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source: orxonox.OLD/trunk/src/lib/math/matrix.cc @ 5666

Last change on this file since 5666 was 5666, checked in by patrick, 19 years ago

trunk/math: working on eigenvectors, almost got it

File size: 3.3 KB
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1
2#include <stdio.h>
3#include <math.h>
4#include "matrix.h"
5
6
7Vector Matrix::eigenValues() const
8{
9  Vector eigVl;
10
11  float a = 0;
12  float b = 0;
13
14  float c[3];
15
16  // c[0] is the determinante of mat
17  c[0] = this->m11 * this->m22 * this->m33 +
18      2* this->m12 * this->m13 * this->m23 -
19      this->m11 * this->m23 * this->m23 -
20      this->m22 * this->m13 * this->m13 -
21      this->m33 * this->m12 * this->m12;
22
23  // c[1] is the trace of a
24  c[1] = this->m11 * this->m22 -
25      this->m12 * this->m12 +
26      this->m11 * this->m33 -
27      this->m13 * this->m13 +
28      this->m22 * this->m33 -
29      this->m23 * this->m23;
30
31  // c[2] is the sum of the diagonal elements
32  c[2] = this->m11 +
33      this->m22 +
34      this->m33;
35
36
37  // Computing the roots:
38  a = (3.0*c[1] - c[2]*c[2]) / 3.0;
39  b = (-2.0*c[2]*c[2]*c[2] + 9.0*c[1]*c[2] - 27.0*c[0]) / 27.0;
40
41  float Q = b*b/4.0 + a*a*a/27.0;
42
43  // 3 distinct Roots
44  if (Q < 0)
45  {
46    printf("good\n");
47    float psi = atan2(sqrt(-Q), -b/2.0);
48    float p = sqrt((b/2.0)*(b/2.0) - Q);
49
50    eigVl.x = c[2]/3.0 + 2 * pow(p, 1/3.0) * cos(psi/3.0);
51    eigVl.y = c[2]/3.0 - pow(p, 1/3.0) * (cos(psi/3.0)
52        + sqrt(3.0) * sin(psi/3.0));
53    eigVl.z = c[2]/3.0 - pow(p, 1/3.0) * (cos(psi/3.0)
54        - sqrt(3.0) * sin(psi/3.0));
55
56  }
57  // 2 Distinct Roots
58  else if (Q == 0)
59  {
60    eigVl.x = c[2]/3.0 + pow(b/2.0, 1.0/3.0);
61    eigVl.y = c[2]/3.0 + pow(b/2.0, 1.0/3.0);
62    eigVl.z = c[2]/3.0 + 2* pow(b/2.0, 1.0/3.0);
63  }
64  // 1 Root (not calculating anything.)
65  else if (Q > 0)
66  {
67    printf("A is multiple of Identity matrix (lambda * I3))\n");
68    eigVl.x = eigVl.y = eigVl.z = 1;
69  }
70  printf("%f %f %f\n", eigVl.x, eigVl.y, eigVl.z);
71  return eigVl;
72
73}
74
75void Matrix::eigenVectors(Vector& a, Vector& b, Vector& c) const
76{
77  Vector eigVl = this->eigenValues();
78
79  float eigVc[9];
80  // EigenVectors
81  for (int i = 0; i < 3; ++i)
82  {
83    printf (":: i = %d\n", i);
84    Matrix M = *this -  Matrix::identity() * eigVl.x;
85    Vector m1, m2, m3;
86
87    M.getTransposed().toVectors(m1, m2, m3);
88
89    Vector u1, u2, u3;
90
91    u1 = m2.cross(m3); u1 /= u1.len();
92    u2 = m3.cross(m1); u2 /= u2.len();
93    u3 = m1.cross(m2); u3 /= u3.len();
94
95    printf("%f, %f, %f\n", u1.x, u1.y, u1.z);
96    printf("%f, %f, %f\n", u2.x, u2.y, u2.z);
97    printf("%f, %f, %f\n", u3.x, u3.y, u3.z);
98
99//     u1 = M*u1;
100//     u2 = M*u2;
101//     u3 = M*u3;
102    //
103//     printf("%f, %f, %f\n", u1.x, u1.y, u1.z);
104//     printf("%f, %f, %f\n", u2.x, u2.y, u2.z);
105//     printf("%f, %f, %f\n", u3.x, u3.y, u3.z);
106//     printf("\n\n");
107  }
108
109  Vector eigVc[3];
110  /* eigenvec test */
111  for(int i = 0; i < 3; i++)
112  {
113    eigVc[i].x =-1/this->m13*(this->m33 - eigValue[i]) + (this->m32*(-this->m31*this->m32 + this->m12*this->m33 - this->m12*eigValue[i])) /
114        this->m13*(-this->m13*this->m22 - this->m12*this->m23 + this->m13*eigValue[i]);
115    eigVc[i].y = -( -this->m13*this->m23 + this->m12*this->m33 - this->m12*eigValue[i]) /
116        (-this->m31*this->m22 + this->m12*this->m23 + this->m13*eigValue[i]);
117    eigVc[i].z = 1.0f;
118
119
120    printf("home brewn: %f, %f, %f\n", eigVc[i].x, eigVc[i].y, eigVc[i].z);
121
122  }
123
124
125
126  this->debug();
127}
128
129
130void Matrix::debug() const
131{
132  printf("input: | %f | %f | %f |\n", this->m11, this->m12, this->m13 );
133  printf("       | %f | %f | %f |\n", this->m21, this->m22, this->m23 );
134  printf("       | %f | %f | %f |\n", this->m31, this->m32, this->m33 );
135
136}
137
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