Function

SparseSolve(_:_:_:)

Solves the equation Factored * x = b for the vector of single-precision values x in place, and without any internal memory allocations.

Declaration

func SparseSolve(_ Factored: SparseOpaqueFactorization_Float, _ xb: DenseVector_Float, _ workspace: UnsafeMutableRawPointer)

Parameters

Factored

The factored matrix to solve.

xb

On input, the vector b. On return it is overwritten with the vector x. If A has dimension m x n, then this parameter must have length k, where k = max(m,n).

workspace

Discussion

If the factorization is A = QR and the system is underdetermined, the solution of minimum norm x is returned.

If the factorization is A = QR and the system is overdetermined, the least squares solution arg min AX - B is returned.

In the case of a factorization of type SparseFactorizationCholeskyAtA, the factorization is in fact of AA, so the solution returned is for the system AAX = B.

See Also

Direct Solving Functions with User-Defined Workspace

func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double, UnsafeMutableRawPointer)

Solves the equation Factored * x = b for the vector of double-precision values x in place, and without any internal memory allocations.

func SparseSolve(SparseOpaqueFactorization_Double, DenseVector_Double, DenseVector_Double, UnsafeMutableRawPointer)

Solves the equation Factored * x = b for the vector of double-precision values x without any internal memory allocations.

func SparseSolve(SparseOpaqueFactorization_Float, DenseVector_Float, DenseVector_Float, UnsafeMutableRawPointer)

Solves the equation Factored * x = b for the vector of single-precision values x without any internal memory allocations.