Real Partial-Systolic QR Decomposition

QR decomposition for real-valued matrices

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

Description

The Real Partial-Systolic QR Decomposition block uses QR decomposition to compute R and C = Q'B, where QR = A, and A and B are real-valued matrices. The least-squares solution to Ax = B is x = R\C. R is an upper triangular matrix and Q is an orthogonal matrix. To compute C = Q', set B to be the identity matrix.

When Regularization parameter is nonzero, the Real Partial-Systolic QR Decomposition block transforms $\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]$ in-place to $R=Q\text{'}\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]$ and $\left[\begin{array}{c}{0}_{n,p}\\ B\end{array}\right]$ in-place to $C=Q\text{'}\left[\begin{array}{c}{0}_{n,p}\\ B\end{array}\right]$ where λ is the regularization parameter, QR is the economy size QR decomposition of $\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]$, A is an m-by-n matrix, p is the number of columns in B, In = `eye(n)`, and 0n,p = `zeros(n,p)`.

Ports

Input

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Rows of real matrix A, specified as a vector. A is an m-by-n matrix where m ≥ 2 and n ≥ 2. 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 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`

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 value at `ready` is 1 (`true`), the block captures the values on 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`

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

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Economy size QR decomposition matrix R, returned as a scalar or vector. R is an upper triangular matrix. The size of matrix R is n-by-n. R has the same data type as A.

Data Types: `single` | `double` | `fixed point`

Economy size QR decomposition matrix C=Q'B, returned as a scalar or vector. C has the same number of rows as R. C has the same data type as B.

Data Types: `single` | `double` | `fixed point`

Whether output data is valid, returned as a Boolean scalar. This control signal indicates when the data at output ports `R` and `C` is valid. When this value is 1 (`true`), the block has successfully computed the R and C matrices. When this value is 0 (`false`), the output data is not valid.

Data Types: `Boolean`

Whether block is ready, returned as a Boolean scalar. This control signal that 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

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Number of rows in input matrices A and B, specified as a positive integer-valued scalar.

Programmatic Use

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

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`

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

Programmatic Use

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

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`

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Version History

Introduced in R2020b