5028371039

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Committed by hahnec

Commit Message

fix(fun): consider new stateless function for torch v2.0.1

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71.43

/torchimize/functions/parallel/gda_fun_parallel.py

__author__ = "Christopher Hahne"
__email__ = "inbox@christopherhahne.de"
__license__ = """
    Copyright (c) 2022 Christopher Hahne <inbox@christopherhahne.de>
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
    This program 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 General Public License for more details.
    You should have received a copy of the GNU General Public License
    along with this program. If not, see <http://www.gnu.org/licenses/>.
"""

import torch
from typing import Union, Callable, Tuple, List

from torchimize.functions.jacobian import jacobian_approx_t


def gradient_descent_parallel(
        p: torch.Tensor,
        function: Callable, 
        jac_function: Callable = None,
        args: Union[Tuple, List] = (),
        wvec: torch.Tensor = None,
        ftol: float = 1e-8,
        ptol: float = 1e-8,
        gtol: float = 1e-8,
        l: float = 1.,
        max_iter: int = 100,
    ) -> List[torch.Tensor]:
    """
    Gradient Descent implementation for parallel least-squares fitting of non-linear functions with conditions.

    :param p: initial value(s)
    :param function: user-provided function which takes p (and additional arguments) as input
    :param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
    :param args: optional arguments passed to function
    :param wvec: weights vector used in reduction of multiple costs
    :param ftol: relative change in cost function as stop condition
    :param ptol: relative change in independant variables as stop condition
    :param gtol: maximum gradient tolerance as stop condition
    :param l: step size damping parameter
    :param max_iter: maximum number of iterations
    :return: list of results
    """

    if len(args) > 0:
        # pass optional arguments to function
        fun = lambda p: function(p, *args)
    else:
        fun = function

    if jac_function is None:
        # use numerical Jacobian if analytical is not provided
        jac_fun = lambda p: jacobian_approx_t(p, f=fun)
    else:
        jac_fun = lambda p: jac_function(p, *args)

    assert len(p.shape) == 2, 'parameter tensor is supposed to have 2 dims, but has %s' % str(len(p.shape))

    wvec = torch.ones(1, device=p.device, dtype=p.dtype) if wvec is None else wvec

    p_list = []
    f_prev = torch.zeros(1, device=p.device, dtype=p.dtype)
    while len(p_list) < max_iter:
        p, f, h = newton_raphson_step(p, fun, jac_fun, wvec, l)
        p_list.append(p.clone())
        g = h/l

        # stop conditions
        gcon = torch.max(abs(g)) < gtol
        pcon = (h**2).sum()**.5 < ptol*(ptol + (p**2).sum()**.5)
        fcon = ((f_prev-f)**2).sum() < ((ftol*f)**2).sum() if f_prev.shape == f.shape else False
        f_prev = f.clone()
        
        if gcon or pcon or fcon:
            break

    return p_list


def gradient_descent_parallel_plain(
        p: torch.Tensor,
        function: Callable, 
        jac_function: Callable,
        wvec: torch.Tensor,
        l: float = 1.,
        max_iter: int = 100,
    ) -> torch.Tensor:
    """
    Gradient Descent implementation for parallel least-squares fitting of non-linear functions without conditions.

    :param p: initial value(s)
    :param function: user-provided function which takes p (and additional arguments) as input
    :param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
    :param wvec: weights vector used in reduction of multiple costs
    :param l: step size damping parameter
    :param max_iter: maximum number of iterations
    :return: result
    """

    for _ in range(max_iter):
        p = newton_raphson_step(p, function=function, jac_function=jac_function, wvec=wvec, l=l)[0]

    return p


def newton_raphson_step(
        p: torch.Tensor,
        function: Callable,
        jac_function: Callable,
        wvec: torch.Tensor,
        l: float = 1.,
    ) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
    """
    Gradient Descent step function for parallel least-squares fitting of non-linear functions

    :param p: current guess
    :param function: user-provided function which takes p (and additional arguments) as input
    :param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
    :param wvec: weights vector used in reduction of multiple costs
    :param l: step size damping parameter
    :return: list of results
    """

    fc = function(p)
    jc = jac_function(p)
    f = torch.einsum('bcp,c->bp', fc, wvec)
    j = torch.einsum('bcpi,c->bpi', jc, wvec)
    try:
        h = torch.linalg.lstsq(j.double(), f.double(), rcond=None, driver=None)[0].to(dtype=p.dtype)
    except torch._C._LinAlgError:
        jmin_rank = min(j.shape[1:])
        rank_mask = torch.linalg.matrix_rank(j) < jmin_rank
        j[rank_mask] = torch.eye(*j.shape[1:], dtype=j.dtype, device=j.device)
        h = torch.linalg.lstsq(j.double(), f.double(), rcond=None, driver=None)[0].to(dtype=p.dtype)

    p -= l*h

    return p, f, h

1	__author__ = "Christopher Hahne"	3✔
2	__email__ = "inbox@christopherhahne.de"	3✔
3	__license__ = """	3✔
4	Copyright (c) 2022 Christopher Hahne <inbox@christopherhahne.de>
5	This program is free software: you can redistribute it and/or modify
6	it under the terms of the GNU General Public License as published by
7	the Free Software Foundation, either version 3 of the License, or
8	(at your option) any later version.
9	This program is distributed in the hope that it will be useful,
10	but WITHOUT ANY WARRANTY; without even the implied warranty of
11	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12	GNU General Public License for more details.
13	You should have received a copy of the GNU General Public License
14	along with this program. If not, see <http://www.gnu.org/licenses/>.
15	"""
16
17	import torch	3✔
18	from typing import Union, Callable, Tuple, List	3✔
19
20	from torchimize.functions.jacobian import jacobian_approx_t	3✔
21
22
23	def gradient_descent_parallel(	3✔
24	p: torch.Tensor,
25	function: Callable,
26	jac_function: Callable = None,
27	args: Union[Tuple, List] = (),
28	wvec: torch.Tensor = None,
29	ftol: float = 1e-8,
30	ptol: float = 1e-8,
31	gtol: float = 1e-8,
32	l: float = 1.,
33	max_iter: int = 100,
34	) -> List[torch.Tensor]:
35	"""
36	Gradient Descent implementation for parallel least-squares fitting of non-linear functions with conditions.
37
38	:param p: initial value(s)
39	:param function: user-provided function which takes p (and additional arguments) as input
40	:param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
41	:param args: optional arguments passed to function
42	:param wvec: weights vector used in reduction of multiple costs
43	:param ftol: relative change in cost function as stop condition
44	:param ptol: relative change in independant variables as stop condition
45	:param gtol: maximum gradient tolerance as stop condition
46	:param l: step size damping parameter
47	:param max_iter: maximum number of iterations
48	:return: list of results
49	"""
50
51	if len(args) > 0:	3!
52	# pass optional arguments to function
53	fun = lambda p: function(p, *args)	3✔
54	else:
55	fun = function	×
56
57	if jac_function is None:	3!
58	# use numerical Jacobian if analytical is not provided
59	jac_fun = lambda p: jacobian_approx_t(p, f=fun)	×
60	else:
61	jac_fun = lambda p: jac_function(p, *args)	3✔
62
63	assert len(p.shape) == 2, 'parameter tensor is supposed to have 2 dims, but has %s' % str(len(p.shape))	3✔
64
65	wvec = torch.ones(1, device=p.device, dtype=p.dtype) if wvec is None else wvec	3✔
66
67	p_list = []	3✔
68	f_prev = torch.zeros(1, device=p.device, dtype=p.dtype)	3✔
69	while len(p_list) < max_iter:	3✔
70	p, f, h = newton_raphson_step(p, fun, jac_fun, wvec, l)	3✔
71	p_list.append(p.clone())	3✔
72	g = h/l	3✔
73
74	# stop conditions
75	gcon = torch.max(abs(g)) < gtol	3✔
76	pcon = (h2).sum().5 < ptol(ptol + (p2).sum()*.5)	3✔
77	fcon = ((f_prev-f)*2).sum() < ((ftolf)**2).sum() if f_prev.shape == f.shape else False	3✔
78	f_prev = f.clone()	3✔
79
80	if gcon or pcon or fcon:	3!
81	break	×
82
83	return p_list	3✔
84
85
86	def gradient_descent_parallel_plain(	3✔
87	p: torch.Tensor,
88	function: Callable,
89	jac_function: Callable,
90	wvec: torch.Tensor,
91	l: float = 1.,
92	max_iter: int = 100,
93	) -> torch.Tensor:
94	"""
95	Gradient Descent implementation for parallel least-squares fitting of non-linear functions without conditions.
96
97	:param p: initial value(s)
98	:param function: user-provided function which takes p (and additional arguments) as input
99	:param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
100	:param wvec: weights vector used in reduction of multiple costs
101	:param l: step size damping parameter
102	:param max_iter: maximum number of iterations
103	:return: result
104	"""
105
106	for _ in range(max_iter):	×
107	p = newton_raphson_step(p, function=function, jac_function=jac_function, wvec=wvec, l=l)[0]	×
108
109	return p	×
110
111
112	def newton_raphson_step(	3✔
113	p: torch.Tensor,
114	function: Callable,
115	jac_function: Callable,
116	wvec: torch.Tensor,
117	l: float = 1.,
118	) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
119	"""
120	Gradient Descent step function for parallel least-squares fitting of non-linear functions
121
122	:param p: current guess
123	:param function: user-provided function which takes p (and additional arguments) as input
124	:param jac_fun: user-provided Jacobian function which takes p (and additional arguments) as input
125	:param wvec: weights vector used in reduction of multiple costs
126	:param l: step size damping parameter
127	:return: list of results
128	"""
129
130	fc = function(p)	3✔
131	jc = jac_function(p)	3✔
132	f = torch.einsum('bcp,c->bp', fc, wvec)	3✔
133	j = torch.einsum('bcpi,c->bpi', jc, wvec)	3✔
134	try:	3✔
135	h = torch.linalg.lstsq(j.double(), f.double(), rcond=None, driver=None)[0].to(dtype=p.dtype)	3✔
136	except torch._C._LinAlgError:	×
137	jmin_rank = min(j.shape[1:])	×
138	rank_mask = torch.linalg.matrix_rank(j) < jmin_rank	×
139	j[rank_mask] = torch.eye(*j.shape[1:], dtype=j.dtype, device=j.device)	×
140	h = torch.linalg.lstsq(j.double(), f.double(), rcond=None, driver=None)[0].to(dtype=p.dtype)	×
141
142	p -= l*h	3✔
143
144	return p, f, h	3✔

hahnec / torchimize / 5028371039

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