def solve(a, b):
"""
Solve a linear matrix equation, or system of linear scalar equations
using Gausian elimination.
:param a: Coefficient matrix
:type a: array_like, shape (M, M)
:param b: Ordinate or "dependent variable" values
:type b: array_like, shape (M,) or (M, N)
:return: Solution to the system a x = b
:rtype: ndarray, shape (M,) or (M, N) depending on b
:raises: :py:exc:`LinAlgError` If `a` is singular or not square.
**Examples:**
Solve the system of equations ``3 * x0 + x1 = 9`` and ``x0 + 2 * x1 = 8``:
>>> import bohrium as np
>>> 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.dot(a, x) == b).all()
True
"""
if not (len(a.shape) == 2 and a.shape[0] == a.shape[1]):
raise la.LinAlgError("a is not square")
w = gauss(np.hstack((a, b[:, np.newaxis])))
lc = w.shape[1] - 1
x = w[:, lc].copy()
def loop_body(lc, x, w):
c = get_iterator(1)
x[:c] -= w[:c, c] * x[c:c + 1]
# for c in range(lc - 1, 0, -1):
# x[:c] -= w[:c, c] * x[c:c + 1]
# np.flush()
return x
def solve(a, b):
"""
Solve a linear matrix equation, or system of linear scalar equations
using Gausian elimination.
:param a: Coefficient matrix
:type a: array_like, shape (M, M)
:param b: Ordinate or "dependent variable" values
:type b: array_like, shape (M,) or (M, N)
:return: Solution to the system a x = b
:rtype: ndarray, shape (M,) or (M, N) depending on b
:raises: :py:exc:`LinAlgError` If `a` is singular or not square.
**Examples:**
Solve the system of equations ``3 * x0 + x1 = 9`` and ``x0 + 2 * x1 = 8``:
>>> import bohrium as np
>>> 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.dot(a, x) == b).all()
True
"""
if not (len(a.shape) == 2 and a.shape[0] == a.shape[1]):
raise la.LinAlgError("a is not square")
w = gauss(np.hstack((a,b[:,np.newaxis])))
lc = w.shape[1]-1
x = w[:,lc].copy()
for c in xrange(lc-1,0,-1):
x[:c] -= w[:c,c] * x[c:c+1]
np.flush(x)
return x