mxnet.np.linalg.solve¶
-
solve
(a, b)¶ Solve a linear matrix equation, or system of linear scalar equations.
Computes the “exact” solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = b.
- Parameters
a ((.., M, M) ndarray) – Coefficient matrix.
b ({(.., M,), (.., M, K)}, ndarray) – Ordinate or “dependent variable” values.
- Returns
x – Solution to the system a x = b. Returned shape is identical to b.
- Return type
{(.., M,), (.., M, K)} ndarray
- Raises
MXNetError – If a is singular or not square.
Notes
Broadcasting rules apply, see the numpy.linalg documentation for details.
The solutions are computed using LAPACK routine
_gesv
.a must be square and of full-rank, i.e., all rows (or, equivalently, columns) must be linearly independent; if either is not true, use lstsq for the least-squares best “solution” of the system/equation.
Examples
Solve the system of equations
3 * x0 + x1 = 9
andx0 + 2 * x1 = 8
:>>> a = np.array([[3,1], [1,2]]) >>> b = np.array([9,8]) >>> x = np.linalg.solve(a, b) >>> x array([2., 3.])
Check that the solution is correct:
>>> np.allclose(np.dot(a, x), b) True