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Real Partial-Systolic Q-less QR Decomposition with Forgetting Factor

Q-less QR decomposition for real-valued matrices with infinite number of rows

  • Library:
  • Fixed-Point Designer / Matrices and Linear Algebra / Matrix Factorizations

  • Real Partial Systolic Q-less QR Decomposition with Forgetting Factor block

Description

The Real Partial-Systolic Q-less QR Decomposition with Forgetting Factor block uses QR decomposition to compute the economy size upper-triangular R factor of the QR decomposition A = QR, without computing Q. A is an infinitely tall real-valued matrix representing streaming data.

The solution to A'Ax = B is x = R\R'\b.

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 A uses a fixed-point data type, A must be signed and use binary-point scaling. Slope-bias representation is not supported for fixed-point data types.

Data Types: single | double | fixed point

Whether inputs are 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 value of ready 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

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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Economy size QR decomposition matrix R multiplied by the Forgetting factor parameter, returned as a matrix. R is an upper triangular matrix. The output at R has the same data type as the input at A(i,:).

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 R is valid. When this value is 1 (true), the block has successfully computed the matrix R. When this value is 0 (false), the output data is not valid.

Data Types: Boolean

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 validIn 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

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Number of columns in input matrix A, specified as a positive integer-valued scalar.

Programmatic Use

Block Parameter: n
Type: character vector
Values: positive integer-valued scalar
Default: 4

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: positive integer-valued scalar
Default: 0.99

Algorithms

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Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced in R2020b