---
title: "SparseSolve(_:_:_:_:_:)"
framework: accelerate
role: symbol
role_heading: Function
path: "accelerate/sparsesolve(_:_:_:_:_:)-9nzvm"
---

# SparseSolve(_:_:_:_:_:)

Solves the equation Ax = b for vectors of single-precision values using the specified iterative method and preconditioner type.

## Declaration

```swift
func SparseSolve(_ method: SparseIterativeMethod, _ A: SparseMatrix_Float, _ b: DenseVector_Float, _ x: DenseVector_Float, _ Preconditioner: SparsePreconditioner_t) -> SparseIterativeStatus_t
```

## Parameters

- `method`: The iterative method.
- `A`: The matrix A.
- `b`: The vector b.
- `x`: The vector x.
- `Preconditioner`: The preconditioner to apply.

## Return Value

Return Value A SparseIterativeStatus_t enumeration that represents the status of the iterative solve.

## Discussion

Discussion Use this function to solve a system of linear equations using a factored coefficient matrix. Preconditioning the coefficient matrix can reduce the number of iterations the function requires to converge the system. The following figure shows two systems of equations where the coefficient matrix is sparse:

The following code solves this system by applying a diagonal scaling preconditioner and using the least squares minimum residual method: /// Create the coefficient matrix _A_. let rowIndices: [Int32] =    [ 0,  1, 1,  2] let columnIndices: [Int32] = [ 2,  0, 2,  1] let aValues: [Float] =       [10, 20, 5, 50]

let A = SparseConvertFromCoordinate(3, 3,                                     4, 1,                                     SparseAttributes_t(),                                     rowIndices, columnIndices,                                     aValues)

defer {     SparseCleanup(A) }

/// Create the right-hand-side vector, _b_. var bValues: [Float] = [30, 35, 100] var xValues = [Float](repeating: .nan, count: bValues.count)

bValues.withUnsafeMutableBufferPointer { bPtr in     xValues.withUnsafeMutableBufferPointer { xPtr in                  let b = DenseVector_Float(count: 3,                                   data: bPtr.baseAddress!)                  let x = DenseVector_Float(count: 3,                                   data: xPtr.baseAddress!)                  SparseSolve(SparseLSMR(),                     A, b, x,                     SparsePreconditionerDiagScaling)     } } On return, xValues contains the values [1.0, 2.0, 3.0].

## See Also

### Iterative sparse solve functions with preconditioner

- [SparseSolve(_:_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:_:)-1qwax.md)
- [SparseSolve(_:_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:_:)-3aphv.md)
- [SparseSolve(_:_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:_:)-5vs11.md)
- [SparseSolve(_:_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:_:)-6i1nx.md)
- [SparseSolve(_:_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:_:)-7wnum.md)