spsolve_with_known

compas.numerical.spsolve_with_known(A, b, x, known)[source]

Solve (sparse) a system of linear equations with part of solution known.

Parameters

  • A (array) – Coefficient matrix (sparse) represented as an (m x n) array.

  • b (array) – Right-hand-side represented as an (m x 1) array.

  • x (array) – Unknowns/knowns represented as an (n x 1) array.

  • known (list) – The indices of the known elements of x.

Returns

array – (n x 1) vector solution.

Notes

Computes the solution (using spsolve) of the system of linear equations.

\[\mathbf{A} \mathbf{x} = \mathbf{b}\]

Same function as solve_with_known, but for sparse matrix A.

Examples

>>> A = array([[2, 1, 3], [2, 6, 8], [6, 8, 18]])
>>> b = array([[1], [3], [5]])
>>> x = array([[0.3], [0], [0]])
>>> x = solve_with_known(A, b, x, [0])
>>> allclose(x, array([[0.3], [0.4], [0.0]]))
True