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Fixed-Point Matrix Operations in Simulink

Optimized fixed-point math and matrix operations blocks for efficient HDL code

Use the Fixed-Point Designer™ library of blocks to perform fixed-point math operations.

Use the Fixed-Point Designer HDL Optimized library of blocks to perform fixed-point math and matrix operations and generate efficient HDL code. These blocks model design patterns for systems of linear equations and core matrix operations, such as QR decomposition, for hardware-efficient implementation on FPGAs. Generate HDL code for designs that incorporate these blocks using HDL Coder™.

Blocks

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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

Divide

Real Divide HDL OptimizedDivide one real input by another and generate optimized HDL code
Complex Divide HDL OptimizedDivide one input by another and generate optimized HDL code
Divide by Constant HDL OptimizedDivide input by a constant and round to integer and generate optimized HDL code
Divide by Constant and RoundDivide input by a constant and round to integer

Modulo

Modulo by Constant HDL OptimizedPerform mod operation with a constant denominator and generate optimized HDL code
Modulo by ConstantPerform modulo operation with a constant denominator

Reciprocal

Normalized Reciprocal HDL OptimizedComputes normalized reciprocal and generates optimized HDL code
Real Reciprocal HDL OptimizedCompute reciprocal and generate optimized HDL code

Trigonometric

Hyperbolic Tangent HDL OptimizedComputes CORDIC-based hyperbolic tangent and generates optimized HDL code

Solve 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
Complex Burst Matrix Solve Using QR DecompositionCompute the value of x in the equation Ax = B for complex-valued matrices using QR decomposition
Real Partial-Systolic Matrix Solve Using QR DecompositionCompute value of x in the equation Ax = B for real-valued matrices using QR decomposition
Complex Partial-Systolic Matrix Solve Using QR DecompositionCompute value of x in the equation Ax = B for complex-valued matrices using QR decomposition

Solve 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
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
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
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
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
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

Solve A'AX = B with Infinitely Tall A Matrix

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
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
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
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

QR Decomposition

Real Burst QR DecompositionQR decomposition for real-valued matrices
Complex Burst QR DecompositionQR decomposition for complex-valued matrices
Real Partial-Systolic QR DecompositionQR decomposition for real-valued matrices
Complex Partial-Systolic QR DecompositionQR decomposition for complex-valued matrices

Q-less QR Decomposition

Real Burst Q-less QR DecompositionQ-less QR decomposition for real-valued matrices
Complex Burst Q-less QR DecompositionQ-less QR decomposition for complex-valued matrices
Real Burst Q-less QR Decomposition Whole R OutputQ-less QR decomposition for real-valued matrices
Complex Burst Q-less QR Decomposition Whole R OutputQ-less QR decomposition for complex-valued matrices
Real Partial-Systolic Q-less QR DecompositionQ-less QR decomposition for real-valued matrices
Complex Partial-Systolic Q-less QR DecompositionQ-less QR decomposition for complex-valued matrices

Q-less QR Decomposition with Forgetting Factor

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

Functions

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

Topics

Math Operations

General

Linear System Solvers: Solve AX = B

Linear System Solvers: Solve A'AX = B

Linear System Solvers: Solve A'AX = B with Infinitely Tall A Matrix

Matrix Factorizations: QR Decomposition

Matrix Factorizations: Q-less QR Decomposition

Matrix Factorizations: Q-less QR Decomposition with Forgetting Factor

Analytically Determine Fixed-Point Data Types for Linear System Solvers and Matrix Factorizations