(A, x, b, Dinv=None, blocksize=1, iterations=1, omega=1.0)
Perform block Jacobi iteration on the linear system Ax=b.

    Parameters
    ----------
    A : csr_matrix or bsr_matrix
        Sparse NxN matrix
    x : ndarray
        Approximate solution (length N)
    b : ndarray
        Right-hand side (length N)
    Dinv : array
        Array holding block diagonal inverses of A
        size (N/blocksize, blocksize, blocksize)
    blocksize : int
        Desired dimension of blocks
    iterations : int
        Number of iterations to perform
    omega : scalar
        Damping parameter

    Returns
    -------
    Nothing, x will be modified in place.

    Examples
    --------
    >>> # Use block Jacobi as a Stand-Alone Solver
    >>> from pyamg.relaxation.relaxation import block_jacobi
    >>> from pyamg.gallery import poisson
    >>> from pyamg.util.linalg import norm
    >>> import numpy as np
    >>> A = poisson((10,10), format='csr')
    >>> x0 = np.zeros((A.shape[0],1))
    >>> b = np.ones((A.shape[0],1))
    >>> block_jacobi(A, x0, b, blocksize=4, iterations=10, omega=1.0)
    >>> print(f'{norm(b-A*x0):2.4}')
    4.665
    >>> #
    >>> # Use block Jacobi as the Multigrid Smoother
    >>> from pyamg import smoothed_aggregation_solver
    >>> opts = {'omega': 4.0/3.0, 'iterations' : 2, 'blocksize' : 4}
    >>> sa = smoothed_aggregation_solver(A, B=np.ones((A.shape[0],1)),
    ...        coarse_solver='pinv', max_coarse=50,
    ...        presmoother=('block_jacobi', opts),
    ...        postsmoother=('block_jacobi', opts))
    >>> x0=np.zeros((A.shape[0],1))
    >>> residuals=[]
    >>> x = sa.solve(b, x0=x0, tol=1e-8, residuals=residuals)
Perform block Jacobi iteration on the linear system Ax=b.
Perform block Jacobi iteration on the linear system Ax = b .
def block_jacobi(A, x, b, Dinv=None, blocksize=1, iterations=1, omega=1.0):
    """Perform block Jacobi iteration on the linear system Ax=b.

    Parameters
    ----------
    A : csr_matrix or bsr_matrix
        Sparse NxN matrix
    x : ndarray
        Approximate solution (length N)
    b : ndarray
        Right-hand side (length N)
    Dinv : array
        Array holding block diagonal inverses of A
        size (N/blocksize, blocksize, blocksize)
    blocksize : int
        Desired dimension of blocks
    iterations : int
        Number of iterations to perform
    omega : scalar
        Damping parameter

    Returns
    -------
    Nothing, x will be modified in place.

    Examples
    --------
    >>> # Use block Jacobi as a Stand-Alone Solver
    >>> from pyamg.relaxation.relaxation import block_jacobi
    >>> from pyamg.gallery import poisson
    >>> from pyamg.util.linalg import norm
    >>> import numpy as np
    >>> A = poisson((10,10), format='csr')
    >>> x0 = np.zeros((A.shape[0],1))
    >>> b = np.ones((A.shape[0],1))
    >>> block_jacobi(A, x0, b, blocksize=4, iterations=10, omega=1.0)
    >>> print(f'{norm(b-A*x0):2.4}')
    4.665
    >>> #
    >>> # Use block Jacobi as the Multigrid Smoother
    >>> from pyamg import smoothed_aggregation_solver
    >>> opts = {'omega': 4.0/3.0, 'iterations' : 2, 'blocksize' : 4}
    >>> sa = smoothed_aggregation_solver(A, B=np.ones((A.shape[0],1)),
    ...        coarse_solver='pinv', max_coarse=50,
    ...        presmoother=('block_jacobi', opts),
    ...        postsmoother=('block_jacobi', opts))
    >>> x0=np.zeros((A.shape[0],1))
    >>> residuals=[]
    >>> x = sa.solve(b, x0=x0, tol=1e-8, residuals=residuals)

    """
    A, x, b = make_system(A, x, b, formats=['csr', 'bsr'])
    A = A.tobsr(blocksize=(blocksize, blocksize))

    if Dinv is None:
        Dinv = get_block_diag(A, blocksize=blocksize, inv_flag=True)
    elif Dinv.shape[0] != int(A.shape[0]/blocksize):
        raise ValueError('Dinv and A have incompatible dimensions')
    elif (Dinv.shape[1] != blocksize) or (Dinv.shape[2] != blocksize):
        raise ValueError('Dinv and blocksize are incompatible')

    sweep = slice(None)
    (row_start, row_stop, row_step) = sweep.indices(int(A.shape[0]/blocksize))

    if (row_stop - row_start) * row_step <= 0:  # no work to do
        return

    temp = np.empty_like(x)

    # Create uniform type, convert possibly complex scalars to length 1 arrays
    [omega] = type_prep(A.dtype, [omega])

    for _iter in range(iterations):
        amg_core.block_jacobi(A.indptr, A.indices, np.ravel(A.data),
                              x, b, np.ravel(Dinv), temp,
                              row_start, row_stop, row_step,
                              omega, blocksize)
def block_jacobi ( A , x , b , Dinv = None , blocksize = 1 , iterations = 1 , omega = 1.0 ) : A , x , b = make_system ( A , x , b , formats = [ 'csr' , 'bsr' ] ) A = A . tobsr ( blocksize = ( blocksize , blocksize ) ) if Dinv is None : Dinv = get_block_diag ( A , blocksize = blocksize , inv_flag = True ) elif Dinv . shape [ 0 ] != int ( A . shape [ 0 ] / blocksize ) : raise ValueError ( 'Dinv and A have incompatible dimensions' ) elif ( Dinv . shape [ 1 ] != blocksize ) or ( Dinv . shape [ 2 ] != blocksize ) : raise ValueError ( 'Dinv and blocksize are incompatible' ) sweep = slice ( None ) ( row_start , row_stop , row_step ) = sweep . indices ( int ( A . shape [ 0 ] / blocksize ) ) if ( row_stop - row_start ) * row_step <= 0 : # no work to do return temp = np . empty_like ( x ) # Create uniform type, convert possibly complex scalars to length 1 arrays [ omega ] = type_prep ( A . dtype , [ omega ] ) for _iter in range ( iterations ) : amg_core . block_jacobi ( A . indptr , A . indices , np . ravel ( A . data ) , x , b , np . ravel ( Dinv ) , temp , row_start , row_stop , row_step , omega , blocksize )