code/validation/Python/0004498_abs.py

# Copyright (C) 2015-2022 by the RBniCS authors
#
# This file is part of RBniCS.
#
# SPDX-License-Identifier: LGPL-3.0-or-later

from math import fabs
from ufl.core.operator import Operator
from rbnics.backends.dolfin.matrix import Matrix
from rbnics.backends.dolfin.vector import Vector
from rbnics.backends.dolfin.function import Function
from rbnics.backends.dolfin.wrapping import (function_from_ufl_operators, get_global_dof_coordinates,
                                             get_global_dof_component, to_petsc4py)
from rbnics.utils.decorators import backend_for, overload
from rbnics.utils.mpi import parallel_max


# abs function to compute maximum absolute value of an expression, matrix or vector (for EIM).
# To be used in combination with max even though here we actually carry out both the max and the abs!
@backend_for("dolfin", inputs=((Matrix.Type(), Vector.Type(), Function.Type(), Operator), ))
def abs(expression):
    return _abs(expression)


@overload
def _abs(matrix: Matrix.Type()):
    # Note: PETSc offers a method MatGetRowMaxAbs, but it is not wrapped in petsc4py. We do the same by hand
    mat = to_petsc4py(matrix)
    row_start, row_end = mat.getOwnershipRange()
    i_max, j_max = None, None
    value_max = None
    for i in range(row_start, row_end):
        cols, vals = mat.getRow(i)
        for (c, v) in zip(cols, vals):
            if value_max is None or fabs(v) > fabs(value_max):
                i_max = i
                j_max = c
                value_max = v
    assert i_max is not None
    assert j_max is not None
    assert value_max is not None
    #
    mpi_comm = mat.comm.tompi4py()
    (global_value_max, global_ij_max) = parallel_max(value_max, (i_max, j_max), fabs, mpi_comm)
    return AbsOutput(global_value_max, global_ij_max)


@overload
def _abs(vector: Vector.Type()):
    # Note: PETSc offers VecAbs and VecMax, but for symmetry with the matrix case we do the same by hand
    vec = to_petsc4py(vector)
    row_start, row_end = vec.getOwnershipRange()
    i_max = None
    value_max = None
    for i in range(row_start, row_end):
        val = vec.getValue(i)
        if value_max is None or fabs(val) > fabs(value_max):
            i_max = i
            value_max = val
    assert i_max is not None
    assert value_max is not None
    #
    mpi_comm = vec.comm.tompi4py()
    (global_value_max, global_i_max) = parallel_max(value_max, (i_max, ), fabs, mpi_comm)
    return AbsOutput(global_value_max, global_i_max)


@overload
def _abs(expression: (Function.Type(), Operator)):
    function = function_from_ufl_operators(expression)
    space = function.function_space()
    abs_output = abs(function.vector())
    value_max = abs_output.max_abs_return_value
    global_dof_max = abs_output.max_abs_return_location
    assert len(global_dof_max) == 1
    global_dof_max = global_dof_max[0]
    coordinates_max = get_global_dof_coordinates(global_dof_max, space)
    component_max = get_global_dof_component(global_dof_max, space)
    # Prettify print
    coordinates_max_component_max_dof_max = PrettyTuple(coordinates_max, component_max, global_dof_max)
    return AbsOutput(value_max, coordinates_max_component_max_dof_max)


# Auxiliary class to signal to the max() function that it is dealing with an output of the abs() method
class AbsOutput(object):
    def __init__(self, max_abs_return_value, max_abs_return_location):
        self.max_abs_return_value = max_abs_return_value
        self.max_abs_return_location = max_abs_return_location


class PrettyTuple(tuple):
    def __new__(cls, arg0, arg1, arg2):
        return tuple.__new__(cls, (arg0, arg1, arg2))

    def __str__(self):
        output = str(self[0])
        if self[1] >= 0:
            output += " at component " + str(self[1])
        return output