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 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.
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, 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
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
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https://numpy.org/doc/1.22/reference/generated/numpy.linalg.solve.html