# Sparse Symbolic Factorization Functions Calculate the symbolic factorization of a matrix, and solve systems using precalculated symbolic factorizations. ## Topics ### Matrix symbolic factorization functions [`func SparseFactor(SparseFactorization_t, SparseMatrixStructure) -> SparseOpaqueSymbolicFactorization`](/documentation/Accelerate/SparseFactor(_:_:)-3697o) Returns a symbolic factorization of the requested type for a specified sparsity structure. [`func SparseFactor(SparseFactorization_t, SparseMatrixStructure, SparseSymbolicFactorOptions) -> SparseOpaqueSymbolicFactorization`](/documentation/Accelerate/SparseFactor(_:_:_:)-45gsz) Returns a symbolic factorization of the requested type for a single-precision matrix with the specified structure. ### Matrix factorizations using precalculated symbolic factorization [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Double) -> SparseOpaqueFactorization_Double`](/documentation/Accelerate/SparseFactor(_:_:)-58oq8) Returns the factorization of a sparse matrix of double-precision values that corresponds to the supplied symbolic factorization. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Float) -> SparseOpaqueFactorization_Float`](/documentation/Accelerate/SparseFactor(_:_:)-1p6im) Returns the factorization of a sparse matrix of single-precision values that corresponds to the supplied symbolic factorization. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Double, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Double`](/documentation/Accelerate/SparseFactor(_:_:_:)-3ddg) Returns the factorization of a sparse matrix of double-precision values that corresponds to the supplied symbolic factorization using specified options. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Float, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Float`](/documentation/Accelerate/SparseFactor(_:_:_:)-797fl) Returns the factorization of a sparse matrix of single-precision values that corresponds to the supplied symbolic factorization using specified options. ### Matrix factorizations using precalculated symbolic factorization with user-defined workspace [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Double, SparseNumericFactorOptions, UnsafeMutableRawPointer?, UnsafeMutableRawPointer?) -> SparseOpaqueFactorization_Double`](/documentation/Accelerate/SparseFactor(_:_:_:_:_:)-68hki) Returns the factorization of a sparse matrix of double-precision values that corresponds to the supplied symbolic factorization using user-defined workspace and factor storage. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Float, SparseNumericFactorOptions, UnsafeMutableRawPointer?, UnsafeMutableRawPointer?) -> SparseOpaqueFactorization_Float`](/documentation/Accelerate/SparseFactor(_:_:_:_:_:)-8afz) Returns the factorization of a sparse matrix of single-precision values that corresponds to the supplied symbolic factorization using user-defined workspace and factor storage. ### Supporting types [`struct SparseOpaqueSymbolicFactorization`](/documentation/Accelerate/SparseOpaqueSymbolicFactorization) A semi-opaque type that represents symbolic matrix factorization. [`struct SparseFactorization_t`](/documentation/Accelerate/SparseFactorization_t) Constants that define the factorization type. [`struct SparseSymbolicFactorOptions`](/documentation/Accelerate/SparseSymbolicFactorOptions) A structure that contains options that affect the symbolic stage of a sparse factorization. ### Complex factorization functions [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Complex_Float) -> SparseOpaqueFactorization_Complex_Float`](/documentation/Accelerate/SparseFactor(_:_:)-7a3l4) Returns the factorization of a sparse matrix of complex float values corresponding to the supplied symbolic factorization. [`func SparseFactor(SparseFactorization_t, SparseMatrixStructureComplex, SparseSymbolicFactorOptions) -> SparseOpaqueSymbolicFactorization`](/documentation/Accelerate/SparseFactor(_:_:_:)-6s9g) Returns a symbolic factorization of the requested type for a complex matrix with the given structure, with the supplied options. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Complex_Float, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Complex_Float`](/documentation/Accelerate/SparseFactor(_:_:_:)-7kqvi) Returns the factorization of a sparse matrix of complex float values corresponding to the supplied symbolic factorization, using the specified options. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Complex_Double, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Complex_Double`](/documentation/Accelerate/SparseFactor(_:_:_:)-9ypz5) Returns the factorization of a sparse matrix of complex double values corresponding to the supplied symbolic factorization, using the specified options. [`func SparseFactor(SparseFactorization_t, SparseMatrix_Complex_Double, SparseSymbolicFactorOptions, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Complex_Double`](/documentation/Accelerate/SparseFactor(_:_:_:_:)-6hqfp) Returns the specified factorization of a sparse matrix of complex double values, using the specified options. [`func SparseFactor(SparseFactorization_t, SparseMatrix_Complex_Float, SparseSymbolicFactorOptions, SparseNumericFactorOptions) -> SparseOpaqueFactorization_Complex_Float`](/documentation/Accelerate/SparseFactor(_:_:_:_:)-9ykfp) Returns the specified factorization of a sparse matrix of complex float values, using the specified options. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Complex_Float, SparseNumericFactorOptions, UnsafeMutableRawPointer?, UnsafeMutableRawPointer?) -> SparseOpaqueFactorization_Complex_Float`](/documentation/Accelerate/SparseFactor(_:_:_:_:_:)-2dqfv) Returns the factorization of a sparse matrix of complex float values corresponding to the supplied symbolic factorization, using the specified options and without any internal memory allocations. [`func SparseFactor(SparseOpaqueSymbolicFactorization, SparseMatrix_Complex_Double, SparseNumericFactorOptions, UnsafeMutableRawPointer?, UnsafeMutableRawPointer?) -> SparseOpaqueFactorization_Complex_Double`](/documentation/Accelerate/SparseFactor(_:_:_:_:_:)-7j0dm) Returns the factorization of a sparse matrix of complex double values corresponding to the supplied symbolic factorization, using the specified options and without any internal memory allocations. --- Copyright © 2026 Apple Inc. 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