Bullet Collision Detection & Physics Library: btConjugateGradient.h Source File

Bullet Collision Detection & Physics Library

btConjugateGradient.h
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1 /*
2 Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
3
4 Bullet Continuous Collision Detection and Physics Library
5 Copyright (c) 2019 Google Inc. http://bulletphysics.org
6 This software is provided 'as-is', without any express or implied warranty.
7 In no event will the authors be held liable for any damages arising from the use of this software.
8 Permission is granted to anyone to use this software for any purpose,
9 including commercial applications, and to alter it and redistribute it freely,
10 subject to the following restrictions:
11 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
12 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
13 3. This notice may not be removed or altered from any source distribution.
14 */
15
16 #ifndef BT_CONJUGATE_GRADIENT_H
17 #define BT_CONJUGATE_GRADIENT_H
18 #include <iostream>
19 #include <cmath>
20 #include <limits>
21 #include <LinearMath/btAlignedObjectArray.h>
22 #include <LinearMath/btVector3.h>
23 #include "LinearMath/btQuickprof.h"
24 template <class MatrixX>
25 class btConjugateGradient
26 {
27 typedef btAlignedObjectArray<btVector3> TVStack;
28 TVStack r,p,z,temp;
29 int max_iterations;
30 btScalar tolerance_squared;
31 public:
32 btConjugateGradient(const int max_it_in)
33 : max_iterations(max_it_in)
34 {
35 tolerance_squared = 1e-5;
36 }
37
38 virtual ~btConjugateGradient(){}
39
40 // return the number of iterations taken
41 int solve(MatrixX& A, TVStack& x, const TVStack& b, bool verbose = false)
42 {
43 BT_PROFILE("CGSolve");
44 btAssert(x.size() == b.size());
45 reinitialize(b);
46 // r = b - A * x --with assigned dof zeroed out
47 A.multiply(x, temp);
48 r = sub(b, temp);
49 A.project(r);
50 // z = M^(-1) * r
51 A.precondition(r, z);
52 A.project(z);
53 btScalar r_dot_z = dot(z,r);
54 if (r_dot_z <= tolerance_squared) {
55 if (verbose)
56 {
57 std::cout << "Iteration = 0" << std::endl;
58 std::cout << "Two norm of the residual = " << r_dot_z << std::endl;
59 }
60 return 0;
61 }
62 p = z;
63 btScalar r_dot_z_new = r_dot_z;
64 for (int k = 1; k <= max_iterations; k++) {
65 // temp = A*p
66 A.multiply(p, temp);
67 A.project(temp);
68 if (dot(p,temp) < SIMD_EPSILON)
69 {
70 if (verbose)
71 std::cout << "Encountered negative direction in CG!" << std::endl;
72 if (k == 1)
73 {
74 x = b;
75 }
76 return k;
77 }
78 // alpha = r^T * z / (p^T * A * p)
79 btScalar alpha = r_dot_z_new / dot(p, temp);
80 // x += alpha * p;
81 multAndAddTo(alpha, p, x);
82 // r -= alpha * temp;
83 multAndAddTo(-alpha, temp, r);
84 // z = M^(-1) * r
85 A.precondition(r, z);
86 r_dot_z = r_dot_z_new;
87 r_dot_z_new = dot(r,z);
88 if (r_dot_z_new < tolerance_squared) {
89 if (verbose)
90 {
91 std::cout << "ConjugateGradient iterations " << k << std::endl;
92 }
93 return k;
94 }
95
96 btScalar beta = r_dot_z_new/r_dot_z;
97 p = multAndAdd(beta, p, z);
98 }
99 if (verbose)
100 {
101 std::cout << "ConjugateGradient max iterations reached " << max_iterations << std::endl;
102 }
103 return max_iterations;
104 }
105
106 void reinitialize(const TVStack& b)
107 {
108 r.resize(b.size());
109 p.resize(b.size());
110 z.resize(b.size());
111 temp.resize(b.size());
112 }
113
114 TVStack sub(const TVStack& a, const TVStack& b)
115 {
116 // c = a-b
117 btAssert(a.size() == b.size());
118 TVStack c;
119 c.resize(a.size());
120 for (int i = 0; i < a.size(); ++i)
121 {
122 c[i] = a[i] - b[i];
123 }
124 return c;
125 }
126
127 btScalar squaredNorm(const TVStack& a)
128 {
129 return dot(a,a);
130 }
131
132 btScalar dot(const TVStack& a, const TVStack& b)
133 {
134 btScalar ans(0);
135 for (int i = 0; i < a.size(); ++i)
136 ans += a[i].dot(b[i]);
137 return ans;
138 }
139
140 void multAndAddTo(btScalar s, const TVStack& a, TVStack& result)
141 {
142 // result += s*a
143 btAssert(a.size() == result.size());
144 for (int i = 0; i < a.size(); ++i)
145 result[i] += s * a[i];
146 }
147
148 TVStack multAndAdd(btScalar s, const TVStack& a, const TVStack& b)
149 {
150 // result = a*s + b
151 TVStack result;
152 result.resize(a.size());
153 for (int i = 0; i < a.size(); ++i)
154 result[i] = s * a[i] + b[i];
155 return result;
156 }
157 };
158 #endif /* btConjugateGradient_h */
SIMD_EPSILON
#define SIMD_EPSILON
Definition: btScalar.h:543
btScalar
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
Definition: btScalar.h:314
btConjugateGradient::p
TVStack p
Definition: btConjugateGradient.h:28
btConjugateGradient::solve
int solve(MatrixX &A, TVStack &x, const TVStack &b, bool verbose=false)
Definition: btConjugateGradient.h:41
btConjugateGradient::btConjugateGradient
btConjugateGradient(const int max_it_in)
Definition: btConjugateGradient.h:32
btConjugateGradient::temp
TVStack temp
Definition: btConjugateGradient.h:28
btConjugateGradient
Definition: btConjugateGradient.h:26
btConjugateGradient::r
TVStack r
Definition: btConjugateGradient.h:28
btVector3.h
btAssert
#define btAssert(x)
Definition: btScalar.h:153
btConjugateGradient::tolerance_squared
btScalar tolerance_squared
Definition: btConjugateGradient.h:30
btAlignedObjectArray::resize
void resize(int newsize, const T &fillData=T())
Definition: btAlignedObjectArray.h:203
btConjugateGradient::max_iterations
int max_iterations
Definition: btConjugateGradient.h:29
btConjugateGradient::z
TVStack z
Definition: btConjugateGradient.h:28
btConjugateGradient::reinitialize
void reinitialize(const TVStack &b)
Definition: btConjugateGradient.h:106
btAlignedObjectArray< btVector3 >
btConjugateGradient::sub
TVStack sub(const TVStack &a, const TVStack &b)
Definition: btConjugateGradient.h:114
btConjugateGradient::multAndAddTo
void multAndAddTo(btScalar s, const TVStack &a, TVStack &result)
Definition: btConjugateGradient.h:140
btConjugateGradient::multAndAdd
TVStack multAndAdd(btScalar s, const TVStack &a, const TVStack &b)
Definition: btConjugateGradient.h:148
btConjugateGradient::squaredNorm
btScalar squaredNorm(const TVStack &a)
Definition: btConjugateGradient.h:127
btQuickprof.h
btConjugateGradient::dot
btScalar dot(const TVStack &a, const TVStack &b)
Definition: btConjugateGradient.h:132
btAlignedObjectArray.h
btConjugateGradient::TVStack
btAlignedObjectArray< btVector3 > TVStack
Definition: btConjugateGradient.h:27
btConjugateGradient::~btConjugateGradient
virtual ~btConjugateGradient()
Definition: btConjugateGradient.h:38
BT_PROFILE
#define BT_PROFILE(name)
Definition: btQuickprof.h:198
btAlignedObjectArray::size
int size() const
return the number of elements in the array
Definition: btAlignedObjectArray.h:142