Gain
Multiply input by constant
Libraries:
Simulink /
Commonly Used Blocks
Simulink /
Math Operations
HDL Coder /
Commonly Used Blocks
HDL Coder /
HDL Floating Point Operations
HDL Coder /
Math Operations
Description
The Gain block multiplies the input by a constant value, or gain. The input and the gain can each be a scalar, vector, or matrix.
You specify the value of gain in the Gain parameter. The Multiplication parameter lets you specify element-wise or matrix multiplication. For matrix multiplication, this parameter also lets you indicate the order of the multiplicands.
The gain is converted from doubles to the data type specified in the block mask offline using round-to-nearest and saturation. The input and gain are then multiplied, and the result is converted to the output data type using the specified rounding and overflow modes.
Examples
Multiply Constant by Gain
Open and simulate the model named SimpleGain
.
mdl = "SimpleGain";
open_system(mdl)
sim(mdl);
This model represents the equation:
The Constant block provides a constant value of 2
to the Gain block.
The Gain block multiplies its input by 5
.
The Display block displays the result of the multiplication.
Extended Examples
Simulation of Bouncing Ball
Uses two models of a bouncing ball to show different approaches to modeling hybrid dynamic systems with Zeno behavior. Zeno behavior is informally characterized by an infinite number of events occurring in a finite time interval for certain hybrid systems. As the ball loses energy, the ball collides with the ground in successively smaller intervals of time.
Model Stick-Slip Friction and Hard Stops in Mass-Spring-Damper System
One way you can incorporate hard stops and friction changes from stick-slip motion into a mass-spring-damper model.
Engine Timing Model with Closed Loop Control
Develop and implement a closed loop control algorithm for the open loop engine model described in Model Engine Timing Using Triggered Subsystems. In this example, the model sldemo_enginewc
contains a controller that regulates engine speed using a fast throttle actuator such that changes in load torque have minimal effect. The controller is implemented using a discrete PI controller.
Ports
Input
Port_1 — Input signal
scalar | vector | matrix
The Gain block accepts real or complex-valued scalar, vector, or matrix input. The Gain block supports fixed-point data types. If the input of the Gain block is real and gain is complex, the output is complex.
Data Types: half
| single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| Boolean
| fixed point
Complex Number Support: Yes
Output
Port_1 — Input multiplied by gain
scalar | vector | matrix
The Gain block outputs the input multiplied by a constant gain value. When the input to the Gain block is real and gain is complex, the output is complex.
Data Types: half
| single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| Boolean
| fixed point
Complex Number Support: Yes
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
Main
Gain — Value by which to multiply the input
1
(default) | real or complex-valued scalar, vector, or matrix
Specify the value by which to multiply the input. The gain can be a real or complex-valued scalar, vector, or matrix.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | Gain |
Values: | '1' (default) | real or complex-valued scalar, vector, or matrix in
quotes |
Multiplication — Specify the multiplication mode
Element-wise(K.*u)
(default) | Matrix(K*u)
| Matrix(u*K)
| Matrix(K*u) (u vector)
Specify one of these multiplication modes:
Element-wise(K.*u)
— Each element of the input is multiplied by each element of the gain. The block performs expansions, if necessary, so that the input and gain have the same dimensions.Matrix(K*u)
— The input and gain are matrix-multiplied with the input as the second operand.Matrix(u*K)
— The input and gain are matrix-multiplied with the input as the first operand.Matrix(K*u) (u vector)
— The input and gain are matrix multiplied with the input as the second operand. This mode is identical toMatrix(K*u)
, except for how dimensions are determined.Suppose that
K
is anm-by-n
matrix.Matrix(K*u)(u vector)
sets the input to a vector of lengthn
and the output to a vector of lengthm
. In contrast,Matrix(K*u)
uses propagation to determine dimensions for the input and output. For anm-by-n
gain matrix, the input can propagate to ann-by-q
matrix, and the output becomes anm-by-q
matrix.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | Multiplication |
Values: | 'Element-wise(K.*u)' (default) | 'Matrix(K*u)' | 'Matrix(u*K)' | 'Matrix(K*u) (u vector)' |
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
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | SampleTime |
Values: | "-1" (default) | scalar or vector in quotes |
Signal Attributes
Output minimum — Minimum output value for range checking
[]
(default) | scalar
Lower value of the output range that the software checks.
The software 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 fixed-point 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).
Tips
Output minimum does not saturate or clip the actual output signal. Use the Saturation block instead.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | OutMin |
Values: | '[]' (default) | scalar in quotes |
Output maximum — Maximum output value for range checking
[]
(default) | scalar
Upper value of the output range that the software checks.
The software 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 fixed-point 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).
Tips
Output maximum does not saturate or clip the actual output signal. Use the Saturation block instead.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | OutMax |
Values: | '[]' (default) | scalar in quotes |
Output data type — Specify the output data type
Inherit: Inherit via internal
rule
(default) | Inherit: Keep MSB
| Inherit: Match scaling
| Inherit: Inherit via back
propagation
| Inherit: Same as input
| double
| single
| half
| int8
| uint8
| int16
| uint16
| int32
| int64
| uint64
| uint32
| 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
.
When you select an inherited option, the block exhibits these behaviors:
Inherit: Inherit via internal rule
— The software 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 32-bit Generic)
, in other words, a generic 32-bit 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, the software displays an error in the Diagnostic Viewer.Inherit: Keep MSB
– The software chooses a data type that maintains the full range of the operation, then reduces the precision of the output to a size appropriate for the embedded target hardware.Tip
For more efficient generated code, clear Saturate on integer overflow.
This rule never produces overflows.
Inherit: Match scaling
– The software chooses a data type whose scaling matches the scaling of the input types. If the full range of the type does not fit on the embedded target hardware, the range is reduced yielding a type appropriate for the embedded target hardware. This rule can produce overflows.It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If these internal rules do not 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 Fixed-Point Tool to propose data types for your model. For more information, seefxptdlg
(Fixed-Point Designer).To specify your own inheritance rule, use
Inherit: Inherit via back propagation
and 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 the data type of the driving block.Inherit: Same as input
— Use the data type of the input signal.
Dependencies
When the input is a floating-point data type smaller than single precision, the
Inherit: Inherit via internal rule
output data type depends on the setting of the Inherit floating-point 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
single-precision data type. For example, half
and
int16
are smaller than single
precision.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | OutDataTypeStr |
Values: | 'Inherit: Inherit via internal
rule' (default) | 'Inherit: Keep MSB' | 'Inherit: Match scaling' | 'Inherit: Inherit via back
propagation' | 'Inherit: Same as input' | 'double' | 'single' | 'half' | 'int8' | 'uint8' | 'int16' | 'uint16' | 'int32' | 'uint32' | 'int64' | 'uint64' | 'fixdt(1,16)' | 'fixdt(1,16,0)' | 'fixdt(1,16,2^0,0)' | '<data type expression>' |
Lock output data type setting against changes by the fixed-point tools — Option to prevent fixed-point tools from overriding Output data type
off
(default) | on
Select this parameter to prevent the fixed-point tools from overriding the Output data type you specify on the block. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | LockScale |
Values: | 'off' (default) | 'on' |
Integer rounding mode — Rounding mode for fixed-point operations
Floor
(default) | Ceiling
| Convergent
| Nearest
| Round
| Simplest
| Zero
Specify the rounding mode for fixed-point operations. For more information, see Rounding Modes (Fixed-Point 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
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | RndMeth |
Values: | 'Floor' (default) | 'Ceiling' | 'Convergent' | 'Nearest' | 'Round' | 'Simplest' | 'Zero' |
Saturate on integer overflow — Method of overflow action
off
(default) | on
Specify whether overflows saturate or wrap.
on
— Overflows saturate to either the minimum or maximum value that the data type can represent.off
— Overflows wrap to the appropriate value that the data type can represent.
For example, the maximum value that the signed 8-bit integer int8
can represent is 127. Any block operation result greater than this maximum value causes
overflow of the 8-bit integer.
With this parameter selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.
With this parameter cleared, the software interprets the overflow-causing value as
int8
, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed asint8
is -126.
Tips
Consider selecting this parameter when your model has a possible overflow and you want explicit saturation protection in the generated code.
Consider clearing this parameter when you want to optimize efficiency of your generated code. Clearing this parameter also helps you to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.
When you select this parameter, 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.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | SaturateOnIntegerOverflow |
Values: | 'off' (default) | 'on' |
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
— Built-in data types. SelectingBuilt in
enables a second menu/text box to the right where you can select a built-in data type.Fixed point
— Fixed-point data types. SelectingFixed point
enables additional parameters that you can use to specify a fixed-point 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 fixed-point 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 fixed-point data is signed or unsigned. Signed data can represent positive and negative values, but unsigned data represents positive values only.
Signed
, specifies the fixed-point data as signed.Unsigned
, specifies the fixed-point 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 Fixed-Point Data Type.
Dependencies
To enable this parameter, set Mode to
Fixed point
.
Scaling — Method for scaling fixed-point data
Best precision
(default) | Binary point
| Slope and bias
Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors. For more information, see Specifying a Fixed-Point Data Type.
Dependencies
To enable this parameter, set Mode to
Fixed point
.
Slope — Specify slope for the fixed-point data type
2^0
(default) | positive, real-valued scalar
Specify slope for the fixed-point data type. For more information, see Specifying a Fixed-Point Data Type.
Dependencies
To enable this parameter, set Scaling to
Slope and bias
.
Bias — Specify bias for the fixed-point data type
0
(default) | real-valued scalar
Specify bias for the fixed-point data type as any real number. For more information, see Specifying a Fixed-Point Data Type.
Dependencies
To enable this parameter, set Scaling to
Slope and bias
.
Fraction length — Specify fraction length for fixed-point data type
0
(default) | scalar integer
Specify fraction length for fixed-point data type as a positive or negative integer. For more information, see Specifying a Fixed-Point Data Type.
Dependencies
To enable this parameter, set Scaling to
Binary point
.
Parameter Attributes
Parameter minimum — Specify the minimum value of gain
[]
(default) | scalar
Specify the minimum value of gain. The default value is []
(unspecified). The software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | ParamMin |
Values: | '[]' (default) | scalar in quotes |
Parameter maximum — Specify the maximum value of gain
[]
(default) | scalar
Specify the maximum value of gain. The default value is []
(unspecified). The software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | ParamMax |
Values: | '[]' (default) | scalar in quotes |
Parameter data type — Specify the data type of the Gain parameter
Inherit: Inherit via internal
rule
(default) | Inherit: Same as input
| Inherit: Inherit from 'Gain'
| double
| single
| half
| int8
| uint8
| int16
| uint16
| int32
| uint32
| int64
| uint64
| fixdt(1,16)
| fixdt(1,16,0)
| fixdt(1,16,2^0,0)
| <data type expression>
Specify the data type of the Gain parameter.
Setting Parameter data type to
Inherit: Inherit via internal rule
lets
the Gain block select a data type based on an internal
heuristic that looks at the current gain value and provides a full
precision data type to represent the current gain value. When you update
the diagram, the software deduces a data type to fit the gain value
3
with high precision and no range loss. For
example, with this heuristic, if the specified gain value is
3
, the Gain block deduces a
selected data type of sfix32_En29
. Consequently, this
deduced data type cannot hold values greater than 4
.
During simulation, if you tune the gain value to 6
,
an overflow occurs in the selected data type and the behavior is
unexpected.
While tuning a parameter with this Parameter data type setting, specify the Parameter Minimum and Parameter Maximum parameters. These settings tell the software about the range of values you want during the simulation and allows the software to provide a full precision data type with sufficient range to allow safe tuning of the gain value within the specified range.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter: | ParamDataTypeStr |
Values: | 'Inherit: Inherit via internal
rule' (default) | 'Inherit: Same as input' | 'Inherit: Inherit from 'Gain'' | 'double' | 'single' | 'half' | 'int8' | 'uint8' | 'int16' | 'uint16' | 'int32' | 'uint32' | 'int64' | 'uint64' | 'fixdt(1,16)' | 'fixdt(1,16,0)' | 'fixdt(1,16,2^0,0)' | '<data type expression>' |
Block Characteristics
Data Types |
|
Direct Feedthrough |
|
Multidimensional Signals |
|
Variable-Size Signals |
|
Zero-Crossing Detection |
|
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.
You can use a tunable parameter in a Gain block intended for HDL code generation. For details, see Generate DUT Ports for Tunable Parameters (HDL Coder).
ConstMultiplierOptimization | Description |
---|---|
none (Default) | By default, HDL Coder does not perform CSD or FCSD optimizations. Code generated for the Gain block retains multiplier operations. |
csd | When you specify this option, the generated code decreases the area used by the model while maintaining or increasing clock speed, using canonical signed digit (CSD) techniques. CSD replaces multiplier operations with add and subtract operations. CSD minimizes the number of addition operations required for constant multiplication by representing binary numbers with a minimum count of nonzero digits. |
fcsd | This option uses factored CSD (FCSD) techniques, which replace multiplier operations with shift and add/subtract operations on certain factors of the operands. These factors are generally prime but can also be a number close to a power of 2, which favors area reduction. You can achieve a greater area reduction with FCSD at the cost of decreasing clock speed. |
auto | When you specify this option, the coder chooses between
the CSD or FCSD optimizations. The coder chooses the
optimization that yields the most area-efficient
implementation, based on the number of adders required. When
you specify |
General | |
---|---|
ConstMultiplierOptimization | Canonical signed digit (CSD) or factored CSD optimization. The
default is |
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
|
Note
For certain values of the Gain parameter, native
floating point implements the algorithm differently instead of using
multipliers. For example, if you set the Gain parameter
to 1
, the generated model uses a wire to pass the input
to the output. If you set the Gain parameter to
-1
, the generated model shows a Unary
Minus block that inverts the polarity of the input signal. This
implementation reduces the latency and resource usage on the target
platform.
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 floating-point
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 |
This block supports code generation for complex signals.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.
Version History
Introduced before R2006a
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