Fixed-Point Matrix Operations in Simulink

Optimized fixed-point math and matrix operations blocks for efficient HDL code

Use the Fixed-Point Designer™ library of blocks to perform fixed-point math operations.

Use the Fixed-Point Designer HDL Optimized library of blocks to perform fixed-point math and matrix operations and generate efficient HDL code. These blocks model design patterns for systems of linear equations and core matrix operations, such as QR decomposition, for hardware-efficient implementation on FPGAs. Generate HDL code for designs that incorporate these blocks using HDL Coder™.

Blocks

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Coordinate Transformations

Euler to NED Transformation HDL Optimized

Computes Euler to North-East-Down transformation using pipelined or burst architecture and generates optimized HDL code (Since R2022b)

Math Operations

Divide

Real Divide HDL Optimized	Divide one real input by another and generate optimized HDL code (Since R2021a)
Complex Divide HDL Optimized	Divide one input by another and generate optimized HDL code (Since R2021a)
Divide by Constant HDL Optimized	Divide input by a constant and round to integer and generate optimized HDL code (Since R2021a)
Divide by Constant and Round	Divide input by a constant and round to integer (Since R2021a)
CORDIC Sigmoid HDL Optimized	CORDIC-based sigmoid activation (Since R2024a)
CORDIC Square Root HDL Optimized	CORDIC-based approximation of square root (Since R2024a)

Modulo

Modulo by Constant HDL Optimized	Perform mod operation with a constant denominator and generate optimized HDL code (Since R2021a)
Modulo by Constant	Perform modulo operation with a constant denominator (Since R2021a)

Reciprocal

Normalized Reciprocal HDL Optimized	Computes normalized reciprocal and generates optimized HDL code (Since R2020a)
Real Reciprocal HDL Optimized	Compute reciprocal and generate optimized HDL code (Since R2021a)

Trigonometric

Hyperbolic Tangent HDL Optimized

Computes CORDIC-based hyperbolic tangent and generates optimized HDL code (Since R2020a)

Linear System Solvers

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 (Since R2020b)
Complex Partial-Systolic Matrix Solve Using QR Decomposition	Compute value of x in the equation Ax = B for complex-valued matrices using QR decomposition (Since R2020b)
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 (Since R2020a)
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 (Since R2020a)
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 (Since R2020b)
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 (Since R2020b)

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 (Since R2020b)
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 (Since R2020b)

Matrix Factorizations

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 (Since R2020b)
Complex Partial-Systolic QR Decomposition	QR decomposition for complex-valued matrices (Since R2020b)
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 (Since R2020a)
Complex Burst Q-less QR Decomposition	Q-less QR decomposition for complex-valued matrices (Since R2020a)
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 (Since R2020b)
Complex Partial-Systolic Q-less QR Decomposition	Q-less QR decomposition for complex-valued matrices (Since R2020b)

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 (Since R2020b)
Complex Partial-Systolic Q-less QR Decomposition with Forgetting Factor	Q-less QR decomposition for complex-valued matrices with infinite number of rows (Since R2020b)

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

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Analytically Determine Fixed-Point Data Types for Linear System Solvers and Matrix Factorizations

`fixed.qrFixedpointTypes`	Determine fixed-point types for transforming A and R and B to C=Q'B in-place, where QR=A is QR decomposition of A (Since R2021b)
`fixed.qlessqrFixedpointTypes`	Determine fixed-point types for transforming A to R in-place, where R is upper-triangular factor of QR decomposition of A, without computing Q (Since R2021b)
`fixed.realQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of real-valued AX=B using QR decomposition (Since R2021b)
`fixed.complexQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of complex-valued AX=B using QR decomposition (Since R2021b)
`fixed.realQlessQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of real-valued A'AX=B using QR decomposition (Since R2021b)
`fixed.complexQlessQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of complex-valued A'AX=B using QR decomposition (Since R2021b)
`fixed.realSingularValueLowerBound`	Estimate lower bound for smallest singular value of real-valued matrix (Since R2021b)
`fixed.complexSingularValueLowerBound`	Estimate lower bound for smallest singular value of complex-valued matrix (Since R2021b)
`fixed.singularValueUpperBound`	Upper bound of largest singular value of matrix (Since R2022b)
`fixed.realConditionNumberUpperBound`	Estimate of upper bound for 2-norm condition number of real-valued matrix (Since R2022b)
`fixed.complexConditionNumberUpperBound`	Estimate of upper bound for 2-norm condition number of complex-valued matrix (Since R2022b)
`fixed.forgettingFactor`	Compute forgetting factor required for streaming input data (Since R2021b)
`fixed.forgettingFactorInverse`	Compute the inverse of the forgetting factor required for streaming input data (Since R2021b)
`fixed.realQuantizationNoiseStandardDeviation`	Estimate standard deviation of quantization noise of real-valued signal (Since R2021b)
`fixed.complexQuantizationNoiseStandardDeviation`	Estimate standard deviation of quantization noise of complex-valued signal (Since R2021b)

Compute Latency of Blocks

`embblk.latency.systolicQRBlockTiming`	Compute throughput and latency of Systolic QR Decomposition block (Since R2024a)
`embblk.latency.systolicQRMatrixSolverBlockTiming`	Compute throughput and latency of Systolic Matrix Solve Using QR Decomposition block (Since R2024a)
`embblk.latency.cordicSqrtHDLOptimizedLatency`	Compute throughput and latency of Systolic QR Decomposition block (Since R2024a)

Topics

Math Operations

Implement Hardware-Efficient Hyperbolic Tangent
Implement a hardware-efficient hyperbolic tangent.
How to Use HDL Optimized Normalized Reciprocal
This example shows how and when to use the normalizedReciprocal function and the Normalized Reciprocal HDL Optimized block to compute the normalized reciprocal of an input.
Implement Hardware-Efficient Real Divide HDL Optimized
How to use the Real Divide HDL Optimized block.
Customize Output Value of Real Divide HDL Optimized Block When Denominator Is Zero
Use the divideByZero port to customize the value of the block output when division by zero occurs.
Implement Hardware-Efficient Complex Divide HDL Optimized
How to use the Complex Divide HDL Optimized block.
Implement HDL Optimized Modulo by Constant
How to use the Modulo by Constant HDL Optimized block.

General

Choose a Block for HDL-Optimized Fixed-Point Matrix Operations
How to choose a block from the Fixed-Point Designer HDL Support library.

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
Use fixed.realQRMatrixSolveFixedpointTypes to 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 the fixed.realQRMatrixSolveFixedpointTypes function 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
Use fixed.complexQRFixedpointTypes to 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 the fixed.complexQRMatrixSolveFixedpointTypes function 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
Use fixed.realQlessQRFixedpointTypes to 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 the fixed.realQlessQRMatrixSolveFixedpointTypes function 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
Use fixed.complexQlessQRFixedpointTypes to 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 the fixed.complexQlessQRMatrixSolveFixedpointTypes function to analytically determine fixed-point types for the solution of the complex least-squares matrix equation
Determine Fixed-Point Types for QR Decomposition
Use fixed.qrFixedpointTypes to determine fixed-point types for computation of QR decomposition.
Determine Fixed-Point Types for Q-less QR Decomposition
Use fixed.qlessqrFixedpointTypes to determine fixed-point types for computation of Q-less QR decomposition.
Estimate Standard Deviation of Quantization Noise of Real-Valued Signal
Use fixed.realQuantizationNoiseStandardDeviation to estimate standard deviation of quantization noise.
Estimate Standard Deviation of Quantization Noise of Complex-Valued Signal
Use fixed.complexQuantizationNoiseStandardDeviation to estimate standard deviation of quantization noise.
Compute Forgetting Factor Required for Streaming Input Data
Use fixed.forgettingFactor and fixed.forgettingFactorInverse to compute forgetting factor.

Featured Examples

Fixed-Point HDL-Optimized Minimum-Variance Distortionless-Response (MVDR) Beamformer

Implement a hardware-efficient MVDR beamformer.

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Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array

Implement Hardware-Efficient QR Decomposition Using CORDIC in a Systolic Array.

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Implement HDL-Optimized CORDIC-Based Square Root for Positive Real Numbers

Implement HDL-optimized CORDIC-based square root for positive real numbers.

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