forked from rchen8/algorithms
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Matrix.java
139 lines (113 loc) · 3.87 KB
/
Matrix.java
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
import java.util.Arrays;
public class Matrix {
private static double determinant(double[][] matrix) {
if (matrix.length != matrix[0].length)
throw new IllegalStateException("invalid dimensions");
if (matrix.length == 2)
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
double det = 0;
for (int i = 0; i < matrix[0].length; i++)
det += Math.pow(-1, i) * matrix[0][i]
* determinant(minor(matrix, 0, i));
return det;
}
private static double[][] inverse(double[][] matrix) {
double[][] inverse = new double[matrix.length][matrix.length];
// minors and cofactors
for (int i = 0; i < matrix.length; i++)
for (int j = 0; j < matrix[i].length; j++)
inverse[i][j] = Math.pow(-1, i + j)
* determinant(minor(matrix, i, j));
// adjugate and determinant
double det = 1.0 / determinant(matrix);
for (int i = 0; i < inverse.length; i++) {
for (int j = 0; j <= i; j++) {
double temp = inverse[i][j];
inverse[i][j] = inverse[j][i] * det;
inverse[j][i] = temp * det;
}
}
return inverse;
}
private static double[][] minor(double[][] matrix, int row, int column) {
double[][] minor = new double[matrix.length - 1][matrix.length - 1];
for (int i = 0; i < matrix.length; i++)
for (int j = 0; i != row && j < matrix[i].length; j++)
if (j != column)
minor[i < row ? i : i - 1][j < column ? j : j - 1] = matrix[i][j];
return minor;
}
private static double[][] multiply(double[][] a, double[][] b) {
if (a[0].length != b.length)
throw new IllegalStateException("invalid dimensions");
double[][] matrix = new double[a.length][b[0].length];
for (int i = 0; i < a.length; i++) {
for (int j = 0; j < b[0].length; j++) {
double sum = 0;
for (int k = 0; k < a[i].length; k++)
sum += a[i][k] * b[k][j];
matrix[i][j] = sum;
}
}
return matrix;
}
private static double[][] rref(double[][] matrix) {
double[][] rref = new double[matrix.length][];
for (int i = 0; i < matrix.length; i++)
rref[i] = Arrays.copyOf(matrix[i], matrix[i].length);
int r = 0;
for (int c = 0; c < rref[0].length && r < rref.length; c++) {
int j = r;
for (int i = r + 1; i < rref.length; i++)
if (Math.abs(rref[i][c]) > Math.abs(rref[j][c]))
j = i;
if (Math.abs(rref[j][c]) < 0.00001)
continue;
double[] temp = rref[j];
rref[j] = rref[r];
rref[r] = temp;
double s = 1.0 / rref[r][c];
for (j = 0; j < rref[0].length; j++)
rref[r][j] *= s;
for (int i = 0; i < rref.length; i++) {
if (i != r) {
double t = rref[i][c];
for (j = 0; j < rref[0].length; j++)
rref[i][j] -= t * rref[r][j];
}
}
r++;
}
return rref;
}
private static double[][] transpose(double[][] matrix) {
double[][] transpose = new double[matrix[0].length][matrix.length];
for (int i = 0; i < matrix.length; i++)
for (int j = 0; j < matrix[i].length; j++)
transpose[j][i] = matrix[i][j];
return transpose;
}
public static void main(String[] args) {
// example 1 - solving a system of equations
double[][] a = { { 1, 1, 1 }, { 0, 2, 5 }, { 2, 5, -1 } };
double[][] b = { { 6 }, { -4 }, { 27 } };
double[][] matrix = multiply(inverse(a), b);
for (double[] i : matrix)
System.out.println(Arrays.toString(i));
System.out.println();
// example 2 - example 1 using reduced row echelon form
a = new double[][]{ { 1, 1, 1, 6 }, { 0, 2, 5, -4 }, { 2, 5, -1, 27 } };
matrix = rref(a);
for (double[] i : matrix)
System.out.println(Arrays.toString(i));
System.out.println();
// example 3 - solving a normal equation for linear regression
double[][] x = { { 2104, 5, 1, 45 }, { 1416, 3, 2, 40 },
{ 1534, 3, 2, 30 }, { 852, 2, 1, 36 } };
double[][] y = { { 460 }, { 232 }, { 315 }, { 178 } };
matrix = multiply(
multiply(inverse(multiply(transpose(x), x)), transpose(x)), y);
for (double[] i : matrix)
System.out.println(Arrays.toString(i));
}
}