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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 ceilDiv Round the result of division toward positive infinity fixed.cordicDivide Fixed-point divide using CORDIC fixed.cordicReciprocal Fixed-point reciprocal using CORDIC fixDiv Round the result of division toward zero floorDiv Round the result of division toward negative infinity nearestDiv Round the result of division toward the nearest integer modByConstant Modulus after division by a constant denominator
 fixed.backwardSubstitute Solve upper-triangular system of equations through backward substitution fixed.forwardSubstitute Solve lower-triangular system of equations through forward substitution fixed.qlessQR Q-less QR decomposition fixed.qlessQRUpdate Update QR factorization fixed.qrAB Compute C = Q'*B and upper-triangular factor R fixed.qrMatrixSolve Solve system of linear equations Ax = B for x using QR decomposition fixed.qlessQRMatrixSolve Solve system of linear equations (A'A)x = B for x using Q-less QR decomposition
 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 and matrix solution using diagonal loading using QR decomposition fixed.complexQRMatrixSolveFixedpointTypes Determine fixed-point types for matrix solution of complex-valued AX=B and matrix solution using diagonal loading 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.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

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.

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