# 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

## Functions

## Topics

### Math Operations

**Implement Hardware-Efficient Hyperbolic Tangent**

Implement a hardware-efficient hyperbolic tangent.**How to Use HDL Optimized Normalized Reciprocal**

This example shows how and when to use the`normalizedReciprocal`

function and the Normalized Reciprocal HDL Optimized block to compute the normalized reciprocal of an input.**Implement Hardware-Efficient Real Divide HDL Optimized**

How to use the Real Divide HDL Optimized block.**Implement Hardware-Efficient Complex Divide HDL Optimized**

How to use the Complex Divide HDL Optimized block.**Implement HDL Optimized Modulo By Constant**

How to use the Modulo by Constant HDL Optimized block.

### Linear System Solvers: Burst Implementation

**Implement Hardware-Efficient Real Burst Matrix Solve Using QR Decomposition**

How to use the Real Burst Matrix Solve Using QR Decomposition block.**Implement Hardware-Efficient Real Burst Matrix Solve Using QR Decomposition with Tikhonov Regularization**

This example shows how to use the Real Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Real Burst Matrix Solve Using Q-less QR Decomposition**

How to use the Real Burst Matrix Solve Using Q-less QR Decomposition block.**Implement Hardware-Efficient Real Burst Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization**

This example shows how to use the Real Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Complex Burst Matrix Solve Using QR Decomposition**

How to use the Complex Burst Matrix Solve Using QR Decomposition block.**Implement Hardware-Efficient Complex Burst Matrix Solve Using QR Decomposition with Tikhonov Regularization**

This example shows how to use the Complex Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Complex Burst Matrix Solve Using Q-less QR Decomposition**

How to use the Complex Burst Matrix Solve Using Q-less QR Decomposition block.**Implement Hardware-Efficient Complex Burst Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization**

This example shows how to use the Complex Burst Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation

### Linear System Solvers: Partial-Systolic Implementation

**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition**

How to use the Real Partial-Systolic Matrix Solve Using QR Decomposition block.**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition with Diagonal Loading**

How to use the Real Partial-Systolic Matrix Solve Using QR Decomposition Block with diagonal loading.**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using QR Decomposition with Tikhonov Regularization**

This example shows how to use the Real Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition**

How to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block.**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor**

How to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block.**Implement Hardware-Efficient Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization**

This example shows how to use the Real Partial-Systolic Matrix Solve Using Q-less QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition**

How to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block.**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition with Diagonal Loading**

How to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition Block with diagonal loading.**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using QR Decomposition with Tikhonov Regularization**

This example shows how to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition**

How to use the Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition block.**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor**

How to use the Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Forgetting Factor block.**Implement Hardware-Efficient Complex Partial-Systolic Matrix Solve Using Q-less QR Decomposition with Tikhonov Regularization**

This example shows how to use the Complex Partial-Systolic Matrix Solve Using QR Decomposition block to solve the regularized least-squares matrix equation

### Matrix Factorizations: Burst Implementation

**Implement Hardware-Efficient Real Burst QR Decomposition**

How to use the Real Burst QR Decomposition block.**Implement Hardware-Efficient Real Burst Q-less QR Decomposition**

How to use the Real Burst Q-less QR Decomposition block.**Implement Hardware-Efficient Complex Burst QR Decomposition**

How to use the Complex Burst QR Decomposition block.**Implement Hardware-Efficient Complex Burst Q-less QR Decomposition**

How to use the Complex Burst Q-less QR Decomposition block.

### Matrix Factorizations: Partial-Systolic Implementation

**Implement Hardware-Efficient Real Partial-Systolic QR Decomposition**

How to use the Real Partial-Systolic QR Decomposition block.**Implement Hardware-Efficient Real Partial-Systolic Q-less QR Decomposition**

How to use the Real Partial-Systolic Q-less QR Decomposition block.**Implement Hardware-Efficient Real Partial-Systolic Q-less QR with Forgetting Factor**

How to use the Real Partial-Systolic Q-less QR Decomposition with Forgetting Factor block.**Implement Hardware-Efficient Complex Partial-Systolic QR Decomposition**

How to use the Complex Partial-Systolic QR Decomposition block.**Implement Hardware-Efficient Complex Partial-Systolic Q-less QR Decomposition**

How to use the Complex Partial-Systolic Q-less QR Decomposition block.**Implement Hardware-Efficient Complex Partial-Systolic Q-less QR with Forgetting Factor**

How to use the Complex Partial-Systolic Q-less QR Decomposition with Forgetting Factor block.

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

**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.**Determine Fixed-Point Types for Complex Least-Squares Matrix Solve with Tikhonov Regularization**

This example shows how to use the`fixed.complexQRMatrixSolveFixedpointTypes`

function to analytically determine fixed-point types for the solution of the complex least-squares matrix equation**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.