numpy.linalg.solve — NumPy v1.11 Manual (original) (raw)
numpy.linalg.solve(a, b)[source]¶
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) array_like Coefficient matrix. b : {(..., M,), (..., M, K)}, array_like Ordinate or “dependent variable” values. |
|---|---|
| Returns: | x : {(..., M,), (..., M, K)} ndarray Solution to the system a x = b. Returned shape is identical to b. |
| Raises: | LinAlgError If a is singular or not square. |
Notes
New in version 1.8.0.
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, uselstsq for the least-squares best “solution” of the system/equation.
References
| [R43] | G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 22. |
|---|
Examples
Solve the system of equations 3 * x0 + x1 = 9 and x0 + 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