romtools.composite_vector_space

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 45
 46from typing import List
 47import numpy as np
 48from romtools.vector_space import VectorSpace
 49
 50
 51class CompositeVectorSpace:
 52    '''
 53    Constructs a composite vector space out of a list of vector spaces
 54    Different vector spaces need to have the same number of spatial DOFs
 55    '''
 56
 57    def __init__(self, list_of_vector_spaces: List[VectorSpace]):
 58        '''
 59        Inputs: list_of_vector_spaces: list[VectorSpace] containing the list of vector spaces to combine
 60        '''
 61        # Computed dimensions and ensure vector spaces are compatable
 62        self.__get_extent_and_check_compatability(list_of_vector_spaces)
 63
 64        # Construct basis as a list of local bases
 65        self.__construct_compact_basis(list_of_vector_spaces)
 66
 67    def extents(self) -> np.ndarray:
 68        return self.__extent
 69
 70    def get_shift_vector(self) -> np.ndarray:
 71        return self.__construct_global_shift_vector()
 72
 73    def get_basis(self) -> np.ndarray:
 74        return self.__construct_full_basis()
 75
 76    def get_compact_basis(self) -> List[np.ndarray]:
 77        return self.__compact_basis
 78
 79    def get_compact_shift_vector(self) -> List[np.ndarray]:
 80        return self.__compact_shift_vector
 81
 82    def __get_extent_and_check_compatability(self, list_of_vector_spaces):
 83        # Checks that dimensions of the vector spaces match
 84        # and assigns self.__extent
 85        dims = np.zeros(len(list_of_vector_spaces))
 86        n_vector_spaces = len(list_of_vector_spaces)
 87        n_vars = 0
 88        total_number_of_bases = 0
 89        for i in range(0, n_vector_spaces):
 90            local_vector_space = list_of_vector_spaces[i]
 91            local_vector_space_dimensions = local_vector_space.get_basis().shape
 92            n_vars += local_vector_space_dimensions[0]
 93            dims[i] = local_vector_space_dimensions[1]
 94            total_number_of_bases += local_vector_space_dimensions[2]
 95
 96        nx = int(dims[0])
 97        n_vars = int(n_vars)
 98        total_number_of_bases = int(total_number_of_bases)
 99        self.__extent = np.array([n_vars, nx, total_number_of_bases], dtype='int')
100        assert np.allclose(np.diff(dims),
101                           np.zeros(dims.size-1)
102               ), "Error constructing composite vector space, not all spaces have the same spatial dimension"
103
104    def __construct_global_shift_vector(self):
105        # Constructs the shift vector for the composite vector space
106        shift_vector = self.__compact_shift_vector[0]
107        for local_shift_vector in self.__compact_shift_vector[1:]:
108            shift_vector = np.append(shift_vector, local_shift_vector, axis=0)
109        return shift_vector
110
111    def __construct_full_basis(self):
112        # Constructs a dense basis for the composite vector space
113        basis = np.zeros((self.__extent[0], self.__extent[1], self.__extent[2]))
114        start_var_index = 0
115        start_basis_index = 0
116        for local_basis in self.__compact_basis:
117            dim = local_basis.shape
118            basis[start_var_index:start_var_index+dim[0], :, start_basis_index:start_basis_index+dim[2]] = local_basis
119            start_var_index += dim[0]
120            start_basis_index += dim[2]
121        return basis
122
123    def __construct_compact_basis(self, list_of_vector_spaces):
124        # Constructs a list of bases.
125        # This is much more efficient in terms of memory
126        self.__compact_basis = [space.get_basis() for space in list_of_vector_spaces]
127        self.__compact_shift_vector = [space.get_shift_vector() for space in list_of_vector_spaces]