Multiply input by constant

Math Operations

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 the 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 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.

The Gain block accepts a real or complex scalar, vector, or
matrix of any numeric data type that Simulink^{®} supports. The Gain
block supports fixed-point data types. If the input of the Gain block
is real and the gain is complex, the output is complex.

For more information, see Data Types Supported by Simulink in the Simulink documentation.

The **Main** pane of the
Gain block dialog box appears as follows:

The **Signal Attributes** pane
of the Gain block dialog box appears as follows:

The **Parameter Attributes** pane
of the Gain block dialog box appears as follows:

Specify the value by which to multiply the input.

Default: 1 |

Minimum: value of Parameter
minimum parameter |

Maximum: value of Parameter
maximum parameter |

The gain can be a scalar, vector, or matrix.

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

Specify the multiplication mode.

**Default:** `Element-wise(K.*u)`

`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.

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

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.

Lower value of the output range that Simulink checks.

**Default:** `[]`

(unspecified)

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

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 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.

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

Parameter: `OutMin` |

Type: character vector |

Value: `'[ ]'` |

Default: `'[ ]'` |

Upper value of the output range that Simulink checks.

**Default:** `[]`

(unspecified)

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

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 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.

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

Parameter: `OutMax` |

Type: character vector |

Value: `'[ ]'` |

Default: `'[ ]'` |

Specify the output data type.

**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. 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)`

, i.e., 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.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 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 input`

Use data type of 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`

.

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

See Control Signal Data Types for more information.

Select the category of data to specify.

**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 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.

Clicking the **Show data type assistant** button
enables this parameter.

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

Specify data type override mode for this signal.

**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.

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.

This parameter appears only when the **Mode** is ```
Built
in
```

or `Fixed point`

.

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

**Default:** `Signed`

`Signed`

Specify the fixed-point data as signed.

`Unsigned`

Specify the fixed-point data as unsigned.

Selecting **Mode** > ```
Fixed
point
```

enables this parameter.

For more information, see Specifying a Fixed-Point Data Type.

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

**Default:** `16`

**Minimum:** `0`

**Maximum:** `32`

Selecting **Mode** > ```
Fixed
point
```

enables this parameter.

For more information, see Specifying a Fixed-Point Data Type.

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

**Default:** ```
Binary
point
```

`Binary point`

Specify binary point location.

`Slope and bias`

Enter slope and bias.

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**

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

Specify fraction length for fixed-point data type.

**Default:** `0`

Binary points can be positive or negative integers.

Selecting **Scaling** > ```
Binary
point
```

enables this parameter.

For more information, see Specifying a Fixed-Point Data Type.

Specify slope for the fixed-point data type.

**Default:** `2^0`

Specify any positive real number.

Selecting **Scaling** > ```
Slope
and bias
```

enables this parameter.

For more information, see Specifying a Fixed-Point Data Type.

Specify bias for the fixed-point data type.

**Default:** `0`

Specify any real number.

Selecting **Scaling** > ```
Slope
and bias
```

enables this parameter.

For more information, see Specifying a Fixed-Point Data Type.

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

**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.

Parameter: `LockScale` |

Type: character vector |

Value: `'off'` | `'on'` |

Default: `'off'` |

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

Specify the rounding mode for fixed-point operations.

**Default:** `Floor`

`Ceiling`

Rounds both 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 both 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`

Automatically chooses between round toward floor and round toward zero to generate rounding code that is as efficient as possible.

`Zero`

Rounds number toward zero. Equivalent to the MATLAB

`fix`

function.

Parameter: `RndMeth` |

Type: character vector |

Value: `'Ceiling'` | `'Convergent'` | `'Floor'` | `'Nearest'` | `'Round'` | `'Simplest'` | `'Zero'` |

Default: `'Floor'` |

For more information, see Rounding (Fixed-Point Designer) in the Fixed-Point Designer documentation.

Specify whether overflows saturate.

**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.

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.

Parameter: `SaturateOnIntegerOverflow` |

Type: character vector |

Value: `'off'` | `'on'` |

Default: `'off'` |

Specify the minimum value of the gain.

Default: `[]` |

The default value is `[]`

(unspecified). Simulink 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

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

Specify the maximum value of the gain.

Default: `[]` |

The default value is `[]`

(unspecified). Simulink 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

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

Specify the data type of the **Gain** parameter.

**Default:** ```
Inherit:
Inherit via internal rule
```

`Inherit: Inherit via internal rule`

Use an internal rule to inherit the data type.

`Inherit: Same as input`

Use data type of sole input signal.

`Inherit: Inherit from 'Gain'`

Use data type of the

**Gain**value. For example:If you set Gain to... The parameter data type inherits... `2`

`double`

`single(2)`

`single`

`int8(2)`

`int8`

`double`

Data type is

`double`

.`single`

Data type is

`single`

.`int8`

Data type is

`int8`

.`uint8`

Data type is

`uint8`

.`int16`

Data type is

`int16`

.`uint16`

Data type is

`uint16`

.`int32`

Data type is

`int32`

.`uint32`

Data type is

`uint32`

.`fixdt(1,16)`

Data type is

`fixdt(1,16)`

.`fixdt(1,16,0)`

Data type is

`fixdt(1,16,0)`

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

Data type is

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

.`<data type expression>`

Use a data type object, for example,

`Simulink.NumericType`

.

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

Select the category of data to specify.

**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)`Same as input`

`Inherit from 'Gain'`

`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.

Clicking the **Show data type assistant** button
enables this parameter.

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

See Specify Data Types Using Data Type Assistant in the Simulink documentation.

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

**Default:** ```
Best
precision
```

`Binary point`

Specify binary point location.

`Slope and bias`

Enter slope and bias.

`Best precision`

Specify best-precision values.

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**

For more information, see Specifying a Fixed-Point Data Type.

The following Simulink examples show how to use the Gain block:

Data Types | Double | Single | Boolean | Base Integer | Fixed-Point |

Sample Time | Inherited from driving block |

Direct Feedthrough | Yes |

Multidimensional Signals | Yes |

Variable-Size Signals | Yes |

Zero-Crossing Detection | No |

Code Generation | Yes |

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