flopscope.numpy.linalg.solve

fnp.linalg.solve(a, b)[flopscope source][numpy source]

Solve a linear matrix equation, or system of linear scalar equations.

Adapted from NumPy docs np.linalg.solve

Arealinalg

Typecustom

Cost

4×

n^3

Flopscope Context

Solve Ax=b. Cost: $n^3$.

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 (..., M) if b is shape (M,) and (..., M, K) if b is (..., M, K), where the "..." part is broadcasted between a and b.

Raises

:LinAlgError: If a is singular or not square.

Notes

Broadcasting rules apply, see the flops.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.

Changed in version 2.0.

References

footnote

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 and 3 * x0 + 5 * x1 = 2:

>>> import flopscope.numpy as fnp
>>> a = flops.array([[1, 2], [3, 5]])
>>> b = flops.array([1, 2])
>>> x = flops.linalg.solve(a, b)
>>> x
array([-1.,  1.])

Check that the solution is correct:

>>> flops.allclose(flops.dot(a, x), b)
True