---
title: "SparseSolve(_:_:_:)"
framework: accelerate
role: symbol
role_heading: Function
path: "accelerate/sparsesolve(_:_:_:)-7ltk8"
---

# SparseSolve(_:_:_:)

Solves the system Ax=b for x, using the supplied SparseOpaqueFactorization_Complex_Double of A, in place.

## Declaration

```swift
func SparseSolve(_ Factored: SparseOpaqueFactorization_Complex_Double, _ xb: DenseVector_Complex_Double, _ workspace: UnsafeMutableRawPointer)
```

## Parameters

- `Factored`: A factorization of A.
- `xb`: On entry, the right-hand side b. On return, the solution vector x. If A has dimension m x n, then xb must have length k, where k=max(m,n).
- `workspace`: Scratch space of size Factored.solveWorkspaceRequiredStatic + 1*Factored.solveWorkspaceRequiredPerRHS * 2. This memory must be 16-byte aligned (any allocation returned by malloc() has this property).

## Discussion

Discussion If the factorization is A=QR and the system is underdetermined, the solution of minimum norm || x ||_2 is returned. If the factorization is A=QR and the system is overdetermined, the least squares solution arg min_x || Ax - b ||_2 is returned. In the case of a factorization of type=SparseCholeskyAtA, the factorization is in fact of A^T A, so the solution returned is for the system A^TAx=b.

## See Also

### Complex direct solving functions

- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-4fydu.md)
- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-1psgz.md)
- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-4fydu.md)
- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-5apxy.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-3482l.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-3hev5.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-3qkkl.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-76ge0.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-7day5.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-85y2u.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-90ojf.md)