MATLAB의 고정소수점 행렬 연산

효율적인 코드를 위한 최적화된 고정소수점 수학 연산, 행렬 솔버 및 행렬 분해 함수

다음 함수를 사용하여 고정소수점 수학 연산과 행렬 연산을 수행하고 효율적인 코드를 생성할 수 있습니다. 이러한 함수는 선형 연립방정식의 해를 구하고, 임베디드 장치에 효율적인 방식으로 행렬 분해를 수행합니다.

함수

수학 연산

`ceilDiv`	나눗셈 결과를 양수 무한대 방향으로 올림 (R2021a 이후)
`fixed.cordicDivide`	Fixed-point divide using CORDIC (R2020b 이후)
`fixed.cordicReciprocal`	Fixed-point reciprocal using CORDIC (R2021b 이후)
`fixDiv`	나눗셈 결과를 0 방향으로 반올림 (R2021a 이후)
`floorDiv`	나눗셈 결과를 음수 무한대 방향으로 내림 (R2021a 이후)
`nearestDiv`	나눗셈 결과를 가장 가까운 정수 방향으로 반올림 (R2021a 이후)
`modByConstant`	Modulus after division by a constant denominator (R2021a 이후)

선형 시스템 솔버 및 행렬 분해

`fixed.backwardSubstitute`	후진 대입을 통해 상부 삼각 연립방정식 풀기 (R2020b 이후)
`fixed.forwardSubstitute`	전진 대입을 통해 하부 삼각 연립방정식 풀기 (R2020b 이후)
`fixed.jacobiSVD`	Fixed-point Jacobi singular value decomposition (R2023a 이후)
`fixed.qlessQR`	Q-less QR decomposition (R2020b 이후)
`fixed.qlessQRUpdate`	Update QR factorization (R2020b 이후)
`fixed.qrAB`	Compute C = Q'B and upper-triangular factor R (R2020b 이후)
`fixed.qrMatrixSolve`	Solve system of linear equations Ax = B for x using QR decomposition (R2020b 이후)
`fixed.qlessQRMatrixSolve`	Solve system of linear equations (A'A)X = B for X using Q-less QR decomposition (R2020b 이후)
`fixed.svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (R2022b 이후)
`svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (R2022b 이후)

선형 시스템 솔버와 행렬 분해를 위해 해석적으로 고정소수점 데이터형 확인

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

도움말 항목

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.
Tikhonov 정규화를 사용하여 복소수 최소제곱 행렬 해의 고정소수점 데이터형 결정하기
이 예제에서는 fixed.complexQRMatrixSolveFixedpointTypes 함수를 사용하여 복소수 최소제곱 행렬 방정식 해의 고정소수점 데이터형을 해석적으로 결정하는 방법을 보여줍니다.
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.