Complex PartialSystolic Matrix Solve Using QR Decomposition
Compute value of x in Ax = B for complexvalued matrices using QR decomposition
 Library:
FixedPoint Designer HDL Support / Matrices and Linear Algebra / Linear System Solvers
Description
The Complex PartialSystolic Matrix Solve Using QR Decomposition block solves the system of linear equations Ax = B using QR decomposition, where A and B are complexvalued matrices. To compute x = A^{1}, set B to be the identity matrix.
Ports
Input
A(i,:)
— Rows of matrix A
vector
Rows of 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
Complex Number Support: Yes
B(i,:)
— Rows of matrix B
vector
Rows of matrix B, specified as a vector. 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
validIn
— Whether inputs are valid
Boolean
scalar
Whether inputs are valid, specified as a Boolean scalar. This control signal
indicates when the data from the A(i,:) and
B(i,:) input ports are valid. When this value is
1
(true
) and the ready
value is 1
(true
), the block captures the values
at the A(i,:) and B(i,:) input ports. When
this value is 0
(false
), the block ignores the
input samples.
After sending a true
validIn signal, there may be some delay before
ready is set to false
. To ensure all data is
processed, you must wait until ready is set to
false
before sending another true
validIn 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
validIn
value is 1 (true
), the block begins
a new subframe.
Data Types: Boolean
Output
X(i, :)
— Rows of matrix X
scalar  vector
Rows of matrix X, returned as a scalar or vector.
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(i,:) is
valid. When this value is 1 (true
), the block has successfully
computed a row of matrix X. When this value is 0
(false
), the output data is not valid.
Data Types: Boolean
ready
— Whether block is ready
Boolean
scalar
Whether the block is ready, 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 the validIn
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
validIn signal, there may be some delay before
ready is set to false
. To ensure all data is
processed, you must wait until ready is set to
false
before sending another true
validIn signal.
Data Types: Boolean
Parameters
Number of rows in matrices A and B
— Number of rows in input matrices A and B
4
(default)  positive integervalued scalar
Number of rows in input matrices A and B, specified as a positive integervalued scalar.
Programmatic Use
Block Parameter:
m 
Type: character vector 
Values: positive integervalued scalar 
Default:
4 
Number of columns in matrix A
— Number of columns in input matrix A
4
(default)  positive integervalued scalar
Number of columns in input matrix A, 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 input matrix B
1
(default)  positive integervalued scalar
Number of columns in input matrix B, specified as a positive integervalued scalar.
Programmatic Use
Block Parameter:
p 
Type: character vector 
Values: positive integervalued scalar 
Default:
1 
Regularization parameter
— Regularization parameter
0 (default)  nonnegative scalar
Regularization parameter, specified as a nonnegative scalar. Small, positive values of the regularization parameter can improve the conditioning of the problem and reduce the variance of the estimates. While biased, the reduced variance of the estimate often results in a smaller mean squared error when compared to leastsquares estimates.
Programmatic Use
Block Parameter:
k 
Type: character vector 
Values: positive integervalued scalar 
Default:
0 
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
Real PartialSystolic Matrix Solve Using QR Decomposition  Complex PartialSystolic Matrix Solve Using Qless QR Decomposition  Complex Burst Matrix Solve Using QR Decomposition
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