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Minimum values of input or sequence of inputs

**Library:**DSP System Toolbox / Statistics

The Minimum block identifies the value and position
of the smallest element in each row or column of the input, or along
vectors of a specified dimension of the input. It can also compute
the minimum value of the entire input. The Minimum block
can also track the minimum values in a sequence of inputs over a period
of time. The **Mode** parameter specifies the block's
mode of operation and can be set to one of the following:

`Value`

— The block outputs the minimum values in the specified dimension.`Index`

— The block outputs the index array of the minimum values in the specified dimension.`Value and Index`

— The block outputs the minimum values and the corresponding index array in the specified dimension.`Running`

— The block tracks the minimum values in a sequence of inputs over a period of time.

You can specify the dimension using the **Find the minimum
value over** parameter.

The **Running** mode in the Minimum block
will be removed in a future release. To compute the running minimum
in Simulink^{®}, use the Moving Minimum block
instead.

`In`

— Data inputvector | matrix |

The block accepts real-valued or complex-valued multichannel and multidimensional inputs. The input can be floating-point, fixed-point, or Boolean. Real fixed-point inputs can be either signed or unsigned. Complex fixed-point inputs must be signed.

This port is unnamed until you set the **Mode** parameter
to `Running`

and the **Reset port** parameter
to any option other than `None`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `uint8`

| `uint16`

| `uint32`

| `Boolean`

| `fixed point`

**Complex Number Support: **Yes

`Rst`

— Reset portscalar

Specify the reset event that causes the block to reset the running
minimum. The sample time of the **Rst** input must
be a positive integer multiple of the input sample time.

To enable this port, set the **Mode** parameter
to `Running`

and the **Reset port** parameter
to any option other than `None`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `uint8`

| `uint16`

| `uint32`

| `Boolean`

`Val`

— Minimum values along the specified dimensionscalar | vector | matrix |

The data type of the minimum value matches the data type of the input.

When the **Mode** parameter is set to either ```
Value
and Index
```

or `Value`

, the following
applies:

The size of the dimension for which the block computes the minimum value is 1. The sizes of all other dimensions match those of the input array. For example, when the input is an

*M*-by-*N*-by-*P*array, with the dimension set to`1`

, the block outputs a 1-by-*N*-by-*P*array. When the dimension is set to`3`

, the block outputs a two-dimensional*M*-by-*N*matrix.When the input is an

*M*-by-*N*matrix, with the dimension set to`1`

, the block outputs a 1-by-*N*matrix.

If you specify the block to compute the minimum value over the entire input, the block outputs a scalar.

When the **Mode** parameter is set `Running`

,
the block tracks the minimum value of each channel in a time sequence
of *M*-by-*N* inputs. In this mode,
you must also specify the **Input processing** parameter
as one of the following:

`Elements as channels (sample based)`

— The block treats each element of the input as a separate channel. For a three-dimensional input signal of size*M*-by-*N*-by-*P*, the block outputs an*M*-by-*N*-by-*P*array. Each*y*element of the output contains the minimum value observed in element_{ijk}*u*for all inputs since the last reset._{ijk}When a reset event occurs, the running minimum

*y*in the current frame is reset to the element_{ijk}*u*._{ijk}`Columns as channels (frame based)`

— The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size*M*-by-*N*, the block outputs an*M*-by-*N*matrix. Each element*y*of the output contains the minimum value observed in the_{ij}*j*th column of all inputs since the last reset, up to and including element*u*of the current input._{ij}When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.

The block resets the running minimum whenever a reset
event is detected at the optional **Rst** port. The
reset sample time must be a positive integer multiple of the input
sample time.

To enable this port, set the **Mode** parameter
to either `Value and Index`

or `Value`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `uint8`

| `uint16`

| `uint32`

| `Boolean`

| `fixed point`

**Complex Number Support: **Yes

`Idx`

— Index of the minimum values along the specified dimensionscalar | vector | matrix |

When the input is `double`

, the index values
are also `double`

. Otherwise, the index values are `uint32`

.

To enable this port, set the **Mode** parameter
to either `Value and Index`

or `Index`

.

**Data Types: **`double`

| `uint32`

`Mode`

— Mode in which the block operates`Value and Index`

(default) | `Value`

| `Index`

| `Running`

When the **Mode** parameter is set to:

`Value`

— The block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input at each sample time, and outputs the array*y*. Each element in*y*is the minimum value in the corresponding column, row, vector, or entire input. The output*y*depends on the setting of the**Find the minimum value over**parameter. Consider a three dimensional input signal of size*M*-by-*N*-by-*P*. Set**Find the minimum value over**to:`Each row`

— The output*y*at each sample time consists of an*M*-by-1-by-*P*array, where each element contains the minimum value of each vector over the second dimension of the input. For an input that is an*M*-by-*N*matrix, the output at each sample time is an*M*-by-1 column vector.`Each column`

— The output*y*at each sample time consists of a 1-by-*N*-by-*P*array, where each element contains the minimum value of each vector over the first dimension of the input. For an input that is an*M*-by-*N*matrix, the output at each sample time is a 1-by-*N*row vector.In this mode, the block treats length-

*M*unoriented vector inputs as*M*-by-1 column vectors.`Entire input`

— The output*y*at each sample time is a scalar that contains the minimum value in the*M*-by-*N*-by-*P*input matrix.`Specified dimension`

— The output*y*at each sample time depends on**Dimension**. If**Dimension**is set to`1`

, the output is the same as when you select`Each column`

. If**Dimension**is set to`2`

, the output is the same as when you select`Each row`

. If**Dimension**is set to`3`

, the output at each sample time is an*M*-by-*N*matrix containing the minimum value of each vector over the third dimension of the input.

**Complex Inputs**For complex inputs, the block selects the value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input that has the minimum magnitude squared in the following figure. For complex value $$u=a+bi$$, the magnitude squared is $${a}^{2}+{b}^{2}$$.

`Index`

— The block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input, and outputs the index array*I*. Each element in*I*is an integer indexing the minimum value in the corresponding column, row, vector, or entire input. The output*I*depends on the setting of the**Find the minimum value over**parameter. Consider a three dimensional input signal of size*M*-by-*N*-by-*P*:`Each row`

— The output*I*at each sample time consists of an*M*-by-1-by-*P*array, where each element contains the index of the minimum value of each vector over the second dimension of the input. For an input that is an*M*-by-*N*matrix, the output at each sample time is an*M*-by-1 column vector.`Each column`

— The output*I*at each sample time consists of a 1-by-*N*-by-*P*array, where each element contains the index of the minimum value of each vector over the first dimension of the input. For an input that is an*M*-by-*N*matrix, the output at each sample time is a 1-by-*N*row vector.In this mode, the block treats length-

*M*unoriented vector inputs as*M*-by-1 column vectors.`Entire input`

— The output*I*at each sample time is a 1-by-3 vector that contains the location of the minimum value in the*M*-by-*N*-by-*P*input matrix. For an input that is an*M*-by-*N*matrix, the output is a 1-by-2 vector.`Specified dimension`

— The output*I*at each sample time depends on**Dimension**. If**Dimension**is set to 1, the output is the same as when you select`Each column`

. If**Dimension**is set to 2, the output is the same as when you select`Each row`

. If**Dimension**is set to 3, the output at each sample time is an*M*-by-*N*matrix containing the indices of the minimum values of each vector over the third dimension of the input.

When a minimum value occurs more than once, the computed index corresponds to the first occurrence. For example, when the input is the column vector

`[3 2 1 2 3]'`

, the computed one-based index of the minimum value is`1`

, rather than`5`

when`Each column`

is selected.`Value and Index`

— The block outputs the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input, and the corresponding index array*I*.`Running`

— The block tracks the minimum value of each channel in a time sequence of*M*-by-*N*inputs. The block resets the running minimum whenever a reset event is detected at the optional`Rst`

port. The reset sample time must be a positive integer multiple of the input sample time. In this mode, you must also specify the**Input processing**parameter as one of the following:`Elements as channels (sample based)`

— The block treats each element of the input as a separate channel. For a three-dimensional input signal of size*M*-by-*N*-by-*P*, the block outputs an*M*-by-*N*-by-*P*array. Each*y*element of the output contains the minimum value observed in element_{ijk}*u*for all inputs since the last reset._{ijk}When a reset event occurs, the running minimum

*y*in the current frame is reset to the element_{ijk}*u*._{ijk}`Columns as channels (frame based)`

— The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size*M*-by-*N*, the block outputs an*M*-by-*N*matrix. Each element*y*of the output contains the minimum value observed in the_{ij}*j*th column of all inputs since the last reset, up to and including element*u*of the current input._{ij}When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.

The block resets the running minimum whenever a reset event is detected at the optional

**Rst**port. The reset sample time must be a positive integer multiple of the input sample time.**Running Mode for Variable-Size Inputs**When the input is a variable-size signal, and you set the

**Mode**to`Running`

, then:If you set the

**Input processing**parameter to`Elements as channels (sample based)`

, the state is reset.If you set the

**Input processing**parameter to`Columns as channels (frame based)`

, then:When the input size difference is in the number of channels (columns), the state is reset.

When the input size difference is in the length of channels (rows), there is no reset and the running operation is carried out as usual.

`Index base`

— Base of the minimum value index`One`

(default) | `Zero`

Specify whether the index of the minimum value is reported using one-based or zero-based numbering.

To enable this parameter, set **Mode** to either `Index`

or ```
Value
and Index
```

.

`Find the minimum value over`

— Dimension over which the block computes the minimum value`Each column`

(default) | `Each row`

| `Entire input`

| `Specified dimension`

`Each column`

— The block outputs the minimum value over each column.`Each row`

— The block outputs the minimum value over each row.`Entire input`

— The block outputs the minimum value over the entire input.`Specified dimension`

— The block outputs the minimum value over the dimension specified in the**Dimension**parameter.

To enable this parameter, set **Mode** to ```
Value
and Index
```

, `Value`

, or `Index`

.

`Dimension`

— Custom dimension`1`

(default) | scalarSpecify the dimension (one-based value) of the input signal over which the block computes the minimum. The value of this parameter must be greater than 0 and less than the number of dimensions in the input signal.

To enable this parameter, set **Find the minimum value
over** to `Specified dimension`

.

`Input processing`

— Method to process the input in running mode`Columns as channels (frame based)`

(default) | `Elements as channels (sample based)`

`Columns as channels (frame based)`

— The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size*M*-by-*N*, the block outputs an*M*-by-*N*matrix. Each element*y*of the output contains the minimum value observed in the_{ij}*j*th column of all inputs since the last reset, up to and including element*u*of the current input._{ij}When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.

`Elements as channels (sample based)`

— The block treats each element of the input as a separate channel. For a three-dimensional input signal of size*M*-by-*N*-by-*P*, the block outputs an*M*-by-*N*-by-*P*array. Each*y*element of the output contains the minimum value observed in element_{ijk}*u*for all inputs since the last reset._{ijk}When a reset event occurs, the running minimum

*y*in the current frame is reset to the element_{ijk}*u*._{ijk}

To enable this parameter, set **Mode** to `Running`

.

`Reset port`

— Reset event`None`

(default) | `Rising edge`

| `Falling edge`

| `Either edge`

| `Non-zero sample`

The block resets the running minimum whenever a reset event
is detected at the optional **Rst** port. The reset
sample time must be a positive integer which is a multiple of the
input sample time.

`None`

— Disables the**Rst**port.`Rising edge`

— Triggers a reset operation when the**Rst**input does one of the following:Rises from a negative value to a positive value or zero.

Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero.

`Falling edge`

— Triggers a reset operation when the**Rst**input does one of the following:Falls from a positive value to a negative value or zero.

Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero.

`Either edge`

— Triggers a reset operation when the**Rst**input is a`Rising edge`

or`Falling edge`

.`Non-zero sample`

— Triggers a reset operation at each sample time that the**Rst**input is not zero.### Note

When running simulations in the Simulink

`MultiTasking`

mode, reset signals have a one-sample latency. Therefore, when the block detects a reset event, there is a one-sample delay at the reset port rate before the block applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

To enable this parameter, set **Mode** to `Running`

.

To use these parameters, the data input must be complex fixed-point.

`Rounding mode`

— Method of rounding operation`Floor`

(default) | `Ceiling`

| `Convergent`

| `Nearest`

| `Round`

| `Simplest`

| `Zero`

Specify the rounding mode for fixed-point operations as one of the following:

`Floor`

`Ceiling`

`Convergent`

`Nearest`

`Round`

`Simplest`

`Zero`

For more details, see rounding mode.

The **Rounding mode** and **Saturate
on integer overflow** parameters have no effect on numeric
results when all these conditions are met:

**Product output**data type is`Inherit: Inherit via internal rule`

.**Accumulator**data type is`Inherit: Inherit via internal rule`

.

With these data type settings, the block operates in full-precision mode.

`Saturate on integer overflow`

— Method of overflow actionoff (default) | on

When you select this parameter, the block saturates the result of its
fixed-point operation. When you clear this parameter, the block wraps
the result of its fixed-point operation. For details on
`saturate`

and `wrap`

, see overflow
mode for fixed-point operations.

The **Rounding mode** and **Saturate on
integer overflow** parameters have no effect on numeric
results when all these conditions are met:

**Product output**data type is`Inherit: Inherit via internal rule`

.**Accumulator**data type is`Inherit: Inherit via internal rule`

.

With these data type settings, the block operates in full-precision mode.

`Product output`

— Product output data type`Inherit: Same as input`

(default) | `fixdt([],16,0)`

**Product output** specifies the data type
of the output of a product operation in the Minimum block.
For more information on the product output data type, see Multiplication Data Types.

`Inherit: Same as input`

— The block specifies the product output data type to be the same as the input data type.`fixdt([],16,0)`

— The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the **Product output** data
type by using the **Data Type Assistant**. To use
the assistant, click the **Show data type assistant** button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

`Accumulator`

— Accumulator data type`Inherit: Same as product output`

(default) | `Inherit: Same as input`

| `fixdt([],16,0)`

**Accumulator** specifies the data type of
the output of an accumulation operation in the Minimum block.

`Inherit: Same as product output`

— The block specifies the accumulator data type to be the same as the product output data type.`Inherit: Same as input`

— The block specifies the accumulator data type to be the same as the input data type.`fixdt([],16,0)`

— The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the **Accumulator** data
type by using the **Data Type Assistant**. To use
the assistant, click the **Show data type assistant** button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

`Lock data type settings against changes by the fixed-point tools`

— Prevent fixed-point tools from overriding data typesoff (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block dialog box.

When you set **Mode** to one of `Value`

, `Index`

,
or `Value and Index`

, and specify a dimension,
the block produces results identical to the MATLAB^{®} `min`

function,
when it is called as `[y,I] = min(u,[],D)`

.

`u`

is the data input.`D`

is the dimension.`y`

is the minimum value.`I`

is the index of the minimum value.

The minimum value along the entire input is identical to calling
the `min`

function as `[y,I] = min(u(:))`

.

When you set **Mode** to `Running`

,
and **Input processing** to ```
Columns
as channels (frame based)
```

, the block treats each column
of the input as a separate channel. In this example, the block processes
a two-channel signal with a frame size of three under these settings.

The block outputs the minimum value over each channel since the last reset. At t = 2, the reset event occurs. The minimum value in the second column changes to 6, and then 2, even though these values are greater than 1, which was the minimum value since the previous reset event.

When you set **Mode** to `Running`

,
and **Input processing** to ```
Elements
as channels (sample based)
```

, the block treats each element
of the input as a separate channel. In this example, the block processes
a two-channel signal with a frame size of three under these settings.

Each element *y _{ij}* of
the output contains the minimum value observed in element

Generate C and C++ code using Simulink® Coder™.

Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

This block supports HDL code generation using HDL Coder™. HDL Coder provides additional configuration options that affect HDL implementation and synthesized logic. For more information on implementations, properties, and restrictions for HDL code generation, see Minimum.

Design and simulate fixed-point algorithms using Fixed-Point Designer™.

The parameters on the **Data Types Tab** of
the block are used only for complex fixed-point inputs. The sum of
the squares of the real and imaginary parts of such an input are formed
before a comparison is made, as described under the 'Mode' parameter
in Main Tab. The results of the squares of the
real and imaginary parts are placed into the product output data type.
The result of the sum of the squares is placed into the accumulator
data type. These parameters are ignored for other types of inputs.

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