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scinote-web/vendor/assets/javascripts/numeric.js
aignatov-bio 1c81994e01
Add license text to vendor files (#1861)
2019-07-03 09:18:30 +02:00

3266 lines
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JavaScript
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// Copyright (C) 2011 by Sébastien Loisel and is distributed under the MIT license
"use strict";
var numeric = (typeof exports === "undefined")?(function numeric() {}):(exports);
if(typeof global !== "undefined") { global.numeric = numeric; }
numeric.version = "1.2.6";
// 1. Utility functions
numeric.bench = function bench (f,interval) {
var t1,t2,n,i;
if(typeof interval === "undefined") { interval = 15; }
n = 0.5;
t1 = new Date();
while(1) {
n*=2;
for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
while(i>0) { f(); i--; }
t2 = new Date();
if(t2-t1 > interval) break;
}
for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
while(i>0) { f(); i--; }
t2 = new Date();
return 1000*(3*n-1)/(t2-t1);
}
numeric._myIndexOf = (function _myIndexOf(w) {
var n = this.length,k;
for(k=0;k<n;++k) if(this[k]===w) return k;
return -1;
});
numeric.myIndexOf = (Array.prototype.indexOf)?Array.prototype.indexOf:numeric._myIndexOf;
numeric.Function = Function;
numeric.precision = 4;
numeric.largeArray = 50;
numeric.prettyPrint = function prettyPrint(x) {
function fmtnum(x) {
if(x === 0) { return '0'; }
if(isNaN(x)) { return 'NaN'; }
if(x<0) { return '-'+fmtnum(-x); }
if(isFinite(x)) {
var scale = Math.floor(Math.log(x) / Math.log(10));
var normalized = x / Math.pow(10,scale);
var basic = normalized.toPrecision(numeric.precision);
if(parseFloat(basic) === 10) { scale++; normalized = 1; basic = normalized.toPrecision(numeric.precision); }
return parseFloat(basic).toString()+'e'+scale.toString();
}
return 'Infinity';
}
var ret = [];
function foo(x) {
var k;
if(typeof x === "undefined") { ret.push(Array(numeric.precision+8).join(' ')); return false; }
if(typeof x === "string") { ret.push('"'+x+'"'); return false; }
if(typeof x === "boolean") { ret.push(x.toString()); return false; }
if(typeof x === "number") {
var a = fmtnum(x);
var b = x.toPrecision(numeric.precision);
var c = parseFloat(x.toString()).toString();
var d = [a,b,c,parseFloat(b).toString(),parseFloat(c).toString()];
for(k=1;k<d.length;k++) { if(d[k].length < a.length) a = d[k]; }
ret.push(Array(numeric.precision+8-a.length).join(' ')+a);
return false;
}
if(x === null) { ret.push("null"); return false; }
if(typeof x === "function") {
ret.push(x.toString());
var flag = false;
for(k in x) { if(x.hasOwnProperty(k)) {
if(flag) ret.push(',\n');
else ret.push('\n{');
flag = true;
ret.push(k);
ret.push(': \n');
foo(x[k]);
} }
if(flag) ret.push('}\n');
return true;
}
if(x instanceof Array) {
if(x.length > numeric.largeArray) { ret.push('...Large Array...'); return true; }
var flag = false;
ret.push('[');
for(k=0;k<x.length;k++) { if(k>0) { ret.push(','); if(flag) ret.push('\n '); } flag = foo(x[k]); }
ret.push(']');
return true;
}
ret.push('{');
var flag = false;
for(k in x) { if(x.hasOwnProperty(k)) { if(flag) ret.push(',\n'); flag = true; ret.push(k); ret.push(': \n'); foo(x[k]); } }
ret.push('}');
return true;
}
foo(x);
return ret.join('');
}
numeric.parseDate = function parseDate(d) {
function foo(d) {
if(typeof d === 'string') { return Date.parse(d.replace(/-/g,'/')); }
if(!(d instanceof Array)) { throw new Error("parseDate: parameter must be arrays of strings"); }
var ret = [],k;
for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
return ret;
}
return foo(d);
}
numeric.parseFloat = function parseFloat_(d) {
function foo(d) {
if(typeof d === 'string') { return parseFloat(d); }
if(!(d instanceof Array)) { throw new Error("parseFloat: parameter must be arrays of strings"); }
var ret = [],k;
for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
return ret;
}
return foo(d);
}
numeric.parseCSV = function parseCSV(t) {
var foo = t.split('\n');
var j,k;
var ret = [];
var pat = /(([^'",]*)|('[^']*')|("[^"]*")),/g;
var patnum = /^\s*(([+-]?[0-9]+(\.[0-9]*)?(e[+-]?[0-9]+)?)|([+-]?[0-9]*(\.[0-9]+)?(e[+-]?[0-9]+)?))\s*$/;
var stripper = function(n) { return n.substr(0,n.length-1); }
var count = 0;
for(k=0;k<foo.length;k++) {
var bar = (foo[k]+",").match(pat),baz;
if(bar.length>0) {
ret[count] = [];
for(j=0;j<bar.length;j++) {
baz = stripper(bar[j]);
if(patnum.test(baz)) { ret[count][j] = parseFloat(baz); }
else ret[count][j] = baz;
}
count++;
}
}
return ret;
}
numeric.toCSV = function toCSV(A) {
var s = numeric.dim(A);
var i,j,m,n,row,ret;
m = s[0];
n = s[1];
ret = [];
for(i=0;i<m;i++) {
row = [];
for(j=0;j<m;j++) { row[j] = A[i][j].toString(); }
ret[i] = row.join(', ');
}
return ret.join('\n')+'\n';
}
numeric.getURL = function getURL(url) {
var client = new XMLHttpRequest();
client.open("GET",url,false);
client.send();
return client;
}
numeric.imageURL = function imageURL(img) {
function base64(A) {
var n = A.length, i,x,y,z,p,q,r,s;
var key = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=";
var ret = "";
for(i=0;i<n;i+=3) {
x = A[i];
y = A[i+1];
z = A[i+2];
p = x >> 2;
q = ((x & 3) << 4) + (y >> 4);
r = ((y & 15) << 2) + (z >> 6);
s = z & 63;
if(i+1>=n) { r = s = 64; }
else if(i+2>=n) { s = 64; }
ret += key.charAt(p) + key.charAt(q) + key.charAt(r) + key.charAt(s);
}
return ret;
}
function crc32Array (a,from,to) {
if(typeof from === "undefined") { from = 0; }
if(typeof to === "undefined") { to = a.length; }
var table = [0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D];
var crc = -1, y = 0, n = a.length,i;
for (i = from; i < to; i++) {
y = (crc ^ a[i]) & 0xFF;
crc = (crc >>> 8) ^ table[y];
}
return crc ^ (-1);
}
var h = img[0].length, w = img[0][0].length, s1, s2, next,k,length,a,b,i,j,adler32,crc32;
var stream = [
137, 80, 78, 71, 13, 10, 26, 10, // 0: PNG signature
0,0,0,13, // 8: IHDR Chunk length
73, 72, 68, 82, // 12: "IHDR"
(w >> 24) & 255, (w >> 16) & 255, (w >> 8) & 255, w&255, // 16: Width
(h >> 24) & 255, (h >> 16) & 255, (h >> 8) & 255, h&255, // 20: Height
8, // 24: bit depth
2, // 25: RGB
0, // 26: deflate
0, // 27: no filter
0, // 28: no interlace
-1,-2,-3,-4, // 29: CRC
-5,-6,-7,-8, // 33: IDAT Chunk length
73, 68, 65, 84, // 37: "IDAT"
// RFC 1950 header starts here
8, // 41: RFC1950 CMF
29 // 42: RFC1950 FLG
];
crc32 = crc32Array(stream,12,29);
stream[29] = (crc32>>24)&255;
stream[30] = (crc32>>16)&255;
stream[31] = (crc32>>8)&255;
stream[32] = (crc32)&255;
s1 = 1;
s2 = 0;
for(i=0;i<h;i++) {
if(i<h-1) { stream.push(0); }
else { stream.push(1); }
a = (3*w+1+(i===0))&255; b = ((3*w+1+(i===0))>>8)&255;
stream.push(a); stream.push(b);
stream.push((~a)&255); stream.push((~b)&255);
if(i===0) stream.push(0);
for(j=0;j<w;j++) {
for(k=0;k<3;k++) {
a = img[k][i][j];
if(a>255) a = 255;
else if(a<0) a=0;
else a = Math.round(a);
s1 = (s1 + a )%65521;
s2 = (s2 + s1)%65521;
stream.push(a);
}
}
stream.push(0);
}
adler32 = (s2<<16)+s1;
stream.push((adler32>>24)&255);
stream.push((adler32>>16)&255);
stream.push((adler32>>8)&255);
stream.push((adler32)&255);
length = stream.length - 41;
stream[33] = (length>>24)&255;
stream[34] = (length>>16)&255;
stream[35] = (length>>8)&255;
stream[36] = (length)&255;
crc32 = crc32Array(stream,37);
stream.push((crc32>>24)&255);
stream.push((crc32>>16)&255);
stream.push((crc32>>8)&255);
stream.push((crc32)&255);
stream.push(0);
stream.push(0);
stream.push(0);
stream.push(0);
// a = stream.length;
stream.push(73); // I
stream.push(69); // E
stream.push(78); // N
stream.push(68); // D
stream.push(174); // CRC1
stream.push(66); // CRC2
stream.push(96); // CRC3
stream.push(130); // CRC4
return 'data:image/png;base64,'+base64(stream);
}
// 2. Linear algebra with Arrays.
numeric._dim = function _dim(x) {
var ret = [];
while(typeof x === "object") { ret.push(x.length); x = x[0]; }
return ret;
}
numeric.dim = function dim(x) {
var y,z;
if(typeof x === "object") {
y = x[0];
if(typeof y === "object") {
z = y[0];
if(typeof z === "object") {
return numeric._dim(x);
}
return [x.length,y.length];
}
return [x.length];
}
return [];
}
numeric.mapreduce = function mapreduce(body,init) {
return Function('x','accum','_s','_k',
'if(typeof accum === "undefined") accum = '+init+';\n'+
'if(typeof x === "number") { var xi = x; '+body+'; return accum; }\n'+
'if(typeof _s === "undefined") _s = numeric.dim(x);\n'+
'if(typeof _k === "undefined") _k = 0;\n'+
'var _n = _s[_k];\n'+
'var i,xi;\n'+
'if(_k < _s.length-1) {\n'+
' for(i=_n-1;i>=0;i--) {\n'+
' accum = arguments.callee(x[i],accum,_s,_k+1);\n'+
' }'+
' return accum;\n'+
'}\n'+
'for(i=_n-1;i>=1;i-=2) { \n'+
' xi = x[i];\n'+
' '+body+';\n'+
' xi = x[i-1];\n'+
' '+body+';\n'+
'}\n'+
'if(i === 0) {\n'+
' xi = x[i];\n'+
' '+body+'\n'+
'}\n'+
'return accum;'
);
}
numeric.mapreduce2 = function mapreduce2(body,setup) {
return Function('x',
'var n = x.length;\n'+
'var i,xi;\n'+setup+';\n'+
'for(i=n-1;i!==-1;--i) { \n'+
' xi = x[i];\n'+
' '+body+';\n'+
'}\n'+
'return accum;'
);
}
numeric.same = function same(x,y) {
var i,n;
if(!(x instanceof Array) || !(y instanceof Array)) { return false; }
n = x.length;
if(n !== y.length) { return false; }
for(i=0;i<n;i++) {
if(x[i] === y[i]) { continue; }
if(typeof x[i] === "object") { if(!same(x[i],y[i])) return false; }
else { return false; }
}
return true;
}
numeric.rep = function rep(s,v,k) {
if(typeof k === "undefined") { k=0; }
var n = s[k], ret = Array(n), i;
if(k === s.length-1) {
for(i=n-2;i>=0;i-=2) { ret[i+1] = v; ret[i] = v; }
if(i===-1) { ret[0] = v; }
return ret;
}
for(i=n-1;i>=0;i--) { ret[i] = numeric.rep(s,v,k+1); }
return ret;
}
numeric.dotMMsmall = function dotMMsmall(x,y) {
var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0;
p = x.length; q = y.length; r = y[0].length;
ret = Array(p);
for(i=p-1;i>=0;i--) {
foo = Array(r);
bar = x[i];
for(k=r-1;k>=0;k--) {
woo = bar[q-1]*y[q-1][k];
for(j=q-2;j>=1;j-=2) {
i0 = j-1;
woo += bar[j]*y[j][k] + bar[i0]*y[i0][k];
}
if(j===0) { woo += bar[0]*y[0][k]; }
foo[k] = woo;
}
ret[i] = foo;
}
return ret;
}
numeric._getCol = function _getCol(A,j,x) {
var n = A.length, i;
for(i=n-1;i>0;--i) {
x[i] = A[i][j];
--i;
x[i] = A[i][j];
}
if(i===0) x[0] = A[0][j];
}
numeric.dotMMbig = function dotMMbig(x,y){
var gc = numeric._getCol, p = y.length, v = Array(p);
var m = x.length, n = y[0].length, A = new Array(m), xj;
var VV = numeric.dotVV;
var i,j,k,z;
--p;
--m;
for(i=m;i!==-1;--i) A[i] = Array(n);
--n;
for(i=n;i!==-1;--i) {
gc(y,i,v);
for(j=m;j!==-1;--j) {
z=0;
xj = x[j];
A[j][i] = VV(xj,v);
}
}
return A;
}
numeric.dotMV = function dotMV(x,y) {
var p = x.length, q = y.length,i;
var ret = Array(p), dotVV = numeric.dotVV;
for(i=p-1;i>=0;i--) { ret[i] = dotVV(x[i],y); }
return ret;
}
numeric.dotVM = function dotVM(x,y) {
var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0,s1,s2,s3,baz,accum;
p = x.length; q = y[0].length;
ret = Array(q);
for(k=q-1;k>=0;k--) {
woo = x[p-1]*y[p-1][k];
for(j=p-2;j>=1;j-=2) {
i0 = j-1;
woo += x[j]*y[j][k] + x[i0]*y[i0][k];
}
if(j===0) { woo += x[0]*y[0][k]; }
ret[k] = woo;
}
return ret;
}
numeric.dotVV = function dotVV(x,y) {
var i,n=x.length,i1,ret = x[n-1]*y[n-1];
for(i=n-2;i>=1;i-=2) {
i1 = i-1;
ret += x[i]*y[i] + x[i1]*y[i1];
}
if(i===0) { ret += x[0]*y[0]; }
return ret;
}
numeric.dot = function dot(x,y) {
var d = numeric.dim;
switch(d(x).length*1000+d(y).length) {
case 2002:
if(y.length < 10) return numeric.dotMMsmall(x,y);
else return numeric.dotMMbig(x,y);
case 2001: return numeric.dotMV(x,y);
case 1002: return numeric.dotVM(x,y);
case 1001: return numeric.dotVV(x,y);
case 1000: return numeric.mulVS(x,y);
case 1: return numeric.mulSV(x,y);
case 0: return x*y;
default: throw new Error('numeric.dot only works on vectors and matrices');
}
}
numeric.diag = function diag(d) {
var i,i1,j,n = d.length, A = Array(n), Ai;
for(i=n-1;i>=0;i--) {
Ai = Array(n);
i1 = i+2;
for(j=n-1;j>=i1;j-=2) {
Ai[j] = 0;
Ai[j-1] = 0;
}
if(j>i) { Ai[j] = 0; }
Ai[i] = d[i];
for(j=i-1;j>=1;j-=2) {
Ai[j] = 0;
Ai[j-1] = 0;
}
if(j===0) { Ai[0] = 0; }
A[i] = Ai;
}
return A;
}
numeric.getDiag = function(A) {
var n = Math.min(A.length,A[0].length),i,ret = Array(n);
for(i=n-1;i>=1;--i) {
ret[i] = A[i][i];
--i;
ret[i] = A[i][i];
}
if(i===0) {
ret[0] = A[0][0];
}
return ret;
}
numeric.identity = function identity(n) { return numeric.diag(numeric.rep([n],1)); }
numeric.pointwise = function pointwise(params,body,setup) {
if(typeof setup === "undefined") { setup = ""; }
var fun = [];
var k;
var avec = /\[i\]$/,p,thevec = '';
var haveret = false;
for(k=0;k<params.length;k++) {
if(avec.test(params[k])) {
p = params[k].substring(0,params[k].length-3);
thevec = p;
} else { p = params[k]; }
if(p==='ret') haveret = true;
fun.push(p);
}
fun[params.length] = '_s';
fun[params.length+1] = '_k';
fun[params.length+2] = (
'if(typeof _s === "undefined") _s = numeric.dim('+thevec+');\n'+
'if(typeof _k === "undefined") _k = 0;\n'+
'var _n = _s[_k];\n'+
'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
'if(_k < _s.length-1) {\n'+
' for(i=_n-1;i>=0;i--) ret[i] = arguments.callee('+params.join(',')+',_s,_k+1);\n'+
' return ret;\n'+
'}\n'+
setup+'\n'+
'for(i=_n-1;i!==-1;--i) {\n'+
' '+body+'\n'+
'}\n'+
'return ret;'
);
return Function.apply(null,fun);
}
numeric.pointwise2 = function pointwise2(params,body,setup) {
if(typeof setup === "undefined") { setup = ""; }
var fun = [];
var k;
var avec = /\[i\]$/,p,thevec = '';
var haveret = false;
for(k=0;k<params.length;k++) {
if(avec.test(params[k])) {
p = params[k].substring(0,params[k].length-3);
thevec = p;
} else { p = params[k]; }
if(p==='ret') haveret = true;
fun.push(p);
}
fun[params.length] = (
'var _n = '+thevec+'.length;\n'+
'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
setup+'\n'+
'for(i=_n-1;i!==-1;--i) {\n'+
body+'\n'+
'}\n'+
'return ret;'
);
return Function.apply(null,fun);
}
numeric._biforeach = (function _biforeach(x,y,s,k,f) {
if(k === s.length-1) { f(x,y); return; }
var i,n=s[k];
for(i=n-1;i>=0;i--) { _biforeach(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
});
numeric._biforeach2 = (function _biforeach2(x,y,s,k,f) {
if(k === s.length-1) { return f(x,y); }
var i,n=s[k],ret = Array(n);
for(i=n-1;i>=0;--i) { ret[i] = _biforeach2(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
return ret;
});
numeric._foreach = (function _foreach(x,s,k,f) {
if(k === s.length-1) { f(x); return; }
var i,n=s[k];
for(i=n-1;i>=0;i--) { _foreach(x[i],s,k+1,f); }
});
numeric._foreach2 = (function _foreach2(x,s,k,f) {
if(k === s.length-1) { return f(x); }
var i,n=s[k], ret = Array(n);
for(i=n-1;i>=0;i--) { ret[i] = _foreach2(x[i],s,k+1,f); }
return ret;
});
/*numeric.anyV = numeric.mapreduce('if(xi) return true;','false');
numeric.allV = numeric.mapreduce('if(!xi) return false;','true');
numeric.any = function(x) { if(typeof x.length === "undefined") return x; return numeric.anyV(x); }
numeric.all = function(x) { if(typeof x.length === "undefined") return x; return numeric.allV(x); }*/
numeric.ops2 = {
add: '+',
sub: '-',
mul: '*',
div: '/',
mod: '%',
and: '&&',
or: '||',
eq: '===',
neq: '!==',
lt: '<',
gt: '>',
leq: '<=',
geq: '>=',
band: '&',
bor: '|',
bxor: '^',
lshift: '<<',
rshift: '>>',
rrshift: '>>>'
};
numeric.opseq = {
addeq: '+=',
subeq: '-=',
muleq: '*=',
diveq: '/=',
modeq: '%=',
lshifteq: '<<=',
rshifteq: '>>=',
rrshifteq: '>>>=',
bandeq: '&=',
boreq: '|=',
bxoreq: '^='
};
numeric.mathfuns = ['abs','acos','asin','atan','ceil','cos',
'exp','floor','log','round','sin','sqrt','tan',
'isNaN','isFinite'];
numeric.mathfuns2 = ['atan2','pow','max','min'];
numeric.ops1 = {
neg: '-',
not: '!',
bnot: '~',
clone: ''
};
numeric.mapreducers = {
any: ['if(xi) return true;','var accum = false;'],
all: ['if(!xi) return false;','var accum = true;'],
sum: ['accum += xi;','var accum = 0;'],
prod: ['accum *= xi;','var accum = 1;'],
norm2Squared: ['accum += xi*xi;','var accum = 0;'],
norminf: ['accum = max(accum,abs(xi));','var accum = 0, max = Math.max, abs = Math.abs;'],
norm1: ['accum += abs(xi)','var accum = 0, abs = Math.abs;'],
sup: ['accum = max(accum,xi);','var accum = -Infinity, max = Math.max;'],
inf: ['accum = min(accum,xi);','var accum = Infinity, min = Math.min;']
};
(function () {
var i,o;
for(i=0;i<numeric.mathfuns2.length;++i) {
o = numeric.mathfuns2[i];
numeric.ops2[o] = o;
}
for(i in numeric.ops2) {
if(numeric.ops2.hasOwnProperty(i)) {
o = numeric.ops2[i];
var code, codeeq, setup = '';
if(numeric.myIndexOf.call(numeric.mathfuns2,i)!==-1) {
setup = 'var '+o+' = Math.'+o+';\n';
code = function(r,x,y) { return r+' = '+o+'('+x+','+y+')'; };
codeeq = function(x,y) { return x+' = '+o+'('+x+','+y+')'; };
} else {
code = function(r,x,y) { return r+' = '+x+' '+o+' '+y; };
if(numeric.opseq.hasOwnProperty(i+'eq')) {
codeeq = function(x,y) { return x+' '+o+'= '+y; };
} else {
codeeq = function(x,y) { return x+' = '+x+' '+o+' '+y; };
}
}
numeric[i+'VV'] = numeric.pointwise2(['x[i]','y[i]'],code('ret[i]','x[i]','y[i]'),setup);
numeric[i+'SV'] = numeric.pointwise2(['x','y[i]'],code('ret[i]','x','y[i]'),setup);
numeric[i+'VS'] = numeric.pointwise2(['x[i]','y'],code('ret[i]','x[i]','y'),setup);
numeric[i] = Function(
'var n = arguments.length, i, x = arguments[0], y;\n'+
'var VV = numeric.'+i+'VV, VS = numeric.'+i+'VS, SV = numeric.'+i+'SV;\n'+
'var dim = numeric.dim;\n'+
'for(i=1;i!==n;++i) { \n'+
' y = arguments[i];\n'+
' if(typeof x === "object") {\n'+
' if(typeof y === "object") x = numeric._biforeach2(x,y,dim(x),0,VV);\n'+
' else x = numeric._biforeach2(x,y,dim(x),0,VS);\n'+
' } else if(typeof y === "object") x = numeric._biforeach2(x,y,dim(y),0,SV);\n'+
' else '+codeeq('x','y')+'\n'+
'}\nreturn x;\n');
numeric[o] = numeric[i];
numeric[i+'eqV'] = numeric.pointwise2(['ret[i]','x[i]'], codeeq('ret[i]','x[i]'),setup);
numeric[i+'eqS'] = numeric.pointwise2(['ret[i]','x'], codeeq('ret[i]','x'),setup);
numeric[i+'eq'] = Function(
'var n = arguments.length, i, x = arguments[0], y;\n'+
'var V = numeric.'+i+'eqV, S = numeric.'+i+'eqS\n'+
'var s = numeric.dim(x);\n'+
'for(i=1;i!==n;++i) { \n'+
' y = arguments[i];\n'+
' if(typeof y === "object") numeric._biforeach(x,y,s,0,V);\n'+
' else numeric._biforeach(x,y,s,0,S);\n'+
'}\nreturn x;\n');
}
}
for(i=0;i<numeric.mathfuns2.length;++i) {
o = numeric.mathfuns2[i];
delete numeric.ops2[o];
}
for(i=0;i<numeric.mathfuns.length;++i) {
o = numeric.mathfuns[i];
numeric.ops1[o] = o;
}
for(i in numeric.ops1) {
if(numeric.ops1.hasOwnProperty(i)) {
setup = '';
o = numeric.ops1[i];
if(numeric.myIndexOf.call(numeric.mathfuns,i)!==-1) {
if(Math.hasOwnProperty(o)) setup = 'var '+o+' = Math.'+o+';\n';
}
numeric[i+'eqV'] = numeric.pointwise2(['ret[i]'],'ret[i] = '+o+'(ret[i]);',setup);
numeric[i+'eq'] = Function('x',
'if(typeof x !== "object") return '+o+'x\n'+
'var i;\n'+
'var V = numeric.'+i+'eqV;\n'+
'var s = numeric.dim(x);\n'+
'numeric._foreach(x,s,0,V);\n'+
'return x;\n');
numeric[i+'V'] = numeric.pointwise2(['x[i]'],'ret[i] = '+o+'(x[i]);',setup);
numeric[i] = Function('x',
'if(typeof x !== "object") return '+o+'(x)\n'+
'var i;\n'+
'var V = numeric.'+i+'V;\n'+
'var s = numeric.dim(x);\n'+
'return numeric._foreach2(x,s,0,V);\n');
}
}
for(i=0;i<numeric.mathfuns.length;++i) {
o = numeric.mathfuns[i];
delete numeric.ops1[o];
}
for(i in numeric.mapreducers) {
if(numeric.mapreducers.hasOwnProperty(i)) {
o = numeric.mapreducers[i];
numeric[i+'V'] = numeric.mapreduce2(o[0],o[1]);
numeric[i] = Function('x','s','k',
o[1]+
'if(typeof x !== "object") {'+
' xi = x;\n'+
o[0]+';\n'+
' return accum;\n'+
'}'+
'if(typeof s === "undefined") s = numeric.dim(x);\n'+
'if(typeof k === "undefined") k = 0;\n'+
'if(k === s.length-1) return numeric.'+i+'V(x);\n'+
'var xi;\n'+
'var n = x.length, i;\n'+
'for(i=n-1;i!==-1;--i) {\n'+
' xi = arguments.callee(x[i]);\n'+
o[0]+';\n'+
'}\n'+
'return accum;\n');
}
}
}());
numeric.truncVV = numeric.pointwise(['x[i]','y[i]'],'ret[i] = round(x[i]/y[i])*y[i];','var round = Math.round;');
numeric.truncVS = numeric.pointwise(['x[i]','y'],'ret[i] = round(x[i]/y)*y;','var round = Math.round;');
numeric.truncSV = numeric.pointwise(['x','y[i]'],'ret[i] = round(x/y[i])*y[i];','var round = Math.round;');
numeric.trunc = function trunc(x,y) {
if(typeof x === "object") {
if(typeof y === "object") return numeric.truncVV(x,y);
return numeric.truncVS(x,y);
}
if (typeof y === "object") return numeric.truncSV(x,y);
return Math.round(x/y)*y;
}
numeric.inv = function inv(x) {
var s = numeric.dim(x), abs = Math.abs, m = s[0], n = s[1];
var A = numeric.clone(x), Ai, Aj;
var I = numeric.identity(m), Ii, Ij;
var i,j,k,x;
for(j=0;j<n;++j) {
var i0 = -1;
var v0 = -1;
for(i=j;i!==m;++i) { k = abs(A[i][j]); if(k>v0) { i0 = i; v0 = k; } }
Aj = A[i0]; A[i0] = A[j]; A[j] = Aj;
Ij = I[i0]; I[i0] = I[j]; I[j] = Ij;
x = Aj[j];
for(k=j;k!==n;++k) Aj[k] /= x;
for(k=n-1;k!==-1;--k) Ij[k] /= x;
for(i=m-1;i!==-1;--i) {
if(i!==j) {
Ai = A[i];
Ii = I[i];
x = Ai[j];
for(k=j+1;k!==n;++k) Ai[k] -= Aj[k]*x;
for(k=n-1;k>0;--k) { Ii[k] -= Ij[k]*x; --k; Ii[k] -= Ij[k]*x; }
if(k===0) Ii[0] -= Ij[0]*x;
}
}
}
return I;
}
numeric.det = function det(x) {
var s = numeric.dim(x);
if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: det() only works on square matrices'); }
var n = s[0], ret = 1,i,j,k,A = numeric.clone(x),Aj,Ai,alpha,temp,k1,k2,k3;
for(j=0;j<n-1;j++) {
k=j;
for(i=j+1;i<n;i++) { if(Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
if(k !== j) {
temp = A[k]; A[k] = A[j]; A[j] = temp;
ret *= -1;
}
Aj = A[j];
for(i=j+1;i<n;i++) {
Ai = A[i];
alpha = Ai[j]/Aj[j];
for(k=j+1;k<n-1;k+=2) {
k1 = k+1;
Ai[k] -= Aj[k]*alpha;
Ai[k1] -= Aj[k1]*alpha;
}
if(k!==n) { Ai[k] -= Aj[k]*alpha; }
}
if(Aj[j] === 0) { return 0; }
ret *= Aj[j];
}
return ret*A[j][j];
}
numeric.transpose = function transpose(x) {
var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
for(j=0;j<n;j++) ret[j] = Array(m);
for(i=m-1;i>=1;i-=2) {
A1 = x[i];
A0 = x[i-1];
for(j=n-1;j>=1;--j) {
Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
--j;
Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
}
if(j===0) {
Bj = ret[0]; Bj[i] = A1[0]; Bj[i-1] = A0[0];
}
}
if(i===0) {
A0 = x[0];
for(j=n-1;j>=1;--j) {
ret[j][0] = A0[j];
--j;
ret[j][0] = A0[j];
}
if(j===0) { ret[0][0] = A0[0]; }
}
return ret;
}
numeric.negtranspose = function negtranspose(x) {
var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
for(j=0;j<n;j++) ret[j] = Array(m);
for(i=m-1;i>=1;i-=2) {
A1 = x[i];
A0 = x[i-1];
for(j=n-1;j>=1;--j) {
Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
--j;
Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
}
if(j===0) {
Bj = ret[0]; Bj[i] = -A1[0]; Bj[i-1] = -A0[0];
}
}
if(i===0) {
A0 = x[0];
for(j=n-1;j>=1;--j) {
ret[j][0] = -A0[j];
--j;
ret[j][0] = -A0[j];
}
if(j===0) { ret[0][0] = -A0[0]; }
}
return ret;
}
numeric._random = function _random(s,k) {
var i,n=s[k],ret=Array(n), rnd;
if(k === s.length-1) {
rnd = Math.random;
for(i=n-1;i>=1;i-=2) {
ret[i] = rnd();
ret[i-1] = rnd();
}
if(i===0) { ret[0] = rnd(); }
return ret;
}
for(i=n-1;i>=0;i--) ret[i] = _random(s,k+1);
return ret;
}
numeric.random = function random(s) { return numeric._random(s,0); }
numeric.norm2 = function norm2(x) { return Math.sqrt(numeric.norm2Squared(x)); }
numeric.linspace = function linspace(a,b,n) {
if(typeof n === "undefined") n = Math.max(Math.round(b-a)+1,1);
if(n<2) { return n===1?[a]:[]; }
var i,ret = Array(n);
n--;
for(i=n;i>=0;i--) { ret[i] = (i*b+(n-i)*a)/n; }
return ret;
}
numeric.getBlock = function getBlock(x,from,to) {
var s = numeric.dim(x);
function foo(x,k) {
var i,a = from[k], n = to[k]-a, ret = Array(n);
if(k === s.length-1) {
for(i=n;i>=0;i--) { ret[i] = x[i+a]; }
return ret;
}
for(i=n;i>=0;i--) { ret[i] = foo(x[i+a],k+1); }
return ret;
}
return foo(x,0);
}
numeric.setBlock = function setBlock(x,from,to,B) {
var s = numeric.dim(x);
function foo(x,y,k) {
var i,a = from[k], n = to[k]-a;
if(k === s.length-1) { for(i=n;i>=0;i--) { x[i+a] = y[i]; } }
for(i=n;i>=0;i--) { foo(x[i+a],y[i],k+1); }
}
foo(x,B,0);
return x;
}
numeric.getRange = function getRange(A,I,J) {
var m = I.length, n = J.length;
var i,j;
var B = Array(m), Bi, AI;
for(i=m-1;i!==-1;--i) {
B[i] = Array(n);
Bi = B[i];
AI = A[I[i]];
for(j=n-1;j!==-1;--j) Bi[j] = AI[J[j]];
}
return B;
}
numeric.blockMatrix = function blockMatrix(X) {
var s = numeric.dim(X);
if(s.length<4) return numeric.blockMatrix([X]);
var m=s[0],n=s[1],M,N,i,j,Xij;
M = 0; N = 0;
for(i=0;i<m;++i) M+=X[i][0].length;
for(j=0;j<n;++j) N+=X[0][j][0].length;
var Z = Array(M);
for(i=0;i<M;++i) Z[i] = Array(N);
var I=0,J,ZI,k,l,Xijk;
for(i=0;i<m;++i) {
J=N;
for(j=n-1;j!==-1;--j) {
Xij = X[i][j];
J -= Xij[0].length;
for(k=Xij.length-1;k!==-1;--k) {
Xijk = Xij[k];
ZI = Z[I+k];
for(l = Xijk.length-1;l!==-1;--l) ZI[J+l] = Xijk[l];
}
}
I += X[i][0].length;
}
return Z;
}
numeric.tensor = function tensor(x,y) {
if(typeof x === "number" || typeof y === "number") return numeric.mul(x,y);
var s1 = numeric.dim(x), s2 = numeric.dim(y);
if(s1.length !== 1 || s2.length !== 1) {
throw new Error('numeric: tensor product is only defined for vectors');
}
var m = s1[0], n = s2[0], A = Array(m), Ai, i,j,xi;
for(i=m-1;i>=0;i--) {
Ai = Array(n);
xi = x[i];
for(j=n-1;j>=3;--j) {
Ai[j] = xi * y[j];
--j;
Ai[j] = xi * y[j];
--j;
Ai[j] = xi * y[j];
--j;
Ai[j] = xi * y[j];
}
while(j>=0) { Ai[j] = xi * y[j]; --j; }
A[i] = Ai;
}
return A;
}
// 3. The Tensor type T
numeric.T = function T(x,y) { this.x = x; this.y = y; }
numeric.t = function t(x,y) { return new numeric.T(x,y); }
numeric.Tbinop = function Tbinop(rr,rc,cr,cc,setup) {
var io = numeric.indexOf;
if(typeof setup !== "string") {
var k;
setup = '';
for(k in numeric) {
if(numeric.hasOwnProperty(k) && (rr.indexOf(k)>=0 || rc.indexOf(k)>=0 || cr.indexOf(k)>=0 || cc.indexOf(k)>=0) && k.length>1) {
setup += 'var '+k+' = numeric.'+k+';\n';
}
}
}
return Function(['y'],
'var x = this;\n'+
'if(!(y instanceof numeric.T)) { y = new numeric.T(y); }\n'+
setup+'\n'+
'if(x.y) {'+
' if(y.y) {'+
' return new numeric.T('+cc+');\n'+
' }\n'+
' return new numeric.T('+cr+');\n'+
'}\n'+
'if(y.y) {\n'+
' return new numeric.T('+rc+');\n'+
'}\n'+
'return new numeric.T('+rr+');\n'
);
}
numeric.T.prototype.add = numeric.Tbinop(
'add(x.x,y.x)',
'add(x.x,y.x),y.y',
'add(x.x,y.x),x.y',
'add(x.x,y.x),add(x.y,y.y)');
numeric.T.prototype.sub = numeric.Tbinop(
'sub(x.x,y.x)',
'sub(x.x,y.x),neg(y.y)',
'sub(x.x,y.x),x.y',
'sub(x.x,y.x),sub(x.y,y.y)');
numeric.T.prototype.mul = numeric.Tbinop(
'mul(x.x,y.x)',
'mul(x.x,y.x),mul(x.x,y.y)',
'mul(x.x,y.x),mul(x.y,y.x)',
'sub(mul(x.x,y.x),mul(x.y,y.y)),add(mul(x.x,y.y),mul(x.y,y.x))');
numeric.T.prototype.reciprocal = function reciprocal() {
var mul = numeric.mul, div = numeric.div;
if(this.y) {
var d = numeric.add(mul(this.x,this.x),mul(this.y,this.y));
return new numeric.T(div(this.x,d),div(numeric.neg(this.y),d));
}
return new T(div(1,this.x));
}
numeric.T.prototype.div = function div(y) {
if(!(y instanceof numeric.T)) y = new numeric.T(y);
if(y.y) { return this.mul(y.reciprocal()); }
var div = numeric.div;
if(this.y) { return new numeric.T(div(this.x,y.x),div(this.y,y.x)); }
return new numeric.T(div(this.x,y.x));
}
numeric.T.prototype.dot = numeric.Tbinop(
'dot(x.x,y.x)',
'dot(x.x,y.x),dot(x.x,y.y)',
'dot(x.x,y.x),dot(x.y,y.x)',
'sub(dot(x.x,y.x),dot(x.y,y.y)),add(dot(x.x,y.y),dot(x.y,y.x))'
);
numeric.T.prototype.transpose = function transpose() {
var t = numeric.transpose, x = this.x, y = this.y;
if(y) { return new numeric.T(t(x),t(y)); }
return new numeric.T(t(x));
}
numeric.T.prototype.transjugate = function transjugate() {
var t = numeric.transpose, x = this.x, y = this.y;
if(y) { return new numeric.T(t(x),numeric.negtranspose(y)); }
return new numeric.T(t(x));
}
numeric.Tunop = function Tunop(r,c,s) {
if(typeof s !== "string") { s = ''; }
return Function(
'var x = this;\n'+
s+'\n'+
'if(x.y) {'+
' '+c+';\n'+
'}\n'+
r+';\n'
);
}
numeric.T.prototype.exp = numeric.Tunop(
'return new numeric.T(ex)',
'return new numeric.T(mul(cos(x.y),ex),mul(sin(x.y),ex))',
'var ex = numeric.exp(x.x), cos = numeric.cos, sin = numeric.sin, mul = numeric.mul;');
numeric.T.prototype.conj = numeric.Tunop(
'return new numeric.T(x.x);',
'return new numeric.T(x.x,numeric.neg(x.y));');
numeric.T.prototype.neg = numeric.Tunop(
'return new numeric.T(neg(x.x));',
'return new numeric.T(neg(x.x),neg(x.y));',
'var neg = numeric.neg;');
numeric.T.prototype.sin = numeric.Tunop(
'return new numeric.T(numeric.sin(x.x))',
'return x.exp().sub(x.neg().exp()).div(new numeric.T(0,2));');
numeric.T.prototype.cos = numeric.Tunop(
'return new numeric.T(numeric.cos(x.x))',
'return x.exp().add(x.neg().exp()).div(2);');
numeric.T.prototype.abs = numeric.Tunop(
'return new numeric.T(numeric.abs(x.x));',
'return new numeric.T(numeric.sqrt(numeric.add(mul(x.x,x.x),mul(x.y,x.y))));',
'var mul = numeric.mul;');
numeric.T.prototype.log = numeric.Tunop(
'return new numeric.T(numeric.log(x.x));',
'var theta = new numeric.T(numeric.atan2(x.y,x.x)), r = x.abs();\n'+
'return new numeric.T(numeric.log(r.x),theta.x);');
numeric.T.prototype.norm2 = numeric.Tunop(
'return numeric.norm2(x.x);',
'var f = numeric.norm2Squared;\n'+
'return Math.sqrt(f(x.x)+f(x.y));');
numeric.T.prototype.inv = function inv() {
var A = this;
if(typeof A.y === "undefined") { return new numeric.T(numeric.inv(A.x)); }
var n = A.x.length, i, j, k;
var Rx = numeric.identity(n),Ry = numeric.rep([n,n],0);
var Ax = numeric.clone(A.x), Ay = numeric.clone(A.y);
var Aix, Aiy, Ajx, Ajy, Rix, Riy, Rjx, Rjy;
var i,j,k,d,d1,ax,ay,bx,by,temp;
for(i=0;i<n;i++) {
ax = Ax[i][i]; ay = Ay[i][i];
d = ax*ax+ay*ay;
k = i;
for(j=i+1;j<n;j++) {
ax = Ax[j][i]; ay = Ay[j][i];
d1 = ax*ax+ay*ay;
if(d1 > d) { k=j; d = d1; }
}
if(k!==i) {
temp = Ax[i]; Ax[i] = Ax[k]; Ax[k] = temp;
temp = Ay[i]; Ay[i] = Ay[k]; Ay[k] = temp;
temp = Rx[i]; Rx[i] = Rx[k]; Rx[k] = temp;
temp = Ry[i]; Ry[i] = Ry[k]; Ry[k] = temp;
}
Aix = Ax[i]; Aiy = Ay[i];
Rix = Rx[i]; Riy = Ry[i];
ax = Aix[i]; ay = Aiy[i];
for(j=i+1;j<n;j++) {
bx = Aix[j]; by = Aiy[j];
Aix[j] = (bx*ax+by*ay)/d;
Aiy[j] = (by*ax-bx*ay)/d;
}
for(j=0;j<n;j++) {
bx = Rix[j]; by = Riy[j];
Rix[j] = (bx*ax+by*ay)/d;
Riy[j] = (by*ax-bx*ay)/d;
}
for(j=i+1;j<n;j++) {
Ajx = Ax[j]; Ajy = Ay[j];
Rjx = Rx[j]; Rjy = Ry[j];
ax = Ajx[i]; ay = Ajy[i];
for(k=i+1;k<n;k++) {
bx = Aix[k]; by = Aiy[k];
Ajx[k] -= bx*ax-by*ay;
Ajy[k] -= by*ax+bx*ay;
}
for(k=0;k<n;k++) {
bx = Rix[k]; by = Riy[k];
Rjx[k] -= bx*ax-by*ay;
Rjy[k] -= by*ax+bx*ay;
}
}
}
for(i=n-1;i>0;i--) {
Rix = Rx[i]; Riy = Ry[i];
for(j=i-1;j>=0;j--) {
Rjx = Rx[j]; Rjy = Ry[j];
ax = Ax[j][i]; ay = Ay[j][i];
for(k=n-1;k>=0;k--) {
bx = Rix[k]; by = Riy[k];
Rjx[k] -= ax*bx - ay*by;
Rjy[k] -= ax*by + ay*bx;
}
}
}
return new numeric.T(Rx,Ry);
}
numeric.T.prototype.get = function get(i) {
var x = this.x, y = this.y, k = 0, ik, n = i.length;
if(y) {
while(k<n) {
ik = i[k];
x = x[ik];
y = y[ik];
k++;
}
return new numeric.T(x,y);
}
while(k<n) {
ik = i[k];
x = x[ik];
k++;
}
return new numeric.T(x);
}
numeric.T.prototype.set = function set(i,v) {
var x = this.x, y = this.y, k = 0, ik, n = i.length, vx = v.x, vy = v.y;
if(n===0) {
if(vy) { this.y = vy; }
else if(y) { this.y = undefined; }
this.x = x;
return this;
}
if(vy) {
if(y) { /* ok */ }
else {
y = numeric.rep(numeric.dim(x),0);
this.y = y;
}
while(k<n-1) {
ik = i[k];
x = x[ik];
y = y[ik];
k++;
}
ik = i[k];
x[ik] = vx;
y[ik] = vy;
return this;
}
if(y) {
while(k<n-1) {
ik = i[k];
x = x[ik];
y = y[ik];
k++;
}
ik = i[k];
x[ik] = vx;
if(vx instanceof Array) y[ik] = numeric.rep(numeric.dim(vx),0);
else y[ik] = 0;
return this;
}
while(k<n-1) {
ik = i[k];
x = x[ik];
k++;
}
ik = i[k];
x[ik] = vx;
return this;
}
numeric.T.prototype.getRows = function getRows(i0,i1) {
var n = i1-i0+1, j;
var rx = Array(n), ry, x = this.x, y = this.y;
for(j=i0;j<=i1;j++) { rx[j-i0] = x[j]; }
if(y) {
ry = Array(n);
for(j=i0;j<=i1;j++) { ry[j-i0] = y[j]; }
return new numeric.T(rx,ry);
}
return new numeric.T(rx);
}
numeric.T.prototype.setRows = function setRows(i0,i1,A) {
var j;
var rx = this.x, ry = this.y, x = A.x, y = A.y;
for(j=i0;j<=i1;j++) { rx[j] = x[j-i0]; }
if(y) {
if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
for(j=i0;j<=i1;j++) { ry[j] = y[j-i0]; }
} else if(ry) {
for(j=i0;j<=i1;j++) { ry[j] = numeric.rep([x[j-i0].length],0); }
}
return this;
}
numeric.T.prototype.getRow = function getRow(k) {
var x = this.x, y = this.y;
if(y) { return new numeric.T(x[k],y[k]); }
return new numeric.T(x[k]);
}
numeric.T.prototype.setRow = function setRow(i,v) {
var rx = this.x, ry = this.y, x = v.x, y = v.y;
rx[i] = x;
if(y) {
if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
ry[i] = y;
} else if(ry) {
ry = numeric.rep([x.length],0);
}
return this;
}
numeric.T.prototype.getBlock = function getBlock(from,to) {
var x = this.x, y = this.y, b = numeric.getBlock;
if(y) { return new numeric.T(b(x,from,to),b(y,from,to)); }
return new numeric.T(b(x,from,to));
}
numeric.T.prototype.setBlock = function setBlock(from,to,A) {
if(!(A instanceof numeric.T)) A = new numeric.T(A);
var x = this.x, y = this.y, b = numeric.setBlock, Ax = A.x, Ay = A.y;
if(Ay) {
if(!y) { this.y = numeric.rep(numeric.dim(this),0); y = this.y; }
b(x,from,to,Ax);
b(y,from,to,Ay);
return this;
}
b(x,from,to,Ax);
if(y) b(y,from,to,numeric.rep(numeric.dim(Ax),0));
}
numeric.T.rep = function rep(s,v) {
var T = numeric.T;
if(!(v instanceof T)) v = new T(v);
var x = v.x, y = v.y, r = numeric.rep;
if(y) return new T(r(s,x),r(s,y));
return new T(r(s,x));
}
numeric.T.diag = function diag(d) {
if(!(d instanceof numeric.T)) d = new numeric.T(d);
var x = d.x, y = d.y, diag = numeric.diag;
if(y) return new numeric.T(diag(x),diag(y));
return new numeric.T(diag(x));
}
numeric.T.eig = function eig() {
if(this.y) { throw new Error('eig: not implemented for complex matrices.'); }
return numeric.eig(this.x);
}
numeric.T.identity = function identity(n) { return new numeric.T(numeric.identity(n)); }
numeric.T.prototype.getDiag = function getDiag() {
var n = numeric;
var x = this.x, y = this.y;
if(y) { return new n.T(n.getDiag(x),n.getDiag(y)); }
return new n.T(n.getDiag(x));
}
// 4. Eigenvalues of real matrices
numeric.house = function house(x) {
var v = numeric.clone(x);
var s = x[0] >= 0 ? 1 : -1;
var alpha = s*numeric.norm2(x);
v[0] += alpha;
var foo = numeric.norm2(v);
if(foo === 0) { /* this should not happen */ throw new Error('eig: internal error'); }
return numeric.div(v,foo);
}
numeric.toUpperHessenberg = function toUpperHessenberg(me) {
var s = numeric.dim(me);
if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: toUpperHessenberg() only works on square matrices'); }
var m = s[0], i,j,k,x,v,A = numeric.clone(me),B,C,Ai,Ci,Q = numeric.identity(m),Qi;
for(j=0;j<m-2;j++) {
x = Array(m-j-1);
for(i=j+1;i<m;i++) { x[i-j-1] = A[i][j]; }
if(numeric.norm2(x)>0) {
v = numeric.house(x);
B = numeric.getBlock(A,[j+1,j],[m-1,m-1]);
C = numeric.tensor(v,numeric.dot(v,B));
for(i=j+1;i<m;i++) { Ai = A[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Ai[k] -= 2*Ci[k-j]; }
B = numeric.getBlock(A,[0,j+1],[m-1,m-1]);
C = numeric.tensor(numeric.dot(B,v),v);
for(i=0;i<m;i++) { Ai = A[i]; Ci = C[i]; for(k=j+1;k<m;k++) Ai[k] -= 2*Ci[k-j-1]; }
B = Array(m-j-1);
for(i=j+1;i<m;i++) B[i-j-1] = Q[i];
C = numeric.tensor(v,numeric.dot(v,B));
for(i=j+1;i<m;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
}
}
return {H:A, Q:Q};
}
numeric.epsilon = 2.220446049250313e-16;
numeric.QRFrancis = function(H,maxiter) {
if(typeof maxiter === "undefined") { maxiter = 10000; }
H = numeric.clone(H);
var H0 = numeric.clone(H);
var s = numeric.dim(H),m=s[0],x,v,a,b,c,d,det,tr, Hloc, Q = numeric.identity(m), Qi, Hi, B, C, Ci,i,j,k,iter;
if(m<3) { return {Q:Q, B:[ [0,m-1] ]}; }
var epsilon = numeric.epsilon;
for(iter=0;iter<maxiter;iter++) {
for(j=0;j<m-1;j++) {
if(Math.abs(H[j+1][j]) < epsilon*(Math.abs(H[j][j])+Math.abs(H[j+1][j+1]))) {
var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[j,j]),maxiter);
var QH2 = numeric.QRFrancis(numeric.getBlock(H,[j+1,j+1],[m-1,m-1]),maxiter);
B = Array(j+1);
for(i=0;i<=j;i++) { B[i] = Q[i]; }
C = numeric.dot(QH1.Q,B);
for(i=0;i<=j;i++) { Q[i] = C[i]; }
B = Array(m-j-1);
for(i=j+1;i<m;i++) { B[i-j-1] = Q[i]; }
C = numeric.dot(QH2.Q,B);
for(i=j+1;i<m;i++) { Q[i] = C[i-j-1]; }
return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,j+1))};
}
}
a = H[m-2][m-2]; b = H[m-2][m-1];
c = H[m-1][m-2]; d = H[m-1][m-1];
tr = a+d;
det = (a*d-b*c);
Hloc = numeric.getBlock(H, [0,0], [2,2]);
if(tr*tr>=4*det) {
var s1,s2;
s1 = 0.5*(tr+Math.sqrt(tr*tr-4*det));
s2 = 0.5*(tr-Math.sqrt(tr*tr-4*det));
Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
numeric.mul(Hloc,s1+s2)),
numeric.diag(numeric.rep([3],s1*s2)));
} else {
Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
numeric.mul(Hloc,tr)),
numeric.diag(numeric.rep([3],det)));
}
x = [Hloc[0][0],Hloc[1][0],Hloc[2][0]];
v = numeric.house(x);
B = [H[0],H[1],H[2]];
C = numeric.tensor(v,numeric.dot(v,B));
for(i=0;i<3;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<m;k++) Hi[k] -= 2*Ci[k]; }
B = numeric.getBlock(H, [0,0],[m-1,2]);
C = numeric.tensor(numeric.dot(B,v),v);
for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<3;k++) Hi[k] -= 2*Ci[k]; }
B = [Q[0],Q[1],Q[2]];
C = numeric.tensor(v,numeric.dot(v,B));
for(i=0;i<3;i++) { Qi = Q[i]; Ci = C[i]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
var J;
for(j=0;j<m-2;j++) {
for(k=j;k<=j+1;k++) {
if(Math.abs(H[k+1][k]) < epsilon*(Math.abs(H[k][k])+Math.abs(H[k+1][k+1]))) {
var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[k,k]),maxiter);
var QH2 = numeric.QRFrancis(numeric.getBlock(H,[k+1,k+1],[m-1,m-1]),maxiter);
B = Array(k+1);
for(i=0;i<=k;i++) { B[i] = Q[i]; }
C = numeric.dot(QH1.Q,B);
for(i=0;i<=k;i++) { Q[i] = C[i]; }
B = Array(m-k-1);
for(i=k+1;i<m;i++) { B[i-k-1] = Q[i]; }
C = numeric.dot(QH2.Q,B);
for(i=k+1;i<m;i++) { Q[i] = C[i-k-1]; }
return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,k+1))};
}
}
J = Math.min(m-1,j+3);
x = Array(J-j);
for(i=j+1;i<=J;i++) { x[i-j-1] = H[i][j]; }
v = numeric.house(x);
B = numeric.getBlock(H, [j+1,j],[J,m-1]);
C = numeric.tensor(v,numeric.dot(v,B));
for(i=j+1;i<=J;i++) { Hi = H[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Hi[k] -= 2*Ci[k-j]; }
B = numeric.getBlock(H, [0,j+1],[m-1,J]);
C = numeric.tensor(numeric.dot(B,v),v);
for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=j+1;k<=J;k++) Hi[k] -= 2*Ci[k-j-1]; }
B = Array(J-j);
for(i=j+1;i<=J;i++) B[i-j-1] = Q[i];
C = numeric.tensor(v,numeric.dot(v,B));
for(i=j+1;i<=J;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
}
}
throw new Error('numeric: eigenvalue iteration does not converge -- increase maxiter?');
}
numeric.eig = function eig(A,maxiter) {
var QH = numeric.toUpperHessenberg(A);
var QB = numeric.QRFrancis(QH.H,maxiter);
var T = numeric.T;
var n = A.length,i,k,flag = false,B = QB.B,H = numeric.dot(QB.Q,numeric.dot(QH.H,numeric.transpose(QB.Q)));
var Q = new T(numeric.dot(QB.Q,QH.Q)),Q0;
var m = B.length,j;
var a,b,c,d,p1,p2,disc,x,y,p,q,n1,n2;
var sqrt = Math.sqrt;
for(k=0;k<m;k++) {
i = B[k][0];
if(i === B[k][1]) {
// nothing
} else {
j = i+1;
a = H[i][i];
b = H[i][j];
c = H[j][i];
d = H[j][j];
if(b === 0 && c === 0) continue;
p1 = -a-d;
p2 = a*d-b*c;
disc = p1*p1-4*p2;
if(disc>=0) {
if(p1<0) x = -0.5*(p1-sqrt(disc));
else x = -0.5*(p1+sqrt(disc));
n1 = (a-x)*(a-x)+b*b;
n2 = c*c+(d-x)*(d-x);
if(n1>n2) {
n1 = sqrt(n1);
p = (a-x)/n1;
q = b/n1;
} else {
n2 = sqrt(n2);
p = c/n2;
q = (d-x)/n2;
}
Q0 = new T([[q,-p],[p,q]]);
Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
} else {
x = -0.5*p1;
y = 0.5*sqrt(-disc);
n1 = (a-x)*(a-x)+b*b;
n2 = c*c+(d-x)*(d-x);
if(n1>n2) {
n1 = sqrt(n1+y*y);
p = (a-x)/n1;
q = b/n1;
x = 0;
y /= n1;
} else {
n2 = sqrt(n2+y*y);
p = c/n2;
q = (d-x)/n2;
x = y/n2;
y = 0;
}
Q0 = new T([[q,-p],[p,q]],[[x,y],[y,-x]]);
Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
}
}
}
var R = Q.dot(A).dot(Q.transjugate()), n = A.length, E = numeric.T.identity(n);
for(j=0;j<n;j++) {
if(j>0) {
for(k=j-1;k>=0;k--) {
var Rk = R.get([k,k]), Rj = R.get([j,j]);
if(numeric.neq(Rk.x,Rj.x) || numeric.neq(Rk.y,Rj.y)) {
x = R.getRow(k).getBlock([k],[j-1]);
y = E.getRow(j).getBlock([k],[j-1]);
E.set([j,k],(R.get([k,j]).neg().sub(x.dot(y))).div(Rk.sub(Rj)));
} else {
E.setRow(j,E.getRow(k));
continue;
}
}
}
}
for(j=0;j<n;j++) {
x = E.getRow(j);
E.setRow(j,x.div(x.norm2()));
}
E = E.transpose();
E = Q.transjugate().dot(E);
return { lambda:R.getDiag(), E:E };
};
// 5. Compressed Column Storage matrices
numeric.ccsSparse = function ccsSparse(A) {
var m = A.length,n,foo, i,j, counts = [];
for(i=m-1;i!==-1;--i) {
foo = A[i];
for(j in foo) {
j = parseInt(j);
while(j>=counts.length) counts[counts.length] = 0;
if(foo[j]!==0) counts[j]++;
}
}
var n = counts.length;
var Ai = Array(n+1);
Ai[0] = 0;
for(i=0;i<n;++i) Ai[i+1] = Ai[i] + counts[i];
var Aj = Array(Ai[n]), Av = Array(Ai[n]);
for(i=m-1;i!==-1;--i) {
foo = A[i];
for(j in foo) {
if(foo[j]!==0) {
counts[j]--;
Aj[Ai[j]+counts[j]] = i;
Av[Ai[j]+counts[j]] = foo[j];
}
}
}
return [Ai,Aj,Av];
}
numeric.ccsFull = function ccsFull(A) {
var Ai = A[0], Aj = A[1], Av = A[2], s = numeric.ccsDim(A), m = s[0], n = s[1], i,j,j0,j1,k;
var B = numeric.rep([m,n],0);
for(i=0;i<n;i++) {
j0 = Ai[i];
j1 = Ai[i+1];
for(j=j0;j<j1;++j) { B[Aj[j]][i] = Av[j]; }
}
return B;
}
numeric.ccsTSolve = function ccsTSolve(A,b,x,bj,xj) {
var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, max = Math.max,n=0;
if(typeof bj === "undefined") x = numeric.rep([m],0);
if(typeof bj === "undefined") bj = numeric.linspace(0,x.length-1);
if(typeof xj === "undefined") xj = [];
function dfs(j) {
var k;
if(x[j] !== 0) return;
x[j] = 1;
for(k=Ai[j];k<Ai[j+1];++k) dfs(Aj[k]);
xj[n] = j;
++n;
}
var i,j,j0,j1,k,l,l0,l1,a;
for(i=bj.length-1;i!==-1;--i) { dfs(bj[i]); }
xj.length = n;
for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
for(i=bj.length-1;i!==-1;--i) { j = bj[i]; x[j] = b[j]; }
for(i=xj.length-1;i!==-1;--i) {
j = xj[i];
j0 = Ai[j];
j1 = max(Ai[j+1],j0);
for(k=j0;k!==j1;++k) { if(Aj[k] === j) { x[j] /= Av[k]; break; } }
a = x[j];
for(k=j0;k!==j1;++k) {
l = Aj[k];
if(l !== j) x[l] -= a*Av[k];
}
}
return x;
}
numeric.ccsDFS = function ccsDFS(n) {
this.k = Array(n);
this.k1 = Array(n);
this.j = Array(n);
}
numeric.ccsDFS.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv) {
var m = 0,foo,n=xj.length;
var k = this.k, k1 = this.k1, j = this.j,km,k11;
if(x[J]!==0) return;
x[J] = 1;
j[0] = J;
k[0] = km = Ai[J];
k1[0] = k11 = Ai[J+1];
while(1) {
if(km >= k11) {
xj[n] = j[m];
if(m===0) return;
++n;
--m;
km = k[m];
k11 = k1[m];
} else {
foo = Pinv[Aj[km]];
if(x[foo] === 0) {
x[foo] = 1;
k[m] = km;
++m;
j[m] = foo;
km = Ai[foo];
k1[m] = k11 = Ai[foo+1];
} else ++km;
}
}
}
numeric.ccsLPSolve = function ccsLPSolve(A,B,x,xj,I,Pinv,dfs) {
var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
var Bi = B[0], Bj = B[1], Bv = B[2];
var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
i0 = Bi[I];
i1 = Bi[I+1];
xj.length = 0;
for(i=i0;i<i1;++i) { dfs.dfs(Pinv[Bj[i]],Ai,Aj,x,xj,Pinv); }
for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
for(i=i0;i!==i1;++i) { j = Pinv[Bj[i]]; x[j] = Bv[i]; }
for(i=xj.length-1;i!==-1;--i) {
j = xj[i];
j0 = Ai[j];
j1 = Ai[j+1];
for(k=j0;k<j1;++k) { if(Pinv[Aj[k]] === j) { x[j] /= Av[k]; break; } }
a = x[j];
for(k=j0;k<j1;++k) {
l = Pinv[Aj[k]];
if(l !== j) x[l] -= a*Av[k];
}
}
return x;
}
numeric.ccsLUP1 = function ccsLUP1(A,threshold) {
var m = A[0].length-1;
var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
var x = numeric.rep([m],0), xj = numeric.rep([m],0);
var i,j,k,j0,j1,a,e,c,d,K;
var sol = numeric.ccsLPSolve, max = Math.max, abs = Math.abs;
var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
var dfs = new numeric.ccsDFS(m);
if(typeof threshold === "undefined") { threshold = 1; }
for(i=0;i<m;++i) {
sol(L,A,x,xj,i,Pinv,dfs);
a = -1;
e = -1;
for(j=xj.length-1;j!==-1;--j) {
k = xj[j];
if(k <= i) continue;
c = abs(x[k]);
if(c > a) { e = k; a = c; }
}
if(abs(x[i])<threshold*a) {
j = P[i];
a = P[e];
P[i] = a; Pinv[a] = i;
P[e] = j; Pinv[j] = e;
a = x[i]; x[i] = x[e]; x[e] = a;
}
a = Li[i];
e = Ui[i];
d = x[i];
Lj[a] = P[i];
Lv[a] = 1;
++a;
for(j=xj.length-1;j!==-1;--j) {
k = xj[j];
c = x[k];
xj[j] = 0;
x[k] = 0;
if(k<=i) { Uj[e] = k; Uv[e] = c; ++e; }
else { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
}
Li[i+1] = a;
Ui[i+1] = e;
}
for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
return {L:L, U:U, P:P, Pinv:Pinv};
}
numeric.ccsDFS0 = function ccsDFS0(n) {
this.k = Array(n);
this.k1 = Array(n);
this.j = Array(n);
}
numeric.ccsDFS0.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv,P) {
var m = 0,foo,n=xj.length;
var k = this.k, k1 = this.k1, j = this.j,km,k11;
if(x[J]!==0) return;
x[J] = 1;
j[0] = J;
k[0] = km = Ai[Pinv[J]];
k1[0] = k11 = Ai[Pinv[J]+1];
while(1) {
if(isNaN(km)) throw new Error("Ow!");
if(km >= k11) {
xj[n] = Pinv[j[m]];
if(m===0) return;
++n;
--m;
km = k[m];
k11 = k1[m];
} else {
foo = Aj[km];
if(x[foo] === 0) {
x[foo] = 1;
k[m] = km;
++m;
j[m] = foo;
foo = Pinv[foo];
km = Ai[foo];
k1[m] = k11 = Ai[foo+1];
} else ++km;
}
}
}
numeric.ccsLPSolve0 = function ccsLPSolve0(A,B,y,xj,I,Pinv,P,dfs) {
var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
var Bi = B[0], Bj = B[1], Bv = B[2];
var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
i0 = Bi[I];
i1 = Bi[I+1];
xj.length = 0;
for(i=i0;i<i1;++i) { dfs.dfs(Bj[i],Ai,Aj,y,xj,Pinv,P); }
for(i=xj.length-1;i!==-1;--i) { j = xj[i]; y[P[j]] = 0; }
for(i=i0;i!==i1;++i) { j = Bj[i]; y[j] = Bv[i]; }
for(i=xj.length-1;i!==-1;--i) {
j = xj[i];
l = P[j];
j0 = Ai[j];
j1 = Ai[j+1];
for(k=j0;k<j1;++k) { if(Aj[k] === l) { y[l] /= Av[k]; break; } }
a = y[l];
for(k=j0;k<j1;++k) y[Aj[k]] -= a*Av[k];
y[l] = a;
}
}
numeric.ccsLUP0 = function ccsLUP0(A,threshold) {
var m = A[0].length-1;
var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
var y = numeric.rep([m],0), xj = numeric.rep([m],0);
var i,j,k,j0,j1,a,e,c,d,K;
var sol = numeric.ccsLPSolve0, max = Math.max, abs = Math.abs;
var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
var dfs = new numeric.ccsDFS0(m);
if(typeof threshold === "undefined") { threshold = 1; }
for(i=0;i<m;++i) {
sol(L,A,y,xj,i,Pinv,P,dfs);
a = -1;
e = -1;
for(j=xj.length-1;j!==-1;--j) {
k = xj[j];
if(k <= i) continue;
c = abs(y[P[k]]);
if(c > a) { e = k; a = c; }
}
if(abs(y[P[i]])<threshold*a) {
j = P[i];
a = P[e];
P[i] = a; Pinv[a] = i;
P[e] = j; Pinv[j] = e;
}
a = Li[i];
e = Ui[i];
d = y[P[i]];
Lj[a] = P[i];
Lv[a] = 1;
++a;
for(j=xj.length-1;j!==-1;--j) {
k = xj[j];
c = y[P[k]];
xj[j] = 0;
y[P[k]] = 0;
if(k<=i) { Uj[e] = k; Uv[e] = c; ++e; }
else { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
}
Li[i+1] = a;
Ui[i+1] = e;
}
for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
return {L:L, U:U, P:P, Pinv:Pinv};
}
numeric.ccsLUP = numeric.ccsLUP0;
numeric.ccsDim = function ccsDim(A) { return [numeric.sup(A[1])+1,A[0].length-1]; }
numeric.ccsGetBlock = function ccsGetBlock(A,i,j) {
var s = numeric.ccsDim(A),m=s[0],n=s[1];
if(typeof i === "undefined") { i = numeric.linspace(0,m-1); }
else if(typeof i === "number") { i = [i]; }
if(typeof j === "undefined") { j = numeric.linspace(0,n-1); }
else if(typeof j === "number") { j = [j]; }
var p,p0,p1,P = i.length,q,Q = j.length,r,jq,ip;
var Bi = numeric.rep([n],0), Bj=[], Bv=[], B = [Bi,Bj,Bv];
var Ai = A[0], Aj = A[1], Av = A[2];
var x = numeric.rep([m],0),count=0,flags = numeric.rep([m],0);
for(q=0;q<Q;++q) {
jq = j[q];
var q0 = Ai[jq];
var q1 = Ai[jq+1];
for(p=q0;p<q1;++p) {
r = Aj[p];
flags[r] = 1;
x[r] = Av[p];
}
for(p=0;p<P;++p) {
ip = i[p];
if(flags[ip]) {
Bj[count] = p;
Bv[count] = x[i[p]];
++count;
}
}
for(p=q0;p<q1;++p) {
r = Aj[p];
flags[r] = 0;
}
Bi[q+1] = count;
}
return B;
}
numeric.ccsDot = function ccsDot(A,B) {
var Ai = A[0], Aj = A[1], Av = A[2];
var Bi = B[0], Bj = B[1], Bv = B[2];
var sA = numeric.ccsDim(A), sB = numeric.ccsDim(B);
var m = sA[0], n = sA[1], o = sB[1];
var x = numeric.rep([m],0), flags = numeric.rep([m],0), xj = Array(m);
var Ci = numeric.rep([o],0), Cj = [], Cv = [], C = [Ci,Cj,Cv];
var i,j,k,j0,j1,i0,i1,l,p,a,b;
for(k=0;k!==o;++k) {
j0 = Bi[k];
j1 = Bi[k+1];
p = 0;
for(j=j0;j<j1;++j) {
a = Bj[j];
b = Bv[j];
i0 = Ai[a];
i1 = Ai[a+1];
for(i=i0;i<i1;++i) {
l = Aj[i];
if(flags[l]===0) {
xj[p] = l;
flags[l] = 1;
p = p+1;
}
x[l] = x[l] + Av[i]*b;
}
}
j0 = Ci[k];
j1 = j0+p;
Ci[k+1] = j1;
for(j=p-1;j!==-1;--j) {
b = j0+j;
i = xj[j];
Cj[b] = i;
Cv[b] = x[i];
flags[i] = 0;
x[i] = 0;
}
Ci[k+1] = Ci[k]+p;
}
return C;
}
numeric.ccsLUPSolve = function ccsLUPSolve(LUP,B) {
var L = LUP.L, U = LUP.U, P = LUP.P;
var Bi = B[0];
var flag = false;
if(typeof Bi !== "object") { B = [[0,B.length],numeric.linspace(0,B.length-1),B]; Bi = B[0]; flag = true; }
var Bj = B[1], Bv = B[2];
var n = L[0].length-1, m = Bi.length-1;
var x = numeric.rep([n],0), xj = Array(n);
var b = numeric.rep([n],0), bj = Array(n);
var Xi = numeric.rep([m+1],0), Xj = [], Xv = [];
var sol = numeric.ccsTSolve;
var i,j,j0,j1,k,J,N=0;
for(i=0;i<m;++i) {
k = 0;
j0 = Bi[i];
j1 = Bi[i+1];
for(j=j0;j<j1;++j) {
J = LUP.Pinv[Bj[j]];
bj[k] = J;
b[J] = Bv[j];
++k;
}
bj.length = k;
sol(L,b,x,bj,xj);
for(j=bj.length-1;j!==-1;--j) b[bj[j]] = 0;
sol(U,x,b,xj,bj);
if(flag) return b;
for(j=xj.length-1;j!==-1;--j) x[xj[j]] = 0;
for(j=bj.length-1;j!==-1;--j) {
J = bj[j];
Xj[N] = J;
Xv[N] = b[J];
b[J] = 0;
++N;
}
Xi[i+1] = N;
}
return [Xi,Xj,Xv];
}
numeric.ccsbinop = function ccsbinop(body,setup) {
if(typeof setup === "undefined") setup='';
return Function('X','Y',
'var Xi = X[0], Xj = X[1], Xv = X[2];\n'+
'var Yi = Y[0], Yj = Y[1], Yv = Y[2];\n'+
'var n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;\n'+
'var Zi = numeric.rep([n+1],0), Zj = [], Zv = [];\n'+
'var x = numeric.rep([m],0),y = numeric.rep([m],0);\n'+
'var xk,yk,zk;\n'+
'var i,j,j0,j1,k,p=0;\n'+
setup+
'for(i=0;i<n;++i) {\n'+
' j0 = Xi[i]; j1 = Xi[i+1];\n'+
' for(j=j0;j!==j1;++j) {\n'+
' k = Xj[j];\n'+
' x[k] = 1;\n'+
' Zj[p] = k;\n'+
' ++p;\n'+
' }\n'+
' j0 = Yi[i]; j1 = Yi[i+1];\n'+
' for(j=j0;j!==j1;++j) {\n'+
' k = Yj[j];\n'+
' y[k] = Yv[j];\n'+
' if(x[k] === 0) {\n'+
' Zj[p] = k;\n'+
' ++p;\n'+
' }\n'+
' }\n'+
' Zi[i+1] = p;\n'+
' j0 = Xi[i]; j1 = Xi[i+1];\n'+
' for(j=j0;j!==j1;++j) x[Xj[j]] = Xv[j];\n'+
' j0 = Zi[i]; j1 = Zi[i+1];\n'+
' for(j=j0;j!==j1;++j) {\n'+
' k = Zj[j];\n'+
' xk = x[k];\n'+
' yk = y[k];\n'+
body+'\n'+
' Zv[j] = zk;\n'+
' }\n'+
' j0 = Xi[i]; j1 = Xi[i+1];\n'+
' for(j=j0;j!==j1;++j) x[Xj[j]] = 0;\n'+
' j0 = Yi[i]; j1 = Yi[i+1];\n'+
' for(j=j0;j!==j1;++j) y[Yj[j]] = 0;\n'+
'}\n'+
'return [Zi,Zj,Zv];'
);
};
(function() {
var k,A,B,C;
for(k in numeric.ops2) {
if(isFinite(eval('1'+numeric.ops2[k]+'0'))) A = '[Y[0],Y[1],numeric.'+k+'(X,Y[2])]';
else A = 'NaN';
if(isFinite(eval('0'+numeric.ops2[k]+'1'))) B = '[X[0],X[1],numeric.'+k+'(X[2],Y)]';
else B = 'NaN';
if(isFinite(eval('1'+numeric.ops2[k]+'0')) && isFinite(eval('0'+numeric.ops2[k]+'1'))) C = 'numeric.ccs'+k+'MM(X,Y)';
else C = 'NaN';
numeric['ccs'+k+'MM'] = numeric.ccsbinop('zk = xk '+numeric.ops2[k]+'yk;');
numeric['ccs'+k] = Function('X','Y',
'if(typeof X === "number") return '+A+';\n'+
'if(typeof Y === "number") return '+B+';\n'+
'return '+C+';\n'
);
}
}());
numeric.ccsScatter = function ccsScatter(A) {
var Ai = A[0], Aj = A[1], Av = A[2];
var n = numeric.sup(Aj)+1,m=Ai.length;
var Ri = numeric.rep([n],0),Rj=Array(m), Rv = Array(m);
var counts = numeric.rep([n],0),i;
for(i=0;i<m;++i) counts[Aj[i]]++;
for(i=0;i<n;++i) Ri[i+1] = Ri[i] + counts[i];
var ptr = Ri.slice(0),k,Aii;
for(i=0;i<m;++i) {
Aii = Aj[i];
k = ptr[Aii];
Rj[k] = Ai[i];
Rv[k] = Av[i];
ptr[Aii]=ptr[Aii]+1;
}
return [Ri,Rj,Rv];
}
numeric.ccsGather = function ccsGather(A) {
var Ai = A[0], Aj = A[1], Av = A[2];
var n = Ai.length-1,m = Aj.length;
var Ri = Array(m), Rj = Array(m), Rv = Array(m);
var i,j,j0,j1,p;
p=0;
for(i=0;i<n;++i) {
j0 = Ai[i];
j1 = Ai[i+1];
for(j=j0;j!==j1;++j) {
Rj[p] = i;
Ri[p] = Aj[j];
Rv[p] = Av[j];
++p;
}
}
return [Ri,Rj,Rv];
}
// The following sparse linear algebra routines are deprecated.
numeric.sdim = function dim(A,ret,k) {
if(typeof ret === "undefined") { ret = []; }
if(typeof A !== "object") return ret;
if(typeof k === "undefined") { k=0; }
if(!(k in ret)) { ret[k] = 0; }
if(A.length > ret[k]) ret[k] = A.length;
var i;
for(i in A) {
if(A.hasOwnProperty(i)) dim(A[i],ret,k+1);
}
return ret;
};
numeric.sclone = function clone(A,k,n) {
if(typeof k === "undefined") { k=0; }
if(typeof n === "undefined") { n = numeric.sdim(A).length; }
var i,ret = Array(A.length);
if(k === n-1) {
for(i in A) { if(A.hasOwnProperty(i)) ret[i] = A[i]; }
return ret;
}
for(i in A) {
if(A.hasOwnProperty(i)) ret[i] = clone(A[i],k+1,n);
}
return ret;
}
numeric.sdiag = function diag(d) {
var n = d.length,i,ret = Array(n),i1,i2,i3;
for(i=n-1;i>=1;i-=2) {
i1 = i-1;
ret[i] = []; ret[i][i] = d[i];
ret[i1] = []; ret[i1][i1] = d[i1];
}
if(i===0) { ret[0] = []; ret[0][0] = d[i]; }
return ret;
}
numeric.sidentity = function identity(n) { return numeric.sdiag(numeric.rep([n],1)); }
numeric.stranspose = function transpose(A) {
var ret = [], n = A.length, i,j,Ai;
for(i in A) {
if(!(A.hasOwnProperty(i))) continue;
Ai = A[i];
for(j in Ai) {
if(!(Ai.hasOwnProperty(j))) continue;
if(typeof ret[j] !== "object") { ret[j] = []; }
ret[j][i] = Ai[j];
}
}
return ret;
}
numeric.sLUP = function LUP(A,tol) {
throw new Error("The function numeric.sLUP had a bug in it and has been removed. Please use the new numeric.ccsLUP function instead.");
};
numeric.sdotMM = function dotMM(A,B) {
var p = A.length, q = B.length, BT = numeric.stranspose(B), r = BT.length, Ai, BTk;
var i,j,k,accum;
var ret = Array(p),reti;
for(i=p-1;i>=0;i--) {
reti = [];
Ai = A[i];
for(k=r-1;k>=0;k--) {
accum = 0;
BTk = BT[k];
for(j in Ai) {
if(!(Ai.hasOwnProperty(j))) continue;
if(j in BTk) { accum += Ai[j]*BTk[j]; }
}
if(accum) reti[k] = accum;
}
ret[i] = reti;
}
return ret;
}
numeric.sdotMV = function dotMV(A,x) {
var p = A.length, Ai, i,j;
var ret = Array(p), accum;
for(i=p-1;i>=0;i--) {
Ai = A[i];
accum = 0;
for(j in Ai) {
if(!(Ai.hasOwnProperty(j))) continue;
if(x[j]) accum += Ai[j]*x[j];
}
if(accum) ret[i] = accum;
}
return ret;
}
numeric.sdotVM = function dotMV(x,A) {
var i,j,Ai,alpha;
var ret = [], accum;
for(i in x) {
if(!x.hasOwnProperty(i)) continue;
Ai = A[i];
alpha = x[i];
for(j in Ai) {
if(!Ai.hasOwnProperty(j)) continue;
if(!ret[j]) { ret[j] = 0; }
ret[j] += alpha*Ai[j];
}
}
return ret;
}
numeric.sdotVV = function dotVV(x,y) {
var i,ret=0;
for(i in x) { if(x[i] && y[i]) ret+= x[i]*y[i]; }
return ret;
}
numeric.sdot = function dot(A,B) {
var m = numeric.sdim(A).length, n = numeric.sdim(B).length;
var k = m*1000+n;
switch(k) {
case 0: return A*B;
case 1001: return numeric.sdotVV(A,B);
case 2001: return numeric.sdotMV(A,B);
case 1002: return numeric.sdotVM(A,B);
case 2002: return numeric.sdotMM(A,B);
default: throw new Error('numeric.sdot not implemented for tensors of order '+m+' and '+n);
}
}
numeric.sscatter = function scatter(V) {
var n = V[0].length, Vij, i, j, m = V.length, A = [], Aj;
for(i=n-1;i>=0;--i) {
if(!V[m-1][i]) continue;
Aj = A;
for(j=0;j<m-2;j++) {
Vij = V[j][i];
if(!Aj[Vij]) Aj[Vij] = [];
Aj = Aj[Vij];
}
Aj[V[j][i]] = V[j+1][i];
}
return A;
}
numeric.sgather = function gather(A,ret,k) {
if(typeof ret === "undefined") ret = [];
if(typeof k === "undefined") k = [];
var n,i,Ai;
n = k.length;
for(i in A) {
if(A.hasOwnProperty(i)) {
k[n] = parseInt(i);
Ai = A[i];
if(typeof Ai === "number") {
if(Ai) {
if(ret.length === 0) {
for(i=n+1;i>=0;--i) ret[i] = [];
}
for(i=n;i>=0;--i) ret[i].push(k[i]);
ret[n+1].push(Ai);
}
} else gather(Ai,ret,k);
}
}
if(k.length>n) k.pop();
return ret;
}
// 6. Coordinate matrices
numeric.cLU = function LU(A) {
var I = A[0], J = A[1], V = A[2];
var p = I.length, m=0, i,j,k,a,b,c;
for(i=0;i<p;i++) if(I[i]>m) m=I[i];
m++;
var L = Array(m), U = Array(m), left = numeric.rep([m],Infinity), right = numeric.rep([m],-Infinity);
var Ui, Uj,alpha;
for(k=0;k<p;k++) {
i = I[k];
j = J[k];
if(j<left[i]) left[i] = j;
if(j>right[i]) right[i] = j;
}
for(i=0;i<m-1;i++) { if(right[i] > right[i+1]) right[i+1] = right[i]; }
for(i=m-1;i>=1;i--) { if(left[i]<left[i-1]) left[i-1] = left[i]; }
var countL = 0, countU = 0;
for(i=0;i<m;i++) {
U[i] = numeric.rep([right[i]-left[i]+1],0);
L[i] = numeric.rep([i-left[i]],0);
countL += i-left[i]+1;
countU += right[i]-i+1;
}
for(k=0;k<p;k++) { i = I[k]; U[i][J[k]-left[i]] = V[k]; }
for(i=0;i<m-1;i++) {
a = i-left[i];
Ui = U[i];
for(j=i+1;left[j]<=i && j<m;j++) {
b = i-left[j];
c = right[i]-i;
Uj = U[j];
alpha = Uj[b]/Ui[a];
if(alpha) {
for(k=1;k<=c;k++) { Uj[k+b] -= alpha*Ui[k+a]; }
L[j][i-left[j]] = alpha;
}
}
}
var Ui = [], Uj = [], Uv = [], Li = [], Lj = [], Lv = [];
var p,q,foo;
p=0; q=0;
for(i=0;i<m;i++) {
a = left[i];
b = right[i];
foo = U[i];
for(j=i;j<=b;j++) {
if(foo[j-a]) {
Ui[p] = i;
Uj[p] = j;
Uv[p] = foo[j-a];
p++;
}
}
foo = L[i];
for(j=a;j<i;j++) {
if(foo[j-a]) {
Li[q] = i;
Lj[q] = j;
Lv[q] = foo[j-a];
q++;
}
}
Li[q] = i;
Lj[q] = i;
Lv[q] = 1;
q++;
}
return {U:[Ui,Uj,Uv], L:[Li,Lj,Lv]};
};
numeric.cLUsolve = function LUsolve(lu,b) {
var L = lu.L, U = lu.U, ret = numeric.clone(b);
var Li = L[0], Lj = L[1], Lv = L[2];
var Ui = U[0], Uj = U[1], Uv = U[2];
var p = Ui.length, q = Li.length;
var m = ret.length,i,j,k;
k = 0;
for(i=0;i<m;i++) {
while(Lj[k] < i) {
ret[i] -= Lv[k]*ret[Lj[k]];
k++;
}
k++;
}
k = p-1;
for(i=m-1;i>=0;i--) {
while(Uj[k] > i) {
ret[i] -= Uv[k]*ret[Uj[k]];
k--;
}
ret[i] /= Uv[k];
k--;
}
return ret;
};
numeric.cgrid = function grid(n,shape) {
if(typeof n === "number") n = [n,n];
var ret = numeric.rep(n,-1);
var i,j,count;
if(typeof shape !== "function") {
switch(shape) {
case 'L':
shape = function(i,j) { return (i>=n[0]/2 || j<n[1]/2); }
break;
default:
shape = function(i,j) { return true; };
break;
}
}
count=0;
for(i=1;i<n[0]-1;i++) for(j=1;j<n[1]-1;j++)
if(shape(i,j)) {
ret[i][j] = count;
count++;
}
return ret;
}
numeric.cdelsq = function delsq(g) {
var dir = [[-1,0],[0,-1],[0,1],[1,0]];
var s = numeric.dim(g), m = s[0], n = s[1], i,j,k,p,q;
var Li = [], Lj = [], Lv = [];
for(i=1;i<m-1;i++) for(j=1;j<n-1;j++) {
if(g[i][j]<0) continue;
for(k=0;k<4;k++) {
p = i+dir[k][0];
q = j+dir[k][1];
if(g[p][q]<0) continue;
Li.push(g[i][j]);
Lj.push(g[p][q]);
Lv.push(-1);
}
Li.push(g[i][j]);
Lj.push(g[i][j]);
Lv.push(4);
}
return [Li,Lj,Lv];
}
numeric.cdotMV = function dotMV(A,x) {
var ret, Ai = A[0], Aj = A[1], Av = A[2],k,p=Ai.length,N;
N=0;
for(k=0;k<p;k++) { if(Ai[k]>N) N = Ai[k]; }
N++;
ret = numeric.rep([N],0);
for(k=0;k<p;k++) { ret[Ai[k]]+=Av[k]*x[Aj[k]]; }
return ret;
}
// 7. Splines
numeric.Spline = function Spline(x,yl,yr,kl,kr) { this.x = x; this.yl = yl; this.yr = yr; this.kl = kl; this.kr = kr; }
numeric.Spline.prototype._at = function _at(x1,p) {
var x = this.x;
var yl = this.yl;
var yr = this.yr;
var kl = this.kl;
var kr = this.kr;
var x1,a,b,t;
var add = numeric.add, sub = numeric.sub, mul = numeric.mul;
a = sub(mul(kl[p],x[p+1]-x[p]),sub(yr[p+1],yl[p]));
b = add(mul(kr[p+1],x[p]-x[p+1]),sub(yr[p+1],yl[p]));
t = (x1-x[p])/(x[p+1]-x[p]);
var s = t*(1-t);
return add(add(add(mul(1-t,yl[p]),mul(t,yr[p+1])),mul(a,s*(1-t))),mul(b,s*t));
}
numeric.Spline.prototype.at = function at(x0) {
if(typeof x0 === "number") {
var x = this.x;
var n = x.length;
var p,q,mid,floor = Math.floor,a,b,t;
p = 0;
q = n-1;
while(q-p>1) {
mid = floor((p+q)/2);
if(x[mid] <= x0) p = mid;
else q = mid;
}
return this._at(x0,p);
}
var n = x0.length, i, ret = Array(n);
for(i=n-1;i!==-1;--i) ret[i] = this.at(x0[i]);
return ret;
}
numeric.Spline.prototype.diff = function diff() {
var x = this.x;
var yl = this.yl;
var yr = this.yr;
var kl = this.kl;
var kr = this.kr;
var n = yl.length;
var i,dx,dy;
var zl = kl, zr = kr, pl = Array(n), pr = Array(n);
var add = numeric.add, mul = numeric.mul, div = numeric.div, sub = numeric.sub;
for(i=n-1;i!==-1;--i) {
dx = x[i+1]-x[i];
dy = sub(yr[i+1],yl[i]);
pl[i] = div(add(mul(dy, 6),mul(kl[i],-4*dx),mul(kr[i+1],-2*dx)),dx*dx);
pr[i+1] = div(add(mul(dy,-6),mul(kl[i], 2*dx),mul(kr[i+1], 4*dx)),dx*dx);
}
return new numeric.Spline(x,zl,zr,pl,pr);
}
numeric.Spline.prototype.roots = function roots() {
function sqr(x) { return x*x; }
function heval(y0,y1,k0,k1,x) {
var A = k0*2-(y1-y0);
var B = -k1*2+(y1-y0);
var t = (x+1)*0.5;
var s = t*(1-t);
return (1-t)*y0+t*y1+A*s*(1-t)+B*s*t;
}
var ret = [];
var x = this.x, yl = this.yl, yr = this.yr, kl = this.kl, kr = this.kr;
if(typeof yl[0] === "number") {
yl = [yl];
yr = [yr];
kl = [kl];
kr = [kr];
}
var m = yl.length,n=x.length-1,i,j,k,y,s,t;
var ai,bi,ci,di, ret = Array(m),ri,k0,k1,y0,y1,A,B,D,dx,cx,stops,z0,z1,zm,t0,t1,tm;
var sqrt = Math.sqrt;
for(i=0;i!==m;++i) {
ai = yl[i];
bi = yr[i];
ci = kl[i];
di = kr[i];
ri = [];
for(j=0;j!==n;j++) {
if(j>0 && bi[j]*ai[j]<0) ri.push(x[j]);
dx = (x[j+1]-x[j]);
cx = x[j];
y0 = ai[j];
y1 = bi[j+1];
k0 = ci[j]/dx;
k1 = di[j+1]/dx;
D = sqr(k0-k1+3*(y0-y1)) + 12*k1*y0;
A = k1+3*y0+2*k0-3*y1;
B = 3*(k1+k0+2*(y0-y1));
if(D<=0) {
z0 = A/B;
if(z0>x[j] && z0<x[j+1]) stops = [x[j],z0,x[j+1]];
else stops = [x[j],x[j+1]];
} else {
z0 = (A-sqrt(D))/B;
z1 = (A+sqrt(D))/B;
stops = [x[j]];
if(z0>x[j] && z0<x[j+1]) stops.push(z0);
if(z1>x[j] && z1<x[j+1]) stops.push(z1);
stops.push(x[j+1]);
}
t0 = stops[0];
z0 = this._at(t0,j);
for(k=0;k<stops.length-1;k++) {
t1 = stops[k+1];
z1 = this._at(t1,j);
if(z0 === 0) {
ri.push(t0);
t0 = t1;
z0 = z1;
continue;
}
if(z1 === 0 || z0*z1>0) {
t0 = t1;
z0 = z1;
continue;
}
var side = 0;
while(1) {
tm = (z0*t1-z1*t0)/(z0-z1);
if(tm <= t0 || tm >= t1) { break; }
zm = this._at(tm,j);
if(zm*z1>0) {
t1 = tm;
z1 = zm;
if(side === -1) z0*=0.5;
side = -1;
} else if(zm*z0>0) {
t0 = tm;
z0 = zm;
if(side === 1) z1*=0.5;
side = 1;
} else break;
}
ri.push(tm);
t0 = stops[k+1];
z0 = this._at(t0, j);
}
if(z1 === 0) ri.push(t1);
}
ret[i] = ri;
}
if(typeof this.yl[0] === "number") return ret[0];
return ret;
}
numeric.spline = function spline(x,y,k1,kn) {
var n = x.length, b = [], dx = [], dy = [];
var i;
var sub = numeric.sub,mul = numeric.mul,add = numeric.add;
for(i=n-2;i>=0;i--) { dx[i] = x[i+1]-x[i]; dy[i] = sub(y[i+1],y[i]); }
if(typeof k1 === "string" || typeof kn === "string") {
k1 = kn = "periodic";
}
// Build sparse tridiagonal system
var T = [[],[],[]];
switch(typeof k1) {
case "undefined":
b[0] = mul(3/(dx[0]*dx[0]),dy[0]);
T[0].push(0,0);
T[1].push(0,1);
T[2].push(2/dx[0],1/dx[0]);
break;
case "string":
b[0] = add(mul(3/(dx[n-2]*dx[n-2]),dy[n-2]),mul(3/(dx[0]*dx[0]),dy[0]));
T[0].push(0,0,0);
T[1].push(n-2,0,1);
T[2].push(1/dx[n-2],2/dx[n-2]+2/dx[0],1/dx[0]);
break;
default:
b[0] = k1;
T[0].push(0);
T[1].push(0);
T[2].push(1);
break;
}
for(i=1;i<n-1;i++) {
b[i] = add(mul(3/(dx[i-1]*dx[i-1]),dy[i-1]),mul(3/(dx[i]*dx[i]),dy[i]));
T[0].push(i,i,i);
T[1].push(i-1,i,i+1);
T[2].push(1/dx[i-1],2/dx[i-1]+2/dx[i],1/dx[i]);
}
switch(typeof kn) {
case "undefined":
b[n-1] = mul(3/(dx[n-2]*dx[n-2]),dy[n-2]);
T[0].push(n-1,n-1);
T[1].push(n-2,n-1);
T[2].push(1/dx[n-2],2/dx[n-2]);
break;
case "string":
T[1][T[1].length-1] = 0;
break;
default:
b[n-1] = kn;
T[0].push(n-1);
T[1].push(n-1);
T[2].push(1);
break;
}
if(typeof b[0] !== "number") b = numeric.transpose(b);
else b = [b];
var k = Array(b.length);
if(typeof k1 === "string") {
for(i=k.length-1;i!==-1;--i) {
k[i] = numeric.ccsLUPSolve(numeric.ccsLUP(numeric.ccsScatter(T)),b[i]);
k[i][n-1] = k[i][0];
}
} else {
for(i=k.length-1;i!==-1;--i) {
k[i] = numeric.cLUsolve(numeric.cLU(T),b[i]);
}
}
if(typeof y[0] === "number") k = k[0];
else k = numeric.transpose(k);
return new numeric.Spline(x,y,y,k,k);
}
// 8. FFT
numeric.fftpow2 = function fftpow2(x,y) {
var n = x.length;
if(n === 1) return;
var cos = Math.cos, sin = Math.sin, i,j;
var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
j = n/2;
for(i=n-1;i!==-1;--i) {
--j;
xo[j] = x[i];
yo[j] = y[i];
--i;
xe[j] = x[i];
ye[j] = y[i];
}
fftpow2(xe,ye);
fftpow2(xo,yo);
j = n/2;
var t,k = (-6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
for(i=n-1;i!==-1;--i) {
--j;
if(j === -1) j = n/2-1;
t = k*i;
ci = cos(t);
si = sin(t);
x[i] = xe[j] + ci*xo[j] - si*yo[j];
y[i] = ye[j] + ci*yo[j] + si*xo[j];
}
}
numeric._ifftpow2 = function _ifftpow2(x,y) {
var n = x.length;
if(n === 1) return;
var cos = Math.cos, sin = Math.sin, i,j;
var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
j = n/2;
for(i=n-1;i!==-1;--i) {
--j;
xo[j] = x[i];
yo[j] = y[i];
--i;
xe[j] = x[i];
ye[j] = y[i];
}
_ifftpow2(xe,ye);
_ifftpow2(xo,yo);
j = n/2;
var t,k = (6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
for(i=n-1;i!==-1;--i) {
--j;
if(j === -1) j = n/2-1;
t = k*i;
ci = cos(t);
si = sin(t);
x[i] = xe[j] + ci*xo[j] - si*yo[j];
y[i] = ye[j] + ci*yo[j] + si*xo[j];
}
}
numeric.ifftpow2 = function ifftpow2(x,y) {
numeric._ifftpow2(x,y);
numeric.diveq(x,x.length);
numeric.diveq(y,y.length);
}
numeric.convpow2 = function convpow2(ax,ay,bx,by) {
numeric.fftpow2(ax,ay);
numeric.fftpow2(bx,by);
var i,n = ax.length,axi,bxi,ayi,byi;
for(i=n-1;i!==-1;--i) {
axi = ax[i]; ayi = ay[i]; bxi = bx[i]; byi = by[i];
ax[i] = axi*bxi-ayi*byi;
ay[i] = axi*byi+ayi*bxi;
}
numeric.ifftpow2(ax,ay);
}
numeric.T.prototype.fft = function fft() {
var x = this.x, y = this.y;
var n = x.length, log = Math.log, log2 = log(2),
p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
var k, c = (-3.141592653589793238462643383279502884197169399375105820/n),t;
var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
for(k=0;k<n;k++) a[k] = x[k];
if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
cx[0] = 1;
for(k=1;k<=m/2;k++) {
t = c*k*k;
cx[k] = cos(t);
cy[k] = sin(t);
cx[m-k] = cos(t);
cy[m-k] = sin(t)
}
var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
X = X.mul(Y);
numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
X = X.mul(Y);
X.x.length = n;
X.y.length = n;
return X;
}
numeric.T.prototype.ifft = function ifft() {
var x = this.x, y = this.y;
var n = x.length, log = Math.log, log2 = log(2),
p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
var k, c = (3.141592653589793238462643383279502884197169399375105820/n),t;
var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
for(k=0;k<n;k++) a[k] = x[k];
if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
cx[0] = 1;
for(k=1;k<=m/2;k++) {
t = c*k*k;
cx[k] = cos(t);
cy[k] = sin(t);
cx[m-k] = cos(t);
cy[m-k] = sin(t)
}
var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
X = X.mul(Y);
numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
X = X.mul(Y);
X.x.length = n;
X.y.length = n;
return X.div(n);
}
//9. Unconstrained optimization
numeric.gradient = function gradient(f,x) {
var n = x.length;
var f0 = f(x);
if(isNaN(f0)) throw new Error('gradient: f(x) is a NaN!');
var max = Math.max;
var i,x0 = numeric.clone(x),f1,f2, J = Array(n);
var div = numeric.div, sub = numeric.sub,errest,roundoff,max = Math.max,eps = 1e-3,abs = Math.abs, min = Math.min;
var t0,t1,t2,it=0,d1,d2,N;
for(i=0;i<n;i++) {
var h = max(1e-6*f0,1e-8);
while(1) {
++it;
if(it>20) { throw new Error("Numerical gradient fails"); }
x0[i] = x[i]+h;
f1 = f(x0);
x0[i] = x[i]-h;
f2 = f(x0);
x0[i] = x[i];
if(isNaN(f1) || isNaN(f2)) { h/=16; continue; }
J[i] = (f1-f2)/(2*h);
t0 = x[i]-h;
t1 = x[i];
t2 = x[i]+h;
d1 = (f1-f0)/h;
d2 = (f0-f2)/h;
N = max(abs(J[i]),abs(f0),abs(f1),abs(f2),abs(t0),abs(t1),abs(t2),1e-8);
errest = min(max(abs(d1-J[i]),abs(d2-J[i]),abs(d1-d2))/N,h/N);
if(errest>eps) { h/=16; }
else break;
}
}
return J;
}
numeric.uncmin = function uncmin(f,x0,tol,gradient,maxit,callback,options) {
var grad = numeric.gradient;
if(typeof options === "undefined") { options = {}; }
if(typeof tol === "undefined") { tol = 1e-8; }
if(typeof gradient === "undefined") { gradient = function(x) { return grad(f,x); }; }
if(typeof maxit === "undefined") maxit = 1000;
x0 = numeric.clone(x0);
var n = x0.length;
var f0 = f(x0),f1,df0;
if(isNaN(f0)) throw new Error('uncmin: f(x0) is a NaN!');
var max = Math.max, norm2 = numeric.norm2;
tol = max(tol,numeric.epsilon);
var step,g0,g1,H1 = options.Hinv || numeric.identity(n);
var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;
var msg = "";
g0 = gradient(x0);
while(it<maxit) {
if(typeof callback === "function") { if(callback(it,x0,f0,g0,H1)) { msg = "Callback returned true"; break; } }
if(!all(isfinite(g0))) { msg = "Gradient has Infinity or NaN"; break; }
step = neg(dot(H1,g0));
if(!all(isfinite(step))) { msg = "Search direction has Infinity or NaN"; break; }
nstep = norm2(step);
if(nstep < tol) { msg="Newton step smaller than tol"; break; }
t = 1;
df0 = dot(g0,step);
// line search
x1 = x0;
while(it < maxit) {
if(t*nstep < tol) { break; }
s = mul(step,t);
x1 = add(x0,s);
f1 = f(x1);
if(f1-f0 >= 0.1*t*df0 || isNaN(f1)) {
t *= 0.5;
++it;
continue;
}
break;
}
if(t*nstep < tol) { msg = "Line search step size smaller than tol"; break; }
if(it === maxit) { msg = "maxit reached during line search"; break; }
g1 = gradient(x1);
y = sub(g1,g0);
ys = dot(y,s);
Hy = dot(H1,y);
H1 = sub(add(H1,
mul(
(ys+dot(y,Hy))/(ys*ys),
ten(s,s) )),
div(add(ten(Hy,s),ten(s,Hy)),ys));
x0 = x1;
f0 = f1;
g0 = g1;
++it;
}
return {solution: x0, f: f0, gradient: g0, invHessian: H1, iterations:it, message: msg};
}
// 10. Ode solver (Dormand-Prince)
numeric.Dopri = function Dopri(x,y,f,ymid,iterations,msg,events) {
this.x = x;
this.y = y;
this.f = f;
this.ymid = ymid;
this.iterations = iterations;
this.events = events;
this.message = msg;
}
numeric.Dopri.prototype._at = function _at(xi,j) {
function sqr(x) { return x*x; }
var sol = this;
var xs = sol.x;
var ys = sol.y;
var k1 = sol.f;
var ymid = sol.ymid;
var n = xs.length;
var x0,x1,xh,y0,y1,yh,xi;
var floor = Math.floor,h;
var c = 0.5;
var add = numeric.add, mul = numeric.mul,sub = numeric.sub, p,q,w;
x0 = xs[j];
x1 = xs[j+1];
y0 = ys[j];
y1 = ys[j+1];
h = x1-x0;
xh = x0+c*h;
yh = ymid[j];
p = sub(k1[j ],mul(y0,1/(x0-xh)+2/(x0-x1)));
q = sub(k1[j+1],mul(y1,1/(x1-xh)+2/(x1-x0)));
w = [sqr(xi - x1) * (xi - xh) / sqr(x0 - x1) / (x0 - xh),
sqr(xi - x0) * sqr(xi - x1) / sqr(x0 - xh) / sqr(x1 - xh),
sqr(xi - x0) * (xi - xh) / sqr(x1 - x0) / (x1 - xh),
(xi - x0) * sqr(xi - x1) * (xi - xh) / sqr(x0-x1) / (x0 - xh),
(xi - x1) * sqr(xi - x0) * (xi - xh) / sqr(x0-x1) / (x1 - xh)];
return add(add(add(add(mul(y0,w[0]),
mul(yh,w[1])),
mul(y1,w[2])),
mul( p,w[3])),
mul( q,w[4]));
}
numeric.Dopri.prototype.at = function at(x) {
var i,j,k,floor = Math.floor;
if(typeof x !== "number") {
var n = x.length, ret = Array(n);
for(i=n-1;i!==-1;--i) {
ret[i] = this.at(x[i]);
}
return ret;
}
var x0 = this.x;
i = 0; j = x0.length-1;
while(j-i>1) {
k = floor(0.5*(i+j));
if(x0[k] <= x) i = k;
else j = k;
}
return this._at(x,i);
}
numeric.dopri = function dopri(x0,x1,y0,f,tol,maxit,event) {
if(typeof tol === "undefined") { tol = 1e-6; }
if(typeof maxit === "undefined") { maxit = 1000; }
var xs = [x0], ys = [y0], k1 = [f(x0,y0)], k2,k3,k4,k5,k6,k7, ymid = [];
var A2 = 1/5;
var A3 = [3/40,9/40];
var A4 = [44/45,-56/15,32/9];
var A5 = [19372/6561,-25360/2187,64448/6561,-212/729];
var A6 = [9017/3168,-355/33,46732/5247,49/176,-5103/18656];
var b = [35/384,0,500/1113,125/192,-2187/6784,11/84];
var bm = [0.5*6025192743/30085553152,
0,
0.5*51252292925/65400821598,
0.5*-2691868925/45128329728,
0.5*187940372067/1594534317056,
0.5*-1776094331/19743644256,
0.5*11237099/235043384];
var c = [1/5,3/10,4/5,8/9,1,1];
var e = [-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40];
var i = 0,er,j;
var h = (x1-x0)/10;
var it = 0;
var add = numeric.add, mul = numeric.mul, y1,erinf;
var max = Math.max, min = Math.min, abs = Math.abs, norminf = numeric.norminf,pow = Math.pow;
var any = numeric.any, lt = numeric.lt, and = numeric.and, sub = numeric.sub;
var e0, e1, ev;
var ret = new numeric.Dopri(xs,ys,k1,ymid,-1,"");
if(typeof event === "function") e0 = event(x0,y0);
while(x0<x1 && it<maxit) {
++it;
if(x0+h>x1) h = x1-x0;
k2 = f(x0+c[0]*h, add(y0,mul( A2*h,k1[i])));
k3 = f(x0+c[1]*h, add(add(y0,mul(A3[0]*h,k1[i])),mul(A3[1]*h,k2)));
k4 = f(x0+c[2]*h, add(add(add(y0,mul(A4[0]*h,k1[i])),mul(A4[1]*h,k2)),mul(A4[2]*h,k3)));
k5 = f(x0+c[3]*h, add(add(add(add(y0,mul(A5[0]*h,k1[i])),mul(A5[1]*h,k2)),mul(A5[2]*h,k3)),mul(A5[3]*h,k4)));
k6 = f(x0+c[4]*h,add(add(add(add(add(y0,mul(A6[0]*h,k1[i])),mul(A6[1]*h,k2)),mul(A6[2]*h,k3)),mul(A6[3]*h,k4)),mul(A6[4]*h,k5)));
y1 = add(add(add(add(add(y0,mul(k1[i],h*b[0])),mul(k3,h*b[2])),mul(k4,h*b[3])),mul(k5,h*b[4])),mul(k6,h*b[5]));
k7 = f(x0+h,y1);
er = add(add(add(add(add(mul(k1[i],h*e[0]),mul(k3,h*e[2])),mul(k4,h*e[3])),mul(k5,h*e[4])),mul(k6,h*e[5])),mul(k7,h*e[6]));
if(typeof er === "number") erinf = abs(er);
else erinf = norminf(er);
if(erinf > tol) { // reject
h = 0.2*h*pow(tol/erinf,0.25);
if(x0+h === x0) {
ret.msg = "Step size became too small";
break;
}
continue;
}
ymid[i] = add(add(add(add(add(add(y0,
mul(k1[i],h*bm[0])),
mul(k3 ,h*bm[2])),
mul(k4 ,h*bm[3])),
mul(k5 ,h*bm[4])),
mul(k6 ,h*bm[5])),
mul(k7 ,h*bm[6]));
++i;
xs[i] = x0+h;
ys[i] = y1;
k1[i] = k7;
if(typeof event === "function") {
var yi,xl = x0,xr = x0+0.5*h,xi;
e1 = event(xr,ymid[i-1]);
ev = and(lt(e0,0),lt(0,e1));
if(!any(ev)) { xl = xr; xr = x0+h; e0 = e1; e1 = event(xr,y1); ev = and(lt(e0,0),lt(0,e1)); }
if(any(ev)) {
var xc, yc, en,ei;
var side=0, sl = 1.0, sr = 1.0;
while(1) {
if(typeof e0 === "number") xi = (sr*e1*xl-sl*e0*xr)/(sr*e1-sl*e0);
else {
xi = xr;
for(j=e0.length-1;j!==-1;--j) {
if(e0[j]<0 && e1[j]>0) xi = min(xi,(sr*e1[j]*xl-sl*e0[j]*xr)/(sr*e1[j]-sl*e0[j]));
}
}
if(xi <= xl || xi >= xr) break;
yi = ret._at(xi, i-1);
ei = event(xi,yi);
en = and(lt(e0,0),lt(0,ei));
if(any(en)) {
xr = xi;
e1 = ei;
ev = en;
sr = 1.0;
if(side === -1) sl *= 0.5;
else sl = 1.0;
side = -1;
} else {
xl = xi;
e0 = ei;
sl = 1.0;
if(side === 1) sr *= 0.5;
else sr = 1.0;
side = 1;
}
}
y1 = ret._at(0.5*(x0+xi),i-1);
ret.f[i] = f(xi,yi);
ret.x[i] = xi;
ret.y[i] = yi;
ret.ymid[i-1] = y1;
ret.events = ev;
ret.iterations = it;
return ret;
}
}
x0 += h;
y0 = y1;
e0 = e1;
h = min(0.8*h*pow(tol/erinf,0.25),4*h);
}
ret.iterations = it;
return ret;
}
// 11. Ax = b
numeric.LU = function(A, fast) {
fast = fast || false;
var abs = Math.abs;
var i, j, k, absAjk, Akk, Ak, Pk, Ai;
var max;
var n = A.length, n1 = n-1;
var P = new Array(n);
if(!fast) A = numeric.clone(A);
for (k = 0; k < n; ++k) {
Pk = k;
Ak = A[k];
max = abs(Ak[k]);
for (j = k + 1; j < n; ++j) {
absAjk = abs(A[j][k]);
if (max < absAjk) {
max = absAjk;
Pk = j;
}
}
P[k] = Pk;
if (Pk != k) {
A[k] = A[Pk];
A[Pk] = Ak;
Ak = A[k];
}
Akk = Ak[k];
for (i = k + 1; i < n; ++i) {
A[i][k] /= Akk;
}
for (i = k + 1; i < n; ++i) {
Ai = A[i];
for (j = k + 1; j < n1; ++j) {
Ai[j] -= Ai[k] * Ak[j];
++j;
Ai[j] -= Ai[k] * Ak[j];
}
if(j===n1) Ai[j] -= Ai[k] * Ak[j];
}
}
return {
LU: A,
P: P
};
}
numeric.LUsolve = function LUsolve(LUP, b) {
var i, j;
var LU = LUP.LU;
var n = LU.length;
var x = numeric.clone(b);
var P = LUP.P;
var Pi, LUi, LUii, tmp;
for (i=n-1;i!==-1;--i) x[i] = b[i];
for (i = 0; i < n; ++i) {
Pi = P[i];
if (P[i] !== i) {
tmp = x[i];
x[i] = x[Pi];
x[Pi] = tmp;
}
LUi = LU[i];
for (j = 0; j < i; ++j) {
x[i] -= x[j] * LUi[j];
}
}
for (i = n - 1; i >= 0; --i) {
LUi = LU[i];
for (j = i + 1; j < n; ++j) {
x[i] -= x[j] * LUi[j];
}
x[i] /= LUi[i];
}
return x;
}
numeric.solve = function solve(A,b,fast) { return numeric.LUsolve(numeric.LU(A,fast), b); }
// 12. Linear programming
numeric.echelonize = function echelonize(A) {
var s = numeric.dim(A), m = s[0], n = s[1];
var I = numeric.identity(m);
var P = Array(m);
var i,j,k,l,Ai,Ii,Z,a;
var abs = Math.abs;
var diveq = numeric.diveq;
A = numeric.clone(A);
for(i=0;i<m;++i) {
k = 0;
Ai = A[i];
Ii = I[i];
for(j=1;j<n;++j) if(abs(Ai[k])<abs(Ai[j])) k=j;
P[i] = k;
diveq(Ii,Ai[k]);
diveq(Ai,Ai[k]);
for(j=0;j<m;++j) if(j!==i) {
Z = A[j]; a = Z[k];
for(l=n-1;l!==-1;--l) Z[l] -= Ai[l]*a;
Z = I[j];
for(l=m-1;l!==-1;--l) Z[l] -= Ii[l]*a;
}
}
return {I:I, A:A, P:P};
}
numeric.__solveLP = function __solveLP(c,A,b,tol,maxit,x,flag) {
var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
var m = c.length, n = b.length,y;
var unbounded = false, cb,i0=0;
var alpha = 1.0;
var f0,df0,AT = numeric.transpose(A), svd = numeric.svd,transpose = numeric.transpose,leq = numeric.leq, sqrt = Math.sqrt, abs = Math.abs;
var muleq = numeric.muleq;
var norm = numeric.norminf, any = numeric.any,min = Math.min;
var all = numeric.all, gt = numeric.gt;
var p = Array(m), A0 = Array(n),e=numeric.rep([n],1), H;
var solve = numeric.solve, z = sub(b,dot(A,x)),count;
var dotcc = dot(c,c);
var g;
for(count=i0;count<maxit;++count) {
var i,j,d;
for(i=n-1;i!==-1;--i) A0[i] = div(A[i],z[i]);
var A1 = transpose(A0);
for(i=m-1;i!==-1;--i) p[i] = (/*x[i]+*/sum(A1[i]));
alpha = 0.25*abs(dotcc/dot(c,p));
var a1 = 100*sqrt(dotcc/dot(p,p));
if(!isFinite(alpha) || alpha>a1) alpha = a1;
g = add(c,mul(alpha,p));
H = dot(A1,A0);
for(i=m-1;i!==-1;--i) H[i][i] += 1;
d = solve(H,div(g,alpha),true);
var t0 = div(z,dot(A,d));
var t = 1.0;
for(i=n-1;i!==-1;--i) if(t0[i]<0) t = min(t,-0.999*t0[i]);
y = sub(x,mul(d,t));
z = sub(b,dot(A,y));
if(!all(gt(z,0))) return { solution: x, message: "", iterations: count };
x = y;
if(alpha<tol) return { solution: y, message: "", iterations: count };
if(flag) {
var s = dot(c,g), Ag = dot(A,g);
unbounded = true;
for(i=n-1;i!==-1;--i) if(s*Ag[i]<0) { unbounded = false; break; }
} else {
if(x[m-1]>=0) unbounded = false;
else unbounded = true;
}
if(unbounded) return { solution: y, message: "Unbounded", iterations: count };
}
return { solution: x, message: "maximum iteration count exceeded", iterations:count };
}
numeric._solveLP = function _solveLP(c,A,b,tol,maxit) {
var m = c.length, n = b.length,y;
var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
var c0 = numeric.rep([m],0).concat([1]);
var J = numeric.rep([n,1],-1);
var A0 = numeric.blockMatrix([[A , J ]]);
var b0 = b;
var y = numeric.rep([m],0).concat(Math.max(0,numeric.sup(numeric.neg(b)))+1);
var x0 = numeric.__solveLP(c0,A0,b0,tol,maxit,y,false);
var x = numeric.clone(x0.solution);
x.length = m;
var foo = numeric.inf(sub(b,dot(A,x)));
if(foo<0) { return { solution: NaN, message: "Infeasible", iterations: x0.iterations }; }
var ret = numeric.__solveLP(c, A, b, tol, maxit-x0.iterations, x, true);
ret.iterations += x0.iterations;
return ret;
};
numeric.solveLP = function solveLP(c,A,b,Aeq,beq,tol,maxit) {
if(typeof maxit === "undefined") maxit = 1000;
if(typeof tol === "undefined") tol = numeric.epsilon;
if(typeof Aeq === "undefined") return numeric._solveLP(c,A,b,tol,maxit);
var m = Aeq.length, n = Aeq[0].length, o = A.length;
var B = numeric.echelonize(Aeq);
var flags = numeric.rep([n],0);
var P = B.P;
var Q = [];
var i;
for(i=P.length-1;i!==-1;--i) flags[P[i]] = 1;
for(i=n-1;i!==-1;--i) if(flags[i]===0) Q.push(i);
var g = numeric.getRange;
var I = numeric.linspace(0,m-1), J = numeric.linspace(0,o-1);
var Aeq2 = g(Aeq,I,Q), A1 = g(A,J,P), A2 = g(A,J,Q), dot = numeric.dot, sub = numeric.sub;
var A3 = dot(A1,B.I);
var A4 = sub(A2,dot(A3,Aeq2)), b4 = sub(b,dot(A3,beq));
var c1 = Array(P.length), c2 = Array(Q.length);
for(i=P.length-1;i!==-1;--i) c1[i] = c[P[i]];
for(i=Q.length-1;i!==-1;--i) c2[i] = c[Q[i]];
var c4 = sub(c2,dot(c1,dot(B.I,Aeq2)));
var S = numeric._solveLP(c4,A4,b4,tol,maxit);
var x2 = S.solution;
if(x2!==x2) return S;
var x1 = dot(B.I,sub(beq,dot(Aeq2,x2)));
var x = Array(c.length);
for(i=P.length-1;i!==-1;--i) x[P[i]] = x1[i];
for(i=Q.length-1;i!==-1;--i) x[Q[i]] = x2[i];
return { solution: x, message:S.message, iterations: S.iterations };
}
numeric.MPStoLP = function MPStoLP(MPS) {
if(MPS instanceof String) { MPS.split('\n'); }
var state = 0;
var states = ['Initial state','NAME','ROWS','COLUMNS','RHS','BOUNDS','ENDATA'];
var n = MPS.length;
var i,j,z,N=0,rows = {}, sign = [], rl = 0, vars = {}, nv = 0;
var name;
var c = [], A = [], b = [];
function err(e) { throw new Error('MPStoLP: '+e+'\nLine '+i+': '+MPS[i]+'\nCurrent state: '+states[state]+'\n'); }
for(i=0;i<n;++i) {
z = MPS[i];
var w0 = z.match(/\S*/g);
var w = [];
for(j=0;j<w0.length;++j) if(w0[j]!=="") w.push(w0[j]);
if(w.length === 0) continue;
for(j=0;j<states.length;++j) if(z.substr(0,states[j].length) === states[j]) break;
if(j<states.length) {
state = j;
if(j===1) { name = w[1]; }
if(j===6) return { name:name, c:c, A:numeric.transpose(A), b:b, rows:rows, vars:vars };
continue;
}
switch(state) {
case 0: case 1: err('Unexpected line');
case 2:
switch(w[0]) {
case 'N': if(N===0) N = w[1]; else err('Two or more N rows'); break;
case 'L': rows[w[1]] = rl; sign[rl] = 1; b[rl] = 0; ++rl; break;
case 'G': rows[w[1]] = rl; sign[rl] = -1;b[rl] = 0; ++rl; break;
case 'E': rows[w[1]] = rl; sign[rl] = 0;b[rl] = 0; ++rl; break;
default: err('Parse error '+numeric.prettyPrint(w));
}
break;
case 3:
if(!vars.hasOwnProperty(w[0])) { vars[w[0]] = nv; c[nv] = 0; A[nv] = numeric.rep([rl],0); ++nv; }
var p = vars[w[0]];
for(j=1;j<w.length;j+=2) {
if(w[j] === N) { c[p] = parseFloat(w[j+1]); continue; }
var q = rows[w[j]];
A[p][q] = (sign[q]<0?-1:1)*parseFloat(w[j+1]);
}
break;
case 4:
for(j=1;j<w.length;j+=2) b[rows[w[j]]] = (sign[rows[w[j]]]<0?-1:1)*parseFloat(w[j+1]);
break;
case 5: /*FIXME*/ break;
case 6: err('Internal error');
}
}
err('Reached end of file without ENDATA');
}
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