nlcpy.linalg.solve

nlcpy.linalg.solve(a, b)[source]

Solves 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{(…, M,), (…, M, K)} ndarray: Solution to the system a x = b. Returned shape is identical to b.

Note

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.

Examples

Solve the system of equations 3 * x0 + x1 = 9 and x0 + 2 * x1 = 8:

>>> import nlcpy as vp
>>> a = vp.array([[3,1], [1,2]])
>>> b = vp.array([9,8])
>>> x = vp.linalg.solve(a, b)
>>> x
array([2., 3.])