---
title: "SparseSolve(_:_:_:)"
framework: accelerate
role: symbol
role_heading: Function
path: "accelerate/sparsesolve(_:_:_:)-8ikjb"
---

# SparseSolve(_:_:_:)

Solves the system AX=B for X, using the supplied SparseOpaqueFactorization_Complex_Float of A, in place, and without any internal memory allocations.

## Declaration

```swift
func SparseSolve(_ Factored: SparseOpaqueFactorization_Complex_Float, _ XB: DenseMatrix_Complex_Float, _ workspace: UnsafeMutableRawPointer)
```

## Parameters

- `Factored`: A factorization of A.
- `XB`: On entry, the right-hand sides B. On return, the solution vectors X. If A has dimension m x n, then XB must have dimension k x nrhs, where k=max(m,n) and nrhs is the number of right-hand sides to find solutions for.
- `workspace`: Scratch space of size Factored.solveWorkspaceRequiredStatic + nrhs * 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 matrix solving functions

- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-31yj7.md)
- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-3x0vj.md)
- [SparseSolve(_:_:)](accelerate/sparsesolve(_:_:)-4j17a.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-2qlwo.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-2rk1c.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-34okt.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-48njk.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-6pudz.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-7krer.md)
- [SparseSolve(_:_:_:)](accelerate/sparsesolve(_:_:_:)-7qdpl.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-5xn6p.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-6demt.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-6od6k.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-7mtyx.md)