1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
|
#
# This file is part of CasADi.
#
# CasADi -- A symbolic framework for dynamic optimization.
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl,
# KU Leuven. All rights reserved.
# Copyright (C) 2011-2014 Greg Horn
#
# CasADi 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.
#
# CasADi 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 CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
from casadi import *
# Read all about coloring in the seminal paper "What color is your Jacobian?" http://www.cs.odu.edu/~pothen/Papers/sirev2005.pdf
def color(A):
print("="*80)
print("Original:")
print(repr(DM(A,1)))
print("Colored: ")
print(repr(DM(A.uni_coloring(),1)))
A = Sparsity.diag(5)
color(A)
# One direction needed to capture all
color(Sparsity.dense(5,10))
# We need 5 directions.
# The colored response reads: each row corresponds to a direction;
# each column correspond to a row of the original matrix.
color(A+Sparsity.triplet(5,5,[0],[4]))
# First 4 rows can be taken together, the fifth row is taken separately
color(A+Sparsity.triplet(5,5,[4],[0]))
# First 4 rows can be taken together, the fifth row is taken separately
color(A+Sparsity.triplet(5,5,[0]*5,list(range(5))))
# The first row is taken separately.
# The remainding rows are lumped together in one direction.
color(A+Sparsity.triplet(5,5,list(range(5)),[0]*5))
# We need 5 directions.
# Next, we look at star_coloring
def color(A):
print("="*80)
print("Original:")
print(repr(DM(A,1)))
print("Star colored: ")
print(repr(DM(A.star_coloring(1),1)))
color(A)
# One direction needed to capture all
color(Sparsity.dense(5,5))
# We need 5 directions.
color(A+Sparsity.triplet(5,5,[0]*5,list(range(5)))+Sparsity.triplet(5,5,list(range(5)),[0]*5))
# The first row/col is taken separately.
# The remainding rows/cols are lumped together in one direction.
# Let's take an example from the paper
A = DM([[1,1,0,0,0,0],[1,1,1,0,1,1],[0,1,1,1,0,0],[0,0,1,1,0,1],[0,1,0,0,1,0],[0,1,0,1,0,1]])
A = sparsify(A)
color(A.sparsity())
|
