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SparseSolve(_:_:)

Solves the system Ax=b for x, using the supplied SparseOpaqueFactorization_Complex_Double of A, in place.

Declaration

func SparseSolve(_ Factored: SparseOpaqueFactorization_Complex_Double, _ xb: DenseVector_Complex_Double)

Parameters

  • Factored:

    A factorization of A.

  • xb:

    On entry, the right-hand side b. On return, the solution vector x. If A has dimension m x n, then xb must have length k, where k=max(m,n).

Discussion

If the factorization is A=QR and the system is underdetermined, the solution of minimum norm || x ||_2 is returned. If the factorization is A=QR and the system is overdetermined, the least squares solution arg min_x || Ax - b ||_2 is returned. In the case of a factorization of type=SparseCholeskyAtA, the factorization is in fact of A^T A, so the solution returned is for the system A^TAx=b.

See Also

Complex direct solving functions