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#[cfg(test)]
mod test;
use super::CscMatrix;
const NONE: isize = -1;
fn flip(i: isize) -> isize {
-i - 2
}
fn wclear(mark: isize, lemax: isize, w: &mut [isize], n: usize) -> isize {
if mark < 2 || mark + lemax < 0 {
w[..n].iter_mut().for_each(|w_i| {
if *w_i != 0 {
*w_i = 1
}
});
2
} else {
mark
}
}
fn tdfs(
root: isize,
mut count: usize,
head: &mut [isize],
next: &[isize],
post: &mut [isize],
stack: &mut [isize],
) -> usize {
let mut top = 0_isize;
stack[0] = root;
while top >= 0 {
let p = stack[top as usize];
let i = head[p as usize];
if i == NONE {
top -= 1;
post[count] = p;
count += 1;
} else {
head[p as usize] = next[i as usize];
top += 1;
stack[top as usize] = i;
}
}
count
}
impl CscMatrix {
/// Fill-reducing ordering from approximate minimum degree on the pattern of A + Aᵀ.
pub fn amd(&self) -> Vec<usize> {
let n = self.height();
assert_eq!(n, self.width());
if n == 0 {
return Vec::new();
}
let transpose = self.transpose();
let mut cp = vec![0_isize; n + 1];
let mut ci = Vec::<isize>::new();
let mut len = vec![0_isize; n + 1];
(0..n).for_each(|j| {
cp[j] = ci.len() as isize;
let mut a = self.column(j).map(|(i, _)| i).peekable();
let mut b = transpose.column(j).map(|(i, _)| i).peekable();
loop {
let i = match (a.peek(), b.peek()) {
(Some(&x), Some(&y)) => {
if x <= y {
if x == y {
b.next();
}
a.next();
x
} else {
b.next();
y
}
}
(Some(&x), None) => {
a.next();
x
}
(None, Some(&y)) => {
b.next();
y
}
(None, None) => break,
};
if i != j {
ci.push(i as isize);
}
}
len[j] = ci.len() as isize - cp[j];
});
let mut cnz = ci.len() as isize;
let nzmax = cnz + cnz / 5 + 2 * n as isize;
ci.resize(nzmax as usize, 0);
let dense = 16
.max((10.0 * (n as f64).sqrt()) as isize)
.min(n as isize - 2);
let mut nv = vec![1_isize; n + 1];
let mut w = vec![1_isize; n + 1];
let mut elen = vec![0_isize; n + 1];
let mut degree = len.clone();
let mut head = vec![NONE; n + 1];
let mut next = vec![NONE; n + 1];
let mut last = vec![NONE; n + 1];
let mut hhead = vec![NONE; n + 1];
cp[n] = NONE;
elen[n] = -2;
w[n] = 0;
let mut nel = 0_isize;
let mut mindeg = 0_usize;
let mut lemax = 0_isize;
let mut mark = wclear(0, 0, &mut w, n);
(0..n).for_each(|i| {
let d = degree[i];
if d == 0 {
elen[i] = -2;
nel += 1;
cp[i] = NONE;
w[i] = 0;
} else if d > dense {
nv[i] = 0;
elen[i] = NONE;
nel += 1;
cp[i] = flip(n as isize);
nv[n] += 1;
} else {
if head[d as usize] != NONE {
last[head[d as usize] as usize] = i as isize;
}
next[i] = head[d as usize];
head[d as usize] = i as isize;
}
});
while nel < n as isize {
let mut pivot = NONE;
while mindeg < n {
pivot = head[mindeg];
if pivot != NONE {
break;
}
mindeg += 1;
}
let k = pivot as usize;
if next[k] != NONE {
last[next[k] as usize] = NONE;
}
head[mindeg] = next[k];
let elenk = elen[k];
let mut nvk = nv[k];
nel += nvk;
if elenk > 0 && cnz + mindeg as isize >= nzmax {
(0..n).for_each(|j| {
let p = cp[j];
if p >= 0 {
cp[j] = ci[p as usize];
ci[p as usize] = flip(j as isize);
}
});
let mut q = 0_usize;
let mut p = 0_usize;
while (p as isize) < cnz {
let j = flip(ci[p]);
p += 1;
if j >= 0 {
let j = j as usize;
ci[q] = cp[j];
cp[j] = q as isize;
q += 1;
(0..len[j] - 1).for_each(|_| {
ci[q] = ci[p];
q += 1;
p += 1;
});
}
}
cnz = q as isize;
}
let mut dk = 0_isize;
nv[k] = -nvk;
let mut p = cp[k];
let pk1 = if elenk == 0 { p } else { cnz };
let mut pk2 = pk1;
for k1 in 1..=(elenk + 1) {
let (e, mut pj, ln) = if k1 > elenk {
(k, p, len[k] - elenk)
} else {
let e = ci[p as usize] as usize;
p += 1;
(e, cp[e], len[e])
};
(0..ln).for_each(|_| {
let i = ci[pj as usize] as usize;
pj += 1;
let nvi = nv[i];
if nvi > 0 {
dk += nvi;
nv[i] = -nvi;
ci[pk2 as usize] = i as isize;
pk2 += 1;
if next[i] != NONE {
last[next[i] as usize] = last[i];
}
if last[i] != NONE {
next[last[i] as usize] = next[i];
} else {
head[degree[i] as usize] = next[i];
}
}
});
if e != k {
cp[e] = flip(k as isize);
w[e] = 0;
}
}
if elenk != 0 {
cnz = pk2;
}
degree[k] = dk;
cp[k] = pk1;
len[k] = pk2 - pk1;
elen[k] = -2;
mark = wclear(mark, lemax, &mut w, n);
(pk1..pk2).for_each(|pk| {
let i = ci[pk as usize] as usize;
let eln = elen[i];
if eln > 0 {
let nvi = -nv[i];
let wnvi = mark - nvi;
(cp[i]..cp[i] + eln).for_each(|p| {
let e = ci[p as usize] as usize;
if w[e] >= mark {
w[e] -= nvi;
} else if w[e] != 0 {
w[e] = degree[e] + wnvi;
}
});
}
});
(pk1..pk2).for_each(|pk| {
let i = ci[pk as usize] as usize;
let p1 = cp[i];
let p2 = p1 + elen[i];
let mut pn = p1;
let mut hash = 0_usize;
let mut d = 0_isize;
(p1..p2).for_each(|p| {
let e = ci[p as usize] as usize;
if w[e] != 0 {
let dext = w[e] - mark;
if dext > 0 {
d += dext;
ci[pn as usize] = e as isize;
pn += 1;
hash += e;
} else {
cp[e] = flip(k as isize);
w[e] = 0;
}
}
});
elen[i] = pn - p1 + 1;
let p3 = pn;
let p4 = p1 + len[i];
(p2..p4).for_each(|p| {
let j = ci[p as usize] as usize;
let nvj = nv[j];
if nvj > 0 {
d += nvj;
ci[pn as usize] = j as isize;
pn += 1;
hash += j;
}
});
if d == 0 {
cp[i] = flip(k as isize);
let nvi = -nv[i];
dk -= nvi;
nvk += nvi;
nel += nvi;
nv[i] = 0;
elen[i] = NONE;
} else {
degree[i] = degree[i].min(d);
ci[pn as usize] = ci[p3 as usize];
ci[p3 as usize] = ci[p1 as usize];
ci[p1 as usize] = k as isize;
len[i] = pn - p1 + 1;
let hash = hash % n;
next[i] = hhead[hash];
hhead[hash] = i as isize;
last[i] = hash as isize;
}
});
degree[k] = dk;
lemax = lemax.max(dk);
mark = wclear(mark + lemax, lemax, &mut w, n);
(pk1..pk2).for_each(|pk| {
let i = ci[pk as usize] as usize;
if nv[i] < 0 {
let hash = last[i] as usize;
let mut i = hhead[hash];
hhead[hash] = NONE;
while i != NONE && next[i as usize] != NONE {
let iu = i as usize;
let ln = len[iu];
let eln = elen[iu];
(cp[iu] + 1..cp[iu] + ln).for_each(|p| w[ci[p as usize] as usize] = mark);
let mut jlast = iu;
let mut j = next[iu];
while j != NONE {
let ju = j as usize;
let mut ok = len[ju] == ln && elen[ju] == eln;
let mut p = cp[ju] + 1;
while ok && p < cp[ju] + ln {
if w[ci[p as usize] as usize] != mark {
ok = false;
}
p += 1;
}
if ok {
cp[ju] = flip(i);
nv[iu] += nv[ju];
nv[ju] = 0;
elen[ju] = NONE;
j = next[ju];
next[jlast] = j;
} else {
jlast = ju;
j = next[ju];
}
}
i = next[iu];
mark += 1;
}
}
});
let mut p = pk1;
(pk1..pk2).for_each(|pk| {
let i = ci[pk as usize] as usize;
let nvi = -nv[i];
if nvi > 0 {
nv[i] = nvi;
let d = (degree[i] + dk - nvi).min(n as isize - nel - nvi);
if head[d as usize] != NONE {
last[head[d as usize] as usize] = i as isize;
}
next[i] = head[d as usize];
last[i] = NONE;
head[d as usize] = i as isize;
mindeg = mindeg.min(d as usize);
degree[i] = d;
ci[p as usize] = i as isize;
p += 1;
}
});
nv[k] = nvk;
len[k] = p - pk1;
if len[k] == 0 {
cp[k] = NONE;
w[k] = 0;
}
if elenk != 0 {
cnz = p;
}
}
(0..=n).for_each(|i| cp[i] = flip(cp[i]));
head.iter_mut().for_each(|head_i| *head_i = NONE);
(0..n).rev().for_each(|j| {
if nv[j] <= 0 {
next[j] = head[cp[j] as usize];
head[cp[j] as usize] = j as isize;
}
});
(0..=n).rev().for_each(|e| {
if nv[e] > 0 && cp[e] != NONE {
next[e] = head[cp[e] as usize];
head[cp[e] as usize] = e as isize;
}
});
let mut post = vec![0_isize; n + 1];
let mut stack = vec![0_isize; n + 1];
let mut count = 0_usize;
(0..=n).for_each(|i| {
if cp[i] == NONE {
count = tdfs(i as isize, count, &mut head, &next, &mut post, &mut stack);
}
});
post.into_iter()
.filter(|&i| i != n as isize)
.map(|i| i as usize)
.collect()
}
}