1 | // This file is a part of Framsticks SDK. http://www.framsticks.com/ |
---|
2 | // Copyright (C) 1999-2015 Maciej Komosinski and Szymon Ulatowski. |
---|
3 | // See LICENSE.txt for details. |
---|
4 | |
---|
5 | |
---|
6 | #include "matrix_tools.h" |
---|
7 | #include "lapack.h" |
---|
8 | #include <cstdlib> |
---|
9 | #include <cmath> |
---|
10 | #include <cstdio> |
---|
11 | #include <stdlib.h> //malloc(), embarcadero |
---|
12 | #include <math.h> //sqrt(), embarcadero |
---|
13 | |
---|
14 | |
---|
15 | double *Create(int nSize) |
---|
16 | { |
---|
17 | double *matrix = (double *)malloc(nSize * sizeof(double)); |
---|
18 | |
---|
19 | for (int i = 0; i < nSize; i++) |
---|
20 | { |
---|
21 | matrix[i] = 0; |
---|
22 | } |
---|
23 | |
---|
24 | return matrix; |
---|
25 | } |
---|
26 | |
---|
27 | double *Multiply(double *&a, double *&b, int nrow, int ncol, double ncol2, double *&toDel, int delSize) |
---|
28 | { |
---|
29 | double *c = Create(nrow * ncol2); |
---|
30 | int i = 0, j = 0, k = 0; |
---|
31 | |
---|
32 | for (i = 0; i < nrow; i++) |
---|
33 | { |
---|
34 | for (j = 0; j < ncol2; j++) |
---|
35 | { |
---|
36 | for (k = 0; k < ncol; k++) |
---|
37 | c[i * nrow + j] += a[i * nrow + k] * b[k * ncol + j]; |
---|
38 | } |
---|
39 | } |
---|
40 | |
---|
41 | if (delSize != 0) |
---|
42 | free(toDel); |
---|
43 | return c; |
---|
44 | } |
---|
45 | |
---|
46 | double *Power(double *&array, int nrow, int ncol, double pow, double *&toDel, int delSize) |
---|
47 | { |
---|
48 | double *m_Power = Create(nrow * ncol); |
---|
49 | if (pow == 2) |
---|
50 | { |
---|
51 | for (int i = 0; i < nrow; i++) |
---|
52 | { |
---|
53 | for (int j = 0; j < ncol; j++) |
---|
54 | { |
---|
55 | m_Power[i * nrow + j] = array[i * nrow + j] * array[i * nrow + j]; |
---|
56 | } |
---|
57 | |
---|
58 | } |
---|
59 | } |
---|
60 | else |
---|
61 | { |
---|
62 | for (int i = 0; i < nrow; i++) |
---|
63 | { |
---|
64 | for (int j = 0; j < ncol; j++) |
---|
65 | { |
---|
66 | m_Power[i * nrow + j] = sqrt(array[i * nrow + j]); |
---|
67 | } |
---|
68 | |
---|
69 | } |
---|
70 | } |
---|
71 | |
---|
72 | if (delSize != 0) |
---|
73 | free(toDel); |
---|
74 | |
---|
75 | return m_Power; |
---|
76 | } |
---|
77 | |
---|
78 | void Print(double *&mat, int nelems) |
---|
79 | { |
---|
80 | for (int i = 0; i < nelems; i++) |
---|
81 | printf("%6.2f ", mat[i]); |
---|
82 | printf("\n"); |
---|
83 | |
---|
84 | } |
---|
85 | |
---|
86 | double *Transpose(double *&A, int arow, int acol) |
---|
87 | { |
---|
88 | double *result = Create(acol * arow); |
---|
89 | |
---|
90 | for (int i = 0; i < acol; i++) |
---|
91 | for (int j = 0; j < arow; j++) |
---|
92 | { |
---|
93 | result[i * arow + j] = A[j * acol + i]; |
---|
94 | } |
---|
95 | |
---|
96 | return result; |
---|
97 | |
---|
98 | } |
---|
99 | |
---|
100 | /** Computes the SVD of the nSize x nSize distance matrix |
---|
101 | @param vdEigenvalues [OUT] Vector of doubles. On return holds the eigenvalues of the |
---|
102 | decomposed distance matrix (or rather, to be strict, of the matrix of scalar products |
---|
103 | created from the matrix of distances). The vector is assumed to be empty before the function call and |
---|
104 | all variance percentages are pushed at the end of it. |
---|
105 | @param nSize size of the matrix of distances. |
---|
106 | @param pDistances [IN] matrix of distances between parts. |
---|
107 | @param Coordinates [OUT] array of three dimensional coordinates obtained from SVD of pDistances matrix. |
---|
108 | */ |
---|
109 | void MatrixTools::SVD(std::vector<double> &vdEigenvalues, int nSize, double *pDistances, Pt3D *&Coordinates) |
---|
110 | { |
---|
111 | // compute squares of elements of this array |
---|
112 | // compute the matrix B that is the parameter of SVD |
---|
113 | double *B = Create(nSize * nSize); |
---|
114 | { |
---|
115 | // use additional scope to delete temporary matrices |
---|
116 | double *Ones, *Eye, *Z, *D; |
---|
117 | |
---|
118 | D = Create(nSize * nSize); |
---|
119 | D = Power(pDistances, nSize, nSize, 2.0, D, nSize); |
---|
120 | |
---|
121 | Ones = Create(nSize * nSize); |
---|
122 | for (int i = 0; i < nSize; i++) |
---|
123 | for (int j = 0; j < nSize; j++) |
---|
124 | { |
---|
125 | Ones[i * nSize + j] = 1; |
---|
126 | } |
---|
127 | |
---|
128 | Eye = Create(nSize * nSize); |
---|
129 | for (int i = 0; i < nSize; i++) |
---|
130 | { |
---|
131 | for (int j = 0; j < nSize; j++) |
---|
132 | { |
---|
133 | if (i == j) |
---|
134 | { |
---|
135 | Eye[i * nSize + j] = 1; |
---|
136 | } |
---|
137 | else |
---|
138 | { |
---|
139 | Eye[i * nSize + j] = 0; |
---|
140 | } |
---|
141 | } |
---|
142 | } |
---|
143 | |
---|
144 | Z = Create(nSize * nSize); |
---|
145 | for (int i = 0; i < nSize; i++) |
---|
146 | { |
---|
147 | for (int j = 0; j < nSize; j++) |
---|
148 | { |
---|
149 | Z[i * nSize + j] = 1.0 / ((double)nSize) * Ones[i * nSize + j]; |
---|
150 | } |
---|
151 | } |
---|
152 | |
---|
153 | for (int i = 0; i < nSize; i++) |
---|
154 | { |
---|
155 | for (int j = 0; j < nSize; j++) |
---|
156 | { |
---|
157 | Z[i * nSize + j] = Eye[i * nSize + j] - Z[i * nSize + j]; |
---|
158 | } |
---|
159 | } |
---|
160 | |
---|
161 | for (int i = 0; i < nSize; i++) |
---|
162 | { |
---|
163 | for (int j = 0; j < nSize; j++) |
---|
164 | { |
---|
165 | B[i * nSize + j] = Z[i * nSize + j] * -0.5; |
---|
166 | } |
---|
167 | } |
---|
168 | |
---|
169 | B = Multiply(B, D, nSize, nSize, nSize, B, nSize); |
---|
170 | B = Multiply(B, Z, nSize, nSize, nSize, B, nSize); |
---|
171 | |
---|
172 | free(Ones); |
---|
173 | free(Eye); |
---|
174 | free(Z); |
---|
175 | free(D); |
---|
176 | } |
---|
177 | |
---|
178 | double *Eigenvalues = Create(nSize); |
---|
179 | double *S = Create(nSize * nSize); |
---|
180 | |
---|
181 | // call SVD function |
---|
182 | double *Vt = Create(nSize * nSize); |
---|
183 | size_t astep = nSize * sizeof(double); |
---|
184 | Lapack::JacobiSVD(B, astep, Eigenvalues, Vt, astep, nSize, nSize, nSize); |
---|
185 | |
---|
186 | double *W = Transpose(Vt, nSize, nSize); |
---|
187 | |
---|
188 | free(B); |
---|
189 | free(Vt); |
---|
190 | |
---|
191 | for (int i = 0; i < nSize; i++) |
---|
192 | for (int j = 0; j < nSize; j++) |
---|
193 | { |
---|
194 | if (i == j) |
---|
195 | S[i * nSize + j] = Eigenvalues[i]; |
---|
196 | else |
---|
197 | S[i * nSize + j] = 0; |
---|
198 | } |
---|
199 | |
---|
200 | // compute coordinates of points |
---|
201 | double *sqS, *dCoordinates; |
---|
202 | sqS = Power(S, nSize, nSize, 0.5, S, nSize); |
---|
203 | dCoordinates = Multiply(W, sqS, nSize, nSize, nSize, W, nSize); |
---|
204 | free(sqS); |
---|
205 | |
---|
206 | for (int i = 0; i < nSize; i++) |
---|
207 | { |
---|
208 | // set coordinate from the SVD solution |
---|
209 | Coordinates[i].x = dCoordinates[i * nSize]; |
---|
210 | Coordinates[i].y = dCoordinates[i * nSize + 1]; |
---|
211 | if (nSize > 2) |
---|
212 | Coordinates[i].z = dCoordinates[i * nSize + 2]; |
---|
213 | else |
---|
214 | Coordinates[i].z = 0; |
---|
215 | } |
---|
216 | |
---|
217 | // store the eigenvalues in the output vector |
---|
218 | for (int i = 0; i < nSize; i++) |
---|
219 | { |
---|
220 | double dElement = Eigenvalues[i]; |
---|
221 | vdEigenvalues.push_back(dElement); |
---|
222 | } |
---|
223 | |
---|
224 | free(Eigenvalues); |
---|
225 | free(dCoordinates); |
---|
226 | } |
---|