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nonlinear_eigenproblem.py
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Sun, Apr 28, 02:24

nonlinear_eigenproblem.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import numpy as np
import scipy.linalg as scla
#import scipy.sparse as scsp
from rrompy.utilities.base.types import Tuple, List, Np1D, Np2D
from .custom_pinv import customPInv
__all__ = ['linearizeDense', 'eigNonlinearDense', 'eigvalsNonlinearDense']
def linearizeDense(As:List[Np2D], jSupp : int = 1) -> Tuple[Np2D, Np2D]:
N = len(As)
n = As[0].shape[0]
stiff = np.zeros(((N - 1) * n, (N - 1) * n), dtype = As[0].dtype)
mass = np.zeros(((N - 1) * n, (N - 1) * n), dtype = As[0].dtype)
if N > 1:
if isinstance(jSupp, str) and jSupp.upper() == "COMPANION":
II = np.arange(n, (N - 1) * n)
stiff = np.pad(- np.hstack(As[-2 :: -1]),
[[0, (N - 2) * n], [0, 0]], "constant")
stiff[II, II - n] = 1.
mass = np.pad(As[-1], [0, (N - 2) * n], "constant")
mass[II, II] = 1.
else:
for j in range(jSupp):
for k in range(jSupp - j - 1, jSupp):
mass[n * j : n * (j + 1), k * n : (k + 1) * n] = \
As[N - 2 + jSupp - k - j]
for j in range(jSupp - 1, N - 1):
for k in range(jSupp, N - 1 + jSupp - j):
stiff[n * j : n * (j + 1), (k - 1) * n : k * n] = \
- As[jSupp - k + N - 2 - j]
stiff[: n * (jSupp - 1), : n * (jSupp - 1)] = \
mass[: n * (jSupp - 1), n : n * jSupp]
mass[n * jSupp :, n * jSupp :] = stiff[n * (jSupp - 1) : - n,
n * jSupp :]
return stiff, mass
def eigNonlinearDense(As:List[Np2D], jSupp : int = 1,
return_inverse : bool = False,
**kwargs_eig) -> Tuple[Np1D, Np2D]:
stiff, mass = linearizeDense(As, jSupp)
if stiff.shape[0] == 0: return stiff, stiff
ev, P = scla.eig(stiff, mass, overwrite_a = True, overwrite_b = True,
**kwargs_eig)
if not return_inverse: return ev, P
Pinv = customPInv(P)
return ev, P, Pinv
def eigvalsNonlinearDense(As:List[Np2D], jSupp : int = 1,
**kwargs_eigvals) -> Np1D:
stiff, mass = linearizeDense(As, jSupp)
if stiff.shape[0] == 0: return stiff
return scla.eigvals(stiff, mass, overwrite_a = True, **kwargs_eigvals)
#def linearizeSparse(As:List[Np2D], jSupp : int = 1) -> Tuple[Np2D, Np2D]:
# N = len(As)
# n = As[0].shape[0]
# if isinstance(jSupp, str) and jSupp.upper() == "COMPANION":
# II = np.arange(n, (N - 1) * n)
# III = np.arange((N - 2) * n + 1)
# IIII = np.arange(0, n ** 2, n)
# improve management of sparse As...
# Alist = - np.hstack([A.todense() for A in As[-2 :: -1]])
# stiffD = np.concatenate((Alist.flatten(), np.ones((N - 2) * n)))
# stiffP = np.concatenate(((N - 1) * IIII, (N - 1) * n ** 2 + III))
# stiffI = np.concatenate((np.tile(np.arange((N - 1) * n), n), II - n))
# massD = np.concatenate((As[-1].todense().flatten(),
# np.ones((N - 2) * n)))
# massP = np.concatenate((IIII, n ** 2 + III))
# massI = np.concatenate((np.tile(np.arange(n), n), II))
# else:
# compute stiffD, stiffP, stiffI depending on jSupp
# compute massD, massP, massI depending on jSupp
# stiff = scsp.csr_matrix((stiffD, stiffI, stiffP),
# shape = ((N - 1) * n, (N - 1) * n))
# mass = scsp.csr_matrix((massD, massI, massP),
# shape = ((N - 1) * n, (N - 1) * n))
# return stiff, mass
#
#def eigNonlinearSparse(As:List[Np2D], jSupp : int = 1,
# return_inverse : bool = False,
# **kwargs_eig) -> Tuple[Np1D, Np2D]:
# stiff, mass = linearizeSparse(As, jSupp)
# ev, P = scsp.linalg.eig(stiff, M = mass, return_eigenvectors = True,
# **kwargs_eig)
# if not return_inverse: return ev, P
# Pinv = customPInv(P)
# return ev, P, Pinv
#
#def eigvalsNonlinearSparse(As:List[Np2D], jSupp : int = 1,
# **kwargs_eigvals) -> Np1D:
# stiff, mass = linearizeSparse(As, jSupp)
# return scsp.linalg.eig(stiff, M = mass, return_eigenvectors = False,
# **kwargs_eigvals)

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