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Opérations matricielles en virgule fixe dans MATLAB

Solveurs de matrices et fonctions de décomposition de matrices en virgule fixe optimisés et basés sur CORDIC pour un code efficace

Utilisez ces fonctions pour effectuer des opérations matricielles en virgule fixe et générer un code C/C++ efficace. Ces fonctions résolvent des systèmes d’équations linéaires et effectuent les principales opérations matricielles, comme les décompositions QR et en valeurs singulières, avec un algorithme basé sur CORDIC efficace pour les dispositifs embarqués. Utilisez les fonctions Fixed-Point Designer™ incluses pour déterminer de manière analytique les types de données à virgule fixe optimaux, pour les blocs de solveur de système linéaire et de factorisation de matrice.

Pour les implémentations basées sur des blocs Simulink^® de ces algorithmes, consultez Opérations matricielles en virgule fixe dans Simulink. Pour les implémentations basées sur CORDIC ou autre d’opérations mathématiques et optimisées pour les dispositifs embarqués dans MATLAB^® et Simulink, consultez Opérations mathématiques en virgule fixe dans MATLAB et Simulink.

Fonctions

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Solveurs de systèmes linéaires et factorisations de matrices

`fixed.backwardSubstitute`	Solve upper-triangular system of equations through backward substitution
`fixed.forwardSubstitute`	Solve lower-triangular system of equations through forward substitution
`fixed.jacobiSVD`	Fixed-point Jacobi singular value decomposition (depuis R2023a)
`fixed.qlessQR`	Q-less QR decomposition
`fixed.qlessQRUpdate`	Update QR factorization
`fixed.qrAB`	Compute C = Q'B and upper-triangular factor R
`fixed.qrMatrixSolve`	Solve system of linear equations Ax = B for x using QR decomposition
`fixed.qlessQRMatrixSolve`	Solve system of linear equations (A'A)X = B for X using Q-less QR decomposition
`fixed.svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (depuis R2022b)
`svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (depuis R2022b)

Détermination analytique des types de données à virgule fixe pour les solveurs de systèmes linéaires et les factorisations de matrices

`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 (depuis 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 (depuis R2021b)
`fixed.realQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of real-valued AX=B using QR decomposition (depuis R2021b)
`fixed.complexQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of complex-valued AX=B using QR decomposition (depuis R2021b)
`fixed.realQlessQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of real-valued A'AX=B using QR decomposition (depuis R2021b)
`fixed.complexQlessQRMatrixSolveFixedpointTypes`	Determine fixed-point types for matrix solution of complex-valued A'AX=B using QR decomposition (depuis R2021b)
`fixed.realSingularValueLowerBound`	Estimate lower bound for smallest singular value of real-valued matrix (depuis R2021b)
`fixed.complexSingularValueLowerBound`	Estimate lower bound for smallest singular value of complex-valued matrix (depuis R2021b)
`fixed.singularValueUpperBound`	Upper bound of largest singular value of matrix (depuis R2022b)
`fixed.realConditionNumberUpperBound`	Estimate of upper bound for 2-norm condition number of real-valued matrix (depuis R2022b)
`fixed.complexConditionNumberUpperBound`	Estimate of upper bound for 2-norm condition number of complex-valued matrix (depuis R2022b)
`fixed.forgettingFactor`	Compute forgetting factor required for streaming input data (depuis R2021b)
`fixed.forgettingFactorInverse`	Compute the inverse of the forgetting factor required for streaming input data (depuis R2021b)
`fixed.realQuantizationNoiseStandardDeviation`	Estimate standard deviation of quantization noise of real-valued signal (depuis R2021b)
`fixed.complexQuantizationNoiseStandardDeviation`	Estimate standard deviation of quantization noise of complex-valued signal (depuis R2021b)

Rubriques

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.
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
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 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
Compute Forgetting Factor Required for Streaming Input Data
Use fixed.forgettingFactor and fixed.forgettingFactorInverse to compute forgetting factor.
Estimate Standard Deviation of Quantization Noise of Complex-Valued Signal
Use fixed.complexQuantizationNoiseStandardDeviation to estimate standard deviation of quantization noise.
Estimate Standard Deviation of Quantization Noise of Real-Valued Signal
Use fixed.realQuantizationNoiseStandardDeviation to estimate standard deviation of quantization noise.

Sélection d՚exemples

Perform QR Factorization Using CORDIC

Write MATLAB code that works for both floating-point and fixed-point data types. The algorithm used in this example is the QR factorization implemented via CORDIC.

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