# Gain

Multiply input by constant

Libraries:
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 (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

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Open and simulate the model named `SimpleGain`.

```mdl = "SimpleGain"; open_system(mdl) sim(mdl);```

This model represents the equation:

`$2*5=10$`

The Gain block multiplies its input by `5`.

## Ports

### Input

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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`

### Output

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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`

## Parameters

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### Main

Specify the value by which to multiply the input. The gain can be a real or complex-valued scalar, vector, or matrix.

#### Programmatic Use

 Block Parameter: `Gain` Type: character vector Values: `'1'` | real- or complex-valued scalar, vector, or matrix Default: `'1'`

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 to `Matrix(K*u)`, except for how dimensions are determined.

Suppose that `K` is an `m-by-n` matrix. ```Matrix(K*u)(u vector)``` sets the input to a vector of length `n` and the output to a vector of length `m`. In contrast, `Matrix(K*u)` uses propagation to determine dimensions for the input and output. For an `m-by-n` gain matrix, the input can propagate to an `n-by-q` matrix, and the output becomes an `m-by-q` matrix.

#### Programmatic Use

 Parameter: `Multiplication` Type: character vector Value: ```'Element-wise(K.*u)' | 'Matrix(K*u)' | 'Matrix(u*K)' | 'Matrix(K*u) (u vector)'``` Default: `'Element-wise(K.*u)'`

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

Lower value of the output range that Simulink® checks.

Simulink uses the minimum to perform:

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: `'[ ]'`

Upper value of the output range that Simulink checks.

Simulink uses the maximum value to perform:

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: `'[ ]'`

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` — 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 type `int8` by a gain of `int16` and `ASIC/FPGA` is specified as the targeted hardware type, the output data type is `sfix24`. If ```Unspecified (assume 32-bit Generic)```, in other words, a generic 32-bit microprocessor, is specified as the target hardware, the output data type is `int32`. 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.

• `Inherit: Keep MSB`– Simulink 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, deselect the Saturate on integer overflow parameter.

This rule never produces overflows.

• `Inherit: Match scaling`– Simulink 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, see `fxptdlg` (Fixed-Point 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 input` — Use data type of input signal.

#### Dependencies

When 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

 Block Parameter: `OutDataTypeStr` Type: character vector Values: ```'Inherit: Inherit via internal rule'``` | `'Inherit: Keep MSB'` | `'Inherit: Match scaling'` | `'Inherit: Same as input'` | `'Inherit: Inherit via back propagation'` | `'single'` | `'half'` | `'int8'` | `'uint8'` | `'int16'` | `'uint16'` | `'int32'` | `'uint32'` | `'int64'` | `'uint64'` | `'fixdt(1,16)'` | `'fixdt(1,16,0)'` | `'fixdt(1,16,2^0,0)'` | ```''``` Default: ```'Inherit: Inherit via internal rule'```

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

 Block Parameter: `LockScale` Type: character vector Values: `'off' | 'on'` Default: `'off'`

Specify the rounding mode for fixed-point operations. For more information, see Rounding (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

 Block Parameter: `RndMeth` Type: character vector Values: ```'Ceiling' | 'Convergent' | 'Floor' | 'Nearest' | 'Round' | 'Simplest' | 'Zero'``` Default: `'Floor'`

Specify whether overflows saturate or wrap.

ActionRationaleImpact on OverflowsExample

Select this check box (`on`).

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 `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.

Do not select this check box (`off`).

You want to optimize efficiency of your generated code.

You want to avoid overspecifying how a block handles out-of-range 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 `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box 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 as `int8`, is -126.

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'`

Select the category of data to specify.

• `Inherit` — Inheritance rules for data types. Selecting `Inherit` enables a second menu/text box to the right where you can select the inheritance mode.

• `Built in` — Built-in data types. Selecting `Built 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. Selecting `Fixed point` enables additional parameters that you can use to specify a fixed-point data type.

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

#### Dependencies

To enable this parameter, click the button.

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.

#### 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.

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.

#### Dependencies

To enable this parameter, set the Mode to ```Fixed point```.

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`.

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`.

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`.

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`.

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

Specify the minimum value of gain. The default value is `[]` (unspecified). Simulink uses this value to perform:

#### Programmatic Use

 Block Parameter: `ParamMin` Type: character vector Value: scalar Default: ```'[ ]'```

Specify the maximum value of gain. The default value is `[]` (unspecified). Simulink uses this value to perform:

#### Programmatic Use

 Block Parameter: `ParamMax` Type: character vector Value: scalar Default: ```'[ ]'```

Specify the data type of the Gain parameter.

#### Tuning Gain Parameter Value When Parameter Data Type is set to `Inherit via internal rule`

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, Simulink 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 Simulink about the range of values you want during the simulation and allows Simulink to provide a full precision data type with sufficient range to allow safe tuning of the gain value within the specified range.

#### Programmatic Use

 Block Parameter: ``` ParamDataTypeStr``` Type: character vector Values: ```'Inherit: Inherit via internal rule``` | `'Inherit: Same as input'` | `'Inherit: Inherit via back propagation'` | `'single'` | `'half'` | `'int8'` | `'uint8'` | `'int16'` | `'uint16'`, `'int32'` | `'uint32'` | `'int64'` | `'uint64'` | `'fixdt(1,16)'` | `'fixdt(1,16,0)'` | `'fixdt(1,16,2^0,0)'` | ```''``` Default: ```'Inherit: Inherit via internal rule'```

## Block Characteristics

 Data Types `Boolean` | `double` | `fixed point` | `half` | `integer` | `single` Direct Feedthrough `yes` Multidimensional Signals `yes` Variable-Size Signals `yes` Zero-Crossing Detection `no`

## Version History

Introduced before R2006a