SparseFactor(_:_:_:)
Returns the factorization of a sparse matrix of double-precision values that corresponds to the supplied symbolic factorization using specified options.
Declaration
func SparseFactor(_ SymbolicFactor: SparseOpaqueSymbolicFactorization, _ Matrix: SparseMatrix_Double, _ nfoptions: SparseNumericFactorOptions) -> SparseOpaqueFactorization_DoubleParameters
- SymbolicFactor:
A symbolic factorization that returns by calling Sparsefactor(_:_:_:_:_:) 68hki.
- Matrix:
The matrix to factorize.
- nfoptions:
The numeric factor options, such as pivoting parameters.
Return Value
A SparseOpaqueFactorization_Double structure that represents the matrix factorization.
Discussion
Use this function to solve a system of linear equations using a symbolic factorization that SparseFactor(_:_:) creates.
The following figure shows two systems of equations where the coefficient matrix is sparse:
[Image]
The following code solves these two systems by calling SparseFactor(_:_:) and SparseFactor(_:_:):
/// Define the sparsity pattern of matrices `A0` and `A1`.
let rowIndices: [Int32] = [ 0, 1, 1, 2]
let columnIndices: [Int32] = [ 2, 0, 2, 1]
/// Create the single-precision coefficient matrix _A0_.
let a0Values: [Float] = [10, 20, 5, 50]
let A0 = SparseConvertFromCoordinate(3, 3,
4, 1,
SparseAttributes_t(),
rowIndices, columnIndices,
a0Values)
/// Create the double-precision coefficient matrix _A1_.
let a1Values: [Double] = [5, 10, 2.5, 25]
let A1 = SparseConvertFromCoordinate(3, 3,
4, 1,
SparseAttributes_t(),
rowIndices, columnIndices,
a1Values)
/// Compute the symbolic factorization from the structure of either coefficient matrix.
let structure = A0.structure
let symbolicFactorization = SparseFactor(SparseFactorizationQR,
structure)
/// Factorize _A0_ using the symbolic factorization.
let factorization0 = SparseFactor(symbolicFactorization, A0)
/// Solve _A0 · x = b0_ in place.
var b0Values: [Float] = [30, 35, 100]
b0Values.withUnsafeMutableBufferPointer { bPtr in
let xb = DenseVector_Float(count: 3,
data: bPtr.baseAddress!)
SparseSolve(factorization0, xb)
}
/// Factorize _A1_ using the symbolic factorization.
let factorization1 = SparseFactor(symbolicFactorization, A1)
/// Solve _A1 · x = b1_ in place.
var b1Values: [Double] = [60, 70, 200]
b1Values.withUnsafeMutableBufferPointer { bPtr in
let xb = DenseVector_Double(count: 3,
data: bPtr.baseAddress!)
SparseSolve(factorization1, xb)
}
SparseCleanup(A0)
SparseCleanup(A1)
SparseCleanup(factorization0)
SparseCleanup(factorization1)On return, b0Values contains the values [1.0, 2.0, 3.0], and b1Values contains the values [4.0, 8.0, 12.0].