Minimum

Minimum values of input or sequence of inputs

• 

Libraries:
DSP System Toolbox / Statistics
DSP System Toolbox HDL Support / Statistics

Description

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.

Note

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.

Examples

Compute the Minimum

Simulink model example to compute the minimum using the Minimum block.

• Open Script

Compute the Running Minimum

Simulink model example to compute the running minimum using the Minimum block.

• Open Script

Ports

Input

In — Data input

vector | matrix | N-D array

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 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Rst — Reset port

scalar

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.

Dependencies

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

Output

Val — Minimum values along the specified dimension

scalar | vector | matrix | N-D array

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_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.

  When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element 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_ij of the output contains the minimum value observed in the jth column of all inputs since the last reset, up to and including element u_ij of the current input.

  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.

Dependencies

To enable this port, set the Mode parameter to either Value and Index or Value.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Idx — Index of the minimum values along the specified dimension

scalar | vector | matrix | N-D array

When the input is double, the index values are also double. Otherwise, the index values are uint32.

Dependencies

To enable this port, set the Mode parameter to either Value and Index or Index.

Data Types: double | uint32

Parameters

Main Tab

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_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.

    When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element 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_ij of the output contains the minimum value observed in the jth column of all inputs since the last reset, up to and including element u_ij of the current input.

    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.

Dependencies

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.

Dependencies

To enable this parameter, set Mode to Value and Index, Value, or Index.

Dimension — Custom dimension

1 (default) | scalar

Specify 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.

Dependencies

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_ij of the output contains the minimum value observed in the jth column of all inputs since the last reset, up to and including element u_ij of the current input.

  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_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.

  When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element u_ijk.

Dependencies

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).

Dependencies

To enable this parameter, set Mode to Running.

Data Types Tab

Note

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

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.

Saturate on integer overflow — Method of overflow action

off (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.

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 types

off (default) | on

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

Block Characteristics

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

Algorithms

Minimum

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(:)).

Running Minimum

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 u_ij for all inputs since the last reset. The reset event occurs at t = 2. When a reset event occurs, the running minimum, y_ij, in the current frame is reset to the element u_ij.

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.

Limitations

For HDL code generation, the In port must be a vector. In that case, the output Val and Idx ports are scalar.

HDL Architecture

This block has multi-cycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated model or validation model. See Generated Model and Validation Model (HDL Coder).

Architecture	Additional cycles of latency	Description
default Tree	0	Generates a tree structure of comparators.

HDL Block Properties

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 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
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 0. For more details, see InputPipeline (HDL Coder).
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 0. For more details, see OutputPipeline (HDL Coder).
InstantiateStages	Generate a VHDL® entity or Verilog® module for each cascade stage. The default is off. See also InstantiateStages (HDL Coder).
SerialPartition	Specify partitions for Cascade-serial implementations as a vector of the lengths of each partition. The default setting uses the minimum number of stages. See also SerialPartition (HDL Coder).

Version History

Introduced before R2006a