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
|
/*
* Copyright (C) 2013 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.android.gallery3d.filtershow.tools;
import android.util.Log;
public class MatrixFit {
// Simple implementation of a matrix fit in N dimensions.
private static final String LOGTAG = "MatrixFit";
private double[][] mMatrix;
private int mDimension;
private boolean mValid = false;
private static double sEPS = 1.0f/10000000000.0f;
public MatrixFit(double[][] from, double[][] to) {
mValid = fit(from, to);
}
public int getDimension() {
return mDimension;
}
public boolean isValid() {
return mValid;
}
public double[][] getMatrix() {
return mMatrix;
}
public boolean fit(double[][] from, double[][] to) {
if ((from.length != to.length) || (from.length < 1)) {
Log.e(LOGTAG, "from and to must be of same size");
return false;
}
mDimension = from[0].length;
mMatrix = new double[mDimension +1][mDimension + mDimension +1];
if (from.length < mDimension) {
Log.e(LOGTAG, "Too few points => under-determined system");
return false;
}
double[][] q = new double[from.length][mDimension];
for (int i = 0; i < from.length; i++) {
for (int j = 0; j < mDimension; j++) {
q[i][j] = from[i][j];
}
}
double[][] p = new double[to.length][mDimension];
for (int i = 0; i < to.length; i++) {
for (int j = 0; j < mDimension; j++) {
p[i][j] = to[i][j];
}
}
// Make an empty (dim) x (dim + 1) matrix and fill it
double[][] c = new double[mDimension+1][mDimension];
for (int j = 0; j < mDimension; j++) {
for (int k = 0; k < mDimension + 1; k++) {
for (int i = 0; i < q.length; i++) {
double qt = 1;
if (k < mDimension) {
qt = q[i][k];
}
c[k][j] += qt * p[i][j];
}
}
}
// Make an empty (dim+1) x (dim+1) matrix and fill it
double[][] Q = new double[mDimension+1][mDimension+1];
for (int qi = 0; qi < q.length; qi++) {
double[] qt = new double[mDimension + 1];
for (int i = 0; i < mDimension; i++) {
qt[i] = q[qi][i];
}
qt[mDimension] = 1;
for (int i = 0; i < mDimension + 1; i++) {
for (int j = 0; j < mDimension + 1; j++) {
Q[i][j] += qt[i] * qt[j];
}
}
}
// Use a gaussian elimination to solve the linear system
for (int i = 0; i < mDimension + 1; i++) {
for (int j = 0; j < mDimension + 1; j++) {
mMatrix[i][j] = Q[i][j];
}
for (int j = 0; j < mDimension; j++) {
mMatrix[i][mDimension + 1 + j] = c[i][j];
}
}
if (!gaussianElimination(mMatrix)) {
return false;
}
return true;
}
public double[] apply(double[] point) {
if (mDimension != point.length) {
return null;
}
double[] res = new double[mDimension];
for (int j = 0; j < mDimension; j++) {
for (int i = 0; i < mDimension; i++) {
res[j] += point[i] * mMatrix[i][j+ mDimension +1];
}
res[j] += mMatrix[mDimension][j+ mDimension +1];
}
return res;
}
public void printEquation() {
for (int j = 0; j < mDimension; j++) {
String str = "x" + j + "' = ";
for (int i = 0; i < mDimension; i++) {
str += "x" + i + " * " + mMatrix[i][j+mDimension+1] + " + ";
}
str += mMatrix[mDimension][j+mDimension+1];
Log.v(LOGTAG, str);
}
}
private void printMatrix(String name, double[][] matrix) {
Log.v(LOGTAG, "name: " + name);
for (int i = 0; i < matrix.length; i++) {
String str = "";
for (int j = 0; j < matrix[0].length; j++) {
str += "" + matrix[i][j] + " ";
}
Log.v(LOGTAG, str);
}
}
/*
* Transforms the given matrix into a row echelon matrix
*/
private boolean gaussianElimination(double[][] m) {
int h = m.length;
int w = m[0].length;
for (int y = 0; y < h; y++) {
int maxrow = y;
for (int y2 = y + 1; y2 < h; y2++) { // Find max pivot
if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y])) {
maxrow = y2;
}
}
// swap
for (int i = 0; i < mDimension; i++) {
double t = m[y][i];
m[y][i] = m[maxrow][i];
m[maxrow][i] = t;
}
if (Math.abs(m[y][y]) <= sEPS) { // Singular Matrix
return false;
}
for (int y2 = y + 1; y2 < h; y2++) { // Eliminate column y
double c = m[y2][y] / m[y][y];
for (int x = y; x < w; x++) {
m[y2][x] -= m[y][x] * c;
}
}
}
for (int y = h -1; y > -1; y--) { // Back substitution
double c = m[y][y];
for (int y2 = 0; y2 < y; y2++) {
for (int x = w - 1; x > y - 1; x--) {
m[y2][x] -= m[y][x] * m[y2][y] / c;
}
}
m[y][y] /= c;
for (int x = h; x < w; x++) { // Normalize row y
m[y][x] /= c;
}
}
return true;
}
}
|
