numpy.linalg.
solve
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.
Coefficient matrix.
Ordinate or “dependent variable” values.
Solution to the system a x = b. Returned shape is identical to b.
If a is singular or not square.
Notes
New in version 1.8.0.
Broadcasting rules apply, see the numpy.linalg documentation for details.
numpy.linalg
The solutions are computed using LAPACK routine _gesv.
_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.
lstsq
References
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:
3 * x0 + x1 = 9
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