditions and minimize quantization errors. For more information, see Specifying a FixedPoint Data Type.
Dependencies
To enable this parameter, set Mode to
Fixed point
.
Slope — Specify slope for the fixedpoint data type
2^0
(default)  positive, realvalued scalar
Specify slope for the fixedpoint data type. For more information, see Specifying a FixedPoint Data Type.
Dependencies
To enable this parameter, set Scaling to
Slope and bias
.
Bias — Specify bias for the fixedpoint data type
0
(default)  realvalued scalar
Specify bias for the fixedpoint data type as any real number. For more information, see Specifying a FixedPoint Data Type.
Dependencies
To enable this parameter, set Scaling to
Slope and bias
.
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
The Product of Elements block uses these algorithms to perform elementwise operations on inputs of floatingpoint, builtin integer, and fixedpoint types.
Input  ElementWise Operation  Algorithm 

Real scalar,  Multiplication  y = u 
Division  y = 1/u  
Real vector or matrix with elements  Multiplication  y = u1*u2*u3*...*uN 
Division  y = ((((1/u1)/u2)/u3).../uN)  
Complex scalar,
 Multiplication  y = u 
Division  y = 1/u  
Complex vector or matrix with elements
 Multiplication  y = u1*u2*u3*...*uN 
Division  y = ((((1/u1)/u2)/u3).../uN) 
If the specified dimension for elementwise multiplication or division is a row or column of a matrix, the algorithm applies to that row or column. Consider the Complex Division Using the Product of Elements Block example.
The top Product of Elements block collapses the matrix input to a scalar by taking successive inverses of the four elements:
y = ((((1/2+i)/3)/4i)/5)
The bottom Product of Elements block collapses the matrix input to a vector by taking successive inverses along the second dimension:
y(1) = ((1/2+i)/3)
y(2) = ((1/4i)/5)
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
HDL Coder supports Tree
architectures for Product
or Product of Elements blocks that have a single vector input with multiple
elements.
This block has multicycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated model or validation model. See Generated Model and Validation Model (HDL Coder).
Architecture  Additional cycles of latency  Description 

Linear
(default)  0  Generates a linear chain of adders to compute the sum of products. 
Tree  0  Generates a tree structure of adders to compute the sum of products. 
Note
The Product of Element block does not support HDL code
generation with double
data types in the Native
Floating Point
mode.
If you use the block in matrix multiplication mode, you can specify the
DotProductStrategy. This setting determines whether you want to
implement the matrix multiplication by using a tree of adders and multipliers, or use the
MultiplyAccumulate block implementation. The default is Fully
Parallel
.
Note
The DotProductStrategy must be set to Fully
Parallel
when you use the Native Floating Point
mode.
For more information, see DotProductStrategy (HDL Coder).
See also Design Considerations for Matrices and Vectors (HDL Coder).
General  

ConstrainedOutputPipeline  Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is

DSPStyle  Synthesis attributes for multiplier mapping. The default is 
InputPipeline  Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

OutputPipeline  Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

Native Floating Point  

HandleDenormals  Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design.
Denormal numbers are numbers that have magnitudes less than the smallest floatingpoint
number that can be represented without leading zeros in the mantissa. The default is

LatencyStrategy  Specify whether to map the blocks in your design to 
NFPCustomLatency  To specify a value, set
LatencyStrategy to 
MantissaMultiplyStrategy  Specify how to implement the mantissa multiplication operation during code generation.
By using different settings, you can control the DSP usage on the target FPGA device.
The default is 
The default (linear) implementation supports complex data.
Complex division is not supported. For block implementations of the Product block in divide mode or reciprocal mode, see HDL Code Generation on the Divide block reference page.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
Version History
Introduced before R2006a
See Also
Product  Divide  Dot Product
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