<!--
{
  "availability" : [
    "iOS: 18.5.0 -",
    "iPadOS: 18.5.0 -",
    "macCatalyst: 18.5.0 -",
    "macOS: 15.5.0 -",
    "tvOS: 18.5.0 -",
    "visionOS: 2.5.0 -",
    "watchOS: 11.5.0 -"
  ],
  "documentType" : "symbol",
  "framework" : "Accelerate",
  "identifier" : "/documentation/Accelerate/SparseSolve(_:_:_:)-7ltk8",
  "metadataVersion" : "0.1.0",
  "role" : "Function",
  "symbol" : {
    "kind" : "Function",
    "modules" : [
      "Accelerate"
    ],
    "preciseIdentifier" : "c:@F@SparseSolve#$@SA@SparseOpaqueFactorization_Complex_Double#$@SA@DenseVector_Complex_Double#*v#"
  },
  "title" : "SparseSolve(_:_:_:)"
}
-->

# SparseSolve(_:_:_:)

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

```
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

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`.

---

Copyright &copy; 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)