numpy.linalg.solve#
- 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.
See also
scipy.linalg.solve
Similar function in SciPy.
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, use
lstsq
for the least-squares best “solution” of the system/equation.References
- 1
G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 22.
Examples
Solve the system of equations
x0 + 2 * x1 = 1
and3 * x0 + 5 * x1 = 2
:>>> a = np.array([[1, 2], [3, 5]]) >>> b = np.array([1, 2]) >>> x = np.linalg.solve(a, b) >>> x array([-1., 1.])
Check that the solution is correct:
>>> np.allclose(np.dot(a, x), b) True