solve(a, b)
Computes the "exact" solution, x, of the well-determined, i.e., full rank, linear matrix equation :None:None:`ax = b`.
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.
Coefficient matrix.
Ordinate or "dependent variable" values.
If a is singular or not square.
Solution to the system a x = b. Returned shape is identical to b.
Solve a linear matrix equation, or system of linear scalar equations.
scipy.linalg.solve
Similar function in SciPy.
Solve the system of equations x0 + 2 * x1 = 1
and 3 * 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) TrueSee :
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