Opérations matricielles en virgule fixe dans MATLAB

Optimisation des opérations mathématiques en virgule fixe, des solveurs de matrices et des fonctions de décomposition de matrices pour un code efficace

Utilisez ces fonctions pour effectuer des opérations mathématiques et matricielles en virgule fixe, et pour générer un code efficace. Ces fonctions permettent de résoudre des systèmes d'équations linéaires et d'effectuer des décompositions de matrices de manière efficace pour les dispositifs embarqués.

Fonctions

développer tout

Opérations mathématiques

`ceilDiv`	Round the result of division toward positive infinity (depuis R2021a)
`fixed.cordicDivide`	Fixed-point divide using CORDIC (depuis R2020b)
`fixed.cordicReciprocal`	Fixed-point reciprocal using CORDIC (depuis R2021b)
`fixDiv`	Round the result of division toward zero (depuis R2021a)
`floorDiv`	Round the result of division toward negative infinity (depuis R2021a)
`nearestDiv`	Round the result of division toward the nearest integer (depuis R2021a)
`modByConstant`	Modulus after division by a constant denominator (depuis R2021a)

Solveurs de systèmes linéaires et factorisations de matrices

`fixed.backwardSubstitute`	Solve upper-triangular system of equations through backward substitution (depuis R2020b)
`fixed.forwardSubstitute`	Solve lower-triangular system of equations through forward substitution (depuis R2020b)
`fixed.jacobiSVD`	Fixed-point Jacobi singular value decomposition (depuis R2023a)
`fixed.qlessQR`	Q-less QR decomposition (depuis R2020b)
`fixed.qlessQRUpdate`	Update QR factorization (depuis R2020b)
`fixed.qrAB`	Compute C = Q'B and upper-triangular factor R (depuis R2020b)
`fixed.qrMatrixSolve`	Solve system of linear equations Ax = B for x using QR decomposition (depuis R2020b)
`fixed.qlessQRMatrixSolve`	Solve system of linear equations (A'A)X = B for X using Q-less QR decomposition (depuis R2020b)
`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.