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SparseSolve(_:_:_:)

Solves the system Ax=b for x, using the supplied SparseOpaqueFactorization_Complex_Float of A.

Declaration

func SparseSolve(_ Factored: SparseOpaqueFactorization_Complex_Float, _ b: DenseVector_Complex_Float, _ x: DenseVector_Complex_Float)

Parameters

  • Factored:

    A factorization of A.

  • b:

    The right-hand side b to solve for. If A has dimension m x n, then b must have length m.

  • x:

    Vector in which to return solution. If A has dimension m x n, then x must have length 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