├── LICENSE ├── README.md ├── SE3Comp.py ├── SE3CompTest.ipynb └── SE3CompTest.py /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | This PyTorch SE3 composition layer implementation is being inspired by [Torch gvnn ](https://github.com/ankurhanda/gvnn). 2 | Thanks for the advice from Ankur Handa @ankurhanda (https://github.com/ankurhanda)(The author of gvnn). 3 | 4 | Please cite 5 | ``` 6 | @misc{JackyLiuSE3comp18, 7 | author = {Tse-An (Jacky) Liu}, 8 | doi = {10.5281/zenodo.1304166}, 9 | title = {se3comp pytorch}, 10 | year = {2018}, 11 | publisher = {GitHub}, 12 | journal = {GitHub repository}, 13 | howpublished = {\url{https://github.com/HTLife/se3comp_pytorch}} 14 | } 15 | ``` 16 | 17 | ## SE3 composition layer 18 | 19 | Purpose: Compose **global pose Tg** with **related pose xi** 20 | 21 | * **Tg** is a SE3 pose represented with 7 parameters (x, y, z, ww, wx, wy, wz) 22 | * **xi** is a se3 pose represented with 6 parameters (rho1, rho2, rho3, omega_x, omega_y, omega_z) 23 | * Tutorial of lie group SE3: http://ethaneade.com/lie.pdf 24 | 25 | 26 | **Txi**: 4x4 Matrix of the exponential mapping of **xi** (lie.pdf Eqation.84) 27 | **Tg_matrix**: Tg represented in matrix form 28 | **T_composed**: The pose calculated by matrix multiplication of Txi and Tg_matrix 29 | ``` 30 | T_composed = Txi (dot) Tg_matrix 31 | ``` 32 | 33 | 34 | ## Some implementation story 35 | 36 | In [VINet](https://arxiv.org/abs/1701.08376)[1], the author described a important structure called **SE3 composition layer** (Figure.2 in VINet). However, they do not describe this structure in detail. I found some related statement in [2] page.9(which is a journal paper from the same advisor). In this journal paper, I found that gvnn[3] might be their reference of implementing SE3 composition layer. 37 | 38 | Unfortunately, [the source code of gvnn](https://github.com/ankurhanda/gvnn) is written by torch-lua. After taking the kind advice from Ankur Handa, I finished implementing this PyTorch SE3 composition layer. 39 | 40 | 41 | ## Reference 42 | * [1] R.Clark, S.Wang, H.Wen, A.Markham, andN.Trigoni, “VINet: Visual-Inertial Odometry as a Sequence-to-Sequence Learning Problem,” pp. 3995–4001, 2017. 43 | * [2] S.Wang, R.Clark, H.Wen, andN.Trigoni, “End-to-end, sequence-to-sequence probabilistic visual odometry through deep neural networks,” Int. J. Rob. Res., 2017. 44 | * [3] A.Handa, M.Bloesch, V.Pătrăucean, S.Stent, J.McCormac, andA.Davison, “Gvnn: Neural network library for geometric computer vision,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 9915 LNCS, pp. 67–82, 2016. 45 | -------------------------------------------------------------------------------- /SE3Comp.py: -------------------------------------------------------------------------------- 1 | import torch 2 | import torch.nn as nn 3 | 4 | class SE3Comp(nn.Module): 5 | def __init__(self): 6 | super(SE3Comp, self).__init__() 7 | self.threshold_square = 1e-1 8 | self.threshold_cube = 1e-1 9 | 10 | def forward(self, Tg, xi): 11 | """ 12 | Tg: SE(3) R^7 (x, y, z, ww, wx, wy, wz) 13 | Tg = torch.zeros(batchSize, 7, 1) 14 | xi: se(3) R^6 (rho1, rho2, rho3, omega_x, omega_y, omega_z) 15 | xi_vec = torch.zeros(batchSize, 6, 1) 16 | return Composed SE(3) in R^7 format 17 | """ 18 | assert isinstance(Tg, type(torch.zeros(1))),'Tg with wrong datatype, should be torch.Tensor' 19 | assert isinstance(xi, type(torch.zeros(1))),'Tg with wrong datatype, should be torch.Tensor' 20 | 21 | 22 | rho = xi[:, 0:3] 23 | omega = xi[:, 3:6] #torch.Size([batchSize, 3, 1]) 24 | batchSize = xi.size()[0] 25 | R, V = self.so3_RV(torch.squeeze(omega, dim=2)) 26 | Txi = torch.zeros(batchSize,4,4) 27 | Txi[:, 0:3, 0:3] = R 28 | Txi[:, 3,3] = 1.0 29 | Txi[:, 0:3, 3] = torch.squeeze(torch.bmm(V, rho)) 30 | 31 | Tg_matrix = torch.zeros(batchSize,4,4) 32 | Tg_matrix[:, 3, 3] = 1.0 33 | q = Tg[:, 3:7] 34 | Tg_matrix[:, 0:3, 0:3] = self.q_to_Matrix(q) 35 | Tg_matrix[:, 0, 3] = torch.squeeze(Tg[:, 0]) 36 | Tg_matrix[:, 1, 3] = torch.squeeze(Tg[:, 1]) 37 | Tg_matrix[:, 2, 3] = torch.squeeze(Tg[:, 2]) 38 | T_combine_M = torch.bmm(Txi, Tg_matrix) 39 | 40 | return self.batchMtoR7(T_combine_M) 41 | 42 | def batchMtoR7(self,M): 43 | batchSize = M.size()[0] 44 | cat = None 45 | for i in range(batchSize): 46 | a = self.MtoR7(M[i]) 47 | if i == 0: 48 | cat = torch.unsqueeze(a, dim=0) 49 | continue 50 | cat = torch.cat([cat,torch.unsqueeze(a, dim=0)]) 51 | 52 | return cat 53 | 54 | def MtoR7(self,M):#no batch 55 | R7 = torch.zeros(7,1) 56 | 57 | R7[0] = M[ 0, 3] # [2] to [2, 1] 58 | R7[1] = M[ 1, 3] # [2] to [2, 1] 59 | R7[2] = M[ 2, 3] # [2] to [2, 1] 60 | #https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2015/01/matrix-to-quat.pdf 61 | t = 0 62 | if M[2, 2] < 0: 63 | if M[0, 0] > M[1, 1]:# 64 | t = 1 + M[0, 0] - M[1, 1] - M[2, 2] 65 | q = [M[2, 1]-M[1, 2], t, M[0, 1]+M[1, 0], M[2, 0]+M[0, 2]] 66 | else:# 67 | t = 1 - M[0, 0] + M[1, 1] - M[2, 2] 68 | q = [M[0, 2]-M[2, 0], M[0, 1]+M[1, 0], t, M[1, 2]+M[2, 1]] 69 | else: 70 | if M[0, 0] < -M[1, 1]:# 71 | t = 1 - M[0, 0] - M[1, 1] + M[2, 2] 72 | q = [M[1, 0]-M[0, 1], M[2, 0]+M[0, 2], M[1, 2]+M[2, 1], t] 73 | else:# 74 | t = 1 + M[0, 0] + M[1, 1] + M[2, 2] 75 | q = [t, M[2, 1]-M[1, 2], M[0, 2]-M[2, 0], M[1, 0]-M[0, 1]] 76 | R7[3], R7[4], R7[5], R7[6] = q 77 | R7[3] *= 0.5 / torch.sqrt(t) 78 | R7[4] *= 0.5 / torch.sqrt(t) 79 | R7[5] *= 0.5 / torch.sqrt(t) 80 | R7[6] *= 0.5 / torch.sqrt(t) 81 | if R7[3] < 0: 82 | R7[3] *= -1 83 | R7[4] *= -1 84 | R7[5] *= -1 85 | R7[6] *= -1 86 | return R7 87 | 88 | def q_to_Matrix(self, q): 89 | qw = q[:, 0] 90 | qx = q[:, 1] 91 | qy = q[:, 2] 92 | qz = q[:, 3] 93 | M = torch.zeros(q.size()[0], 3, 3) 94 | 95 | M[:, 0, 0] = torch.squeeze( 1 - 2*torch.mul(qy,qy) - 2*torch.mul(qz,qz) ) 96 | M[:, 1, 0] = torch.squeeze( 2*torch.mul(qx,qy) + 2*torch.mul(qz,qw) ) 97 | M[:, 2, 0] = torch.squeeze( 2*torch.mul(qx,qz) - 2*torch.mul(qy,qw) ) 98 | 99 | M[:, 0, 1] = torch.squeeze( 2*torch.mul(qx,qy) - 2*torch.mul(qz,qw) ) 100 | M[:, 1, 1] = torch.squeeze( 1 - 2*torch.mul(qx,qx) - 2*torch.mul(qz,qz) ) 101 | M[:, 2, 1] = torch.squeeze( 2*torch.mul(qy,qz) + 2*torch.mul(qx,qw) ) 102 | 103 | M[:, 0, 2] = torch.squeeze( 2*torch.mul(qx,qz) + 2*torch.mul(qy,qw) ) 104 | M[:, 1, 2] = torch.squeeze( 2*torch.mul(qy,qz) - 2*torch.mul(qx,qw) ) 105 | M[:, 2, 2] = torch.squeeze( 1 - 2*torch.mul(qx,qx) - 2*torch.mul(qy,qy) ) 106 | 107 | return M 108 | 109 | def so3_RV(self, omega): 110 | """ 111 | (3-tuple) 112 | omega = torch.zeros(batchSize, 3) 113 | 114 | return batchx3x3 matrix R after exponential mapping, V 115 | """ 116 | batchSize = omega.size()[0] 117 | omega_x = omega[:, 0] 118 | omega_y = omega[:, 1] 119 | omega_z = omega[:, 2] 120 | 121 | #paramIndex = paramIndex + 3 122 | omega_skew = torch.zeros(batchSize,3,3) 123 | """ 124 | 0 -oz oy 0 125 | oz 0 -ox 0 126 | -oy ox 0 0 127 | 0 0 0 0 128 | """ 129 | omega_skew[:, 1, 0] = omega_z.clone() 130 | omega_skew[:, 2, 0] = -1 * omega_y 131 | 132 | omega_skew[:, 0, 1] = -1 * omega_z 133 | omega_skew[:, 2, 1] = omega_x.clone() 134 | 135 | omega_skew[:, 0, 2] = omega_y.clone() 136 | omega_skew[:, 1, 2] = -1 * omega_x 137 | 138 | omega_skew_sqr = torch.bmm(omega_skew,omega_skew) 139 | theta_sqr = torch.pow(omega_x,2) +\ 140 | torch.pow(omega_y,2) +\ 141 | torch.pow(omega_z,2) 142 | theta = torch.pow(theta_sqr,0.5) 143 | theta_cube = torch.mul(theta_sqr, theta)# 144 | sin_theta = torch.sin(theta) 145 | sin_theta_div_theta = torch.div(sin_theta,theta) 146 | sin_theta_div_theta[sin_theta_div_theta != sin_theta_div_theta] = 0 # set nan to zero 147 | 148 | one_minus_cos_theta = torch.ones(theta.size()) - torch.cos(theta) 149 | one_minus_cos_div_theta_sqr = torch.div(one_minus_cos_theta,theta_sqr) 150 | 151 | theta_minus_sin_theta = theta - torch.sin(theta) 152 | theta_minus_sin_div_theta_cube = torch.div(theta_minus_sin_theta, theta_cube) 153 | 154 | sin_theta_div_theta_tensor = torch.ones(omega_skew.size()) 155 | one_minus_cos_div_theta_sqr_tensor = torch.ones(omega_skew.size()) 156 | theta_minus_sin_div_theta_cube_tensor = torch.ones(omega_skew.size()) 157 | 158 | # sin_theta_div_theta do not need linear approximation 159 | sin_theta_div_theta_tensor = sin_theta_div_theta 160 | 161 | for b in range(batchSize): 162 | if theta_sqr[b] > self.threshold_square: 163 | one_minus_cos_div_theta_sqr_tensor[b] = one_minus_cos_div_theta_sqr[b] 164 | elif theta_sqr[b] < 1e-6: 165 | one_minus_cos_div_theta_sqr_tensor[b] = 0#0.5 166 | else:#Taylor expansion 167 | c = 1.0 / 2.0 168 | c += theta[b]**(4*1) / 720.0#np.math.factorial(6) 169 | c += theta[b]**(4*2) / 3628800.0#np.math.factorial(6+4) 170 | c -= theta[b]**(2) / 24.0#np.math.factorial(4) 171 | c -= theta[b]**(2 + 4) / 40320.0#np.math.factorial(4+4) 172 | one_minus_cos_div_theta_sqr_tensor[b] = c 173 | 174 | if theta_cube[b] > self.threshold_cube: 175 | theta_minus_sin_div_theta_cube_tensor[b] = theta_minus_sin_div_theta_cube[b] 176 | elif theta_sqr[b] < 1e-6: 177 | theta_minus_sin_div_theta_cube_tensor[b] = 0#1.0 / 6.0 178 | else:#Taylor expansion 179 | s = 1.0 / 6.0 180 | s += theta[b]**(4*1) / 5040.0 181 | s += theta[b]**(4*2) / 39916800.0 182 | s -= theta[b]**(2) / 120.0 183 | s -= theta[b]**(2 + 4) / 362880.0 184 | theta_minus_sin_div_theta_cube_tensor[b] = s 185 | 186 | completeTransformation = torch.zeros(batchSize,3,3) 187 | 188 | completeTransformation[:, 0, 0] += 1 189 | completeTransformation[:, 1, 1] += 1 190 | completeTransformation[:, 2, 2] += 1 191 | 192 | sin_theta_div_theta_tensor = torch.unsqueeze(sin_theta_div_theta_tensor, dim=1) 193 | completeTransformation = completeTransformation +\ 194 | self.vecMulMat(sin_theta_div_theta_tensor,omega_skew) +\ 195 | torch.mul(one_minus_cos_div_theta_sqr_tensor, omega_skew_sqr) 196 | 197 | 198 | V = torch.zeros(batchSize,3,3) 199 | V[:, 0, 0] += 1 200 | V[:, 1, 1] += 1 201 | V[:, 2, 2] += 1 202 | V = V + torch.mul(one_minus_cos_div_theta_sqr_tensor, omega_skew) +\ 203 | torch.mul(theta_minus_sin_div_theta_cube_tensor, omega_skew_sqr) 204 | return completeTransformation, V 205 | 206 | def vecMulMat(self, vec, mat): 207 | mat_view = mat.view(vec.size()[0], -1) 208 | out = mat_view * vec 209 | return out.view(mat_view.size()[0], mat.size()[1], -1) 210 | 211 | 212 | 213 | 214 | -------------------------------------------------------------------------------- /SE3CompTest.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Forward" 8 | ] 9 | }, 10 | { 11 | "cell_type": "markdown", 12 | "metadata": { 13 | "ExecuteTime": { 14 | "end_time": "2018-06-23T06:33:40.224305Z", 15 | "start_time": "2018-06-23T06:33:40.080203Z" 16 | }, 17 | "code_folding": [ 18 | 25 19 | ] 20 | }, 21 | "source": [ 22 | "## Generate se3 R6 from SE3 Matrix by Sophus Library\n", 23 | "\n", 24 | "Rotation matrix\n", 25 | "```\n", 26 | "SE3 Matrix\n", 27 | "[ -0.1746031, -0.0317460, 0.9841270; 1\n", 28 | " 0.3492065, -0.9365079, 0.0317460; 2\n", 29 | " 0.9206349, 0.3492065, 0.1746031 ] 3\n", 30 | " 0 0 0 1 \n", 31 | "```\n", 32 | "(SE3 Matrix ==> se3 R6)\n", 33 | "```python\n", 34 | "from sophus import *\n", 35 | "from sympy import *\n", 36 | "q = Quaternion(0.1259882, Matrix([0.6299408, 0.1259882, 0.7559289]))\n", 37 | "xi_SE3 = Se3(So3(q), Matrix([1, 2, 3]))\n", 38 | "xi_se3 = SE3.log()\n", 39 | "```\n", 40 | "xi se3 R6\n", 41 | "```\n", 42 | "se3 R6\n", 43 | "Matrix([[3.48075536975048], [2.34718513399708], [0.874839482491055], [1.83448188157597], [0.366896492801180], [2.20137808316218]])\n", 44 | "```\n", 45 | "Combine Tg pose with xi\n", 46 | "```\n", 47 | "Tg = 1, 2, 3, 0.6324555, 0.3162278, 0.6324555, 0.3162278\n", 48 | "T_combine = xi_SE3_M * Tg_SE3_M\n", 49 | "```\n", 50 | "T_combine\n", 51 | "```\n", 52 | "R^4x4\n", 53 | " [-0.615872887393401, 0.768254002808266, -0.174603012694796, 3.71428578273958], \n", 54 | " [-0.768253903444096, -0.536507791771389, 0.349206445794498, 0.571428888078200], \n", 55 | " [0.174603364513569, 0.349206351769077, 0.920634830550402, 5.14285714642664], \n", 56 | " [0, 0, 0, 1]])\n", 57 | " \n", 58 | " R7\n", 59 | " 3.71428578273958 0.5714288880782 5.14285714642664 0.4383 -0.0000 -0.1992 -0.8765\n", 60 | "```" 61 | ] 62 | }, 63 | { 64 | "cell_type": "code", 65 | "execution_count": 1, 66 | "metadata": { 67 | "ExecuteTime": { 68 | "end_time": "2018-07-01T07:38:28.276023Z", 69 | "start_time": "2018-07-01T07:38:28.122800Z" 70 | } 71 | }, 72 | "outputs": [ 73 | { 74 | "name": "stdout", 75 | "output_type": "stream", 76 | "text": [ 77 | "tensor([[[ 3.7143],\n", 78 | " [ 0.5714],\n", 79 | " [ 5.1429],\n", 80 | " [ 0.4383],\n", 81 | " [-0.0000],\n", 82 | " [-0.1992],\n", 83 | " [-0.8765]],\n", 84 | "\n", 85 | " [[ 0.0000],\n", 86 | " [ 0.0000],\n", 87 | " [ 0.0000],\n", 88 | " [ 1.0000],\n", 89 | " [ 0.0000],\n", 90 | " [ 0.0000],\n", 91 | " [ 0.0000]]])\n" 92 | ] 93 | } 94 | ], 95 | "source": [ 96 | "import torch \n", 97 | "\n", 98 | "import numpy as np\n", 99 | "from SE3Comp import *\n", 100 | "\n", 101 | "batchSize = 2\n", 102 | "Tg = torch.zeros(batchSize, 7, 1)\n", 103 | "xi_vec = torch.zeros(batchSize, 6, 1)\n", 104 | "\n", 105 | "Tg[0, 0] = 1\n", 106 | "Tg[0, 1] = 2\n", 107 | "Tg[0, 2] = 3\n", 108 | "Tg[0, 3] = 0.6324555\n", 109 | "Tg[0, 4] = 0.3162278\n", 110 | "Tg[0, 5] = 0.6324555\n", 111 | "Tg[0, 6] = 0.3162278\n", 112 | "\n", 113 | "# Tg[0, 0] = 0\n", 114 | "# Tg[0, 1] = 0\n", 115 | "# Tg[0, 2] = 0\n", 116 | "# Tg[0, 3] = 0\n", 117 | "# Tg[0, 4] = 0\n", 118 | "# Tg[0, 5] = 0\n", 119 | "# Tg[0, 6] = 0\n", 120 | "xi_vec[0,0] = 3.48075536975048\n", 121 | "xi_vec[0,1] = 2.34718513399708\n", 122 | "xi_vec[0,2] = 0.874839482491055\n", 123 | "xi_vec[0,3] = 1.83448188157597\n", 124 | "xi_vec[0,4] = 0.366896492801180\n", 125 | "xi_vec[0,5] = 2.20137808316218\n", 126 | "\n", 127 | "# xi_vec[0,0] = 0\n", 128 | "# xi_vec[0,1] = 0\n", 129 | "# xi_vec[0,2] = 0\n", 130 | "# xi_vec[0,3] = 0\n", 131 | "# xi_vec[0,4] = 0\n", 132 | "# xi_vec[0,5] = 0\n", 133 | "\n", 134 | "model = SE3Comp()\n", 135 | "\n", 136 | "\n", 137 | "ans = model.forward(Tg, xi_vec)\n", 138 | "print(ans)\n", 139 | "#3.71428578273958 0.5714288880782 5.14285714642664 0.4383 -0.0000 -0.1992 -0.8765" 140 | ] 141 | }, 142 | { 143 | "cell_type": "markdown", 144 | "metadata": {}, 145 | "source": [ 146 | "# Backward" 147 | ] 148 | }, 149 | { 150 | "cell_type": "code", 151 | "execution_count": 1, 152 | "metadata": { 153 | "ExecuteTime": { 154 | "end_time": "2018-07-01T06:38:42.652852Z", 155 | "start_time": "2018-07-01T06:38:42.481634Z" 156 | } 157 | }, 158 | "outputs": [ 159 | { 160 | "ename": "NameError", 161 | "evalue": "name 'nn' is not defined", 162 | "output_type": "error", 163 | "traceback": [ 164 | "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", 165 | "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", 166 | "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptim\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0moptim\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mclass\u001b[0m \u001b[0mtestNet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mModule\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtestNet\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", 167 | "\u001b[0;31mNameError\u001b[0m: name 'nn' is not defined" 168 | ] 169 | } 170 | ], 171 | "source": [ 172 | "import torch.optim as optim\n", 173 | "\n", 174 | "class testNet(nn.Module):\n", 175 | " def __init__(self):\n", 176 | " super(testNet, self).__init__()\n", 177 | " self.se3comp = SE3Comp()\n", 178 | " self.linearTg = nn.Linear(7, 7)\n", 179 | " self.linearXI = nn.Linear(6, 6)\n", 180 | " self.linear3 = nn.Linear(7, 7)\n", 181 | " def forward(self, Tg, xi_vec):\n", 182 | " batchSize = 2\n", 183 | " \n", 184 | " outTg = self.linearTg(Tg.view(batchSize, 1, -1))\n", 185 | " outXI = self.linearXI(xi_vec.view(batchSize,1, -1))\n", 186 | " outC = self.se3comp(outTg.view(batchSize,7,-1) , outXI.view(batchSize, 6, -1))\n", 187 | " outC_squeezed = torch.squeeze(outC)\n", 188 | " \n", 189 | " \n", 190 | " outL = self.linear3(outC_squeezed.view(batchSize, 1, -1))\n", 191 | " \n", 192 | " return outL.view(batchSize, 7, -1)\n", 193 | " \n", 194 | "model = testNet()\n", 195 | "\n", 196 | "optimizer = optim.SGD(filter(lambda p: p.requires_grad, model.parameters()), lr=1e-4)\n", 197 | "criterion = nn.MSELoss()\n", 198 | "\n", 199 | "print('Before optimization\\n')\n", 200 | "for param in model.parameters():\n", 201 | " print(param.data)\n", 202 | "print('==============================\\n') \n", 203 | "\n", 204 | "Tans = torch.zeros(batchSize, 7, 1)\n", 205 | "Tg[0, 0] = 1\n", 206 | "Tg[0, 1] = 2\n", 207 | "Tg[0, 2] = 0\n", 208 | "Tg[0, 3] = 0\n", 209 | "Tg[0, 4] = 0.3162278\n", 210 | "Tg[0, 5] = 0.6324555\n", 211 | "Tg[0, 6] = 0.3162278\n", 212 | "\n", 213 | "EPOCH = 50\n", 214 | "for k in range(EPOCH):\n", 215 | " optimizer.zero_grad()\n", 216 | " output = model(Tg, xi_vec)\n", 217 | " #print('output size: ', output.size())\n", 218 | "\n", 219 | " loss = criterion(output, Tans)\n", 220 | " print(loss)\n", 221 | " loss.register_hook(print)\n", 222 | " loss.backward\n", 223 | " optimizer.step()\n", 224 | "\n", 225 | "print('After optimization\\n')\n", 226 | "for param in model.parameters():\n", 227 | " print(param.data)" 228 | ] 229 | }, 230 | { 231 | "cell_type": "code", 232 | "execution_count": 36, 233 | "metadata": { 234 | "ExecuteTime": { 235 | "end_time": "2018-06-27T10:56:01.644311Z", 236 | "start_time": "2018-06-27T10:56:01.636492Z" 237 | } 238 | }, 239 | "outputs": [ 240 | { 241 | "name": "stdout", 242 | "output_type": "stream", 243 | "text": [ 244 | "tensor([[[ 1., 0., 0.],\n", 245 | " [ 0., 1., 0.],\n", 246 | " [ 0., 0., 1.]],\n", 247 | "\n", 248 | " [[ 1., 0., 0.],\n", 249 | " [ 0., 1., 0.],\n", 250 | " [ 0., 0., 1.]]])\n" 251 | ] 252 | } 253 | ], 254 | "source": [ 255 | "import torch \n", 256 | "\n", 257 | "import numpy as np\n", 258 | "from SE3Comp import *\n", 259 | "\n", 260 | "batchSize = 2\n", 261 | "q = torch.zeros(batchSize, 4, 1)\n", 262 | "q[:,0] = 0\n", 263 | "q[:,1] = 0\n", 264 | "q[:,2] = 0\n", 265 | "q[:,3] = 0\n", 266 | "\n", 267 | "\n", 268 | "def q_to_Matrix(q):\n", 269 | " qw = q[:, 0]\n", 270 | " qx = q[:, 1]\n", 271 | " qy = q[:, 2]\n", 272 | " qz = q[:, 3]\n", 273 | " M = torch.zeros(q.size()[0], 3, 3)\n", 274 | "\n", 275 | " M[:, 0, 0] = torch.squeeze( 1 - 2*torch.mul(qy,qy) - 2*torch.mul(qz,qz) )\n", 276 | " M[:, 1, 0] = torch.squeeze( 2*torch.mul(qx,qy) + 2*torch.mul(qz,qw) )\n", 277 | " M[:, 2, 0] = torch.squeeze( 2*torch.mul(qx,qz) - 2*torch.mul(qy,qw) )\n", 278 | "\n", 279 | " M[:, 0, 1] = torch.squeeze( 2*torch.mul(qx,qy) - 2*torch.mul(qz,qw) )\n", 280 | " M[:, 1, 1] = torch.squeeze( 1 - 2*torch.mul(qx,qx) - 2*torch.mul(qz,qz) )\n", 281 | " M[:, 2, 1] = torch.squeeze( 2*torch.mul(qy,qz) + 2*torch.mul(qx,qw) )\n", 282 | "\n", 283 | " M[:, 0, 2] = torch.squeeze( 2*torch.mul(qx,qz) + 2*torch.mul(qy,qw) )\n", 284 | " M[:, 1, 2] = torch.squeeze( 2*torch.mul(qy,qz) - 2*torch.mul(qx,qw) )\n", 285 | " M[:, 2, 2] = torch.squeeze( 1 - 2*torch.mul(qx,qx) - 2*torch.mul(qy,qy) )\n", 286 | "\n", 287 | " return M\n", 288 | "\n", 289 | "ans = q_to_Matrix(q)\n", 290 | "print(ans)" 291 | ] 292 | }, 293 | { 294 | "cell_type": "code", 295 | "execution_count": 93, 296 | "metadata": { 297 | "ExecuteTime": { 298 | "end_time": "2018-06-27T13:31:59.069539Z", 299 | "start_time": "2018-06-27T13:31:59.062295Z" 300 | } 301 | }, 302 | "outputs": [ 303 | { 304 | "name": "stdout", 305 | "output_type": "stream", 306 | "text": [ 307 | "by formula\n", 308 | "tensor([0.499583472197418, 0.499995833347366, 0.499999958325503, 0.499999996961265, 0.500000041370185, 0.500044450291171, 0.499600361081320,\n", 309 | " 0.000000000000000, 0.000000000000000, 0.000000000000000], dtype=torch.float64)\n", 310 | "by Taylor\n", 311 | "tensor([0.499583472197423, 0.499995833347222, 0.499999958333335, 0.499999999583333, 0.499999999995833, 0.499999999999958, 0.500000000000000,\n", 312 | " 0.500000000000000, 0.500000000000000, 0.500000000000000], dtype=torch.float64)\n" 313 | ] 314 | } 315 | ], 316 | "source": [ 317 | "import numpy as np\n", 318 | "np.set_printoptions(precision=15)\n", 319 | "torch.set_printoptions(precision=15)\n", 320 | "theta = torch.from_numpy(np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9, 1e-10]))\n", 321 | "\n", 322 | "co = (1.0 - torch.cos(theta)) / (theta*theta)\n", 323 | "print('by formula')\n", 324 | "print(co)\n", 325 | "\n", 326 | "co_l = torch.full((theta.shape[0],), 1.0 / 2.0, dtype=torch.float64)\n", 327 | "co_l += torch.pow(theta, (4*1)) / 720.0# 6!\n", 328 | "co_l += theta**(4*2) / 3628800.0# 10!\n", 329 | "co_l -= theta**(2) / 24.0\n", 330 | "co_l -= theta**(2 + 4) / 40320.0\n", 331 | "\n", 332 | "print('by Taylor')\n", 333 | "print(co_l)\n", 334 | "\n", 335 | "\n", 336 | "\n" 337 | ] 338 | }, 339 | { 340 | "cell_type": "code", 341 | "execution_count": 96, 342 | "metadata": { 343 | "ExecuteTime": { 344 | "end_time": "2018-06-27T13:40:57.516584Z", 345 | "start_time": "2018-06-27T13:40:57.510576Z" 346 | } 347 | }, 348 | "outputs": [ 349 | { 350 | "name": "stdout", 351 | "output_type": "stream", 352 | "text": [ 353 | "tensor([0.166583353171851, 0.166665833335744, 0.166666658339004, 0.166666661483190, 0.166667284899440, 0.166653732372284, 0.172053567411030,\n", 354 | " 0.000000000000000, 0.000000000000000, 0.000000000000000], dtype=torch.float64)\n", 355 | "tensor([0.166583353171848, 0.166665833335317, 0.166666658333334, 0.166666666583333, 0.166666666665833, 0.166666666666658, 0.166666666666667,\n", 356 | " 0.166666666666667, 0.166666666666667, 0.166666666666667], dtype=torch.float64)\n" 357 | ] 358 | } 359 | ], 360 | "source": [ 361 | "si = (theta - torch.sin(theta)) / (theta**3)\n", 362 | "print(si)\n", 363 | "\n", 364 | "si_l = torch.full((theta.shape[0],), 1.0 / 6.0, dtype=torch.float64)\n", 365 | "si_l += theta**(4*1) / 5040.0\n", 366 | "si_l += theta**(4*2) / 39916800.0\n", 367 | "si_l -= theta**(2) / 120.0\n", 368 | "si_l -= theta**(2 + 4) / 362880.0\n", 369 | "print(si_l)" 370 | ] 371 | }, 372 | { 373 | "cell_type": "code", 374 | "execution_count": 67, 375 | "metadata": { 376 | "ExecuteTime": { 377 | "end_time": "2018-06-27T12:57:27.515966Z", 378 | "start_time": "2018-06-27T12:57:27.511662Z" 379 | } 380 | }, 381 | "outputs": [], 382 | "source": [ 383 | "co_l_pos = torch.full((theta.shape[0],), 1.0 / 2.0)" 384 | ] 385 | }, 386 | { 387 | "cell_type": "code", 388 | "execution_count": 75, 389 | "metadata": { 390 | "ExecuteTime": { 391 | "end_time": "2018-06-27T13:06:15.347135Z", 392 | "start_time": "2018-06-27T13:06:15.342369Z" 393 | } 394 | }, 395 | "outputs": [ 396 | { 397 | "data": { 398 | "text/plain": [ 399 | "362880" 400 | ] 401 | }, 402 | "execution_count": 75, 403 | "metadata": {}, 404 | "output_type": "execute_result" 405 | } 406 | ], 407 | "source": [ 408 | "np.math.factorial(9) " 409 | ] 410 | }, 411 | { 412 | "cell_type": "code", 413 | "execution_count": 81, 414 | "metadata": { 415 | "ExecuteTime": { 416 | "end_time": "2018-06-27T13:10:29.627207Z", 417 | "start_time": "2018-06-27T13:10:29.621647Z" 418 | } 419 | }, 420 | "outputs": [ 421 | { 422 | "name": "stdout", 423 | "output_type": "stream", 424 | "text": [ 425 | "tensor([ 0.9983, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n", 426 | " 1.0000, 1.0000, 1.0000], dtype=torch.float64)\n" 427 | ] 428 | } 429 | ], 430 | "source": [ 431 | "theta = torch.from_numpy(np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9, 1e-10]))\n", 432 | "one = torch.sin(theta) / theta\n", 433 | "print(one)" 434 | ] 435 | }, 436 | { 437 | "cell_type": "code", 438 | "execution_count": 99, 439 | "metadata": { 440 | "ExecuteTime": { 441 | "end_time": "2018-06-30T16:49:49.171011Z", 442 | "start_time": "2018-06-30T16:49:49.165930Z" 443 | } 444 | }, 445 | "outputs": [ 446 | { 447 | "data": { 448 | "text/plain": [ 449 | "'0.4.0'" 450 | ] 451 | }, 452 | "execution_count": 99, 453 | "metadata": {}, 454 | "output_type": "execute_result" 455 | } 456 | ], 457 | "source": [ 458 | "torch.__version__" 459 | ] 460 | }, 461 | { 462 | "cell_type": "code", 463 | "execution_count": 101, 464 | "metadata": { 465 | "ExecuteTime": { 466 | "end_time": "2018-06-30T16:51:25.465942Z", 467 | "start_time": "2018-06-30T16:51:25.463494Z" 468 | } 469 | }, 470 | "outputs": [ 471 | { 472 | "data": { 473 | "text/plain": [ 474 | "'3.5.2 (default, Nov 23 2017, 16:37:01) \\n[GCC 5.4.0 20160609]'" 475 | ] 476 | }, 477 | "execution_count": 101, 478 | "metadata": {}, 479 | "output_type": "execute_result" 480 | } 481 | ], 482 | "source": [ 483 | "import sys\n", 484 | "sys.version" 485 | ] 486 | }, 487 | { 488 | "cell_type": "code", 489 | "execution_count": 16, 490 | "metadata": { 491 | "ExecuteTime": { 492 | "end_time": "2018-07-01T07:04:32.587022Z", 493 | "start_time": "2018-07-01T07:04:32.581438Z" 494 | } 495 | }, 496 | "outputs": [ 497 | { 498 | "name": "stdout", 499 | "output_type": "stream", 500 | "text": [ 501 | "torch.Size([2])\n", 502 | "torch.Size([2, 2])\n", 503 | "tensor([[ 0.5000, 3.0000],\n", 504 | " [ 2.4000, 9.9000]], dtype=torch.float64)\n" 505 | ] 506 | } 507 | ], 508 | "source": [ 509 | "a = torch.from_numpy(np.array([2, 3], dtype=float))\n", 510 | "print(a.size())\n", 511 | "b = torch.from_numpy(np.array([[0.25, 1.0], [1.2, 3.3]], dtype=float))\n", 512 | "print(b.size())\n", 513 | "# torch.reciprocal(a)\n", 514 | "b = torch.mul(a,b)\n", 515 | "print(b)" 516 | ] 517 | }, 518 | { 519 | "cell_type": "code", 520 | "execution_count": 17, 521 | "metadata": { 522 | "ExecuteTime": { 523 | "end_time": "2018-07-01T07:05:34.675434Z", 524 | "start_time": "2018-07-01T07:05:34.669683Z" 525 | } 526 | }, 527 | "outputs": [ 528 | { 529 | "name": "stdout", 530 | "output_type": "stream", 531 | "text": [ 532 | "torch.Size([2, 1])\n", 533 | "torch.Size([2, 2])\n", 534 | "tensor([[ 0.5000, 2.0000],\n", 535 | " [ 3.6000, 9.9000]], dtype=torch.float64)\n" 536 | ] 537 | } 538 | ], 539 | "source": [ 540 | "a = torch.from_numpy(np.array([[2], [3]], dtype=float))\n", 541 | "print(a.size())\n", 542 | "b = torch.from_numpy(np.array([[0.25, 1.0], [1.2, 3.3]], dtype=float))\n", 543 | "print(b.size())\n", 544 | "# torch.reciprocal(a)\n", 545 | "b = torch.mul(a,b)\n", 546 | "print(b)" 547 | ] 548 | }, 549 | { 550 | "cell_type": "code", 551 | "execution_count": 58, 552 | "metadata": { 553 | "ExecuteTime": { 554 | "end_time": "2018-07-01T07:31:06.587505Z", 555 | "start_time": "2018-07-01T07:31:06.576529Z" 556 | } 557 | }, 558 | "outputs": [ 559 | { 560 | "name": "stdout", 561 | "output_type": "stream", 562 | "text": [ 563 | "torch.Size([2, 1])\n", 564 | "tensor([[ 2.],\n", 565 | " [ 3.]], dtype=torch.float64)\n", 566 | "torch.Size([2, 3, 3])\n", 567 | "torch.Size([2, 9])\n", 568 | "tensor([[ 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n", 569 | " [ 3., 0., 0., 0., 0., 0., 0., 0., 0.]], dtype=torch.float64)\n", 570 | "tensor([[ 2., 0., 0., 0., 0., 0., 0., 0., 0.],\n", 571 | " [ 9., 0., 0., 0., 0., 0., 0., 0., 0.]], dtype=torch.float64)\n", 572 | "tensor([[[ 2., 0., 0.],\n", 573 | " [ 0., 0., 0.],\n", 574 | " [ 0., 0., 0.]],\n", 575 | "\n", 576 | " [[ 9., 0., 0.],\n", 577 | " [ 0., 0., 0.],\n", 578 | " [ 0., 0., 0.]]], dtype=torch.float64)\n" 579 | ] 580 | } 581 | ], 582 | "source": [ 583 | "# a = torch.from_numpy(np.array([2, 3], dtype=float))\n", 584 | "# print(a.size())\n", 585 | "# print(a)\n", 586 | "# a2 = torch.unsqueeze(a, dim=1)\n", 587 | "# print(a2.size())\n", 588 | "# print(a2)\n", 589 | "\n", 590 | "scalar = torch.from_numpy(np.array([2, 3], dtype=float))\n", 591 | "scalar = torch.unsqueeze(scalar, dim=1)\n", 592 | "print(scalar.size())\n", 593 | "print(scalar)\n", 594 | "m = torch.zeros((2,3,3), dtype=torch.float64)\n", 595 | "m[0,0,0] = 1\n", 596 | "m[1,0,0] = 3\n", 597 | "print(m.shape)\n", 598 | "#print(m)\n", 599 | "\n", 600 | "m_view = m.view(scalar.size()[0], -1)\n", 601 | "print(m_view.size())\n", 602 | "print(m_view)\n", 603 | "\n", 604 | "out = m_view * scalar\n", 605 | "print(out)\n", 606 | "\n", 607 | "out_view = out.view(scalar.size()[0], m.size()[1], -1)\n", 608 | "print(out_view)\n", 609 | "# b = torch.from_numpy(, dtype=float))\n", 610 | "# print(b.size())\n", 611 | "# c = torch.bmm(a2,b)" 612 | ] 613 | }, 614 | { 615 | "cell_type": "code", 616 | "execution_count": null, 617 | "metadata": {}, 618 | "outputs": [], 619 | "source": [] 620 | } 621 | ], 622 | "metadata": { 623 | "kernelspec": { 624 | "display_name": "Python 3", 625 | "language": "python", 626 | "name": "python3" 627 | }, 628 | "language_info": { 629 | "codemirror_mode": { 630 | "name": "ipython", 631 | "version": 3 632 | }, 633 | "file_extension": ".py", 634 | "mimetype": "text/x-python", 635 | "name": "python", 636 | "nbconvert_exporter": "python", 637 | "pygments_lexer": "ipython3", 638 | "version": "3.5.2" 639 | }, 640 | "varInspector": { 641 | "cols": { 642 | "lenName": 16, 643 | "lenType": 16, 644 | "lenVar": 40 645 | }, 646 | "kernels_config": { 647 | "python": { 648 | "delete_cmd_postfix": "", 649 | "delete_cmd_prefix": "del ", 650 | "library": "var_list.py", 651 | "varRefreshCmd": "print(var_dic_list())" 652 | }, 653 | "r": { 654 | "delete_cmd_postfix": ") ", 655 | "delete_cmd_prefix": "rm(", 656 | "library": "var_list.r", 657 | "varRefreshCmd": "cat(var_dic_list()) " 658 | } 659 | }, 660 | "types_to_exclude": [ 661 | "module", 662 | "function", 663 | "builtin_function_or_method", 664 | "instance", 665 | "_Feature" 666 | ], 667 | "window_display": false 668 | } 669 | }, 670 | "nbformat": 4, 671 | "nbformat_minor": 2 672 | } 673 | -------------------------------------------------------------------------------- /SE3CompTest.py: -------------------------------------------------------------------------------- 1 | import torch 2 | 3 | import numpy as np 4 | from SE3Comp import * 5 | 6 | batchSize = 1 7 | Tg = torch.zeros(batchSize, 7, 1) 8 | xi_vec = torch.zeros(batchSize, 6, 1) 9 | 10 | 11 | 12 | Tg[0, 0] = 1 13 | Tg[0, 1] = 2 14 | Tg[0, 2] = 3 15 | Tg[0, 3] = 0.6324555 16 | Tg[0, 4] = 0.3162278 17 | Tg[0, 5] = 0.6324555 18 | Tg[0, 6] = 0.3162278 19 | 20 | # Tg[0, 0] = 0 21 | # Tg[0, 1] = 0 22 | # Tg[0, 2] = 0 23 | # Tg[0, 3] = 0 24 | # Tg[0, 4] = 0 25 | # Tg[0, 5] = 0 26 | # Tg[0, 6] = 0 27 | xi_vec[0,0] = 3.48075536975048 28 | xi_vec[0,1] = 2.34718513399708 29 | xi_vec[0,2] = 0.874839482491055 30 | xi_vec[0,3] = 1.83448188157597 31 | xi_vec[0,4] = 0.366896492801180 32 | xi_vec[0,5] = 2.20137808316218 33 | 34 | # xi_vec[0,0] = 0 35 | # xi_vec[0,1] = 0 36 | # xi_vec[0,2] = 0 37 | # xi_vec[0,3] = 0 38 | # xi_vec[0,4] = 0 39 | # xi_vec[0,5] = 0 40 | 41 | model = SE3Comp() 42 | 43 | 44 | ans = model.forward(Tg, xi_vec) 45 | print('The result should be:') 46 | print(' [3.71428578273958 0.5714288880782 5.14285714642664 0.4383 -0.0000 -0.1992 -0.8765]') 47 | print(' [0 0 0 1 0 0 0]') 48 | print('=======Result=======') 49 | print(ans) 50 | #3.71428578273958 0.5714288880782 5.14285714642664 0.4383 -0.0000 -0.1992 -0.8765 51 | --------------------------------------------------------------------------------