Minimum
Minimum values of input or sequence of inputs
 Library:
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.
Ports
Input
In
— Data input
vector  matrix  ND array
The block accepts realvalued or complexvalued multichannel and multidimensional inputs. The input can be floatingpoint, fixedpoint, or Boolean. Real fixedpoint inputs can be either signed or unsigned. Complex fixedpoint 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  ND 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 MbyNbyP array, with the dimension set to
1
, the block outputs a 1byNbyP array. When the dimension is set to3
, the block outputs a twodimensional MbyN matrix.When the input is an MbyN matrix, with the dimension set to
1
, the block outputs a 1byN 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
MbyN 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 threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP 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 Ndimensional input signal, where N > 2. For a twodimensional input signal of size MbyN, the block outputs an MbyN 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  ND 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 MbyNbyP. Set Find the minimum value over to:Each row
— The output y at each sample time consists of an Mby1byP array, where each element contains the minimum value of each vector over the second dimension of the input. For an input that is an MbyN matrix, the output at each sample time is an Mby1 column vector.Each column
— The output y at each sample time consists of a 1byNbyP array, where each element contains the minimum value of each vector over the first dimension of the input. For an input that is an MbyN matrix, the output at each sample time is a 1byN row vector.In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Entire input
— The output y at each sample time is a scalar that contains the minimum value in the MbyNbyP input matrix.Specified dimension
— The output y at each sample time depends on Dimension. If Dimension is set to1
, the output is the same as when you selectEach column
. If Dimension is set to2
, the output is the same as when you selectEach row
. If Dimension is set to3
, the output at each sample time is an MbyN 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 MbyNbyP:Each row
— The output I at each sample time consists of an Mby1byP 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 MbyN matrix, the output at each sample time is an Mby1 column vector.Each column
— The output I at each sample time consists of a 1byNbyP 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 MbyN matrix, the output at each sample time is a 1byN row vector.In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Entire input
— The output I at each sample time is a 1by3 vector that contains the location of the minimum value in the MbyNbyP input matrix. For an input that is an MbyN matrix, the output is a 1by2 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 selectEach column
. If Dimension is set to 2, the output is the same as when you selectEach row
. If Dimension is set to 3, the output at each sample time is an MbyN 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 onebased index of the minimum value is1
, rather than5
whenEach 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 MbyN inputs. The block resets the running minimum whenever a reset event is detected at the optionalRst
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 threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP 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 Ndimensional input signal, where N > 2. For a twodimensional input signal of size MbyN, the block outputs an MbyN 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 VariableSize Inputs
When the input is a variablesize 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 onebased or zerobased 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 (onebased 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 Ndimensional input signal, where N > 2. For a twodimensional input signal of size MbyN, the block outputs an MbyN 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 threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP 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
 Nonzero 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 aRising edge
orFalling edge
.Nonzero 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 onesample latency. Therefore, when the block detects a reset event, there is a onesample 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 TimeBased 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 fixedpoint.
Rounding mode
— Method of rounding operation
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint 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
fixedpoint operation. When you clear this parameter, the block wraps
the result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint 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, binarypoint, scaled, fixedpoint 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, binarypoint, scaled, fixedpoint 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 fixedpoint tools
— Prevent fixedpoint tools from overriding data types
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify in the block dialog box.
Model Examples
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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 twochannel 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 twochannel 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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has multicycle 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. 
Cascade  1, when block has a single vector input port.  This implementation is optimized for latency * area, with medium speed. See Cascade Architecture Best Practices (HDL Coder). 
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

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

InstantiateStages  Generate a VHDL^{®} 
SerialPartition  Specify partitions for Cascadeserial implementations as a vector of the lengths of each partition. The default setting uses the minimum number of stages. See also SerialPartition (HDL Coder). 
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
The parameters on the Data Types Tab of the block are used only for complex fixedpoint 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.
See Also
Functions
Objects
Blocks
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