# Complex Partial-Systolic Q-less QR Decomposition

Q-less QR decomposition for complex-valued matrices

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

## Description

The Complex Partial-Systolic Q-less QR Decomposition block uses QR decomposition to compute the economy size upper-triangular R factor of the QR decomposition A = QR, where A is a complex-valued matrix, without computing Q. The solution to A'Ax = B is x = R\R'\b.

When Regularization parameter is nonzero, the Complex Partial-Systolic Q-less QR Decomposition block computes the upper-triangular factor R of the economy size QR decomposition of $\left[\begin{array}{c}\lambda {I}_{n}\\ A\end{array}\right]$ where λ is the regularization parameter.

## Ports

### Input

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Rows of 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
Complex Number Support: Yes

Whether inputs are valid, specified as a Boolean scalar. This control signal indicates when the data at the A(i,:) input port is valid. When this value is 1 (true) and the value at 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.

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

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 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 matrix A, 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

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

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