numpy.linalg.solve¶

numpy.linalg.
solve
(a, b)[source]¶ Solve a linear matrix equation, or system of linear scalar equations.
Computes the “exact” solution, x, of the welldetermined, 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 fullrank, i.e., all rows (or, equivalently, columns) must be linearly independent; if either is not true, use
lstsq
for the leastsquares best “solution” of the system/equation.References
[R48] 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
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