# 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 (Since R2021a) `fixed.cordicDivide` Fixed-point divide using CORDIC (Since R2020b) `fixed.cordicReciprocal` Fixed-point reciprocal using CORDIC (Since R2021b) `fixDiv` Round the result of division toward zero (Since R2021a) `floorDiv` Round the result of division toward negative infinity (Since R2021a) `nearestDiv` Round the result of division toward the nearest integer (Since R2021a) `modByConstant` Modulus after division by a constant denominator (Since R2021a)
 `fixed.backwardSubstitute` Solve upper-triangular system of equations through backward substitution (Since R2020b) `fixed.forwardSubstitute` Solve lower-triangular system of equations through forward substitution (Since R2020b) `fixed.jacobiSVD` Fixed-point Jacobi singular value decomposition (Since R2023a) `fixed.qlessQR` Q-less QR decomposition (Since R2020b) `fixed.qlessQRUpdate` Update QR factorization (Since R2020b) `fixed.qrAB` Compute C = Q'B and upper-triangular factor R (Since R2020b) `fixed.qrMatrixSolve` Solve system of linear equations Ax = B for x using QR decomposition (Since R2020b) `fixed.qlessQRMatrixSolve` Solve system of linear equations (A'A)X = B for X using Q-less QR decomposition (Since R2020b) `fixed.svd` Fixed-point Golub-Kahan-Reinsch singular value decomposition (Since R2022b) `svd` Fixed-point Golub-Kahan-Reinsch singular value decomposition (Since R2022b)
 `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)