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
// Copyright © 2023 Marvin Beckmann
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
//! This module contains the implementation of the `tensor` product.
use super::MatZq;
use crate::{
error::MathError,
traits::{CompareBase, MatrixDimensions, Tensor},
};
use flint_sys::{fmpz_mat::fmpz_mat_kronecker_product, fmpz_mod_mat::_fmpz_mod_mat_reduce};
impl Tensor for MatZq {
/// Computes the tensor product of `self` with `other`.
///
/// Parameters:
/// - `other`: the value with which the tensor product is computed.
///
/// Returns the tensor product of `self` with `other` and panics if the
/// moduli of the provided matrices mismatch.
///
/// # Examples
/// ```
/// use qfall_math::integer_mod_q::MatZq;
/// use qfall_math::traits::Tensor;
/// use std::str::FromStr;
///
/// let mat_1 = MatZq::from_str("[[1, 1],[2, 2]] mod 7").unwrap();
/// let mat_2 = MatZq::from_str("[[1, 2],[3, 4]] mod 7").unwrap();
///
/// let mat_ab = mat_1.tensor_product(&mat_2);
/// let mat_ba = mat_2.tensor_product(&mat_1);
///
/// let res_ab = "[[1, 2, 1, 2],[3, 4, 3, 4],[2, 4, 2, 4],[6, 1, 6, 1]] mod 7";
/// let res_ba = "[[1, 1, 2, 2],[2, 2, 4, 4],[3, 3, 4, 4],[6, 6, 1, 1]] mod 7";
/// assert_eq!(mat_ab, MatZq::from_str(res_ab).unwrap());
/// assert_eq!(mat_ba, MatZq::from_str(res_ba).unwrap());
/// ```
///
/// # Panics ...
/// - if the moduli of both matrices mismatch.
/// Use [`tensor_product_safe`](crate::integer_mod_q::MatZq::tensor_product_safe) to get an error instead.
fn tensor_product(&self, other: &Self) -> Self {
self.tensor_product_safe(other).unwrap()
}
}
impl MatZq {
/// Computes the tensor product of `self` with `other`.
///
/// Parameters:
/// - `other`: the value with which the tensor product is computed.
///
/// Returns the tensor product of `self` with `other` or an error if the
/// moduli of the provided matrices mismatch.
///
/// # Examples
/// ```
/// use qfall_math::integer_mod_q::MatZq;
/// use std::str::FromStr;
///
/// let mat_1 = MatZq::from_str("[[1, 1],[2, 2]] mod 7").unwrap();
/// let mat_2 = MatZq::from_str("[[1, 2],[3, 4]] mod 7").unwrap();
///
/// let mat_ab = mat_1.tensor_product_safe(&mat_2).unwrap();
/// let mat_ba = mat_2.tensor_product_safe(&mat_1).unwrap();
///
/// let res_ab = "[[1, 2, 1, 2],[3, 4, 3, 4],[2, 4, 2, 4],[6, 1, 6, 1]] mod 7";
/// let res_ba = "[[1, 1, 2, 2],[2, 2, 4, 4],[3, 3, 4, 4],[6, 6, 1, 1]] mod 7";
/// assert_eq!(mat_ab, MatZq::from_str(res_ab).unwrap());
/// assert_eq!(mat_ba, MatZq::from_str(res_ba).unwrap());
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type
/// [`MismatchingModulus`](MathError::MismatchingModulus) if the
/// moduli of the provided matrices mismatch.
pub fn tensor_product_safe(&self, other: &Self) -> Result<Self, MathError> {
if !self.compare_base(other) {
return Err(self.call_compare_base_error(other).unwrap());
}
let mut out = MatZq::new(
self.get_num_rows() * other.get_num_rows(),
self.get_num_columns() * other.get_num_columns(),
self.get_mod(),
);
unsafe {
fmpz_mat_kronecker_product(
&mut out.matrix.mat[0],
&self.matrix.mat[0],
&other.matrix.mat[0],
)
};
unsafe { _fmpz_mod_mat_reduce(&mut out.matrix) }
Ok(out)
}
}
#[cfg(test)]
mod test_tensor {
use crate::{
integer_mod_q::MatZq,
traits::{MatrixDimensions, Tensor},
};
use std::str::FromStr;
/// Ensure that the dimensions of the tensor product are taken over correctly.
#[test]
fn dimensions_fit() {
let mat_1 = MatZq::new(17, 13, 13);
let mat_2 = MatZq::new(3, 4, 13);
let mat_3 = mat_1.tensor_product(&mat_2);
let mat_3_safe = mat_1.tensor_product_safe(&mat_2).unwrap();
assert_eq!(51, mat_3.get_num_rows());
assert_eq!(52, mat_3.get_num_columns());
assert_eq!(&mat_3, &mat_3_safe);
}
/// Ensure that the tensor works correctly with identity.
#[test]
fn identity() {
let identity = MatZq::from_str(&format!("[[1, 0],[0, 1]] mod {}", u128::MAX)).unwrap();
let mat_1 = MatZq::from_str(&format!(
"[[1, {}, 1],[0, {}, -1]] mod {}",
u64::MAX,
i64::MIN,
u128::MAX
))
.unwrap();
let mat_2 = identity.tensor_product(&mat_1);
let mat_3 = mat_1.tensor_product(&identity);
let mat_2_safe = identity.tensor_product_safe(&mat_1).unwrap();
let mat_3_safe = mat_1.tensor_product_safe(&identity).unwrap();
let cmp_mat_2 = MatZq::from_str(&format!(
"[[1, {}, 1, 0, 0, 0], \
[0, {}, -1, 0, 0, 0], \
[0, 0, 0, 1, {}, 1], \
[0, 0, 0, 0, {}, -1]] mod {}",
u64::MAX,
i64::MIN,
u64::MAX,
i64::MIN,
u128::MAX
))
.unwrap();
let cmp_mat_3 = MatZq::from_str(&format!(
"[[1, 0, {}, 0, 1, 0], \
[0, 1, 0, {}, 0, 1], \
[0, 0, {}, 0, -1, 0], \
[0, 0, 0, {}, 0, -1]] mod {}",
u64::MAX,
u64::MAX,
i64::MIN,
i64::MIN,
u128::MAX
))
.unwrap();
assert_eq!(cmp_mat_2, mat_2);
assert_eq!(cmp_mat_3, mat_3);
assert_eq!(cmp_mat_2, mat_2_safe);
assert_eq!(cmp_mat_3, mat_3_safe);
}
/// Ensure the tensor product works where one is a vector and the other is a matrix.
#[test]
fn vector_matrix() {
let vector = MatZq::from_str(&format!("[[1],[-1]] mod {}", u128::MAX)).unwrap();
let mat_1 = MatZq::from_str(&format!(
"[[1, {}, 1],[0, {}, -1]] mod {}",
u64::MAX,
i64::MAX,
u128::MAX
))
.unwrap();
let mat_2 = vector.tensor_product(&mat_1);
let mat_3 = mat_1.tensor_product(&vector);
let mat_2_safe = vector.tensor_product_safe(&mat_1).unwrap();
let mat_3_safe = mat_1.tensor_product_safe(&vector).unwrap();
let cmp_mat_2 = MatZq::from_str(&format!(
"[[1, {}, 1],[0, {}, -1],[-1, -{}, -1],[0, -{}, 1]] mod {}",
u64::MAX,
i64::MAX,
u64::MAX,
i64::MAX,
u128::MAX
))
.unwrap();
let cmp_mat_3 = MatZq::from_str(&format!(
"[[1, {}, 1],[-1, -{}, -1],[0, {}, -1],[0, -{}, 1]] mod {}",
u64::MAX,
u64::MAX,
i64::MAX,
i64::MAX,
u128::MAX
))
.unwrap();
assert_eq!(cmp_mat_2, mat_2);
assert_eq!(cmp_mat_3, mat_3);
assert_eq!(cmp_mat_2, mat_2_safe);
assert_eq!(cmp_mat_3, mat_3_safe);
}
/// Ensure that the tensor product works correctly with two vectors.
#[test]
fn vector_vector() {
let vec_1 = MatZq::from_str(&format!("[[2],[1]] mod {}", u128::MAX)).unwrap();
let vec_2 = MatZq::from_str(&format!(
"[[{}],[{}]] mod {}",
(u64::MAX - 1) / 2,
i64::MIN / 2,
u128::MAX
))
.unwrap();
let vec_3 = vec_1.tensor_product(&vec_2);
let vec_4 = vec_2.tensor_product(&vec_1);
let vec_3_safe = vec_1.tensor_product_safe(&vec_2).unwrap();
let vec_4_safe = vec_2.tensor_product_safe(&vec_1).unwrap();
let cmp_vec_3 = MatZq::from_str(&format!(
"[[{}],[{}],[{}],[{}]] mod {}",
u64::MAX - 1,
i64::MIN,
(u64::MAX - 1) / 2,
i64::MIN / 2,
u128::MAX
))
.unwrap();
let cmp_vec_4 = MatZq::from_str(&format!(
"[[{}],[{}],[{}],[{}]] mod {}",
u64::MAX - 1,
(u64::MAX - 1) / 2,
i64::MIN,
i64::MIN / 2,
u128::MAX
))
.unwrap();
assert_eq!(cmp_vec_3, vec_3);
assert_eq!(cmp_vec_4, vec_4);
assert_eq!(cmp_vec_3, vec_3_safe);
assert_eq!(cmp_vec_4, vec_4_safe);
}
/// Ensure that entries are reduced by the modulus.
#[test]
fn entries_reduced() {
let mat_1 = MatZq::from_str(&format!("[[1, 2],[3, 4]] mod {}", u64::MAX - 58)).unwrap();
let mat_2 = MatZq::from_str(&format!("[[1, 58],[0, -1]] mod {}", u64::MAX - 58)).unwrap();
let mat_3 = mat_1.tensor_product(&mat_2);
let mat_3_safe = mat_1.tensor_product_safe(&mat_2).unwrap();
let mat_3_cmp = MatZq::from_str(&format!(
"[[1, 58, 2, 116],[0, -1, 0, -2],[3, 174, 4, 232],[0, -3, 0, -4]] mod {}",
u64::MAX - 58
))
.unwrap();
assert_eq!(mat_3_cmp, mat_3);
assert_eq!(mat_3_cmp, mat_3_safe);
}
/// Ensure that tensor panics if the moduli mismatch.
#[test]
#[should_panic]
fn mismatching_moduli_tensor_product() {
let mat_1 = MatZq::new(1, 2, u64::MAX);
let mat_2 = MatZq::new(1, 2, u64::MAX - 58);
let _ = mat_1.tensor_product(&mat_2);
}
/// Ensure that tensor_product_safe returns an error if the moduli mismatch.
#[test]
fn mismatching_moduli_tensor_product_safe() {
let mat_1 = MatZq::new(1, 2, u64::MAX);
let mat_2 = MatZq::new(1, 2, u64::MAX - 58);
assert!(mat_1.tensor_product_safe(&mat_2).is_err());
assert!(mat_2.tensor_product_safe(&mat_1).is_err());
}
}