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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™.

Blocchi

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Euler to NED Transformation HDL OptimizedComputes Euler to North-East-Down transformation using pipelined or burst architecture and generates optimized HDL code (Da R2022b)

Divide

Real Divide HDL OptimizedDivide one real input by another and generate optimized HDL code (Da R2021a)
Complex Divide HDL OptimizedDivide one input by another and generate optimized HDL code (Da R2021a)
Divide by Constant HDL OptimizedDivide input by a constant and round to integer and generate optimized HDL code (Da R2021a)
Divide by Constant and RoundDivide input by a constant and round to integer (Da R2021a)

Modulo

Modulo by Constant HDL OptimizedPerform mod operation with a constant denominator and generate optimized HDL code (Da R2021a)
Modulo by ConstantPerform modulo operation with a constant denominator (Da R2021a)

Reciprocal

Normalized Reciprocal HDL OptimizedComputes normalized reciprocal and generates optimized HDL code (Da R2020a)
Real Reciprocal HDL OptimizedCompute reciprocal and generate optimized HDL code (Da R2021a)

Trigonometric

Hyperbolic Tangent HDL OptimizedComputes CORDIC-based hyperbolic tangent and generates optimized HDL code (Da R2020a)

Solve AX = B

Real Burst Matrix Solve Using QR DecompositionCompute the value of x in the equation Ax = B for real-valued matrices using QR decomposition (Da R2019b)
Complex Burst Matrix Solve Using QR DecompositionCompute the value of x in the equation Ax = B for complex-valued matrices using QR decomposition (Da R2019b)
Real Partial-Systolic Matrix Solve Using QR DecompositionCompute value of x in the equation Ax = B for real-valued matrices using QR decomposition (Da R2020b)
Complex Partial-Systolic Matrix Solve Using QR DecompositionCompute value of x in the equation Ax = B for complex-valued matrices using QR decomposition (Da R2020b)

Solve A'AX = B

Real Burst Matrix Solve Using Q-less QR DecompositionCompute the value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition (Da R2020a)
Complex Burst Matrix Solve Using Q-less QR DecompositionCompute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition (Da R2020a)
Real Burst Asynchronous Matrix Solve Using Q-less QR DecompositionCompute the value of X in the equation A'AX = B for real-valued matrices using asynchronous Q-less QR decomposition (Da R2022b)
Complex Burst Asynchronous Matrix Solve Using Q-less QR DecompositionCompute the value of X in the equation A'AX = B for complex-valued matrices using asynchronous Q-less QR decomposition (Da R2022b)
Real Partial-Systolic Matrix Solve Using Q-less QR DecompositionCompute value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition (Da R2020b)
Complex Partial-Systolic Matrix Solve Using Q-less QR DecompositionCompute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition (Da R2020b)

Solve A'AX = B with Infinitely Tall A Matrix

Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting FactorCompute 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 (Da R2022b)
Complex Burst Matrix Solve Using Q-less QR Decomposition with Forgetting FactorCompute 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 (Da R2022b)
Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting FactorCompute value of X in the equation A'AX = B for real-valued matrices with infinite number of rows using Q-less QR decomposition (Da R2020b)
Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting FactorCompute the value of X in the equation A'AX = B for complex-valued matrices with infinite number of rows using Q-less QR decomposition (Da R2020b)

QR Decomposition

Real Burst QR DecompositionQR decomposition for real-valued matrices (Da R2019b)
Complex Burst QR DecompositionQR decomposition for complex-valued matrices (Da R2019b)
Real Partial-Systolic QR DecompositionQR decomposition for real-valued matrices (Da R2020b)
Complex Partial-Systolic QR DecompositionQR decomposition for complex-valued matrices (Da R2020b)

Q-less QR Decomposition

Real Burst Q-less QR DecompositionQ-less QR decomposition for real-valued matrices (Da R2020a)
Complex Burst Q-less QR DecompositionQ-less QR decomposition for complex-valued matrices (Da R2020a)
Real Burst Q-less QR Decomposition Whole R OutputQ-less QR decomposition for real-valued matrices (Da R2022b)
Complex Burst Q-less QR Decomposition Whole R OutputQ-less QR decomposition for complex-valued matrices (Da R2022b)
Real Partial-Systolic Q-less QR DecompositionQ-less QR decomposition for real-valued matrices (Da R2020b)
Complex Partial-Systolic Q-less QR DecompositionQ-less QR decomposition for complex-valued matrices (Da R2020b)

Q-less QR Decomposition with Forgetting Factor

Real Burst Q-less QR Decomposition with Forgetting Factor Whole R OutputQ-less QR decomposition for real-valued matrices with infinite number of rows (Da R2022b)
Complex Burst Q-less QR Decomposition with Forgetting Factor Whole R OutputQ-less QR decomposition for complex-valued matrices with infinite number of rows (Da R2022b)
Real Partial-Systolic Q-less QR Decomposition with Forgetting FactorQ-less QR decomposition for real-valued matrices with infinite number of rows (Da R2020b)
Complex Partial-Systolic Q-less QR Decomposition with Forgetting FactorQ-less QR decomposition for complex-valued matrices with infinite number of rows (Da R2020b)

Singular Value Decomposition

Square Jacobi SVD HDL OptimizedFixed-point singular value decomposition (Da R2023a)
Non-Square Jacobi SVD HDL OptimizedFixed-point singular value decomposition (Da R2023b)

Funzioni

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fixed.qrFixedpointTypesDetermine fixed-point types for transforming A and R and B to C=Q'B in-place, where QR=A is QR decomposition of A (Da R2021b)
fixed.qlessqrFixedpointTypesDetermine fixed-point types for transforming A to R in-place, where R is upper-triangular factor of QR decomposition of A, without computing Q (Da R2021b)
fixed.realQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of real-valued AX=B using QR decomposition (Da R2021b)
fixed.complexQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of complex-valued AX=B using QR decomposition (Da R2021b)
fixed.realQlessQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of real-valued A'AX=B using QR decomposition (Da R2021b)
fixed.complexQlessQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of complex-valued A'AX=B using QR decomposition (Da R2021b)
fixed.realSingularValueLowerBoundEstimate lower bound for smallest singular value of real-valued matrix (Da R2021b)
fixed.complexSingularValueLowerBoundEstimate lower bound for smallest singular value of complex-valued matrix (Da R2021b)
fixed.singularValueUpperBoundUpper bound of largest singular value of matrix (Da R2022b)
fixed.realConditionNumberUpperBoundEstimate of upper bound for 2-norm condition number of real-valued matrix (Da R2022b)
fixed.complexConditionNumberUpperBoundEstimate of upper bound for 2-norm condition number of complex-valued matrix (Da R2022b)
fixed.forgettingFactorCompute forgetting factor required for streaming input data (Da R2021b)
fixed.forgettingFactorInverseCompute the inverse of the forgetting factor required for streaming input data (Da R2021b)
fixed.realQuantizationNoiseStandardDeviationEstimate standard deviation of quantization noise of real-valued signal (Da R2021b)
fixed.complexQuantizationNoiseStandardDeviationEstimate standard deviation of quantization noise of complex-valued signal (Da R2021b)

Argomenti

Math Operations

General

Linear System Solvers: Solve AX = B

Linear System Solvers: Solve A'AX = B

Linear System Solvers: Solve A'AX = B with Infinitely Tall A Matrix

Matrix Factorizations: QR Decomposition

Matrix Factorizations: Q-less QR Decomposition

Matrix Factorizations: Q-less QR Decomposition with Forgetting Factor

Matrix Factorizations: Singular Value Decomposition

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