minimage 0.1.3

Minimum-image convention for periodic parallelepiped cells
Documentation 
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

//! Batched minimum-image squared distances.
//!
//! Orthorhombic differences are a structure-of-arrays kernel: one
//! reciprocal per axis, then `abs` and `round`, the Highway
//! `BatchPeriodicDistSq` arithmetic, issued as AVX when the CPU has
//! it. Restricted triclinic batches use the triangular
//! lamda step. A general `H` hoists the inverse and applies it per
//! row. [`dist2_shifted_many`](crate::Cell::dist2_shifted_many) is
//! Rapaport's linked-cell pair, one lattice shift for a whole bin.

use crate::kernel::{self, n2};
use crate::{Cell, Error};

/// Minimum-image wrap of packed difference vectors.
///
/// `diffs` and `out` are row-major `n` triples. Each row is `q - p`
/// (the cell origin does not enter).
pub fn wrap_many(cell: &Cell, diffs: &[[f64; 3]], out: &mut [[f64; 3]]) -> Result<(), Error> {
    if out.len() != diffs.len() {
        return Err(Error::BufferSize);
    }
    if cell.is_ortho() {
        crate::simd::wrap_many_ortho(cell.widths(), diffs, out);
    } else {
        for (d, o) in diffs.iter().zip(out.iter_mut()) {
            *o = cell.wrap_diff(*d);
        }
    }
    Ok(())
}

/// Squared MIC distances from `p` to each packed candidate in `qs`.
///
/// `qs` is row-major `n` triples. `out` has length `n`.
pub fn dist2_many(cell: &Cell, p: [f64; 3], qs: &[[f64; 3]], out: &mut [f64]) -> Result<(), Error> {
    if out.len() != qs.len() {
        return Err(Error::BufferSize);
    }
    if cell.is_ortho() {
        dist2_many_ortho(cell.widths(), p, qs, out);
    } else if cell.is_restricted() {
        for (q, o) in qs.iter().zip(out.iter_mut()) {
            let d = cell.wrap_diff([q[0] - p[0], q[1] - p[1], q[2] - p[2]]);
            *o = n2(d);
        }
    } else {
        let h = cell.h();
        let hinv = cell.hinv();
        for (q, o) in qs.iter().zip(out.iter_mut()) {
            let d = kernel::general_wrap(h, hinv, [q[0] - p[0], q[1] - p[1], q[2] - p[2]]);
            *o = n2(d);
        }
    }
    Ok(())
}

/// Squared MIC distances for packed pair lists `ps` and `qs`.
///
/// Each slice is row-major `n` triples. `out` has length `n`.
pub fn dist2_pairs(
    cell: &Cell,
    ps: &[[f64; 3]],
    qs: &[[f64; 3]],
    out: &mut [f64],
) -> Result<(), Error> {
    if ps.len() != qs.len() || out.len() != ps.len() {
        return Err(Error::BufferSize);
    }
    if cell.is_ortho() {
        dist2_pairs_ortho(cell.widths(), ps, qs, out);
    } else {
        for i in 0..ps.len() {
            out[i] = cell.dist2(ps[i], qs[i]);
        }
    }
    Ok(())
}

/// Orthorhombic wrap of precomputed differences, one reciprocal per axis.
///
/// `dx`, `dy`, `dz`, and `out` have length `n`. This is the Highway
/// kernel: `dr -= box * round(dr * (1 / box))` after taking `abs`.
pub fn dist2_ortho_diffs(
    dx: &[f64],
    dy: &[f64],
    dz: &[f64],
    bx: f64,
    by: f64,
    bz: f64,
    out: &mut [f64],
) -> Result<(), Error> {
    let n = dx.len().min(dy.len()).min(dz.len()).min(out.len());
    if n == 0 {
        return Ok(());
    }
    if !(bx > 0.0 && by > 0.0 && bz > 0.0) {
        return Err(Error::BadBox);
    }
    crate::simd::dist2_ortho_diffs(&dx[..n], &dy[..n], &dz[..n], bx, by, bz, &mut out[..n]);
    Ok(())
}

pub(crate) fn dist2_pairs_ortho(l: [f64; 3], ps: &[[f64; 3]], qs: &[[f64; 3]], out: &mut [f64]) {
    const CHUNK: usize = 64;
    let mut dx = [0.0; CHUNK];
    let mut dy = [0.0; CHUNK];
    let mut dz = [0.0; CHUNK];
    let mut start = 0;
    while start < ps.len() {
        let n = (ps.len() - start).min(CHUNK);
        for k in 0..n {
            let i = start + k;
            dx[k] = qs[i][0] - ps[i][0];
            dy[k] = qs[i][1] - ps[i][1];
            dz[k] = qs[i][2] - ps[i][2];
        }
        crate::simd::dist2_ortho_diffs(
            &dx[..n],
            &dy[..n],
            &dz[..n],
            l[0],
            l[1],
            l[2],
            &mut out[start..start + n],
        );
        start += n;
    }
}

pub(crate) fn dist2_many_ortho(l: [f64; 3], p: [f64; 3], qs: &[[f64; 3]], out: &mut [f64]) {
    // Squares match the signed wrap, so the SoA kernel is the same
    // distance. Chunks stay on the stack.
    const CHUNK: usize = 64;
    let mut dx = [0.0; CHUNK];
    let mut dy = [0.0; CHUNK];
    let mut dz = [0.0; CHUNK];
    let mut start = 0;
    while start < qs.len() {
        let n = (qs.len() - start).min(CHUNK);
        for (k, q) in qs[start..start + n].iter().enumerate() {
            dx[k] = q[0] - p[0];
            dy[k] = q[1] - p[1];
            dz[k] = q[2] - p[2];
        }
        crate::simd::dist2_ortho_diffs(
            &dx[..n],
            &dy[..n],
            &dz[..n],
            l[0],
            l[1],
            l[2],
            &mut out[start..start + n],
        );
        start += n;
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn batch_matches_scalar_ortho() {
        let cell = Cell::ortho(10.0, 10.0, 10.0).unwrap();
        let p = [0.2, 0.0, 0.0];
        let qs = [[9.4, 0.0, 0.0], [1.0, 0.0, 0.0], [5.0, 0.0, 0.0]];
        let mut out = [0.0; 3];
        dist2_many(&cell, p, &qs, &mut out).unwrap();
        for i in 0..3 {
            assert!((out[i] - cell.dist2(p, qs[i])).abs() < 1e-12);
        }
        assert!((out[0] - 0.64).abs() < 1e-12);
        let wide: Vec<[f64; 3]> = (0..70).map(|i| [f64::from(i) - 20.0, 0.0, 0.0]).collect();
        let mut wide_out = vec![0.0; wide.len()];
        dist2_many(&cell, p, &wide, &mut wide_out).unwrap();
        for (q, got) in wide.iter().zip(wide_out.iter()) {
            assert!((got - cell.dist2(p, *q)).abs() < 1e-12);
        }
    }

    #[test]
    fn diffs_kernel_matches_highway_shape() {
        let dx = [9.2_f64, 0.8, 5.0, 11.0, -3.0];
        let dy = [0.0; 5];
        let dz = [0.0; 5];
        let mut out = [0.0; 5];
        dist2_ortho_diffs(&dx, &dy, &dz, 10.0, 10.0, 10.0, &mut out).unwrap();
        assert!((out[0] - 0.64).abs() < 1e-12);
        assert!((out[1] - 0.64).abs() < 1e-12);
        assert!((out[2] - 25.0).abs() < 1e-12);
        assert!((out[3] - 1.0).abs() < 1e-12);
        assert!((out[4] - 9.0).abs() < 1e-12);
    }

    #[test]
    fn sheared_batch_quarter() {
        let cell =
            Cell::from_lammps_bounds(15.0, 8.660254037844386, 10.0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0)
                .unwrap();
        let p = [0.2, 0.1, 1.0];
        let qs = [[9.7, 0.1, 1.0]];
        let mut out = [0.0];
        dist2_many(&cell, p, &qs, &mut out).unwrap();
        assert!((out[0] - 0.25).abs() < 1e-12);
    }

    #[test]
    fn wrap_many_ortho_face() {
        let cell = Cell::ortho(10.0, 10.0, 10.0).unwrap();
        let diffs = [[9.2, 0.0, 0.0], [0.2, 0.0, 0.0]];
        let mut out = [[0.0; 3]; 2];
        wrap_many(&cell, &diffs, &mut out).unwrap();
        assert!((out[0][0] + 0.8).abs() < 1e-12);
        assert!((out[1][0] - 0.2).abs() < 1e-12);
    }

    #[test]
    fn pairs_match_scalar_including_later_images() {
        let cell = Cell::ortho(10.0, 11.0, 12.0).unwrap();
        let mut ps = vec![[0.0; 3]; 70];
        let mut qs = vec![[0.0; 3]; 70];
        for i in 0..70 {
            let t = f64::from(i as i32) - 20.0;
            ps[i] = [0.2, 0.0, 0.0];
            qs[i] = [t, -18.0, 3.0];
        }
        let mut out = vec![0.0; 70];
        dist2_pairs(&cell, &ps, &qs, &mut out).unwrap();
        for i in 0..70 {
            assert!((out[i] - cell.dist2(ps[i], qs[i])).abs() < 1e-9);
        }
    }

    #[test]
    fn wrap_many_keeps_negative_half() {
        let cell = Cell::ortho(10.0, 10.0, 10.0).unwrap();
        let diffs = [[-5.0, 0.0, 0.0], [5.0, 0.0, 0.0]];
        let mut out = [[0.0; 3]; 2];
        wrap_many(&cell, &diffs, &mut out).unwrap();
        assert!((out[0][0] + 5.0).abs() < 1e-12);
        assert!((out[1][0] + 5.0).abs() < 1e-12);
        for (d, o) in diffs.iter().zip(out.iter()) {
            let s = cell.displacement([0.0, 0.0, 0.0], *d);
            assert!((o[0] - s[0]).abs() < 1e-12);
        }
    }
}