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 elementwise 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 roundtonearest 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:
$$2*5=10$$
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 StickSlip Friction and Hard Stops in MassSpringDamper System
One way you can incorporate hard stops and friction changes from stickslip motion into a massspringdamper 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 complexvalued scalar, vector, or matrix input. The Gain block supports fixedpoint 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 complexvalued scalar, vector, or matrix
Specify the value by which to multiply the input. The gain can be a real or complexvalued 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 complexvalued scalar, vector, or matrix in
quotes 
Multiplication — Specify the multiplication mode
Elementwise(K.*u)
(default)  Matrix(K*u)
 Matrix(u*K)
 Matrix(K*u) (u vector)
Specify one of these multiplication modes:
Elementwise(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 matrixmultiplied with the input as the second operand.Matrix(u*K)
— The input and gain are matrixmultiplied 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 anmbyn
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 anmbyn
gain matrix, the input can propagate to annbyq
matrix, and the output becomes anmbyq
matrix.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
Parameter:  Multiplication 
Values:  'Elementwise(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 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).
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 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).
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 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, 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 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 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 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
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 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
To set the block parameter value programmatically, use
the set_param
function.
Parameter:  LockScale 
Values:  'off' (default)  'on' 
Integer rounding mode — Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint operations. For more information, see Rounding Modes (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
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 8bit integer int8
can represent is 127. Any block operation result greater than this maximum value causes
overflow of the 8bit 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 overflowcausing 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 outofrange 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
— 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
.
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
.
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
.
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 fixedpoint 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 fixedpoint 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 

VariableSize Signals 

ZeroCrossing 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 areaefficient
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 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 
This block supports code generation for complex signals.
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
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