feat:node-modules
This commit is contained in:
houjunxiang
580
node_modules/mathjs/lib/esm/function/algebra/sparse/csAmd.js
generated
vendored
Normal file
580
node_modules/mathjs/lib/esm/function/algebra/sparse/csAmd.js
generated
vendored
Normal file
@@ -0,0 +1,580 @@
|
||||
// Copyright (c) 2006-2024, Timothy A. Davis, All Rights Reserved.
|
||||
// SPDX-License-Identifier: LGPL-2.1+
|
||||
// https://github.com/DrTimothyAldenDavis/SuiteSparse/tree/dev/CSparse/Source
|
||||
import { factory } from '../../../utils/factory.js';
|
||||
import { csFkeep } from './csFkeep.js';
|
||||
import { csFlip } from './csFlip.js';
|
||||
import { csTdfs } from './csTdfs.js';
|
||||
var name = 'csAmd';
|
||||
var dependencies = ['add', 'multiply', 'transpose'];
|
||||
export var createCsAmd = /* #__PURE__ */factory(name, dependencies, _ref => {
|
||||
var {
|
||||
add,
|
||||
multiply,
|
||||
transpose
|
||||
} = _ref;
|
||||
/**
|
||||
* Approximate minimum degree ordering. The minimum degree algorithm is a widely used
|
||||
* heuristic for finding a permutation P so that P*A*P' has fewer nonzeros in its factorization
|
||||
* than A. It is a gready method that selects the sparsest pivot row and column during the course
|
||||
* of a right looking sparse Cholesky factorization.
|
||||
*
|
||||
* @param {Number} order 0: Natural, 1: Cholesky, 2: LU, 3: QR
|
||||
* @param {Matrix} m Sparse Matrix
|
||||
*/
|
||||
return function csAmd(order, a) {
|
||||
// check input parameters
|
||||
if (!a || order <= 0 || order > 3) {
|
||||
return null;
|
||||
}
|
||||
// a matrix arrays
|
||||
var asize = a._size;
|
||||
// rows and columns
|
||||
var m = asize[0];
|
||||
var n = asize[1];
|
||||
// initialize vars
|
||||
var lemax = 0;
|
||||
// dense threshold
|
||||
var dense = Math.max(16, 10 * Math.sqrt(n));
|
||||
dense = Math.min(n - 2, dense);
|
||||
// create target matrix C
|
||||
var cm = _createTargetMatrix(order, a, m, n, dense);
|
||||
// drop diagonal entries
|
||||
csFkeep(cm, _diag, null);
|
||||
// C matrix arrays
|
||||
var cindex = cm._index;
|
||||
var cptr = cm._ptr;
|
||||
|
||||
// number of nonzero elements in C
|
||||
var cnz = cptr[n];
|
||||
|
||||
// allocate result (n+1)
|
||||
var P = [];
|
||||
|
||||
// create workspace (8 * (n + 1))
|
||||
var W = [];
|
||||
var len = 0; // first n + 1 entries
|
||||
var nv = n + 1; // next n + 1 entries
|
||||
var next = 2 * (n + 1); // next n + 1 entries
|
||||
var head = 3 * (n + 1); // next n + 1 entries
|
||||
var elen = 4 * (n + 1); // next n + 1 entries
|
||||
var degree = 5 * (n + 1); // next n + 1 entries
|
||||
var w = 6 * (n + 1); // next n + 1 entries
|
||||
var hhead = 7 * (n + 1); // last n + 1 entries
|
||||
|
||||
// use P as workspace for last
|
||||
var last = P;
|
||||
|
||||
// initialize quotient graph
|
||||
var mark = _initializeQuotientGraph(n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree);
|
||||
|
||||
// initialize degree lists
|
||||
var nel = _initializeDegreeLists(n, cptr, W, degree, elen, w, dense, nv, head, last, next);
|
||||
|
||||
// minimum degree node
|
||||
var mindeg = 0;
|
||||
|
||||
// vars
|
||||
var i, j, k, k1, k2, e, pj, ln, nvi, pk, eln, p1, p2, pn, h, d;
|
||||
|
||||
// while (selecting pivots) do
|
||||
while (nel < n) {
|
||||
// select node of minimum approximate degree. amd() is now ready to start eliminating the graph. It first
|
||||
// finds a node k of minimum degree and removes it from its degree list. The variable nel keeps track of thow
|
||||
// many nodes have been eliminated.
|
||||
for (k = -1; mindeg < n && (k = W[head + mindeg]) === -1; mindeg++);
|
||||
if (W[next + k] !== -1) {
|
||||
last[W[next + k]] = -1;
|
||||
}
|
||||
// remove k from degree list
|
||||
W[head + mindeg] = W[next + k];
|
||||
// elenk = |Ek|
|
||||
var elenk = W[elen + k];
|
||||
// # of nodes k represents
|
||||
var nvk = W[nv + k];
|
||||
// W[nv + k] nodes of A eliminated
|
||||
nel += nvk;
|
||||
|
||||
// Construct a new element. The new element Lk is constructed in place if |Ek| = 0. nv[i] is
|
||||
// negated for all nodes i in Lk to flag them as members of this set. Each node i is removed from the
|
||||
// degree lists. All elements e in Ek are absorved into element k.
|
||||
var dk = 0;
|
||||
// flag k as in Lk
|
||||
W[nv + k] = -nvk;
|
||||
var p = cptr[k];
|
||||
// do in place if W[elen + k] === 0
|
||||
var pk1 = elenk === 0 ? p : cnz;
|
||||
var pk2 = pk1;
|
||||
for (k1 = 1; k1 <= elenk + 1; k1++) {
|
||||
if (k1 > elenk) {
|
||||
// search the nodes in k
|
||||
e = k;
|
||||
// list of nodes starts at cindex[pj]
|
||||
pj = p;
|
||||
// length of list of nodes in k
|
||||
ln = W[len + k] - elenk;
|
||||
} else {
|
||||
// search the nodes in e
|
||||
e = cindex[p++];
|
||||
pj = cptr[e];
|
||||
// length of list of nodes in e
|
||||
ln = W[len + e];
|
||||
}
|
||||
for (k2 = 1; k2 <= ln; k2++) {
|
||||
i = cindex[pj++];
|
||||
// check node i dead, or seen
|
||||
if ((nvi = W[nv + i]) <= 0) {
|
||||
continue;
|
||||
}
|
||||
// W[degree + Lk] += size of node i
|
||||
dk += nvi;
|
||||
// negate W[nv + i] to denote i in Lk
|
||||
W[nv + i] = -nvi;
|
||||
// place i in Lk
|
||||
cindex[pk2++] = i;
|
||||
if (W[next + i] !== -1) {
|
||||
last[W[next + i]] = last[i];
|
||||
}
|
||||
// check we need to remove i from degree list
|
||||
if (last[i] !== -1) {
|
||||
W[next + last[i]] = W[next + i];
|
||||
} else {
|
||||
W[head + W[degree + i]] = W[next + i];
|
||||
}
|
||||
}
|
||||
if (e !== k) {
|
||||
// absorb e into k
|
||||
cptr[e] = csFlip(k);
|
||||
// e is now a dead element
|
||||
W[w + e] = 0;
|
||||
}
|
||||
}
|
||||
// cindex[cnz...nzmax] is free
|
||||
if (elenk !== 0) {
|
||||
cnz = pk2;
|
||||
}
|
||||
// external degree of k - |Lk\i|
|
||||
W[degree + k] = dk;
|
||||
// element k is in cindex[pk1..pk2-1]
|
||||
cptr[k] = pk1;
|
||||
W[len + k] = pk2 - pk1;
|
||||
// k is now an element
|
||||
W[elen + k] = -2;
|
||||
|
||||
// Find set differences. The scan1 function now computes the set differences |Le \ Lk| for all elements e. At the start of the
|
||||
// scan, no entry in the w array is greater than or equal to mark.
|
||||
|
||||
// clear w if necessary
|
||||
mark = _wclear(mark, lemax, W, w, n);
|
||||
// scan 1: find |Le\Lk|
|
||||
for (pk = pk1; pk < pk2; pk++) {
|
||||
i = cindex[pk];
|
||||
// check if W[elen + i] empty, skip it
|
||||
if ((eln = W[elen + i]) <= 0) {
|
||||
continue;
|
||||
}
|
||||
// W[nv + i] was negated
|
||||
nvi = -W[nv + i];
|
||||
var wnvi = mark - nvi;
|
||||
// scan Ei
|
||||
for (p = cptr[i], p1 = cptr[i] + eln - 1; p <= p1; p++) {
|
||||
e = cindex[p];
|
||||
if (W[w + e] >= mark) {
|
||||
// decrement |Le\Lk|
|
||||
W[w + e] -= nvi;
|
||||
} else if (W[w + e] !== 0) {
|
||||
// ensure e is a live element, 1st time e seen in scan 1
|
||||
W[w + e] = W[degree + e] + wnvi;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// degree update
|
||||
// The second pass computes the approximate degree di, prunes the sets Ei and Ai, and computes a hash
|
||||
// function h(i) for all nodes in Lk.
|
||||
|
||||
// scan2: degree update
|
||||
for (pk = pk1; pk < pk2; pk++) {
|
||||
// consider node i in Lk
|
||||
i = cindex[pk];
|
||||
p1 = cptr[i];
|
||||
p2 = p1 + W[elen + i] - 1;
|
||||
pn = p1;
|
||||
// scan Ei
|
||||
for (h = 0, d = 0, p = p1; p <= p2; p++) {
|
||||
e = cindex[p];
|
||||
// check e is an unabsorbed element
|
||||
if (W[w + e] !== 0) {
|
||||
// dext = |Le\Lk|
|
||||
var dext = W[w + e] - mark;
|
||||
if (dext > 0) {
|
||||
// sum up the set differences
|
||||
d += dext;
|
||||
// keep e in Ei
|
||||
cindex[pn++] = e;
|
||||
// compute the hash of node i
|
||||
h += e;
|
||||
} else {
|
||||
// aggressive absorb. e->k
|
||||
cptr[e] = csFlip(k);
|
||||
// e is a dead element
|
||||
W[w + e] = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
// W[elen + i] = |Ei|
|
||||
W[elen + i] = pn - p1 + 1;
|
||||
var p3 = pn;
|
||||
var p4 = p1 + W[len + i];
|
||||
// prune edges in Ai
|
||||
for (p = p2 + 1; p < p4; p++) {
|
||||
j = cindex[p];
|
||||
// check node j dead or in Lk
|
||||
var nvj = W[nv + j];
|
||||
if (nvj <= 0) {
|
||||
continue;
|
||||
}
|
||||
// degree(i) += |j|
|
||||
d += nvj;
|
||||
// place j in node list of i
|
||||
cindex[pn++] = j;
|
||||
// compute hash for node i
|
||||
h += j;
|
||||
}
|
||||
// check for mass elimination
|
||||
if (d === 0) {
|
||||
// absorb i into k
|
||||
cptr[i] = csFlip(k);
|
||||
nvi = -W[nv + i];
|
||||
// |Lk| -= |i|
|
||||
dk -= nvi;
|
||||
// |k| += W[nv + i]
|
||||
nvk += nvi;
|
||||
nel += nvi;
|
||||
W[nv + i] = 0;
|
||||
// node i is dead
|
||||
W[elen + i] = -1;
|
||||
} else {
|
||||
// update degree(i)
|
||||
W[degree + i] = Math.min(W[degree + i], d);
|
||||
// move first node to end
|
||||
cindex[pn] = cindex[p3];
|
||||
// move 1st el. to end of Ei
|
||||
cindex[p3] = cindex[p1];
|
||||
// add k as 1st element in of Ei
|
||||
cindex[p1] = k;
|
||||
// new len of adj. list of node i
|
||||
W[len + i] = pn - p1 + 1;
|
||||
// finalize hash of i
|
||||
h = (h < 0 ? -h : h) % n;
|
||||
// place i in hash bucket
|
||||
W[next + i] = W[hhead + h];
|
||||
W[hhead + h] = i;
|
||||
// save hash of i in last[i]
|
||||
last[i] = h;
|
||||
}
|
||||
}
|
||||
// finalize |Lk|
|
||||
W[degree + k] = dk;
|
||||
lemax = Math.max(lemax, dk);
|
||||
// clear w
|
||||
mark = _wclear(mark + lemax, lemax, W, w, n);
|
||||
|
||||
// Supernode detection. Supernode detection relies on the hash function h(i) computed for each node i.
|
||||
// If two nodes have identical adjacency lists, their hash functions wil be identical.
|
||||
for (pk = pk1; pk < pk2; pk++) {
|
||||
i = cindex[pk];
|
||||
// check i is dead, skip it
|
||||
if (W[nv + i] >= 0) {
|
||||
continue;
|
||||
}
|
||||
// scan hash bucket of node i
|
||||
h = last[i];
|
||||
i = W[hhead + h];
|
||||
// hash bucket will be empty
|
||||
W[hhead + h] = -1;
|
||||
for (; i !== -1 && W[next + i] !== -1; i = W[next + i], mark++) {
|
||||
ln = W[len + i];
|
||||
eln = W[elen + i];
|
||||
for (p = cptr[i] + 1; p <= cptr[i] + ln - 1; p++) {
|
||||
W[w + cindex[p]] = mark;
|
||||
}
|
||||
var jlast = i;
|
||||
// compare i with all j
|
||||
for (j = W[next + i]; j !== -1;) {
|
||||
var ok = W[len + j] === ln && W[elen + j] === eln;
|
||||
for (p = cptr[j] + 1; ok && p <= cptr[j] + ln - 1; p++) {
|
||||
// compare i and j
|
||||
if (W[w + cindex[p]] !== mark) {
|
||||
ok = 0;
|
||||
}
|
||||
}
|
||||
// check i and j are identical
|
||||
if (ok) {
|
||||
// absorb j into i
|
||||
cptr[j] = csFlip(i);
|
||||
W[nv + i] += W[nv + j];
|
||||
W[nv + j] = 0;
|
||||
// node j is dead
|
||||
W[elen + j] = -1;
|
||||
// delete j from hash bucket
|
||||
j = W[next + j];
|
||||
W[next + jlast] = j;
|
||||
} else {
|
||||
// j and i are different
|
||||
jlast = j;
|
||||
j = W[next + j];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Finalize new element. The elimination of node k is nearly complete. All nodes i in Lk are scanned one last time.
|
||||
// Node i is removed from Lk if it is dead. The flagged status of nv[i] is cleared.
|
||||
for (p = pk1, pk = pk1; pk < pk2; pk++) {
|
||||
i = cindex[pk];
|
||||
// check i is dead, skip it
|
||||
if ((nvi = -W[nv + i]) <= 0) {
|
||||
continue;
|
||||
}
|
||||
// restore W[nv + i]
|
||||
W[nv + i] = nvi;
|
||||
// compute external degree(i)
|
||||
d = W[degree + i] + dk - nvi;
|
||||
d = Math.min(d, n - nel - nvi);
|
||||
if (W[head + d] !== -1) {
|
||||
last[W[head + d]] = i;
|
||||
}
|
||||
// put i back in degree list
|
||||
W[next + i] = W[head + d];
|
||||
last[i] = -1;
|
||||
W[head + d] = i;
|
||||
// find new minimum degree
|
||||
mindeg = Math.min(mindeg, d);
|
||||
W[degree + i] = d;
|
||||
// place i in Lk
|
||||
cindex[p++] = i;
|
||||
}
|
||||
// # nodes absorbed into k
|
||||
W[nv + k] = nvk;
|
||||
// length of adj list of element k
|
||||
if ((W[len + k] = p - pk1) === 0) {
|
||||
// k is a root of the tree
|
||||
cptr[k] = -1;
|
||||
// k is now a dead element
|
||||
W[w + k] = 0;
|
||||
}
|
||||
if (elenk !== 0) {
|
||||
// free unused space in Lk
|
||||
cnz = p;
|
||||
}
|
||||
}
|
||||
|
||||
// Postordering. The elimination is complete, but no permutation has been computed. All that is left
|
||||
// of the graph is the assembly tree (ptr) and a set of dead nodes and elements (i is a dead node if
|
||||
// nv[i] is zero and a dead element if nv[i] > 0). It is from this information only that the final permutation
|
||||
// is computed. The tree is restored by unflipping all of ptr.
|
||||
|
||||
// fix assembly tree
|
||||
for (i = 0; i < n; i++) {
|
||||
cptr[i] = csFlip(cptr[i]);
|
||||
}
|
||||
for (j = 0; j <= n; j++) {
|
||||
W[head + j] = -1;
|
||||
}
|
||||
// place unordered nodes in lists
|
||||
for (j = n; j >= 0; j--) {
|
||||
// skip if j is an element
|
||||
if (W[nv + j] > 0) {
|
||||
continue;
|
||||
}
|
||||
// place j in list of its parent
|
||||
W[next + j] = W[head + cptr[j]];
|
||||
W[head + cptr[j]] = j;
|
||||
}
|
||||
// place elements in lists
|
||||
for (e = n; e >= 0; e--) {
|
||||
// skip unless e is an element
|
||||
if (W[nv + e] <= 0) {
|
||||
continue;
|
||||
}
|
||||
if (cptr[e] !== -1) {
|
||||
// place e in list of its parent
|
||||
W[next + e] = W[head + cptr[e]];
|
||||
W[head + cptr[e]] = e;
|
||||
}
|
||||
}
|
||||
// postorder the assembly tree
|
||||
for (k = 0, i = 0; i <= n; i++) {
|
||||
if (cptr[i] === -1) {
|
||||
k = csTdfs(i, k, W, head, next, P, w);
|
||||
}
|
||||
}
|
||||
// remove last item in array
|
||||
P.splice(P.length - 1, 1);
|
||||
// return P
|
||||
return P;
|
||||
};
|
||||
|
||||
/**
|
||||
* Creates the matrix that will be used by the approximate minimum degree ordering algorithm. The function accepts the matrix M as input and returns a permutation
|
||||
* vector P. The amd algorithm operates on a symmetrix matrix, so one of three symmetric matrices is formed.
|
||||
*
|
||||
* Order: 0
|
||||
* A natural ordering P=null matrix is returned.
|
||||
*
|
||||
* Order: 1
|
||||
* Matrix must be square. This is appropriate for a Cholesky or LU factorization.
|
||||
* P = M + M'
|
||||
*
|
||||
* Order: 2
|
||||
* Dense columns from M' are dropped, M recreated from M'. This is appropriatefor LU factorization of unsymmetric matrices.
|
||||
* P = M' * M
|
||||
*
|
||||
* Order: 3
|
||||
* This is best used for QR factorization or LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.
|
||||
* P = M' * M
|
||||
*/
|
||||
function _createTargetMatrix(order, a, m, n, dense) {
|
||||
// compute A'
|
||||
var at = transpose(a);
|
||||
|
||||
// check order = 1, matrix must be square
|
||||
if (order === 1 && n === m) {
|
||||
// C = A + A'
|
||||
return add(a, at);
|
||||
}
|
||||
|
||||
// check order = 2, drop dense columns from M'
|
||||
if (order === 2) {
|
||||
// transpose arrays
|
||||
var tindex = at._index;
|
||||
var tptr = at._ptr;
|
||||
// new column index
|
||||
var p2 = 0;
|
||||
// loop A' columns (rows)
|
||||
for (var j = 0; j < m; j++) {
|
||||
// column j of AT starts here
|
||||
var p = tptr[j];
|
||||
// new column j starts here
|
||||
tptr[j] = p2;
|
||||
// skip dense col j
|
||||
if (tptr[j + 1] - p > dense) {
|
||||
continue;
|
||||
}
|
||||
// map rows in column j of A
|
||||
for (var p1 = tptr[j + 1]; p < p1; p++) {
|
||||
tindex[p2++] = tindex[p];
|
||||
}
|
||||
}
|
||||
// finalize AT
|
||||
tptr[m] = p2;
|
||||
// recreate A from new transpose matrix
|
||||
a = transpose(at);
|
||||
// use A' * A
|
||||
return multiply(at, a);
|
||||
}
|
||||
|
||||
// use A' * A, square or rectangular matrix
|
||||
return multiply(at, a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Initialize quotient graph. There are four kind of nodes and elements that must be represented:
|
||||
*
|
||||
* - A live node is a node i (or a supernode) that has not been selected as a pivot nad has not been merged into another supernode.
|
||||
* - A dead node i is one that has been removed from the graph, having been absorved into r = flip(ptr[i]).
|
||||
* - A live element e is one that is in the graph, having been formed when node e was selected as the pivot.
|
||||
* - A dead element e is one that has benn absorved into a subsequent element s = flip(ptr[e]).
|
||||
*/
|
||||
function _initializeQuotientGraph(n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree) {
|
||||
// Initialize quotient graph
|
||||
for (var k = 0; k < n; k++) {
|
||||
W[len + k] = cptr[k + 1] - cptr[k];
|
||||
}
|
||||
W[len + n] = 0;
|
||||
// initialize workspace
|
||||
for (var i = 0; i <= n; i++) {
|
||||
// degree list i is empty
|
||||
W[head + i] = -1;
|
||||
last[i] = -1;
|
||||
W[next + i] = -1;
|
||||
// hash list i is empty
|
||||
W[hhead + i] = -1;
|
||||
// node i is just one node
|
||||
W[nv + i] = 1;
|
||||
// node i is alive
|
||||
W[w + i] = 1;
|
||||
// Ek of node i is empty
|
||||
W[elen + i] = 0;
|
||||
// degree of node i
|
||||
W[degree + i] = W[len + i];
|
||||
}
|
||||
// clear w
|
||||
var mark = _wclear(0, 0, W, w, n);
|
||||
// n is a dead element
|
||||
W[elen + n] = -2;
|
||||
// n is a root of assembly tree
|
||||
cptr[n] = -1;
|
||||
// n is a dead element
|
||||
W[w + n] = 0;
|
||||
// return mark
|
||||
return mark;
|
||||
}
|
||||
|
||||
/**
|
||||
* Initialize degree lists. Each node is placed in its degree lists. Nodes of zero degree are eliminated immediately. Nodes with
|
||||
* degree >= dense are alsol eliminated and merged into a placeholder node n, a dead element. Thes nodes will appera last in the
|
||||
* output permutation p.
|
||||
*/
|
||||
function _initializeDegreeLists(n, cptr, W, degree, elen, w, dense, nv, head, last, next) {
|
||||
// result
|
||||
var nel = 0;
|
||||
// loop columns
|
||||
for (var i = 0; i < n; i++) {
|
||||
// degree @ i
|
||||
var d = W[degree + i];
|
||||
// check node i is empty
|
||||
if (d === 0) {
|
||||
// element i is dead
|
||||
W[elen + i] = -2;
|
||||
nel++;
|
||||
// i is a root of assembly tree
|
||||
cptr[i] = -1;
|
||||
W[w + i] = 0;
|
||||
} else if (d > dense) {
|
||||
// absorb i into element n
|
||||
W[nv + i] = 0;
|
||||
// node i is dead
|
||||
W[elen + i] = -1;
|
||||
nel++;
|
||||
cptr[i] = csFlip(n);
|
||||
W[nv + n]++;
|
||||
} else {
|
||||
var h = W[head + d];
|
||||
if (h !== -1) {
|
||||
last[h] = i;
|
||||
}
|
||||
// put node i in degree list d
|
||||
W[next + i] = W[head + d];
|
||||
W[head + d] = i;
|
||||
}
|
||||
}
|
||||
return nel;
|
||||
}
|
||||
function _wclear(mark, lemax, W, w, n) {
|
||||
if (mark < 2 || mark + lemax < 0) {
|
||||
for (var k = 0; k < n; k++) {
|
||||
if (W[w + k] !== 0) {
|
||||
W[w + k] = 1;
|
||||
}
|
||||
}
|
||||
mark = 2;
|
||||
}
|
||||
// at this point, W [0..n-1] < mark holds
|
||||
return mark;
|
||||
}
|
||||
function _diag(i, j) {
|
||||
return i !== j;
|
||||
}
|
||||
});
|
||||
Reference in New Issue
Block a user