"git@gitlab.mn.tu-dresden.de:osander/dune-gfe.git" did not exist on "121bc4feaa487f6ac3cbeee02edc340321818cdb"
Newer
Older
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
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
clear all
clc
% --- Change PolynomialDisplayStyle ----
% sympref('PolynomialDisplayStyle','ascend');
% sympref('AbbreviateOutput',false);
syms f_plus(v1,v2,q1,q2,q3,b1,b2,b3)
assume( q1 > 0)
assume( q2 > 0)
assume( q3 > 0)
% assume(q3 == q1);
assume(q3 >= q1)
assume(q2 >= q3)
v = [v1; v2];
%should be sqrt(2) instead of 2!
f_plus(v1,v2,q1,q2,q3,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2-2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2);
f_minus(v1,v2,q1,q2,q3,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2+2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2);
% ---- Fix parameters
% f_plus = subs(f_plus,b3,0) % set b3
% f_plus = subs(f_plus,q3,q1)
% f_plus = subs(f_plus,q1,40);
% f_plus = subs(f_plus,q3,63.9);
% f_plus = subs(f_plus,q2,34.9);
% f_plus = subs(f_plus,b1,4);
% f_plus = subs(f_plus,b2,2.4);
% f_plus = subs(f_plus,b3,2.4);
% f_plus = subs(f_plus,q1,40);
% f_plus = subs(f_plus,q3,20);
% f_plus = subs(f_plus,q2,50);
% f_plus = subs(f_plus,b1,5);
% f_plus = subs(f_plus,b2,6);
% f_plus = subs(f_plus,b3,7);
f_plus = subs(f_plus,q1,40);
f_plus = subs(f_plus,q3,63.9);
f_plus = subs(f_plus,q2,70);
rndm1 = randi([1 20],1,1);
rndm2 = randi([1 20],1,1);
rndm3 = randi([1 20],1,1);
f_plus = subs(f_plus,b1,rndm1);
f_plus = subs(f_plus,b2,rndm2);
f_plus = subs(f_plus,b3,rndm3);
f_minus = subs(f_minus,q1,40);
f_minus = subs(f_minus,q3,63.9);
f_minus = subs(f_minus,q2,70);
f_minus = subs(f_minus,b1,rndm1);
f_minus = subs(f_minus,b2,rndm2);
f_minus = subs(f_minus,b3,rndm3);
% Compute Gradient
df_plusx = diff(f_plus,v1);
df_plusy = diff(f_plus,v2);
df_minusx = diff(f_minus,v1);
df_minusy = diff(f_minus,v2);
eq1 = df_plusx == 0;
eq2 = df_plusy == 0;
eqns = [eq1, eq2]
eq3 = df_minusx == 0;
eq4 = df_minusy == 0;
eqns_minus = [eq3, eq4]
S = solve(eqns,v1,v2,'MaxDegree' , 5, 'Real', true);
S_minus = solve(eqns_minus,v1,v2,'MaxDegree' , 5, 'Real', true);
% S = solve(eqns,v1,v2,'MaxDegree' , 5);
% S = solve(eqns,v1,v2,'MaxDegree' , 5, 'IgnoreAnalyticConstraints',true);
% S = solve(eqns,v1,v2,'MaxDegree' , 5, 'IgnoreAnalyticConstraints',true, 'Real', true);
% S = solve(eqns)
A = S.v1;
B = S.v2;
A_minus = S_minus.v1;
B_minus = S_minus.v2;
% A = simplify(A);
% B = simplify(B)
% S_minus = solve(eqns_minus,v1,v2);
% S_minus.v1
% S_minus.v2
%---------- TEST ---------------------
% r = subs(subs(df_plusx,v1,A(3)),v2,B(3));
fprintf('Testing equation grad(f) = 0 with stationary points')
double(subs(subs(df_plusx,v1,A(1)),v2,B(1)))
double(subs(subs(df_plusx,v1,A(2)),v2,B(2)))
double(subs(subs(df_plusx,v1,A(3)),v2,B(3)))
% ------------------------------------
fprintf('print stationary points of f_plus:')
double(A)
double(B)
fprintf('print stationary points of f_minus:')
double(A_minus)
double(B_minus)
% determine global Minimizer from stationary points:
fprintf('function values at stationary points:')
T = arrayfun(@(v1,v2) double(f_plus(v1,v2,q1,q2,q3,b1,b2,b3)),A,B,'UniformOutput', false)
T = cell2mat(T);
Min_plus = min(T, [], 'all')
% determine global Minimizer from stationary points:
fprintf('function values at stationary points:')
T_minus = arrayfun(@(v1,v2) double(f_minus(v1,v2,q1,q2,q3,b1,b2,b3)),A_minus,B_minus,'UniformOutput', false)
T_minus = cell2mat(T_minus);
Min_minus = min(T_minus, [], 'all')
globalMinimizerValue = min(Min_plus,Min_minus)
% Plot function
fsurf(@(x,y) f_plus(x,y,q1,q2,q3,b1,b2,b3))
hold on
plot3(A,B,T,'g*')
% view(90,0)
% view(2)
figure
fsurf(@(x,y) f_minus(x,y,q1,q2,q3,b1,b2,b3))
hold on
plot3(A_minus,B_minus,T,'g*')
%Write to txt-File
fileID = fopen('txt.txt','w');
fprintf(fileID,'%s' , latex(S.v1));
fclose(fileID);