# Sparse Direct Solving Functions (Vector RHS) Solve a system with a right-hand-side dense vector using a factored sparse coefficient matrix. ## Topics ### In-place direct solving functions [`func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-pofy) Solves the system *Ax = x* using the supplied double-precision factorization of *A*. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseVector_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-60ngw) Solves the system *Ax = b* using the supplied single-precision factorization of *A*, in place. ### Out-of-place direct solving functions [`func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double, DenseVector_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-416bj) Solves the system *Ax = b* using the supplied double-precision factorization of *A*. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseVector_Float, DenseVector_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-666oh) Solves the system *Ax = b* using the supplied single-precision factorization of *A*. ### In-place direct solving functions with user-defined workspace [`func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-14nj) Solves the system *Ax = b* using the supplied double-precision factorization of *A*, in place and without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseVector_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-9hs9y) Solves the system *Ax = b* using the supplied single-precision factorization of *A*, in place and without any internal memory allocations. ### Out-of-place direct solving functions with user-defined workspace [`func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double, DenseVector_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-7k9ll) Solves the system *Ax = b* using the supplied double-precision factorization of *A*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseVector_Float, DenseVector_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-6bmr8) Solves the system *Ax = b* using the supplied single-precision factorization of *A*, without any internal memory allocations. ### Complex direct solving functions [`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(SparseOpaqueFactorization_Complex_Double, DenseVector_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-1psgz) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, 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(SparseOpaqueFactorization_Complex_Float, DenseVector_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-5apxy) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseVector_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-3482l) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseVector_Complex_Float, DenseVector_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-3hev5) Solve the equation `Subfactor * x = b` for the vector `x` of complex float values. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseVector_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-3qkkl) Solve the equation `Subfactor * x = b` for the vector `x` of complex float values, in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseVector_Complex_Float, DenseVector_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-76ge0) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`. [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseVector_Complex_Double, DenseVector_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-7day5) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`. [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseVector_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-7ltk8) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseVector_Complex_Double, DenseVector_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-85y2u) Solve the equation `Subfactor * x = b` for the vector `x` of complex double values. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseVector_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-90ojf) Solve the equation `Subfactor * x = b` for the vector `x` of complex double values, in place. --- 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)