SparseFactor(_:_:)

Returns the specified factorization of a sparse matrix of double-precision values.

Declaration

func SparseFactor(_ type: SparseFactorization_t, _ Matrix: SparseMatrix_Double) -> SparseOpaqueFactorization_Double

Parameters

type:
The type of factorization to perform.
Matrix:
The matrix to factorize.

Mentioned in

Solving systems using direct methods

Return Value

A SparseOpaqueFactorization_Double structure that represents the matrix factorization.

Discussion

Use this function to calculate the factorization of a sparse matrix to pass to the direct solve functions. The following figure shows a system of equations where the coefficient matrix is sparse:

[Image]

The following code solves this system with a QR factorization of the coefficient matrix:

/// 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)

/// Factorize _A_.
let factorization = SparseFactor(SparseFactorizationQR, A)

defer {
    SparseCleanup(A)
    SparseCleanup(factorization)
}

/// Create the right-hand-side vector, _b_.
var bValues = [30.0, 35.0, 100.0]

bValues.withUnsafeMutableBufferPointer { bPtr in
    
    let xb = DenseVector_Double(count: 3,
                               data: bPtr.baseAddress!)
    
    SparseSolve(factorization, xb)
}

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

You can use the symbolic factorization that this function returns for multiple numerical factorizations with different numerical values but the same nonzero structure.