---
title: "SparseSolve(_:_:_:_:)"
framework: accelerate
role: symbol
role_heading: Function
path: "accelerate/sparsesolve(_:_:_:_:)-7f1sp"
---

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

Solves the equation Ax = b for vectors of double-precision values using the specified iterative method.

## Declaration

```swift
func SparseSolve(_ method: SparseIterativeMethod, _ A: SparseMatrix_Double, _ b: DenseVector_Double, _ x: DenseVector_Double) -> SparseIterativeStatus_t
```

## Parameters

- `method`: The iterative method.
- `A`: The matrix A.
- `b`: The vector b.
- `x`: The vector x.

## 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. The following figure shows a system of equations where the coefficient matrix is sparse:

The following code solves this system 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: [Double] =      [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: [Double] = [30, 35, 100] var xValues = [Double](repeating: .nan, count: bValues.count)

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

## See Also

### Iterative sparse solve functions

- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-97k3a.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-26fae.md)
- [SparseSolve(_:_:_:_:)](accelerate/sparsesolve(_:_:_:_:)-9yhgp.md)