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Fixed-Point Matrix Operations in MATLAB

Optimized fixed-point math operations, matrix solvers, and matrix decomposition functions for efficient code

Use these functions to perform fixed-point math and matrix operations and generate efficient code. These functions solve systems of linear equations and perform matrix decompositions in a way that is efficient for embedded devices.

Functions

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ceilDivRound the result of division toward positive infinity
fixed.cordicDivideFixed-point divide using CORDIC
fixed.cordicReciprocalFixed-point reciprocal using CORDIC
fixDivRound the result of division toward zero
floorDivRound the result of division toward negative infinity
nearestDivRound the result of division toward the nearest integer
modByConstantModulus after division by a constant denominator
fixed.backwardSubstituteSolve upper-triangular system of equations through backward substitution
fixed.forwardSubstituteSolve lower-triangular system of equations through forward substitution
fixed.qlessQRQ-less QR decomposition
fixed.qlessQRUpdateUpdate QR factorization
fixed.qrABCompute C = Q'*B and upper-triangular factor R
fixed.qrMatrixSolveSolve system of linear equations Ax = B for x using QR decomposition
fixed.qlessQRMatrixSolveSolve system of linear equations (A'A)x = B for x using Q-less QR decomposition
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 and matrix solution using diagonal loading using QR decomposition
fixed.complexQRMatrixSolveFixedpointTypesDetermine fixed-point types for matrix solution of complex-valued AX=B and matrix solution using diagonal loading 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.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

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.

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.

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.

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.

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.