Source code for cla_utils.exercises10

import numpy as np
import numpy.random as random


def arnoldi(A, b, k):
    """
    For a matrix A, apply k iterations of the Arnoldi algorithm,
    using b as the first basis vector.

    :param A: an mxm numpy array
    :param b: m dimensional numpy array, the starting vector
    :param k: integer, the number of iterations

    :return Q: an mx(k+1) dimensional numpy array containing the orthonormal basis
    :return H: a (k+1)xk dimensional numpy array containing the upper \
    Hessenberg matrix
    """

    raise NotImplementedError


def GMRES(A, b, maxit, tol, return_residual_norms=False,
          return_residuals=False):
    """
    For a matrix A, solve Ax=b using the basic GMRES algorithm.

    :param A: an mxm numpy array
    :param b: m dimensional numpy array
    :param maxit: integer, the maximum number of iterations
    :param tol: floating point number, the tolerance for termination
    :param return_residual_norms: logical
    :param return_residuals: logical

    :return x: an m dimensional numpy array, the solution
    :return nits: if converged, the number of iterations required, otherwise \
    equal to -1
    :return rnorms: nits dimensional numpy array containing the norms of \
    the residuals at each iteration
    :return r: mxnits dimensional numpy array, column k contains residual \
    at iteration k
    """
    
    raise NotImplementedError


def get_AA100():
    """
    Get the AA100 matrix.

    :return A: a 100x100 numpy array used in exercises 10.
    """
    AA100 = np.fromfile('AA100.dat', sep=' ')
    AA100 = AA100.reshape((100, 100))
    return AA100


def get_BB100():
    """
    Get the BB100 matrix.

    :return B: a 100x100 numpy array used in exercises 10.
    """
    BB100 = np.fromfile('BB100.dat', sep=' ')
    BB100 = BB100.reshape((100, 100))
    return BB100


def get_CC100():
    """
    Get the CC100 matrix.

    :return C: a 100x100 numpy array used in exercises 10.
    """
    CC100 = np.fromfile('CC100.dat', sep=' ')
    CC100 = CC100.reshape((100, 100))
    return CC100