# Sparse Direct Solving Functions (Matrix RHS) Solve a system with a right-hand-side dense matrix using a factored sparse coefficient matrix. ## Topics ### In-place direct solving functions [`func SparseSolve(SparseOpaqueFactorization_Double, DenseMatrix_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-9j9rw) Solves the system *AX = B* using the supplied double-precision factorization of *A*, in place. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseMatrix_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-1jp0k) 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, DenseMatrix_Double, DenseMatrix_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-3iav7) Solves the system *AX = B* using the supplied double-precision factorization of *A*. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseMatrix_Float, DenseMatrix_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-2rxlq) 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, DenseMatrix_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-l2kw) 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, DenseMatrix_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-749fu) 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, DenseMatrix_Double, DenseMatrix_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-7aj3g) Solves the system *AX = B* using the supplied double-precision factorization of *A*, without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Float, DenseMatrix_Float, DenseMatrix_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-8xma8) Solves the system *AX = B* using the supplied single-precision factorization of *A*, without any internal memory allocations. ### Complex matrix solving functions [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseMatrix_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:)-31yj7) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, in place. [`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(SparseOpaqueFactorization_Complex_Float, DenseMatrix_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:)-4j17a) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, 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(SparseOpaqueFactorization_Complex_Double, DenseMatrix_Complex_Double, DenseMatrix_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-2rk1c) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Double` of A`,` in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseMatrix_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-34okt) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, in place, and without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseMatrix_Complex_Float, DenseMatrix_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-48njk) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Float` of A`,` in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseMatrix_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-6pudz) Solve the equation `Subfactor * X` = B for the matrix `X` of complex double values in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Float, DenseMatrix_Complex_Float, DenseMatrix_Complex_Float)`](/documentation/Accelerate/SparseSolve(_:_:_:)-7krer) Solve the equation `Subfactor * X = B` for the matrix `X` of complex float values, in place. [`func SparseSolve(SparseOpaqueSubfactor_Complex_Double, DenseMatrix_Complex_Double, DenseMatrix_Complex_Double)`](/documentation/Accelerate/SparseSolve(_:_:_:)-7qdpl) Solve the equation `Subfactor * X = B` for the matrix `X` of complex double values, in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseMatrix_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:)-8ikjb) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, in place, and without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseMatrix_Complex_Double, DenseMatrix_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-5xn6p) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, and without any internal memory allocations. [`func SparseSolve(SparseOpaqueFactorization_Complex_Double, DenseVector_Complex_Double, DenseVector_Complex_Double, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-6demt) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Double` of `A`, in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseVector_Complex_Float, DenseVector_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-6od6k) Solves the system `Ax=b` for `x`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, in place. [`func SparseSolve(SparseOpaqueFactorization_Complex_Float, DenseMatrix_Complex_Float, DenseMatrix_Complex_Float, UnsafeMutableRawPointer)`](/documentation/Accelerate/SparseSolve(_:_:_:_:)-7mtyx) Solves the system `AX=B` for `X`, using the supplied `SparseOpaqueFactorization_Complex_Float` of `A`, and without any internal memory allocations. --- 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)