def jacobi(a, b, tol=0.0005):
"""
Solve a linear matrix equation, or system of linear scalar equations
using the Jacobi Method.
: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.jacobi(a, b)
>>> x
array([ 2., 3.])
Check that the solution is correct:
>>> (np.dot(a, x) == b).all()
True
"""
x = np.ones_like(b)
D = 1 / np.diag(a)
R = np.diag(np.diag(a)) - a
T = D[:, np.newaxis] * R
C = D * b
error = tol + 1
while error > tol:
xo = x
x = np.add.reduce(T * x, -1) + C
error = norm(x - xo) / norm(x)
return x
def jacobi(a, b, tol=0.0005):
"""
Solve a linear matrix equation, or system of linear scalar equations
using the Jacobi Method.
: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.jacobi(a, b)
>>> x
array([ 2., 3.])
Check that the solution is correct:
>>> (np.dot(a, x) == b).all()
True
"""
x = np.ones_like(b)
D = 1/np.diag(a)
R = np.diag(np.diag(a)) - a
T = D[:,np.newaxis]*R
C = D*b
error = tol + 1
while error > tol:
xo = x
x = np.add.reduce(T*x,-1) + C
error = norm(x-xo)/norm(x)
return x
def get_drhodS(salt, temp, p):
betaS = 0.78e-3
rho0 = 1024.
return betaS * rho0 * bh.ones_like(temp)