Real PartialSystolic Matrix Solve Using Qless QR Decomposition with Forgetting Factor
Compute value of X in A'AX = B for realvalued matrices with infinite number of rows using Qless QR decomposition
 Library:
FixedPoint Designer HDL Support / Matrices and Linear Algebra / Linear System Solvers
Description
The Real PartialSystolic Matrix Solve Using Qless QR Decomposition with Forgetting Factor block solves the system of linear equations A'AX = B using Qless QR decomposition, where A and B are realvalued matrices. A is an infinitely tall matrix representing streaming data.
Ports
Input
A(i,:)
— Rows of real matrix A
vector
Rows of real matrix A, specified as a vector. A is an mbyn matrix where m ≥ 2 and m ≥ n. If B is single or double, A must be the same data type as B. If A is a fixedpoint data type, A must be signed, use binarypoint scaling, and have the same word length as B. Slopebias representation is not supported for fixedpoint data types.
Data Types: single
 double
 fixed point
B
— Matrix B
matrix
Real matrix B, specified as a matrix. B is an mbyp matrix where m ≥ 2. If A is single or double, B must be the same data type as A. If B is a fixedpoint data type, B must be signed, use binarypoint scaling, and have the same word length as A. Slopebias representation is not supported for fixedpoint data types.
Data Types: single
 double
 fixed point
validInA
— Whether A input is valid
Boolean
scalar
Whether A(i, ;) input is valid, specified as a Boolean
scalar. This control signal indicates when the data from the
A(i,:) input port is valid. When this value is
1
(true
) and the readyA
value is 1
(true
), the block captures the values
at the A(i,:) input port. When this value is 0
(false
), the block ignores the input samples.
After sending a true
validInA signal, there may be some delay before
readyA is set to false
. To ensure all data
is processed, you must wait until readyA is set to
false
before sending another true
validInA signal.
Data Types: Boolean
validInB
— Whether B input is valid
Boolean
scalar
Whether B input is valid, specified as a Boolean scalar. This
control signal indicates when the data from the B input port is
valid. When this value is 1
(true
) and the
readyB value is 1
(true
),
the block captures the values at the B input port. When this
value is 0
(false
), the block ignores the input
samples.
After sending a true
validInB signal, there may be some delay before
readyB is set to false
. To ensure all data
is processed, you must wait until readyB is set to
false
before sending another true
validInB signal.
Data Types: Boolean
restart
— Whether to clear internal states
Boolean
scalar
Whether to clear internal states, specified as a Boolean scalar. When this value
is 1 (true
), the block stops the current calculation and clears all
internal states. When this value is 0 (false
) and the
validInA and validInB values are both 1
(true
), the block begins a new subframe.
Data Types: Boolean
Output
X
— Matrix X
vector  matrix
Matrix X, returned as a vector or matrix.
Data Types: single
 double
 fixed point
validOut
— Whether output data is valid
Boolean
scalar
Whether the output data is valid, returned as a Boolean scalar. This control
signal indicates when the data at the output port X is valid.
When this value is 1
(true
), the block has
successfully computed a row of X. When this value is
0
(false
), the output data is not
valid.
Data Types: Boolean
readyA
— Whether block is ready for input A
Boolean
scalar
Whether the block is ready for input A, returned as a Boolean scalar. This control
signal indicates when the block is ready for new input data. When this value is 1
(true
) and validInA value is 1
(true
), the block accepts input data in the next time step. When
this value is 0 (false
), the block ignores input data in the next
time step.
After sending a true
validInA signal, there may be some delay before
readyA is set to false
. To ensure all data
is processed, you must wait until readyA is set to
false
before sending another true
validInA signal.
Data Types: Boolean
readyB
— Whether block is ready for input B
Boolean
scalar
Whether the block is ready for input B, returned as a Boolean scalar. This control
signal indicates when the block is ready for new input data. When this value is 1
(true
) and validInB value is 1
(true
), the block accepts input data in the next time step. When
this value is 0 (false
), the block ignores input data in the next
time step.
After sending a true
validInB signal, there may be some delay before
readyB is set to false
. To ensure all data
is processed, you must wait until readyB is set to
false
before sending another true
validInB signal.
Data Types: Boolean
Parameters
Number of columns in matrix A and rows in matrix B
— Number of columns in matrix A and rows in matrix B
4
(default)  positive integervalued scalar
Number of columns in matrix A and rows in matrix B, specified as a positive integervalued scalar.
Programmatic Use
Block Parameter:
n 
Type: character vector 
Values: positive integervalued scalar 
Default:
4 
Number of columns in matrix B
— Number of columns in matrix B
1
(default)  positive integervalued scalar
Number of columns in matrix B, specified as a positive integervalued scalar.
Programmatic Use
Block Parameter:
p 
Type: character vector 
Values: positive integervalued scalar 
Default:
1 
Forgetting factor
— Forgetting factor applied before each row of matrix is factored
0.99 (default)  real positive scalar
Forgetting factor applied before each row of the matrix is factored, specified as a real positive scalar. The output is updated as each row of A is input indefinitely.
Programmatic Use
Block Parameter:
forgettingFactor 
Type: character vector 
Values: positive integervalued scalar 
Default:
0.99 
Output datatype
— Data type of output matrix X
fixdt(1,18,14)
(default)  double
 single
 fixdt(1,16,0)
 <data type expression>
Data type of the output matrix X, specified as
fixdt(1,18,14)
, double
,
single
, fixdt(1,16,0)
, or as a userspecified
data type expression. The type can be specified directly, or expressed as a data type
object such as Simulink.NumericType
.
Programmatic Use
Block Parameter:
OutputType 
Type: character vector 
Values:
'fixdt(1,18,14)'  'double' 
'single'  'fixdt(1,16,0)' 
'<data type expression>' 
Default:
'fixdt(1,18,14)' 
Model Examples
Algorithms
Choosing the Implementation Method
Partialsystolic implementations prioritize speed of computations over space constraints, while burst implementations prioritize space constraints at the expense of speed of the operations. The following table illustrates the tradeoffs between the implementations available for matrix decompositions and solving systems of linear equations.
Implementation  Ready  Latency  Area  Sample block or example 

Systolic  C  O(n)  O(mn^{2})  Implement HardwareEfficient QR Decomposition Using CORDIC in a Systolic Array 
PartialSystolic  C  O(m)  O(n^{2})  
PartialSystolic with Forgetting Factor  C  O(n)  O(n^{2})  FixedPoint HDLOptimized MinimumVariance DistortionlessResponse (MVDR) Beamformer 
Burst  O(n)  O(mn^{2})  O(n) 
Where C is a constant proportional to the word length of the data, m is the number of rows in matrix A, and n is the number of columns in matrix A.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Slopebias representation is not supported for fixedpoint data types.
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 a single, default HDL architecture.
General  

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

Supports fixedpoint data types only.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
A and B must be signed, use binarypoint scaling, and have the same word length. Slopebias representation is not supported for fixedpoint data types.
See Also
Blocks
 Complex PartialSystolic Matrix Solve Using Qless QR Decomposition with Forgetting Factor  Real PartialSystolic Matrix Solve Using QR Decomposition  Real PartialSystolic Matrix Solve Using Qless QR Decomposition  Real Burst Matrix Solve Using QR Decomposition
Functions
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