Complex Burst QR Decomposition

QR decomposition for complex-valued matrices

Description

The Complex Burst QR Decomposition block uses QR decomposition to compute R and C = Q'B, where QR = A, and A and B are complex-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.

Creation

model = fixed.getQRFactorizationModel(A, B) generates a model named model containing a QR Decomposition block and data input matrices, A and B.

Ports

Input

A(i,:) — Rows of matrix A

vector

Rows of matrix A, where A is a m-by-n matrix with m, n ≥ 2. If B is single or double, A must be the same data type as B. If A is fixed point, 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

B(i,:) — Rows of matrix B

vector

Rows of matrix B, where B is an m-by-p matrix with m ≥ 2. If A is single or double, B must be the same data type as A. If B is fixed point, 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
Complex Number Support: Yes

validIn — Indicates valid inputs

Boolean scalar

Indicates valid inputs, specified as a Boolean scalar. Control signal that indicates when the data from the A(i,:) and B(i,:) input ports is valid. When this value is 1 (true) and 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.

Data Types: Boolean

restart — Clear internal states

Boolean scalar

Clears internal state, 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

R(i,:) — Rows of upper-triangular matrix R

scalar | vector

Rows of the economy sized QR decomposition matrix R. R is an upper triangular matrix. R has the same data type as A.

Data Types: single | double | fixed point

C(i,:) — Rows of matrix C=Q'B

scalar | vector

Rows of the economy sized QR decomposition matrix C=Q'B. C has the same number of rows as R. C has the same data type as B.

Data Types: single | double | fixed point

validOut — Indicates valid output data

Boolean scalar

Control signal that indicates when the data at output ports R(i,:) and C(i,:) 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

ready — Indicates block is ready

Boolean scalar

Control signal that 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

Number of rows in matrices A and B — Number of rows in matrices A and B

4 (default) | integer-valued scalar

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

Programmatic Use

Block Parameter: m

Type: character vector

Values: integer-valued scalar

Default: '4'

Number of columns in matrix A — Number of columns in matrix A

4 (default) | integer-valued scalar

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

Programmatic Use

Block Parameter: n

Type: character vector

Values: integer-valued scalar

Default: '4'

Number of columns in matrix B — Number of columns in matrix B

4 (default) | integer-valued scalar

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

Programmatic Use

Block Parameter: p

Type: character vector

Values: integer-valued scalar

Default: '1'

Model Examples

Implement Hardware-Efficient Complex Burst QR Decomposition

Demonstrates how to compute the QR decomposition of complex matrices using hardware-efficient MATLAB® code in Simulink®. This model shares computational resources across steps of the QR Decomposition algorithm. It thus uses fewer on chip resources than a fully pipelined approach, while sacrificing some total throughput.

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