xorbits.numpy.linalg.solve#
- xorbits.numpy.linalg.solve(a, b, sym_pos=False, sparse=None)[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 – Solution to the system a x = b. Returned shape is identical to b.
- Return type
{(…, M,), (…, M, K)} ndarray
- 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(numpy.linalg).
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
- sym_posbool
Assume a is symmetric and positive definite. If
True
, use Cholesky decomposition.- sparse: bool, optional
Return sparse value or not.
This docstring was copied from numpy.linalg.