Source code for pymor.discretizers.disk

# -*- coding: utf-8 -*-
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2016 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

from __future__ import absolute_import, division, print_function

import os.path
import ConfigParser

import numpy as np

from pymor.algorithms.timestepping import ImplicitEulerTimeStepper
from pymor.discretizations.basic import StationaryDiscretization
from pymor.discretizations.basic import InstationaryDiscretization
from pymor.operators.constructions import LincombOperator
from pymor.operators.numpy import NumpyMatrixOperator
from pymor.parameters.spaces import CubicParameterSpace
from pymor.parameters.functionals import ExpressionParameterFunctional


[docs]def discretize_stationary_from_disk(parameter_file): """Load a linear affinely decomposed |StationaryDiscretization| from file. The discretization is defined via an `.ini`-style file as follows :: [system-matrices] L_1.mat: l_1(μ_1,...,μ_n) L_2.mat: l_2(μ_1,...,μ_n) ... [rhs-vectors] F_1.mat: f_1(μ_1,...,μ_n) F_2.mat: f_2(μ_1,...,μ_n) ... [parameter] μ_1: a_1,b_1 ... μ_n: a_n,b_n [products] Prod1: P_1.mat Prod2: P_2.mat ... Here, `L_1.mat`, `L_2.mat`, ..., `F_1.mat`, `F_2.mat`, ... are files containing matrices `L_1`, `L_2`, ... and vectors `F_1.mat`, `F_2.mat`, ... which correspond to the affine components of the operator and right-hand side functional. The respective coefficient functionals, are given via the string expressions `l_1(...)`, `l_2(...)`, ..., `f_1(...)` in the (scalar-valued) |Parameter| components `w_1`, ..., `w_n`. The allowed lower and upper bounds `a_i, b_i` for the component `μ_i` are specified in the `[parameters]` section. The resulting operator and right-hand side are then of the form :: L(μ) = l_1(μ)*L_1 + l_2(μ)*L_2+ ... F(μ) = f_1(μ)*F_1 + f_2(μ)*L_2+ ... In the `[products]` section, an optional list of inner products `Prod1`, `Prod2`, .. with corresponding matrices `P_1.mat`, `P_2.mat` can be specified. Example:: [system-matrices] matrix1.mat: 1. matrix2.mat: 1. - theta**2 [rhs-vectors] rhs.mat: 1. [parameter] theta: 0, 0.5 [products] h1: h1.mat l2: mass.mat Parameters ---------- parameter_file Path to the parameter file. Returns ------- discretization The |StationaryDiscretization| that has been generated. """ assert ".ini" == parameter_file[-4:], "Given file is not an .ini file" base_path = os.path.dirname(parameter_file) # Get input from parameter file config = ConfigParser.ConfigParser() config.optionxform = str config.read(parameter_file) # Assert that all needed entries given assert 'system-matrices' in config.sections() assert 'rhs-vectors' in config.sections() assert 'parameter' in config.sections() system_mat = config.items('system-matrices') rhs_vec = config.items('rhs-vectors') parameter = config.items('parameter') # Dict of parameters types and ranges parameter_type = {} parameter_range = {} # get parameters for i in range(len(parameter)): parameter_name = parameter[i][0] parameter_list = tuple(float(j) for j in parameter[i][1].replace(" ", "").split(',')) parameter_range[parameter_name] = parameter_list # Assume scalar parameter dependence parameter_type[parameter_name] = 0 # Create parameter space parameter_space = CubicParameterSpace(parameter_type=parameter_type, ranges=parameter_range) # Assemble operators system_operators, system_functionals = [], [] # get parameter functionals and system matrices for i in range(len(system_mat)): path = os.path.join(base_path, system_mat[i][0]) expr = system_mat[i][1] parameter_functional = ExpressionParameterFunctional(expr, parameter_type=parameter_type) system_operators.append(NumpyMatrixOperator.from_file(path)) system_functionals.append(parameter_functional) system_lincombOperator = LincombOperator(system_operators, coefficients=system_functionals) # get rhs vectors rhs_operators, rhs_functionals = [], [] for i in range(len(rhs_vec)): path = os.path.join(base_path, rhs_vec[i][0]) expr = rhs_vec[i][1] parameter_functional = ExpressionParameterFunctional(expr, parameter_type=parameter_type) op = NumpyMatrixOperator.from_file(path) assert isinstance(op._matrix, np.ndarray) op = op.with_(matrix=op._matrix.reshape((1, -1))) rhs_operators.append(op) rhs_functionals.append(parameter_functional) rhs_lincombOperator = LincombOperator(rhs_operators, coefficients=rhs_functionals) # get products if given if 'products' in config.sections(): product = config.items('products') products = {} for i in range(len(product)): product_name = product[i][0] product_path = os.path.join(base_path, product[i][1]) products[product_name] = NumpyMatrixOperator.from_file(product_path) else: products = None # Create and return stationary discretization return StationaryDiscretization(operator=system_lincombOperator, rhs=rhs_lincombOperator, parameter_space=parameter_space, products=products)
[docs]def discretize_instationary_from_disk(parameter_file, T=None, steps=None, u0=None, time_stepper=None): """Load a linear affinely decomposed |InstationaryDiscretization| from file. Similarly to :func:`discretize_stationary_from_disk`, the discretization is specified via an `ini.`-file of the following form :: [system-matrices] L_1.mat: l_1(μ_1,...,μ_n) L_2.mat: l_2(μ_1,...,μ_n) ... [rhs-vectors] F_1.mat: f_1(μ_1,...,μ_n) F_2.mat: f_2(μ_1,...,μ_n) ... [mass-matrix] D.mat [initial-solution] u0: u0.mat [parameter] μ_1: a_1,b_1 ... μ_n: a_n,b_n [products] Prod1: P_1.mat Prod2: P_2.mat ... [time] T: final time steps: number of time steps Parameters ---------- parameter_file Path to the '.ini' parameter file. T End-time of desired solution. If `None`, the value specified in the parameter file is used. steps Number of time steps to. If `None`, the value specified in the parameter file is used. u0 Initial solution. If `None` the initial solution is obtained from parameter file. time_stepper The desired :class:`time stepper <pymor.algorithms.timestepping.TimeStepperInterface>` to use. If `None`, implicit Euler time stepping is used. Returns ------- discretization The |InstationaryDiscretization| that has been generated. """ assert ".ini" == parameter_file[-4:], "Given file is not an .ini file" base_path = os.path.dirname(parameter_file) # Get input from parameter file config = ConfigParser.ConfigParser() config.optionxform = str config.read(parameter_file) # Assert that all needed entries given assert 'system-matrices' in config.sections() assert 'mass-matrix' in config.sections() assert 'rhs-vectors' in config.sections() assert 'parameter' in config.sections() system_mat = config.items('system-matrices') mass_mat = config.items('mass-matrix') rhs_vec = config.items('rhs-vectors') parameter = config.items('parameter') # Dict of parameters types and ranges parameter_type = {} parameter_range = {} # get parameters for i in range(len(parameter)): parameter_name = parameter[i][0] parameter_list = tuple(float(j) for j in parameter[i][1].replace(" ", "").split(',')) parameter_range[parameter_name] = parameter_list # Assume scalar parameter dependence parameter_type[parameter_name] = 0 # Create parameter space parameter_space = CubicParameterSpace(parameter_type=parameter_type, ranges=parameter_range) # Assemble operators system_operators, system_functionals = [], [] # get parameter functionals and system matrices for i in range(len(system_mat)): path = os.path.join(base_path, system_mat[i][0]) expr = system_mat[i][1] parameter_functional = ExpressionParameterFunctional(expr, parameter_type=parameter_type) system_operators.append(NumpyMatrixOperator.from_file(path)) system_functionals.append(parameter_functional) system_lincombOperator = LincombOperator(system_operators, coefficients=system_functionals) # get rhs vectors rhs_operators, rhs_functionals = [], [] for i in range(len(rhs_vec)): path = os.path.join(base_path, rhs_vec[i][0]) expr = rhs_vec[i][1] parameter_functional = ExpressionParameterFunctional(expr, parameter_type=parameter_type) op = NumpyMatrixOperator.from_file(path) assert isinstance(op._matrix, np.ndarray) op = op.with_(matrix=op._matrix.reshape((1, -1))) rhs_operators.append(op) rhs_functionals.append(parameter_functional) rhs_lincombOperator = LincombOperator(rhs_operators, coefficients=rhs_functionals) # get mass matrix path = os.path.join(base_path, mass_mat[0][1]) mass_operator = NumpyMatrixOperator.from_file(path) # Obtain initial solution if not given if u0 is None: u_0 = config.items('initial-solution') path = os.path.join(base_path, u_0[0][1]) op = NumpyMatrixOperator.from_file(path) assert isinstance(op._matrix, np.ndarray) u0 = op.with_(matrix=op._matrix.reshape((-1, 1))) # get products if given if 'products' in config.sections(): product = config.items('products') products = {} for i in range(len(product)): product_name = product[i][0] product_path = os.path.join(base_path, product[i][1]) products[product_name] = NumpyMatrixOperator.from_file(product_path) else: products = None # Further specifications if 'time' in config.sections(): if T is None: assert 'T' in config.options('time') T = float(config.get('time', 'T')) if steps is None: assert 'steps' in config.options('time') steps = int(config.get('time', 'steps')) # Use implicit euler time stepper if no time-stepper given if time_stepper is None: time_stepper = ImplicitEulerTimeStepper(steps) else: time_stepper = time_stepper(steps) # Create and return instationary discretization return InstationaryDiscretization(operator=system_lincombOperator, rhs=rhs_lincombOperator, parameter_space=parameter_space, initial_data=u0, T=T, time_stepper=time_stepper, mass=mass_operator, products=products)