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Simulink 中的定点矩阵运算

为实现高效的 HDL 代码而进行了优化的定点数学和矩阵运算模块

使用 Fixed-Point Designer™ 模块库执行定点数学运算。

使用模块的 Fixed-Point Designer HDL Optimized 库来执行定点数学和矩阵运算,并生成高效的 HDL 代码。这些模块为线性方程组和核心矩阵运算(例如 QR 分解)进行设计模式建模,以便在 FPGA 上进行硬件高效的实现。使用 HDL Coder™ 为包含这些模块的设计生成 HDL 代码。

模块

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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 (自 R2022b 起)

除法

Real Divide HDL OptimizedDivide one real input by another and generate optimized HDL code (自 R2021a 起)
Complex Divide HDL OptimizedDivide one input by another and generate optimized HDL code (自 R2021a 起)
Divide by Constant HDL OptimizedDivide input by a constant and round to integer and generate optimized HDL code (自 R2021a 起)
Divide by Constant and Round将输入除以常量并舍入到整数 (自 R2021a 起)

Modulo by Constant HDL OptimizedPerform mod operation with a constant denominator and generate optimized HDL code (自 R2021a 起)
Modulo by Constant用常量分母执行取模运算 (自 R2021a 起)

倒数

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

三角函数

Hyperbolic Tangent HDL Optimized计算基于 CORDIC 的双曲正切并生成优化的 HDL 代码 (自 R2020a 起)

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

求解 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 (自 R2020a 起)
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 (自 R2020a 起)
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 (自 R2022b 起)
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 (自 R2022b 起)
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 (自 R2020b 起)
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 (自 R2020b 起)

求解使用无限 tall A 矩阵的 A'AX = B

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 (自 R2022b 起)
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 (自 R2022b 起)
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 (自 R2020b 起)
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 (自 R2020b 起)

QR 分解

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

Q-less QR 分解

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

使用遗忘因子的 Q-less QR 分解

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

奇异值分解

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

函数

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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 (自 R2021b 起)
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 (自 R2021b 起)
fixed.realQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of real-valued AX=B using QR decomposition (自 R2021b 起)
fixed.complexQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of complex-valued AX=B using QR decomposition (自 R2021b 起)
fixed.realQlessQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of real-valued A'AX=B using QR decomposition (自 R2021b 起)
fixed.complexQlessQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of complex-valued A'AX=B using QR decomposition (自 R2021b 起)
fixed.realSingularValueLowerBoundEstimate lower bound for smallest singular value of real-valued matrix (自 R2021b 起)
fixed.complexSingularValueLowerBoundEstimate lower bound for smallest singular value of complex-valued matrix (自 R2021b 起)
fixed.singularValueUpperBoundUpper bound of largest singular value of matrix (自 R2022b 起)
fixed.realConditionNumberUpperBoundEstimate of upper bound for 2-norm condition number of real-valued matrix (自 R2022b 起)
fixed.complexConditionNumberUpperBoundEstimate of upper bound for 2-norm condition number of complex-valued matrix (自 R2022b 起)
fixed.forgettingFactorCompute forgetting factor required for streaming input data (自 R2021b 起)
fixed.forgettingFactorInverseCompute the inverse of the forgetting factor required for streaming input data (自 R2021b 起)
fixed.realQuantizationNoiseStandardDeviationEstimate standard deviation of quantization noise of real-valued signal (自 R2021b 起)
fixed.complexQuantizationNoiseStandardDeviationEstimate standard deviation of quantization noise of complex-valued signal (自 R2021b 起)

主题

数学运算

通用

线性方程组求解器:求解 AX = B

线性方程组求解器:求解 A'AX = B

线性方程组求解器:求解使用无限 tall A 矩阵的 A'AX = B

矩阵分解:QR 分解

矩阵分解:Q-less QR 分解

矩阵分解:使用遗忘因子的 Q-less QR 分解

矩阵分解:奇异值分解

以解析方式确定线性方程组求解器和矩阵分解的定点数据类型