-
Notifications
You must be signed in to change notification settings - Fork 6
/
ptm_polar.cpp
341 lines (295 loc) · 12.9 KB
/
ptm_polar.cpp
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
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
/*******************************************************************************
* -/_|:|_|_\-
*
* This code is a modification of D.L. Theobald's QCP rotation code.
* It has been adapted to calculate the polar decomposition of a 3x3 matrix
* Adaption by P.M. Larsen
*
* Original Author(s): Douglas L. Theobald
* Department of Biochemistry
* MS 009
* Brandeis University
* 415 South St
* Waltham, MA 02453
* USA
*
*
* Pu Liu
* Johnson & Johnson Pharmaceutical Research and Development, L.L.C.
* 665 Stockton Drive
* Exton, PA 19341
* USA
*
*
*
* If you use this QCP rotation calculation method in a publication, please
* reference:
*
* Douglas L. Theobald (2005)
* "Rapid calculation of RMSD using a quaternion-based characteristic
* polynomial."
* Acta Crystallographica A 61(4):478-480.
*
* Pu Liu, Dmitris K. Agrafiotis, and Douglas L. Theobald (2009)
* "Fast determination of the optimal rotational matrix for macromolecular
* superpositions."
* Journal of Computational Chemistry 31(7):1561-1563.
*
*
* Copyright (c) 2009-2013 Pu Liu and Douglas L. Theobald
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are permitted
* provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
* * Neither the name of the <ORGANIZATION> nor the names of its contributors may be used to
* endorse or promote products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
* PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* Source: started anew.
*
* Change History:
* 2009/04/13 Started source
* 2010/03/28 Modified FastCalcRMSDAndRotation() to handle tiny qsqr
* If trying all rows of the adjoint still gives too small
* qsqr, then just return identity matrix. (DLT)
* 2010/06/30 Fixed prob in assigning A[9] = 0 in InnerProduct()
* invalid mem access
* 2011/02/21 Made CenterCoords use weights
* 2011/05/02 Finally changed CenterCoords declaration in qcprot.h
* Also changed some functions to static
* 2011/07/08 put in fabs() to fix taking sqrt of small neg numbers, fp error
* 2012/07/26 minor changes to comments and main.c, more info (v.1.4)
*
* 2016/05/29 QCP method adapted for polar decomposition of a 3x3 matrix,
* for use in Polyhedral Template Matching.
*
******************************************************************************/
#include <cmath>
#include <algorithm>
#include <cstring>
#include "ptm_quat.h"
namespace ptm {
static void matmul_3x3(double* A, double* x, double* b)
{
b[0] = A[0] * x[0] + A[1] * x[3] + A[2] * x[6];
b[3] = A[3] * x[0] + A[4] * x[3] + A[5] * x[6];
b[6] = A[6] * x[0] + A[7] * x[3] + A[8] * x[6];
b[1] = A[0] * x[1] + A[1] * x[4] + A[2] * x[7];
b[4] = A[3] * x[1] + A[4] * x[4] + A[5] * x[7];
b[7] = A[6] * x[1] + A[7] * x[4] + A[8] * x[7];
b[2] = A[0] * x[2] + A[1] * x[5] + A[2] * x[8];
b[5] = A[3] * x[2] + A[4] * x[5] + A[5] * x[8];
b[8] = A[6] * x[2] + A[7] * x[5] + A[8] * x[8];
}
static double matrix_determinant_3x3(double* A)
{
return A[0] * (A[4]*A[8] - A[5]*A[7])
- A[1] * (A[3]*A[8] - A[5]*A[6])
+ A[2] * (A[3]*A[7] - A[4]*A[6]);
}
static void flip_matrix(double* A)
{
for (int i=0;i<9;i++)
A[i] = -A[i];
}
static bool optimal_quaternion(double* A, bool polar, double E0, double* p_nrmsdsq, double* qopt)
{
const double evecprec = 1e-6;
const double evalprec = 1e-11;
double Sxx = A[0], Sxy = A[1], Sxz = A[2],
Syx = A[3], Syy = A[4], Syz = A[5],
Szx = A[6], Szy = A[7], Szz = A[8];
double Sxx2 = Sxx * Sxx, Syy2 = Syy * Syy, Szz2 = Szz * Szz,
Sxy2 = Sxy * Sxy, Syz2 = Syz * Syz, Sxz2 = Sxz * Sxz,
Syx2 = Syx * Syx, Szy2 = Szy * Szy, Szx2 = Szx * Szx;
double fnorm_squared = Sxx2 + Syy2 + Szz2 + Sxy2 + Syz2 + Sxz2 + Syx2 + Szy2 + Szx2;
double SyzSzymSyySzz2 = 2.0 * (Syz * Szy - Syy * Szz);
double Sxx2Syy2Szz2Syz2Szy2 = Syy2 + Szz2 - Sxx2 + Syz2 + Szy2;
double SxzpSzx = Sxz + Szx;
double SyzpSzy = Syz + Szy;
double SxypSyx = Sxy + Syx;
double SyzmSzy = Syz - Szy;
double SxzmSzx = Sxz - Szx;
double SxymSyx = Sxy - Syx;
double SxxpSyy = Sxx + Syy;
double SxxmSyy = Sxx - Syy;
double Sxy2Sxz2Syx2Szx2 = Sxy2 + Sxz2 - Syx2 - Szx2;
double C[3];
C[0] = Sxy2Sxz2Syx2Szx2 * Sxy2Sxz2Syx2Szx2
+ (Sxx2Syy2Szz2Syz2Szy2 + SyzSzymSyySzz2) * (Sxx2Syy2Szz2Syz2Szy2 - SyzSzymSyySzz2)
+ (-(SxzpSzx)*(SyzmSzy)+(SxymSyx)*(SxxmSyy-Szz)) * (-(SxzmSzx)*(SyzpSzy)+(SxymSyx)*(SxxmSyy+Szz))
+ (-(SxzpSzx)*(SyzpSzy)-(SxypSyx)*(SxxpSyy-Szz)) * (-(SxzmSzx)*(SyzmSzy)-(SxypSyx)*(SxxpSyy+Szz))
+ (+(SxypSyx)*(SyzpSzy)+(SxzpSzx)*(SxxmSyy+Szz)) * (-(SxymSyx)*(SyzmSzy)+(SxzpSzx)*(SxxpSyy+Szz))
+ (+(SxypSyx)*(SyzmSzy)+(SxzmSzx)*(SxxmSyy-Szz)) * (-(SxymSyx)*(SyzpSzy)+(SxzmSzx)*(SxxpSyy-Szz));
C[1] = 8.0 * (Sxx*Syz*Szy + Syy*Szx*Sxz + Szz*Sxy*Syx - Sxx*Syy*Szz - Syz*Szx*Sxy - Szy*Syx*Sxz);
C[2] = -2.0 * fnorm_squared;
//Newton-Raphson
double mxEigenV = polar ? sqrt(3 * fnorm_squared) : E0;
if (mxEigenV > evalprec)
{
for (int i=0;i<50;i++)
{
double oldg = mxEigenV;
double x2 = mxEigenV*mxEigenV;
double b = (x2 + C[2])*mxEigenV;
double a = b + C[1];
double delta = ((a * mxEigenV + C[0]) / (2 * x2 * mxEigenV + b + a));
mxEigenV -= delta;
if (fabs(mxEigenV - oldg) < fabs(evalprec * mxEigenV))
break;
}
}
else
{
mxEigenV = 0.0;
}
(*p_nrmsdsq) = std::max(0.0, 2.0 * (E0 - mxEigenV));
double a11 = SxxpSyy + Szz - mxEigenV;
double a12 = SyzmSzy;
double a13 = -SxzmSzx;
double a14 = SxymSyx;
double a21 = SyzmSzy;
double a22 = SxxmSyy - Szz -mxEigenV;
double a23 = SxypSyx;
double a24 = SxzpSzx;
double a31 = a13;
double a32 = a23;
double a33 = Syy - Sxx - Szz - mxEigenV;
double a34 = SyzpSzy;
double a41 = a14;
double a42 = a24;
double a43 = a34;
double a44 = Szz - SxxpSyy - mxEigenV;
double a3344_4334 = a33 * a44 - a43 * a34;
double a3244_4234 = a32 * a44 - a42 * a34;
double a3243_4233 = a32 * a43 - a42 * a33;
double a3143_4133 = a31 * a43 - a41 * a33;
double a3144_4134 = a31 * a44 - a41 * a34;
double a3142_4132 = a31 * a42 - a41 * a32;
double a1324_1423 = a13 * a24 - a14 * a23;
double a1224_1422 = a12 * a24 - a14 * a22;
double a1223_1322 = a12 * a23 - a13 * a22;
double a1124_1421 = a11 * a24 - a14 * a21;
double a1123_1321 = a11 * a23 - a13 * a21;
double a1122_1221 = a11 * a22 - a12 * a21;
double q[4][4];
q[0][0] = a12 * a3344_4334 - a13 * a3244_4234 + a14 * a3243_4233;
q[0][1] = -a11 * a3344_4334 + a13 * a3144_4134 - a14 * a3143_4133;
q[0][2] = a11 * a3244_4234 - a12 * a3144_4134 + a14 * a3142_4132;
q[0][3] = -a11 * a3243_4233 + a12 * a3143_4133 - a13 * a3142_4132;
q[1][0] = a22 * a3344_4334 - a23 * a3244_4234 + a24 * a3243_4233;
q[1][1] = -a21 * a3344_4334 + a23 * a3144_4134 - a24 * a3143_4133;
q[1][2] = a21 * a3244_4234 - a22 * a3144_4134 + a24 * a3142_4132;
q[1][3] = -a21 * a3243_4233 + a22 * a3143_4133 - a23 * a3142_4132;
q[2][0] = a32 * a1324_1423 - a33 * a1224_1422 + a34 * a1223_1322;
q[2][1] = -a31 * a1324_1423 + a33 * a1124_1421 - a34 * a1123_1321;
q[2][2] = a31 * a1224_1422 - a32 * a1124_1421 + a34 * a1122_1221;
q[2][3] = -a31 * a1223_1322 + a32 * a1123_1321 - a33 * a1122_1221;
q[3][0] = a42 * a1324_1423 - a43 * a1224_1422 + a44 * a1223_1322;
q[3][1] = -a41 * a1324_1423 + a43 * a1124_1421 - a44 * a1123_1321;
q[3][2] = a41 * a1224_1422 - a42 * a1124_1421 + a44 * a1122_1221;
q[3][3] = -a41 * a1223_1322 + a42 * a1123_1321 - a43 * a1122_1221;
double qsqr[4];
for (int i=0;i<4;i++)
qsqr[i] = q[i][0]*q[i][0] + q[i][1]*q[i][1] + q[i][2]*q[i][2] + q[i][3]*q[i][3];
int bi = 0;
double max = 0;
for (int i=0;i<4;i++)
{
if (qsqr[i] > max)
{
bi = i;
max = qsqr[i];
}
}
bool too_small = false;
if (qsqr[bi] < evecprec)
{
//if qsqr is still too small, return the identity rotation.
q[bi][0] = 1;
q[bi][1] = 0;
q[bi][2] = 0;
q[bi][3] = 0;
too_small = true;
}
else
{
double normq = sqrt(qsqr[bi]);
q[bi][0] /= normq;
q[bi][1] /= normq;
q[bi][2] /= normq;
q[bi][3] /= normq;
}
memcpy(qopt, q[bi], 4 * sizeof(double));
return !too_small;
}
int polar_decomposition_3x3(double* _A, bool right_sided, double* U, double* P)
{
double A[9];
memcpy(A, _A, 9 * sizeof(double));
double det = matrix_determinant_3x3(A);
if (det < 0)
flip_matrix(A);
double q[4];
double nrmsdsq = 0;
optimal_quaternion(A, true, -1, &nrmsdsq, q);
q[0] = -q[0];
quaternion_to_rotation_matrix(q, U);
if (det < 0)
flip_matrix(U);
double UT[9] = {U[0], U[3], U[6], U[1], U[4], U[7], U[2], U[5], U[8]};
if (right_sided)
matmul_3x3(UT, _A, P);
else
matmul_3x3(_A, UT, P);
return 0;
}
void InnerProduct(double *A, int num, const double (*coords1)[3], double (*coords2)[3], int8_t* permutation)
{
A[0] = A[1] = A[2] = A[3] = A[4] = A[5] = A[6] = A[7] = A[8] = 0.0;
for (int i = 0; i < num; ++i)
{
double x1 = coords1[i][0];
double y1 = coords1[i][1];
double z1 = coords1[i][2];
double x2 = coords2[permutation[i]][0];
double y2 = coords2[permutation[i]][1];
double z2 = coords2[permutation[i]][2];
A[0] += x1 * x2;
A[1] += x1 * y2;
A[2] += x1 * z2;
A[3] += y1 * x2;
A[4] += y1 * y2;
A[5] += y1 * z2;
A[6] += z1 * x2;
A[7] += z1 * y2;
A[8] += z1 * z2;
}
}
int FastCalcRMSDAndRotation(double *A, double E0, double *p_nrmsdsq, double *q, double* U)
{
optimal_quaternion(A, false, E0, p_nrmsdsq, q);
quaternion_to_rotation_matrix(q, U);
return 0;
}
}