# Subfactor Solve Functions Solve systems with the equation *Subfactor * X = B*. ## Topics ### Matrix-solving functions [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseMatrix_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-2oyl1) Solves the equation *Subfactor * X = B* in place for the matrix of double-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseMatrix_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-2tyws) Solves the equation *Subfactor * X = B* in place for the matrix of single-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseMatrix_Double, DenseMatrix_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-1lads) Solves the equation *Subfactor * X = B* for the matrix of double-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseMatrix_Float, DenseMatrix_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-76z89) Solves the equation *Subfactor * X = B* for the matrix of single-precision values *X*. ### Matrix-solving functions with user-defined workspace [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseMatrix_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-8k0w9) Solves the equation *Subfactor * X = B* in place for the matrix of double-precision values *X*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseMatrix_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-9kp2g) Solves the equation *Subfactor * X = B* in place for the matrix of single-precision values *X*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseMatrix_Double, DenseMatrix_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-90z8f) Solves the equation *Subfactor * X = B* for the matrix of double-precision values *X*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseMatrix_Float, DenseMatrix_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-1hhdi) Solves the equation *Subfactor * X = B* for the matrix of single-precision values *X*, without any internal memory allocations. ### Vector-solving functions [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseVector_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-87v8w) Solves the equation *Subfactor * X = B* in place for the vector of double-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseVector_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-6pxrq) Solves the equation *Subfactor * X = B* in place for the vector of single-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseVector_Double, DenseVector_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-g0wb) Solves the equation *Subfactor * X = B* in place for the vector of double-precision values *X*. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseVector_Float, DenseVector_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-5mq7s) Solves the equation *Subfactor * X = B* in place for the vector of single-precision values *X*. ### Vector-solving functions with user-defined workspace [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseVector_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-7auge) Solves the equation *Subfactor * X = B* for the vector of double-precision values *X*, in place and without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseVector_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-1xw9b) Solves the equation *Subfactor * X = B* for the vector of single-precision values *X*, in place and without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Double, DenseVector_Double, DenseVector_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-eaq9) Solves the equation *Subfactor * X = B* for the vector of double-precision values *X*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueSubfactor_Float, DenseVector_Float, DenseVector_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-2p6e3) Solves the equation *Subfactor * X = B* for the vector of single-precision values *X*, without any internal memory allocations. ### Complex subfactor-solving functions [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseMatrix_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-3x0vj) Solve the equation `Subfactor * X = B` for the matrix `X` of complex double values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseVector_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-4fydu) Solve the equation `Subfactor * x = b` for the vector `x` of complex float values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseVector_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-78cl0) Solve the equation `Subfactor * x = b` for the vector `x` of complex double values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseMatrix_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-879na) Solve the equation `Subfactor * X = B` for the matrix `X` of complex float values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseMatrix_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-2qlwo) Solve the equation `Subfactor * X` = B for the matrix `X` of complex float values in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseVector_Complex_Float, DenseVector_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-5stp5) Solve the equation `Subfactor * x = b` for the vector `x` of complex float values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseMatrix_Complex_Float, DenseMatrix_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-6afcf) Solve the equation `Subfactor * X = B` for the matrix `X` of complex float values. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseVector_Complex_Double, DenseVector_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-9ui81) Solve the equation `Subfactor * x = b` for the vector `x` of complex double values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseMatrix_Complex_Double, DenseMatrix_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-9xxqn) Solve the equation `Subfactor * X = B` for the matrix `X` of complex double values. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)