# Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor

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

• Library:
• Fixed-Point Designer HDL Support / 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.

When the regularization parameter is nonzero, the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor initializes the first upper-triangular factor R to λIn before factoring in the rows of A, where λ is the regularization parameter and In = eye(n).

## 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

Real matrix B, specified as a matrix. 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 validInA and validInB values are both 1 (true), the block begins a new subframe.

Data Types: Boolean

### Output

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Matrix X, returned as a vector or matrix.

Data Types: single | double | fixed point

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

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

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

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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: forgettingFactor Type: character vector Values: positive integer-valued scalar Default: 0.99

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)' | '' Default: 'fixdt(1,18,14)'

## Tips

• Use fixed.forgettingFactor to compute the forgetting factor, α, for an infinite number of rows with the equivalent gain of a matrix with m rows.

• Use fixed.forgettingFactorInverse to compute the number of rows, m, of a matrix with equivalent gain corresponding to forgetting factor α

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## Version History

Introduced in R2020b

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