Fixed-Point Matrix Operations in Simulink
R2026bOptimized CORDIC-based fixed-point matrix solvers and matrix
decomposition blocks for efficient HDL code
Use the Fixed-Point Designer™ HDL Optimized library of blocks to perform CORDIC-based fixed-point matrix operations and generate efficient HDL code. These blocks model design patterns for systems of linear equations and perform core matrix operations, such as QR decomposition and singular value decomposition, for hardware-efficient implementation on FPGAs. For help choosing an appropriate block for your application, see Choose a Block for HDL-Optimized Fixed-Point Matrix Operations. Use the included Fixed-Point Designer functions to analytically determine optimal fixed-point data types for the linear system solver and matrix factorization blocks. Generate HDL code for designs that incorporate these blocks using HDL Coder™.
For MATLAB®-based implementations of these algorithms, see Fixed-Point Matrix Operations in MATLAB. For CORDIC-based and other embedded-efficient implementations of math operations in MATLAB and Simulink®, see Fixed-Point Math Operations in MATLAB and Simulink.
Blocks
Solve AX = B
 | Real Burst Matrix Solve Using QR Decomposition | Compute the value of x in the equation Ax = B for real-valued matrices using QR decomposition |
 | Complex Burst Matrix Solve Using QR Decomposition | Compute the value of x in the equation Ax = B for complex-valued matrices using QR decomposition |
 | Real Partial-Systolic Matrix Solve Using QR Decomposition | Compute value of x in the equation Ax = B for real-valued matrices using QR decomposition |
 | Complex Partial-Systolic Matrix Solve Using QR Decomposition | Compute value of x in the equation Ax = B for complex-valued matrices using QR decomposition |
 | Systolic Matrix Solve Using QR Decomposition | Compute value of X in the equation AX = B using QR decomposition (Since R2024a) |
Solve A'AX = B
 | Real Burst Matrix Solve Using Q-less QR Decomposition | Compute the value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition |
 | Complex Burst Matrix Solve Using Q-less QR Decomposition | Compute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition |
 | Real Burst Asynchronous Matrix Solve Using Q-less QR Decomposition | Compute the value of X in the equation A'AX = B for real-valued matrices using asynchronous Q-less QR decomposition (Since R2022b) |
 | Complex Burst Asynchronous Matrix Solve Using Q-less QR Decomposition | Compute the value of X in the equation A'AX = B for complex-valued matrices using asynchronous Q-less QR decomposition (Since R2022b) |
 | Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition | Compute value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition |
 | Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition | Compute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition |
Solve A'AX = B with Infinitely Tall A Matrix
 | Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor | Compute the value of X in the equation A'AX = B for real-valued matrices with infinite number of rows using asynchronous Q-less QR decomposition (Since R2022b) |
 | Complex Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor | Compute the value of X in the equation A'AX = B for complex-valued matrices with infinite number of rows using asynchronous Q-less QR decomposition (Since R2022b) |
 | 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 |
 | Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor | Compute the value of X in the equation A'AX = B for complex-valued matrices with infinite number of rows using Q-less QR decomposition |
QR Decomposition
 | Real Burst QR Decomposition | QR decomposition for real-valued matrices |
 | Complex Burst QR Decomposition | QR decomposition for complex-valued matrices |
 | Real Partial-Systolic QR Decomposition | QR decomposition for real-valued matrices |
 | Complex Partial-Systolic QR Decomposition | QR decomposition for complex-valued matrices |
 | Systolic QR Decomposition | QR decomposition for matrices (Since R2024a) |
Q-less QR Decomposition
 | Real Burst Q-less QR Decomposition | Q-less QR decomposition for real-valued matrices |
 | Complex Burst Q-less QR Decomposition | Q-less QR decomposition for complex-valued matrices |
 | Real Burst Q-less QR Decomposition Whole R Output | Q-less QR decomposition for real-valued matrices (Since R2022b) |
 | Complex Burst Q-less QR Decomposition Whole R Output | Q-less QR decomposition for complex-valued matrices (Since R2022b) |
 | Real Partial-Systolic Q-less QR Decomposition | Q-less QR decomposition for real-valued matrices |
 | Complex Partial-Systolic Q-less QR Decomposition | Q-less QR decomposition for complex-valued matrices |
Q-less QR Decomposition with Forgetting Factor
 | Real Burst Q-less QR Decomposition with Forgetting Factor Whole R Output | Q-less QR decomposition for real-valued matrices with infinite number of rows (Since R2022b) |
 | Complex Burst Q-less QR Decomposition with Forgetting Factor Whole R Output | Q-less QR decomposition for complex-valued matrices with infinite number of rows (Since R2022b) |
 | Real Partial-Systolic Q-less QR Decomposition with Forgetting Factor | Q-less QR decomposition for real-valued matrices with infinite number of rows |
 | Complex Partial-Systolic Q-less QR Decomposition with Forgetting Factor | Q-less QR decomposition for complex-valued matrices with infinite number of rows |
Singular Value Decomposition
 | Square Jacobi SVD HDL Optimized | Fixed-point singular value decomposition (Since R2023a) |
 | Non-Square Jacobi SVD HDL Optimized | Fixed-point singular value decomposition (Since R2023b) |
Functions
Topics
General
- Choose a Block for HDL-Optimized Fixed-Point Matrix Operations
How to choose a block from the Fixed-Point Designer HDL Support library. - Data Type Agent for Partial-Systolic Matrix Solve Using QR Decomposition Blocks
Use the Data Type Agent to recommend fixed-point data types for Partial-Systolic Matrix Solve Using QR Decomposition blocks. (Since R2025a)
Linear System Solvers: Solve AX = B
- Implement Hardware-Efficient Real Burst Matrix Solve Using QR Decomposition
How to use the Real Burst Matrix Solve Using QR Decomposition block. - Implement Hardware-Efficient Real Burst Matrix Solve Using QR Decomposition with Tikhonov Regularization
This example shows how to use the Real Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Complex Burst Matrix Solve Using QR Decomposition
How to use the Complex Burst Matrix Solve Using QR Decomposition block. - Implement Hardware-Efficient Complex Burst Matrix Solve Using QR Decomposition with Tikhonov Regularization
This example shows how to use the Complex Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition
How to use the Real Partial-Systolic Matrix Solve Using QR Decomposition block. - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition with Diagonal Loading
How to use the Real Partial-Systolic Matrix Solve Using QR Decomposition Block with diagonal loading. - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition with Tikhonov Regularization
This example shows how to use the Real Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition
How to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block. - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition with Diagonal Loading
How to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition Block with diagonal loading. - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition with Tikhonov Regularization
This example shows how to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Use Hardware-Efficient Algorithm to Solve Systems of Complex-Valued Linear Equations
Solve a system of complex-valued linear equations using hardware-efficient code.
Linear System Solvers: Solve A'AX = B
- Implement Hardware-Efficient Real Burst Matrix Solve Using Q-less QR Decomposition
How to use the Real Burst Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Real Burst Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization
This example shows how to use the Real Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Complex Burst Matrix Solve Using Q-less QR Decomposition
How to use the Complex Burst Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Complex Burst Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization
This example shows how to use the Complex Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Real Burst Asynchronous Matrix Solve Using Q-less QR Decomposition
This example shows how to implement a hardware-efficient solution to the real-valued matrix equation A'AX=B using the Real Burst Asynchronous Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Complex Burst Asynchronous Matrix Solve Using Q-less QR Decomposition
This example shows how to implement a hardware-efficient solution to the complex-valued matrix equation A'AX=B using the Complex Burst Asynchronous Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition
How to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization
This example shows how to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block to solve the regularized least-squares matrix equation - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition
How to use the Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition block. - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization
This example shows how to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation
Linear System Solvers: Solve A'AX = B with Infinitely Tall A Matrix
- Implement Hardware-Efficient Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor
This example shows how to use the hardware-efficient Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block. - Implement Hardware-Efficient Complex Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor
This example shows how to use the hardware-efficient Complex Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block. - Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor
How to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block. - Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor
How to use the Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block.
Matrix Factorizations: QR Decomposition
- Implement Hardware-Efficient Real Burst QR Decomposition
How to use the Real Burst QR Decomposition block. - Implement Hardware-Efficient Complex Burst QR Decomposition
How to use the Complex Burst QR Decomposition block. - Implement Hardware-Efficient Real Partial-Systolic QR Decomposition
How to use the Real Partial-Systolic QR Decomposition block. - Implement Hardware-Efficient Complex Partial-Systolic QR Decomposition
How to use the Complex Partial-Systolic QR Decomposition block. - Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array
Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array.
Matrix Factorizations: Q-less QR Decomposition
- Implement Hardware-Efficient Real Burst Q-less QR Decomposition
How to use the Real Burst Q-less QR Decomposition block. - Implement Hardware-Efficient Complex Burst Q-less QR Decomposition
How to use the Complex Burst Q-less QR Decomposition block. - Implement Hardware-Efficient Real Partial-Systolic Q-less QR Decomposition
How to use the Real Partial-Systolic Q-less QR Decomposition block. - Implement Hardware-Efficient Complex Partial-Systolic Q-less QR Decomposition
How to use the Complex Partial-Systolic Q-less QR Decomposition block.
Matrix Factorizations: Q-less QR Decomposition with Forgetting Factor
- Implement Hardware-Efficient Real Burst Q-less QR with Forgetting Factor
This example shows how to use the hardware-efficient Real Burst Q-less QR Decomposition with Forgetting Factor Whole R Output block. - Implement Hardware-Efficient Complex Burst Q-less QR with Forgetting Factor
This example shows how to use the hardware-efficient Complex Burst Q-less QR Decomposition with Forgetting Factor Whole R Output block. - Implement Hardware-Efficient Real Partial-Systolic Q-less QR with Forgetting Factor
How to use the Real Partial-Systolic Q-less QR Decomposition with Forgetting Factor block. - Implement Hardware-Efficient Complex Partial-Systolic Q-less QR with Forgetting Factor
How to use the Complex Partial-Systolic Q-less QR Decomposition with Forgetting Factor block.
Matrix Factorizations: Singular Value Decomposition
- Implement HDL Optimized SVD in Feedforward Fashion Without Backpressure
This example shows how to implement a hardware-efficient singular value decomposition (SVD) using the Square Jacobi SVD HDL Optimized block in a feedforward fashion without backpressure. - Implement HDL Optimized SVD with Backpressure Signal and HDL FIFO Block
This example shows how to implement hardware-efficient singular value decomposition (SVD) using the Square Jacobi SVD HDL Optimized block with backpressure control and an HDL FIFO block. - Implement HDL Optimized SVD for Non-Square Matrix with Scalar Input and Simplified AXI4 Protocol
This example shows how to use the Non-Square Jacobi SVD HDL Optimized block to compute the singular value decomposition (SVD) of non-square matrices. - Compute SVD of Non-Square Matrices Using Square Jacobi SVD HDL Optimized Block by Forming Covariance Matrices
This example shows how to use the Square Jacobi SVD HDL Optimized block to compute the singular value decomposition (SVD) of non-square matrices by forming covariance matrices.
Analytically Determine Fixed-Point Data Types for Linear System Solvers and Matrix Factorizations
- Algorithms to Determine Fixed-Point Types for Real Least-Squares Matrix Solve AX=B
Derivation of algorithms for determining fixed-point types for real least-squares matrix solve. - Determine Fixed-Point Types for Real Least-Squares Matrix Solve AX=B
Usefixed.realQRMatrixSolveFixedpointTypesto determine fixed-point types for computation of the real least-squares matrix equation. - Determine Fixed-Point Types for Real Least-Squares Matrix Solve with Tikhonov Regularization
This example shows how to use thefixed.realQRMatrixSolveFixedpointTypesfunction to analytically determine fixed-point types for the solution of the real least-squares matrix equation - Algorithms to Determine Fixed-Point Types for Complex Least-Squares Matrix Solve AX=B
Derivation of algorithms for determining fixed-point types for complex QR matrix solve. - Determine Fixed-Point Types for Complex Least-Squares Matrix Solve AX=B
Usefixed.complexQRFixedpointTypesto determine fixed-point types for computation of the complex least-squares matrix equation. - Determine Fixed-Point Types for Complex Least-Squares Matrix Solve with Tikhonov Regularization
This example shows how to use thefixed.complexQRMatrixSolveFixedpointTypesfunction to analytically determine fixed-point types for the solution of the complex least-squares matrix equation - Algorithms to Determine Fixed-Point Types for Real Q-less QR Matrix Solve A'AX=B
Derivation of algorithms for determining fixed-point types for real Q-less QR matrix solve. - Determine Fixed-Point Types for Real Q-less QR Matrix Solve A'AX=B
Usefixed.realQlessQRFixedpointTypesto determine fixed-point types for computation of the real least-squares matrix equation. - Determine Fixed-Point Types for Real Q-less QR Matrix Solve with Tikhonov Regularization
This example shows how to use thefixed.realQlessQRMatrixSolveFixedpointTypesfunction to analytically determine fixed-point types for the solution of the real least-squares matrix equation - Algorithms to Determine Fixed-Point Types for Complex Q-less QR Matrix Solve A'AX=B
Derivation of algorithms for determining fixed-point types for complex Q-less QR matrix solve. - Determine Fixed-Point Types for Complex Q-less QR Matrix Solve A'AX=B
Usefixed.complexQlessQRFixedpointTypesto determine fixed-point types for computation of the complex least-squares matrix equation. - Determine Fixed-Point Types for Complex Q-less QR Matrix Solve with Tikhonov Regularization
This example shows how to use thefixed.complexQlessQRMatrixSolveFixedpointTypesfunction to analytically determine fixed-point types for the solution of the complex least-squares matrix equation - Determine Fixed-Point Types for QR Decomposition
Usefixed.qrFixedpointTypesto determine fixed-point types for computation of QR decomposition. - Determine Fixed-Point Types for Q-less QR Decomposition
Usefixed.qlessqrFixedpointTypesto determine fixed-point types for computation of Q-less QR decomposition. - Estimate Standard Deviation of Quantization Noise of Real-Valued Signal
Usefixed.realQuantizationNoiseStandardDeviationto estimate standard deviation of quantization noise. - Estimate Standard Deviation of Quantization Noise of Complex-Valued Signal
Usefixed.complexQuantizationNoiseStandardDeviationto estimate standard deviation of quantization noise. - Compute Forgetting Factor Required for Streaming Input Data
Usefixed.forgettingFactorandfixed.forgettingFactorInverseto compute forgetting factor.
Featured Examples
Fixed-Point HDL-Optimized Minimum-Variance Distortionless-Response (MVDR) Beamformer
Implement a hardware-efficient MVDR beamformer.
Implement Hardware-Efficient Jacobi SVD for Two-by-Two Matrices
Implement singular value decomposition for real and complex two-by-two matrices.
Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array
Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array.
Use Hardware-Efficient Algorithm to Solve Systems of Complex-Valued Linear Equations
Solve a system of complex-valued linear equations using hardware-efficient code.
New
Implement HDL-Optimized Real QRD-RLS Adaptive Filtering
Implement real QR decomposition-based recursive least squares (QRD-RLS) adaptive filtering for system identification. The example includes a MATLAB® fixed-point implementation and a Simulink® model implementation optimized for HDL code generation.
