mvpa2.clfs.gpr.NLAsolve¶

`mvpa2.clfs.gpr.``NLAsolve`(a, b)

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. x : {(..., M,), (..., M, K)} ndarray Solution to the system a x = b. Returned shape is identical to `b`. 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, use `lstsq` for the least-squares best “solution” of the system/equation.

References

 [R10] 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` and `x0 + 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
```