Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor
Compute value of X in A'AX = B for real-valued matrices with infinite number of rows using Q-less QR decomposition
- Library:
Fixed-Point Designer / Matrices and Linear Algebra / Linear System Solvers
Description
The Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block solves the system of linear equations A'AX = B using Q-less QR decomposition, where A and B are real-valued 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 m-by-n 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 fixed-point data type, A must be signed, use binary-point scaling, and have the same word length as B. Slope-bias representation is not supported for fixed-point data types.
Data Types: single | double | fixed point
B — Matrix B
matrix
Real matrix B, specified as a matrix. B is an m-by-p matrix where m ≥ 2. If A is single or double, B must be the same data type as A. If B is a fixed-point data type, B must be signed, use binary-point scaling, and have the same word length as A. Slope-bias representation is not supported for fixed-point 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.
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.
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.
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.
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 integer-valued scalar
Number of columns in matrix A and rows in matrix B, specified as a positive integer-valued scalar.
Programmatic Use
Block Parameter:
n |
| Type: character vector |
| Values: positive integer-valued scalar |
Default:
4 |
Number of columns in matrix B — Number of columns in matrix B
1 (default) | positive integer-valued scalar
Number of columns in matrix B, specified as a positive integer-valued scalar.
Programmatic Use
Block Parameter:
p |
| Type: character vector |
| Values: positive integer-valued scalar |
Default:
1 |
Forgetting factor — Forgetting factor applied after each row of matrix is factored
0.99 (default) | real positive scalar
Forgetting factor applied after 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 integer-valued 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 user-specified
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)' |
Algorithms
Choosing the Implementation Method
Partial-systolic 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(mn2) | Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array |
| Partial-Systolic | C | O(m) | O(n2) | |
| Partial-Systolic with Forgetting Factor | C | O(n) | O(n2) | Fixed-Point HDL-Optimized Minimum-Variance Distortionless-Response (MVDR) Beamformer |
| Burst | O(n) | O(mn2) | 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™.
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 fixed-point data types only.
Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.
A and B must be signed, use binary-point scaling, and have the same word length. Slope-bias representation is not supported for fixed-point data types.
See Also
Blocks
- Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor | Real Burst Matrix Solve Using QR Decomposition | Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition | Real Partial-Systolic Matrix Solve Using QR Decomposition