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
|
#
# ev.m
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
L = [
2, -1, 0, -1, 0;
-1, 4, -1, -1, -1;
0, -1, 2, 0, -1;
-1, -1, 0, 3, -1;
0, -1, -1, -1, 3
];
[v, lambda] = eig(L);
function knoten(fn, wert, punkt)
if (wert > 0)
farbe = sprintf("red!%02d", round(100 * wert));
else
farbe = sprintf("blue!%02d", round(-100 * wert));
end
fprintf(fn, "\t\\fill[color=%s] %s circle[radius=0.25];\n",
farbe, punkt);
fprintf(fn, "\t\\draw %s circle[radius=0.25];\n", punkt);
endfunction
function vektor(fn, v, name, lambda)
fprintf(fn, "\\def\\%s{\n", name);
fprintf(fn, "\t\\coordinate (A) at ({0*\\a},0);\n");
fprintf(fn, "\t\\coordinate (B) at ({1*\\a},0);\n");
fprintf(fn, "\t\\coordinate (C) at ({2*\\a},0);\n");
fprintf(fn, "\t\\coordinate (D) at ({0.5*\\a},{-\\b});\n");
fprintf(fn, "\t\\coordinate (E) at ({1.5*\\a},{-\\b});\n");
fprintf(fn, "\t\\draw (A) -- (B);\n");
fprintf(fn, "\t\\draw (A) -- (D);\n");
fprintf(fn, "\t\\draw (B) -- (C);\n");
fprintf(fn, "\t\\draw (B) -- (D);\n");
fprintf(fn, "\t\\draw (B) -- (E);\n");
fprintf(fn, "\t\\draw (C) -- (E);\n");
fprintf(fn, "\t\\draw (D) -- (E);\n");
fprintf(fn, "\t\\node at (-2.8,{-0.5*\\b}) [right] {$\\lambda=%.4f$};\n",
round(1000 * abs(lambda)) / 10000);
w = v / max(abs(v));
knoten(fn, w(1,1), "(A)");
knoten(fn, w(2,1), "(B)");
knoten(fn, w(3,1), "(C)");
knoten(fn, w(4,1), "(D)");
knoten(fn, w(5,1), "(E)");
fprintf(fn, "}\n");
endfunction
function punkt(fn, x, wert)
fprintf(fn, "({%.4f*\\c},{%.4f*\\d})", x, wert);
endfunction
function funktion(fn, v, name, lambda)
fprintf(fn, "\\def\\%s{\n", name);
fprintf(fn, "\t\\draw[color=red,line width=1.4pt]\n\t\t");
punkt(fn, -2, v(1,1));
fprintf(fn, " --\n\t\t");
punkt(fn, -1, v(4,1));
fprintf(fn, " --\n\t\t");
punkt(fn, 0, v(2,1));
fprintf(fn, " --\n\t\t");
punkt(fn, 1, v(5,1));
fprintf(fn, " --\n\t\t");
punkt(fn, 2, v(3,1));
fprintf(fn, ";\n");
fprintf(fn, "\t\\draw[->] ({-2.1*\\c},0) -- ({2.1*\\c},0);\n");
fprintf(fn, "\t\\draw[->] (0,{-1.1*\\d}) -- (0,{1.1*\\d});\n");
for x = (-2:2)
fprintf(fn, "\t\\fill ({%d*\\c},0) circle[radius=0.05];\n", x);
endfor
fprintf(fn, "}\n");
endfunction
fn = fopen("vektoren.tex", "w");
vektor(fn, v(:,1), "vnull", lambda(1,1));
funktion(fn, v(:,1), "fnull", lambda(1,1));
vektor(fn, v(:,2), "vone", lambda(2,2));
funktion(fn, v(:,2), "fone", lambda(2,2));
vektor(fn, v(:,3), "vtwo", lambda(3,3));
funktion(fn, v(:,3), "ftwo", lambda(3,3));
vektor(fn, v(:,4), "vthree", lambda(4,4));
funktion(fn, v(:,4), "fthree", lambda(4,4));
vektor(fn, v(:,5), "vfour", lambda(5,5));
funktion(fn, v(:,5), "ffour", lambda(5,5));
fclose(fn);
|
