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# 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: DenseMatrix_Complex_Double)
```

## 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.

## 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`.

---

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