# 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™.

## Blocs

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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

#### Divide

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

#### Modulo

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

#### Reciprocal

 Normalized Reciprocal HDL Optimized Computes normalized reciprocal and generates optimized HDL code Real Reciprocal HDL Optimized Compute reciprocal and generate optimized HDL code

#### Trigonometric

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

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

#### QR Decomposition

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

#### Q-less QR Decomposition

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

#### Singular Value Decomposition

 Square Jacobi SVD HDL Optimized Fixed-point singular value decomposition

## Fonctions

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