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
use crate::mat::dims::Dimensions;
use crate::mat::Matrix;
use num_traits::identities::{One, Zero};
use num_traits::{cast, sign};
use std::fmt::Display;
impl<T> Matrix<T>
where
T: One + Zero + Clone + Copy,
{
/// Create a new matrix of type `T` with `init` as the default value for each entry.
///
/// # Arguments
///
/// * `rows` - Row count of matrix
/// * `cols` - Column count of matrix
/// * `init` - The initial value of all entries
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// let mat = Matrix::new(3, 4, 9);
/// println!("{}", mat);
///
/// // Output:
/// // 9 9 9 9
/// // 9 9 9 9
/// // 9 9 9 9
/// ```
pub fn new(rows: usize, cols: usize, init: T) -> Matrix<T> {
Matrix::<T> {
dims: Dimensions::new(rows, cols),
matrix: vec![init; rows * cols],
}
}
/// Create a new matrix from a vec.
///
/// # Arguments
///
/// * `rows` - Row count of matrix
/// * `cols` - Column count of matrix
/// * `vec` - Vector of length `rows x cols` where `vec[i * cols + j]` is the entry in row `i` and column `j`
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// # use libmat::matrix;
/// let mat = matrix!{1, 2, 3; 3, 2, 1; 2, 1, 3};
/// println!("{}", mat);
///
/// // Output:
/// // 1 2 3
/// // 3 2 1
/// // 2 1 3
/// ```
pub fn from_vec(rows: usize, cols: usize, vec: Vec<T>) -> Matrix<T> {
if vec.len() != rows * cols {
panic!("vec must have a length of rows * cols");
} else {
Matrix::<T> {
dims: Dimensions::new(rows, cols),
matrix: vec,
}
}
}
/// Get the number of rows
pub fn row_count(&self) -> usize {
self.dims.get_rows()
}
/// Get the number of columns
pub fn col_count(&self) -> usize {
self.dims.get_cols()
}
// pub fn insert_row(&mut self, at: usize, row: &[T]) -> Result<(), MatrixError> {
// if row.len() != self[0].len() {
// Err(MatrixError::IndexOutOfBounds)
// } else if at * self.dims.get_cols() >= self.matrix.len() {
// Err(MatrixError::IndexOutOfBounds)
// } else {
// for i in 0..row.len() {
// self.matrix.insert(at * self.dims.get_cols() + i, row[i]);
// }
// Ok(())
// }
// }
// pub fn insert_col() {}
/// Create an identity matrix of type `T` with dimensions `dim x dim`.
///
/// # Arguments
///
/// * `dim` - The dimensions of a square matrix
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// let mat_a: Matrix<u32> = Matrix::one(3);
/// println!("{}", mat_a);
///
/// // Output:
/// // 1 0 0
/// // 0 1 0
/// // 0 0 1
/// ```
pub fn one(dim: usize) -> Matrix<T> {
let mut res = Matrix::<T>::zero(dim, dim);
for i in 0..dim {
res[i][i] = T::one();
}
res
}
/// Create a zero-matrix of type `T`.
///
/// # Arguments
///
/// * `rows` - Row count of matrix
/// * `cols` - Column count of matrix
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// let mat = Matrix::zero(3, 8);
/// assert_eq!(mat, Matrix::new(3, 8, 0));
/// ```
pub fn zero(rows: usize, cols: usize) -> Matrix<T> {
Self::new(rows, cols, T::zero())
}
/// Create a diagonal matrix of type `T` with entries `init`.
///
/// # Arguments
///
/// * `dim` - The dimensions of a square matrix
/// * `init` - The initial value of diagonal entries
///
/// # Examples
///
/// ```
/// # use libmat::mat::Matrix;
/// let mat = Matrix::diag(3, 1);
/// assert_eq!(mat, Matrix::one(3));
/// ```
pub fn diag(dim: usize, init: T) -> Matrix<T> {
&Matrix::<T>::one(dim) * init
}
/// Creates a diagonal matrix with dimensions `dim x dim` and initial entries specified in `entries`.
pub fn diag_with(dim: usize, entries: &[T]) -> Matrix<T> {
if entries.len() > dim || entries.len() < dim {
panic!("Input slice does not have the correct length.");
}
let mut res_mat = Matrix::one(dim);
for i in 0..dim {
res_mat[i][i] = entries[i];
}
res_mat
}
pub fn lupdecompose(&self) -> Option<(Matrix<f64>, Vec<usize>)>
where
T: sign::Signed + PartialOrd + cast::ToPrimitive,
{
if !self.is_square() {
return None;
}
let mut a = Matrix::zero(self.dims.get_rows(), self.dims.get_cols());
a.matrix = self.matrix.iter().map(|&x| x.to_f64().unwrap()).collect();
let dim = self.dims.get_rows();
let mut imax: usize;
let mut max_a: f64;
let mut p: Vec<usize> = (0..=dim).collect();
for i in 0..dim {
max_a = 0_f64;
imax = i;
for k in i..dim {
// if a.matrix[i * dim + k].abs() > max_a {
// max_a = a.matrix[i * dim + k].abs();
// imax = k;
// }
if a[i][k].abs() > max_a {
max_a = a[i][k].abs();
imax = k;
}
}
if max_a < 0.000001 {
return None;
}
if imax != i {
let j = p[i];
p[i] = p[imax];
p[imax] = j;
let mut t_ij: Matrix<f64> = Matrix::one(self.dims.get_rows());
// t_ij.matrix[i * dim + i] = 0_f64;
// t_ij.matrix[imax * dim + imax] = 0_f64;
// t_ij.matrix[i * dim + imax] = 1_f64;
// t_ij.matrix[imax * dim + i] = 1_f64;
t_ij[i][i] = 0_f64;
t_ij[imax][imax] = 0_f64;
t_ij[i][imax] = 1_f64;
t_ij[imax][i] = 1_f64;
// switch rows i and imax
a = &a * &t_ij;
p[dim] += 1;
}
for j in (i + 1)..dim {
// a.matrix[j * dim + i] = a.matrix[j * dim + i] / a.matrix[i * dim + i];
a[j][i] = a[j][i] / a[i][i];
for k in (i + 1)..dim {
// a.matrix[j * dim + k] =
// a.matrix[j * dim + k] - (a.matrix[j * dim + i] * a.matrix[i * dim + k])
a[j][k] = a[j][k] - a[j][i] * a[i][k];
}
}
}
Some((a, p))
}
/// Calculate the determinant of a square matrix.
///
/// # Caution
///
/// Calculation may not be exact. Be sure to use `round()` when calculating the determinant of a integer matrix.
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// # use libmat::matrix;
/// let mat = matrix!{1, 2, 3; 3, 2, 1; 2, 1, 3};
/// assert_eq!(mat.det(), -12.0);
/// ```
pub fn det(&self) -> f64
where
T: sign::Signed + PartialOrd + Display + cast::ToPrimitive,
{
if self.row_count() != self.col_count() {
panic!("Matrix is not a square.");
}
if let Some((mat, p)) = self.lupdecompose() {
let mut det = mat.matrix[0];
for i in 1..mat.col_count() {
det = det * mat.matrix[i * mat.col_count() + i];
}
if (p[mat.row_count()] - mat.row_count()) % 2 == 0 {
det
} else {
-det
}
} else {
0_f64
}
}
/// Returns true if the matrix is a square matrix, false otherwise.
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// let mat_a: Matrix<i32> = Matrix::one(3);
/// let mat_b: Matrix<f32> = Matrix::zero(3, 4);
/// assert_eq!(mat_a.is_square(), true);
/// assert_eq!(mat_b.is_square(), false);
/// ```
pub fn is_square(&self) -> bool {
self.dims.is_square()
}
/// Transpose a matrix.
///
/// # Example
///
/// ```
/// # use libmat::mat::Matrix;
/// # use libmat::matrix;
/// let mat_a = matrix!{1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12};
/// // 1 2 3 4
/// // 5 6 7 8
/// // 9 10 11 12
/// let mat_b = matrix!{1, 5, 9; 2, 6, 10; 3, 7, 11; 4, 8, 12};
/// // 1 5 9
/// // 2 6 10
/// // 3 7 11
/// // 4 8 12
/// assert_eq!(mat_a.transpose(), mat_b);
/// ```
pub fn transpose(&self) -> Matrix<T> {
let mut vec = Vec::<T>::new();
for i in 0..self.dims.get_cols() {
for j in 0..self.dims.get_rows() {
vec.push(self.matrix[j * self.dims.get_cols() + i]);
}
}
Matrix::<T>::from_vec(self.dims.get_cols(), self.dims.get_rows(), vec)
}
}