scipy.linalg.solve

scipy.linalg.solve(a, b, sym_pos=False, lower=False, overwrite_a=False, overwrite_b=False, debug=False, check_finite=True)

Solve the equation a x = b for x.

Parameters:

a : (M, M) array_like

A square matrix.

b : (M,) or (M, N) array_like

Right-hand side matrix in a x = b.

sym_pos : bool, optional

Assume a is symmetric and positive definite.

lower : bool, optional

Use only data contained in the lower triangle of a, if sym_pos is true. Default is to use upper triangle.

overwrite_a : bool, optional

Allow overwriting data in a (may enhance performance). Default is False.

overwrite_b : bool, optional

Allow overwriting data in b (may enhance performance). Default is False.

check_finite : bool, optional

Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

x : (M,) or (M, N) ndarray

Solution to the system a x = b. Shape of the return matches the shape of b.

Raises:

LinAlgError

If a is singular.

ValueError

If a is not square

Examples

Given a and b, solve for x:

>>> a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])
>>> b = np.array([2, 4, -1])
>>> from scipy import linalg
>>> x = linalg.solve(a, b)
>>> x
array([ 2., -2.,  9.])
>>> np.dot(a, x) == b
array([ True,  True,  True], dtype=bool)