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

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

Declaration

func SparseSolve(_ method: SparseIterativeMethod, _ A: SparseMatrix_Double, _ b: DenseVector_Double, _ x: DenseVector_Double, _ 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.

Mentioned in

Solving systems using iterative methods

Return Value

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

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:

[Image]

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: [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,
                    SparsePreconditionerDiagScaling)
    }
}

On return, xValues contains the values [1.0, 2.0, 3.0].