numpy.linalg.solve
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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 equationax = 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
[1] 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
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Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.16.1/reference/generated/numpy.linalg.solve.html