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Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor

Compute the value of X in the equation A'AX = B for real-valued matrices with infinite number of rows using asynchronous Q-less QR decomposition

  • Library:
  • Fixed-Point Designer HDL Support / Matrices and Linear Algebra / Linear System Solvers

  • Screenshot of Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block

Description

The Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block solves the system of linear equations A'AX = B using asynchronous Q-less QR decomposition, where A and B are real-valued matrices. A is an infinitely tall matrix representing streaming data.

When Regularization parameter is nonzero, the Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block solves the matrix equation

[λInA]'[λInA]X=(λ2In+A'A)X=B

where λ is the regularization parameter, A is an m-by-n matrix, and In = eye(n).

This block operates asynchronously. The forward- and backward-substitution and Q-less QR decomposition run independently using the latest R and B matrices.

Ports

Input

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Rows of real matrix A, specified as a vector. A is an infinitely tall matrix of streaming data. 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

Rows of real matrix B, specified as a vector. B is an n-by-p matrix where n ≥ 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

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

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

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 value at validIn is 1 (true), the block begins a new subframe.

Data Types: Boolean

Output

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Rows of the matrix X, returned as a scalar or vector.

Data Types: single | double | fixed point

Whether the output data is valid, specified as a Boolean scalar. This control signal indicates when the data at output port X is valid. When this value is 1 (true), the block has successfully computed the matrix X. When this value is 0 (false), the output data is not valid.

Data Types: Boolean

Whether block is ready for input A(i,:), 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 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

Whether 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 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

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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, specified as a positive integer-valued scalar.

Programmatic Use

Block Parameter: p
Type: character vector
Values: positive integer-valued scalar
Default: 1

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: forgetting_factor
Type: character vector
Values: real positive scalar
Default: 0

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 least-squares estimates.

Programmatic Use

Block Parameter: regularizationParameter
Type: character vector
Values: real nonnegative scalar
Default: 0

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

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Extended Capabilities

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2022b