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Product of Elements

Copy or invert one scalar input, or collapse one nonscalar input

Math Operations

Description

The Divide and Product blocks are variants of the Product of Elements block.

• For information on the Divide block, see Divide.

• For information on the Product block, see Product.

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 by multiplying together the elements of each row or column or taking 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: Element-wise(.*)

• Number of inputs: *

Setting non-default 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. See the documentation of those two blocks for more information.

Algorithm

The Product of Elements block uses the following algorithms to perform element-wise operations on inputs of floating-point, built-in integer, and fixed-point types:

InputElement-Wise OperationAlgorithm

Real scalar, u

Multiplicationy = u
Divisiony = 1/u

Real vector or matrix, with elements u1, u2, u3, ..., uN

Multiplicationy = u1*u2*u3*...*uN
Divisiony = ((((1/u1)/u2)/u3).../uN)

Complex scalar, u

Multiplicationy = u
Divisiony = 1/u

Complex vector or matrix, with elements u1, u2, u3, ..., uN

Multiplicationy = u1*u2*u3*...*uN
Divisiony = ((((1/u1)/u2)/u3).../uN)

If the specified dimension for element-wise multiplication or division is a row or column of a matrix, the algorithm applies to that row or column. For example, consider the following model:

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)/4-i)/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) = ((1/4-i)/5)

Parameters

Number of inputs

Control two properties of the block:

• The number of input ports on the block

• Whether each input is multiplied or divided into the output

Settings

Default: *

• 1 or *

• Copies a scalar input unchanged

• Collapses a vector input to a scalar by multiplying all elements together

• Collapses a matrix input to a scalar or vector by multiplying elements together based on the Multiply over parameter

• /

• Outputs the arithmetic inverse of a scalar input

• Collapses a vector input to a scalar by taking successive inverses of the elements

• Collapses a matrix input to a scalar or vector by taking successive inverses of elements based on the Multiply over parameter

• Integer value > 1

Has the number of inputs given by the integer value. The block becomes a product block and the input are multiplied together in element-wise mode or matrix mode, as specified by the Multiplication parameter. See Element-wise Mode and Matrix Mode in the Product documentation for more information.

• Unquoted string of two or more * and / characters

Has the number of inputs given by the length of the character vector. The block becomes a product or divide block and multiplies each input that corresponds to a * character into the output. Each input that corresponds to a / character is divided into the output. The operations occur in Element-wise mode or Matrix mode, as specified by the Multiplication parameter. See Element-wise Mode and Matrix Mode in the Product block reference page for more information.

Dependency

Setting Number of inputs to * and selecting Element-wise(.*) for Multiplication enables the following Multiply over parameter.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Multiplication

Specify whether the Product block operates in Element-wise mode or Matrix mode.

Settings

Default: Element-wise(.*)

Element-wise(.*)

Operate in Element-wise mode.

Matrix(*)

Operate in Matrix mode.

Dependency

Selecting Element-wise(.*) and setting Number of inputs to * enable the following parameter:

• Multiply over

Command-Line Information

See Block-Specific Parameters for the command-line information.

Multiply over

Affect multiplication on matrix input.

Settings

Default: All dimensions

All dimensions

Output a scalar that is product of all elements of the matrix, or the product of their inverses, depending on the value of Number of inputs.

Specified dimension

Output a vector, the composition of which depends on the value of the Dimension parameter.

Dependencies

• Enable this parameter by selecting Element-wise(.*) for Multiplication and setting Number of inputs to * or 1 or /.

• Setting this parameter to Specified dimension enables the Dimension parameter.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Dimension

Affect multiplication on matrix input.

Settings

Default: 1

Minimum: 1

Maximum: 2

1

Output a vector that contains an element for each column of the input matrix.

2

Output a vector that contains an element for each row of the input matrix.

Tips

Each element of the output vector contains the product of all elements in the corresponding column or row of the input matrix, or the product of the inverses of those elements, depending on the value of Number of inputs:

• 1 or *

Multiply the values of the column or row elements

• /

Multiply the inverses of the column or row elements

Dependency

Enable this parameter by selecting Specified dimension for Multiply over.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Sample time

 Note:   This parameter is not visible in the block dialog box unless it is explicitly set to a value other than -1. To learn more, see Blocks for Which Sample Time Is Not Recommended.

Require all inputs to have the same data type

Require that all inputs have the same data type.

Settings

Default: Off

On

Require that all inputs have the same data type.

Off

Do not require that all inputs have the same data type.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Output minimum

Lower value of the output range that Simulink® checks.

Settings

Default: [] (unspecified)

Specify this number as a finite, real, double, scalar value.

Simulink uses the minimum to perform:

 Note:   Output minimum does not saturate or clip the actual output signal. Use the Saturation block instead.

Command-Line Information

 Parameter: OutMin Type: character vector Value: '[ ]' Default: '[ ]'

Output maximum

Upper value of the output range that Simulink checks.

Settings

Default: [] (unspecified)

Specify this number as a finite, real, double, scalar value.

Simulink uses the maximum value to perform:

 Note:   Output maximum does not saturate or clip the actual output signal. Use the Saturation block instead.

Command-Line Information

 Parameter: OutMax Type: character vector Value: '[ ]' Default: '[ ]'

Output data type

Specify the output data type.

Settings

Default: Inherit: Inherit via internal rule

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. 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 first input.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

• 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 the first input signal.

double

Output data type is double.

single

Output data type is single.

int8

Output data type is int8.

uint8

Output data type is uint8.

int16

Output data type is int16.

uint16

Output data type is uint16.

int32

Output data type is int32.

uint32

Output data type is uint32.

fixdt(1,16,0)

Output data type is fixed point fixdt(1,16,0).

fixdt(1,16,2^0,0)

Output data type is fixed point fixdt(1,16,2^0,0).

<data type expression>

Use a data type object, for example, Simulink.NumericType.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Show data type assistant

Display the Data Type Assistant.

Settings

The Data Type Assistant helps you set the Output data type parameter.

Mode

Select the category of data to specify.

Settings

Default: Inherit

Inherit

Inheritance rules for data types. Selecting Inherit enables a second menu/text box to the right. Select one of the following choices:

• Inherit via internal rule (default)

• Inherit via back propagation

• Same as first input

Built in

Built-in data types. Selecting Built in enables a second menu/text box to the right. Select one of the following choices:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Fixed-point data types.

Expression

Expressions that evaluate to data types. Selecting Expression enables a second menu/text box to the right, where you can enter the expression.

Dependency

Clicking the Show data type assistant button enables this parameter.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Data type override

Specify data type override mode for this signal.

Settings

Default: Inherit

Inherit

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.

Off

Ignores the data type override setting of its context and uses the fixed-point data type specified for the signal.

Tip

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.

Dependency

This parameter appears only when the Mode is Built in or Fixed point.

Signedness

Specify whether you want the fixed-point data as signed or unsigned.

Settings

Default: Signed

Signed

Specify the fixed-point data as signed.

Unsigned

Specify the fixed-point data as unsigned.

Dependencies

Selecting Mode > Fixed point enables this parameter.

Word length

Specify the bit size of the word that holds the quantized integer.

Default: 16

Minimum: 0

Maximum: 32

Dependencies

Selecting Mode > Fixed point enables this parameter.

Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

Settings

Default: Best precision

Binary point

Specify binary point location.

Slope and bias

Enter slope and bias.

Best precision

Specify best-precision values.

Dependencies

Selecting Mode > Fixed point enables this parameter.

Selecting Binary point enables:

• Fraction length

• Calculate Best-Precision Scaling

Selecting Slope and bias enables:

• Slope

• Bias

• Calculate Best-Precision Scaling

Fraction length

Specify fraction length for fixed-point data type.

Settings

Default: 0

Binary points can be positive or negative integers.

Dependencies

Selecting Scaling > Binary point enables this parameter.

Slope

Specify slope for the fixed-point data type.

Settings

Default: 2^0

Specify any positive real number.

Dependencies

Selecting Scaling > Slope and bias enables this parameter.

Bias

Specify bias for the fixed-point data type.

Settings

Default: 0

Specify any real number.

Dependencies

Selecting Scaling > Slope and bias enables this parameter.

Lock output data type setting against changes by the fixed-point tools

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor.

Settings

Default: Off

On

Locks the output data type setting for this block.

Off

Allows the Fixed-Point Tool and the Fixed-Point Advisor to change the output data type setting for this block.

Command-Line Information

 Parameter: LockScale Type: character vector Value: 'off' | 'on' Default: 'off'

For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Integer rounding mode

Specify the rounding mode for fixed-point operations.

Settings

Default: Floor

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 Fixed-Point 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 Fixed-Point 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 Fixed-Point 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.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Saturate on integer overflow

Specify whether overflows saturate.

Settings

Default: Off

On

Overflows saturate to either the minimum or maximum value that the data type can represent.

For example, an overflow associated with a signed 8-bit integer can saturate to -128 or 127.

Off

Overflows wrap to the appropriate value that the data type can represent.

For example, the number 130 does not fit in a signed 8-bit integer and wraps to -126.

Tips

• Consider selecting this check box when your model has a possible overflow and you want explicit saturation protection in the generated code.

• Consider clearing this check box when you want to optimize efficiency of your generated code.

Clearing this check box also helps you to avoid overspecifying how a block handles out-of-range signals. For more information, see Check for Signal Range Errors.

• When you select this check box, saturation applies to every internal operation on the block, not just the output or result.

• In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

Command-Line Information

 Parameter: SaturateOnIntegerOverflow Type: character vector Value: 'off' | 'on' Default: 'off'

Examples

This table shows the output of the Product of Elements block for example inputs using default block parameter values, except as shown in the table.

Parameter ValuesExamples

Multiplication: Element-wise(.*)

Number of inputs: *

Multiplication: Element-wise(.*)

Number of inputs: /

Multiplication: Element-wise(.*)

Number of inputs: *

Multiplication: Element-wise(.*)

Number of inputs: *

Multiply over: All dimensions

Multiplication: Element-wise(.*)

Number of inputs: *

Multiply over: Specified dimension

Dimension: 1

Multiplication: Element-wise(.*)

Number of inputs: /

Multiply over: Specified dimension

Dimension: 2

Characteristics

 Data Types Double | Single | Boolean | Base Integer | Fixed-Point Multidimensional Signals Yes Variable-Size Signals Yes Code Generation Yes