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Operazioni tra matrici in virgola fissa in MATLAB

Risolutori di matrici in virgola fissa basati su CORDIC e funzioni di scomposizione di matrici ottimizzati per un codice efficiente

Utilizzare queste funzioni per eseguire operazioni tra matrici in virgola fissa e generare codice C/C++ efficiente. Queste funzioni risolvono sistemi di equazioni lineari ed eseguono operazioni di base tra le matrici, come la scomposizione QR e la scomposizione in valori singolari, utilizzando un algoritmo basato su CORDIC, efficiente per i dispositivi embedded. Utilizzare le funzioni Fixed-Point Designer™ incluse per determinare analiticamente i tipi di dati in virgola fissa ottimali per il risolutore di sistemi lineari e i blocchi di fattorizzazione della matrice.

Per le implementazioni di questi algoritmi nel blocco Simulink^®, vedere Operazioni tra matrici in virgola fissa in Simulink. Per implementazioni basate su CORDIC e altre implementazioni efficienti per l'embedded di operazioni matematiche in MATLAB^® e Simulink, vedere Operazioni matematiche in virgola fissa in MATLAB e Simulink.

Funzioni

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Risolutori di sistemi lineari e fattorizzazioni di matrici

`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 (Da 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 (Da R2022b)
`svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (Da R2022b)

Determinazione analitica di tipi di dati in virgola fissa per risolutori di sistemi lineari e fattorizzazioni di matrici

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

Argomenti

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.

Esempi in primo piano

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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