# 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 Optimized Computes Euler to North-East-Down transformation using pipelined or burst architecture and generates optimized HDL code (Since R2022b)

#### Divide

 Real Divide HDL Optimized Divide one real input by another and generate optimized HDL code (Since R2021a) Complex Divide HDL Optimized Divide one input by another and generate optimized HDL code (Since R2021a) Divide by Constant HDL Optimized Divide input by a constant and round to integer and generate optimized HDL code (Since R2021a) Divide by Constant and Round Divide input by a constant and round to integer (Since R2021a)

#### Modulo

 Modulo by Constant HDL Optimized Perform mod operation with a constant denominator and generate optimized HDL code (Since R2021a) Modulo by Constant Perform modulo operation with a constant denominator (Since R2021a)

#### Reciprocal

 Normalized Reciprocal HDL Optimized Computes normalized reciprocal and generates optimized HDL code (Since R2020a) Real Reciprocal HDL Optimized Compute reciprocal and generate optimized HDL code (Since R2021a)

#### Trigonometric

 Hyperbolic Tangent HDL Optimized Computes CORDIC-based hyperbolic tangent and generates optimized HDL code (Since R2020a)

#### Solve AX = B

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

#### Solve A'AX = B

 Real Burst Matrix Solve Using Q-less QR Decomposition Compute the value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition (Since R2020a) Complex Burst Matrix Solve Using Q-less QR Decomposition Compute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition (Since R2020a) Real Burst Asynchronous Matrix Solve Using Q-less QR Decomposition Compute the value of X in the equation A'AX = B for real-valued matrices using asynchronous Q-less QR decomposition (Since R2022b) Complex Burst Asynchronous Matrix Solve Using Q-less QR Decomposition Compute the value of X in the equation A'AX = B for complex-valued matrices using asynchronous Q-less QR decomposition (Since R2022b) Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition Compute value of X in the equation A'AX = B for real-valued matrices using Q-less QR decomposition (Since R2020b) Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition Compute the value of X in the equation A'AX = B for complex-valued matrices using Q-less QR decomposition (Since R2020b)

#### Solve A'AX = B with Infinitely Tall A Matrix

 Real Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor Compute 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 (Since R2022b) Complex Burst Matrix Solve Using Q-less QR Decomposition with Forgetting Factor Compute 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 (Since R2022b) Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor Compute value of X in the equation A'AX = B for real-valued matrices with infinite number of rows using Q-less QR decomposition (Since R2020b) Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor Compute the value of X in the equation A'AX = B for complex-valued matrices with infinite number of rows using Q-less QR decomposition (Since R2020b)

#### QR Decomposition

 Real Burst QR Decomposition QR decomposition for real-valued matrices (Since R2019b) Complex Burst QR Decomposition QR decomposition for complex-valued matrices (Since R2019b) Real Partial-Systolic QR Decomposition QR decomposition for real-valued matrices (Since R2020b) Complex Partial-Systolic QR Decomposition QR decomposition for complex-valued matrices (Since R2020b)

#### Q-less QR Decomposition

 Real Burst Q-less QR Decomposition Q-less QR decomposition for real-valued matrices (Since R2020a) Complex Burst Q-less QR Decomposition Q-less QR decomposition for complex-valued matrices (Since R2020a) Real Burst Q-less QR Decomposition Whole R Output Q-less QR decomposition for real-valued matrices (Since R2022b) Complex Burst Q-less QR Decomposition Whole R Output Q-less QR decomposition for complex-valued matrices (Since R2022b) Real Partial-Systolic Q-less QR Decomposition Q-less QR decomposition for real-valued matrices (Since R2020b) Complex Partial-Systolic Q-less QR Decomposition Q-less QR decomposition for complex-valued matrices (Since R2020b)

#### Q-less QR Decomposition with Forgetting Factor

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

#### Singular Value Decomposition

 Square Jacobi SVD HDL Optimized Fixed-point singular value decomposition (Since R2023a) Non-Square Jacobi SVD HDL Optimized Fixed-point singular value decomposition (Since R2023b)

## Functions

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