From c0f744ed88902594df78d1e5139919603988c5cd Mon Sep 17 00:00:00 2001
From: Amanda Ghassaei <amandaghassaei@gmail.com>
Date: Wed, 14 Jan 2015 15:13:01 -0500
Subject: [PATCH] setting up physical elements
---
dependencies/numeric-1.2.6.js | 4424 +++++++++++++++++++++++++++++
dependencies/numeric-1.2.6.min.js | 3 +
js/models/dmaBeam.js | 57 +
js/models/dmaCell.js | 3 +
js/models/dmaNode.js | 27 +
js/models/dmaPart.js | 27 +
js/models/element.js | 7 -
js/views/importMenu.js | 1 -
js/worker.js | 2 +-
main.html | 3 +
10 files changed, 4545 insertions(+), 9 deletions(-)
create mode 100644 dependencies/numeric-1.2.6.js
create mode 100644 dependencies/numeric-1.2.6.min.js
create mode 100644 js/models/dmaBeam.js
create mode 100644 js/models/dmaCell.js
create mode 100644 js/models/dmaNode.js
create mode 100644 js/models/dmaPart.js
delete mode 100644 js/models/element.js
diff --git a/dependencies/numeric-1.2.6.js b/dependencies/numeric-1.2.6.js
new file mode 100644
index 00000000..44edb9b8
--- /dev/null
+++ b/dependencies/numeric-1.2.6.js
@@ -0,0 +1,4424 @@
+"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');
+}
+// seedrandom.js version 2.0.
+// Author: David Bau 4/2/2011
+//
+// Defines a method Math.seedrandom() that, when called, substitutes
+// an explicitly seeded RC4-based algorithm for Math.random(). Also
+// supports automatic seeding from local or network sources of entropy.
+//
+// Usage:
+//
+// <script src=http://davidbau.com/encode/seedrandom-min.js></script>
+//
+// Math.seedrandom('yipee'); Sets Math.random to a function that is
+// initialized using the given explicit seed.
+//
+// Math.seedrandom(); Sets Math.random to a function that is
+// seeded using the current time, dom state,
+// and other accumulated local entropy.
+// The generated seed string is returned.
+//
+// Math.seedrandom('yowza', true);
+// Seeds using the given explicit seed mixed
+// together with accumulated entropy.
+//
+// <script src="http://bit.ly/srandom-512"></script>
+// Seeds using physical random bits downloaded
+// from random.org.
+//
+// <script src="https://jsonlib.appspot.com/urandom?callback=Math.seedrandom">
+// </script> Seeds using urandom bits from call.jsonlib.com,
+// which is faster than random.org.
+//
+// Examples:
+//
+// Math.seedrandom("hello"); // Use "hello" as the seed.
+// document.write(Math.random()); // Always 0.5463663768140734
+// document.write(Math.random()); // Always 0.43973793770592234
+// var rng1 = Math.random; // Remember the current prng.
+//
+// var autoseed = Math.seedrandom(); // New prng with an automatic seed.
+// document.write(Math.random()); // Pretty much unpredictable.
+//
+// Math.random = rng1; // Continue "hello" prng sequence.
+// document.write(Math.random()); // Always 0.554769432473455
+//
+// Math.seedrandom(autoseed); // Restart at the previous seed.
+// document.write(Math.random()); // Repeat the 'unpredictable' value.
+//
+// Notes:
+//
+// Each time seedrandom('arg') is called, entropy from the passed seed
+// is accumulated in a pool to help generate future seeds for the
+// zero-argument form of Math.seedrandom, so entropy can be injected over
+// time by calling seedrandom with explicit data repeatedly.
+//
+// On speed - This javascript implementation of Math.random() is about
+// 3-10x slower than the built-in Math.random() because it is not native
+// code, but this is typically fast enough anyway. Seeding is more expensive,
+// especially if you use auto-seeding. Some details (timings on Chrome 4):
+//
+// Our Math.random() - avg less than 0.002 milliseconds per call
+// seedrandom('explicit') - avg less than 0.5 milliseconds per call
+// seedrandom('explicit', true) - avg less than 2 milliseconds per call
+// seedrandom() - avg about 38 milliseconds per call
+//
+// LICENSE (BSD):
+//
+// Copyright 2010 David Bau, all rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// 1. Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//
+// 2. Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// 3. Neither the name of this module nor the names of its contributors may
+// be used to endorse or promote products derived from this software
+// without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+/**
+ * All code is in an anonymous closure to keep the global namespace clean.
+ *
+ * @param {number=} overflow
+ * @param {number=} startdenom
+ */
+
+// Patched by Seb so that seedrandom.js does not pollute the Math object.
+// My tests suggest that doing Math.trouble = 1 makes Math lookups about 5%
+// slower.
+numeric.seedrandom = { pow:Math.pow, random:Math.random };
+
+(function (pool, math, width, chunks, significance, overflow, startdenom) {
+
+
+//
+// seedrandom()
+// This is the seedrandom function described above.
+//
+math['seedrandom'] = function seedrandom(seed, use_entropy) {
+ var key = [];
+ var arc4;
+
+ // Flatten the seed string or build one from local entropy if needed.
+ seed = mixkey(flatten(
+ use_entropy ? [seed, pool] :
+ arguments.length ? seed :
+ [new Date().getTime(), pool, window], 3), key);
+
+ // Use the seed to initialize an ARC4 generator.
+ arc4 = new ARC4(key);
+
+ // Mix the randomness into accumulated entropy.
+ mixkey(arc4.S, pool);
+
+ // Override Math.random
+
+ // This function returns a random double in [0, 1) that contains
+ // randomness in every bit of the mantissa of the IEEE 754 value.
+
+ math['random'] = function random() { // Closure to return a random double:
+ var n = arc4.g(chunks); // Start with a numerator n < 2 ^ 48
+ var d = startdenom; // and denominator d = 2 ^ 48.
+ var x = 0; // and no 'extra last byte'.
+ while (n < significance) { // Fill up all significant digits by
+ n = (n + x) * width; // shifting numerator and
+ d *= width; // denominator and generating a
+ x = arc4.g(1); // new least-significant-byte.
+ }
+ while (n >= overflow) { // To avoid rounding up, before adding
+ n /= 2; // last byte, shift everything
+ d /= 2; // right using integer math until
+ x >>>= 1; // we have exactly the desired bits.
+ }
+ return (n + x) / d; // Form the number within [0, 1).
+ };
+
+ // Return the seed that was used
+ return seed;
+};
+
+//
+// ARC4
+//
+// An ARC4 implementation. The constructor takes a key in the form of
+// an array of at most (width) integers that should be 0 <= x < (width).
+//
+// The g(count) method returns a pseudorandom integer that concatenates
+// the next (count) outputs from ARC4. Its return value is a number x
+// that is in the range 0 <= x < (width ^ count).
+//
+/** @constructor */
+function ARC4(key) {
+ var t, u, me = this, keylen = key.length;
+ var i = 0, j = me.i = me.j = me.m = 0;
+ me.S = [];
+ me.c = [];
+
+ // The empty key [] is treated as [0].
+ if (!keylen) { key = [keylen++]; }
+
+ // Set up S using the standard key scheduling algorithm.
+ while (i < width) { me.S[i] = i++; }
+ for (i = 0; i < width; i++) {
+ t = me.S[i];
+ j = lowbits(j + t + key[i % keylen]);
+ u = me.S[j];
+ me.S[i] = u;
+ me.S[j] = t;
+ }
+
+ // The "g" method returns the next (count) outputs as one number.
+ me.g = function getnext(count) {
+ var s = me.S;
+ var i = lowbits(me.i + 1); var t = s[i];
+ var j = lowbits(me.j + t); var u = s[j];
+ s[i] = u;
+ s[j] = t;
+ var r = s[lowbits(t + u)];
+ while (--count) {
+ i = lowbits(i + 1); t = s[i];
+ j = lowbits(j + t); u = s[j];
+ s[i] = u;
+ s[j] = t;
+ r = r * width + s[lowbits(t + u)];
+ }
+ me.i = i;
+ me.j = j;
+ return r;
+ };
+ // For robust unpredictability discard an initial batch of values.
+ // See http://www.rsa.com/rsalabs/node.asp?id=2009
+ me.g(width);
+}
+
+//
+// flatten()
+// Converts an object tree to nested arrays of strings.
+//
+/** @param {Object=} result
+ * @param {string=} prop
+ * @param {string=} typ */
+function flatten(obj, depth, result, prop, typ) {
+ result = [];
+ typ = typeof(obj);
+ if (depth && typ == 'object') {
+ for (prop in obj) {
+ if (prop.indexOf('S') < 5) { // Avoid FF3 bug (local/sessionStorage)
+ try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}
+ }
+ }
+ }
+ return (result.length ? result : obj + (typ != 'string' ? '\0' : ''));
+}
+
+//
+// mixkey()
+// Mixes a string seed into a key that is an array of integers, and
+// returns a shortened string seed that is equivalent to the result key.
+//
+/** @param {number=} smear
+ * @param {number=} j */
+function mixkey(seed, key, smear, j) {
+ seed += ''; // Ensure the seed is a string
+ smear = 0;
+ for (j = 0; j < seed.length; j++) {
+ key[lowbits(j)] =
+ lowbits((smear ^= key[lowbits(j)] * 19) + seed.charCodeAt(j));
+ }
+ seed = '';
+ for (j in key) { seed += String.fromCharCode(key[j]); }
+ return seed;
+}
+
+//
+// lowbits()
+// A quick "n mod width" for width a power of 2.
+//
+function lowbits(n) { return n & (width - 1); }
+
+//
+// The following constants are related to IEEE 754 limits.
+//
+startdenom = math.pow(width, chunks);
+significance = math.pow(2, significance);
+overflow = significance * 2;
+
+//
+// When seedrandom.js is loaded, we immediately mix a few bits
+// from the built-in RNG into the entropy pool. Because we do
+// not want to intefere with determinstic PRNG state later,
+// seedrandom will not call math.random on its own again after
+// initialization.
+//
+mixkey(math.random(), pool);
+
+// End anonymous scope, and pass initial values.
+}(
+ [], // pool: entropy pool starts empty
+ numeric.seedrandom, // math: package containing random, pow, and seedrandom
+ 256, // width: each RC4 output is 0 <= x < 256
+ 6, // chunks: at least six RC4 outputs for each double
+ 52 // significance: there are 52 significant digits in a double
+ ));
+/* This file is a slightly modified version of quadprog.js from Alberto Santini.
+ * It has been slightly modified by Sébastien Loisel to make sure that it handles
+ * 0-based Arrays instead of 1-based Arrays.
+ * License is in resources/LICENSE.quadprog */
+(function(exports) {
+
+function base0to1(A) {
+ if(typeof A !== "object") { return A; }
+ var ret = [], i,n=A.length;
+ for(i=0;i<n;i++) ret[i+1] = base0to1(A[i]);
+ return ret;
+}
+function base1to0(A) {
+ if(typeof A !== "object") { return A; }
+ var ret = [], i,n=A.length;
+ for(i=1;i<n;i++) ret[i-1] = base1to0(A[i]);
+ return ret;
+}
+
+function dpori(a, lda, n) {
+ var i, j, k, kp1, t;
+
+ for (k = 1; k <= n; k = k + 1) {
+ a[k][k] = 1 / a[k][k];
+ t = -a[k][k];
+ //~ dscal(k - 1, t, a[1][k], 1);
+ for (i = 1; i < k; i = i + 1) {
+ a[i][k] = t * a[i][k];
+ }
+
+ kp1 = k + 1;
+ if (n < kp1) {
+ break;
+ }
+ for (j = kp1; j <= n; j = j + 1) {
+ t = a[k][j];
+ a[k][j] = 0;
+ //~ daxpy(k, t, a[1][k], 1, a[1][j], 1);
+ for (i = 1; i <= k; i = i + 1) {
+ a[i][j] = a[i][j] + (t * a[i][k]);
+ }
+ }
+ }
+
+}
+
+function dposl(a, lda, n, b) {
+ var i, k, kb, t;
+
+ for (k = 1; k <= n; k = k + 1) {
+ //~ t = ddot(k - 1, a[1][k], 1, b[1], 1);
+ t = 0;
+ for (i = 1; i < k; i = i + 1) {
+ t = t + (a[i][k] * b[i]);
+ }
+
+ b[k] = (b[k] - t) / a[k][k];
+ }
+
+ for (kb = 1; kb <= n; kb = kb + 1) {
+ k = n + 1 - kb;
+ b[k] = b[k] / a[k][k];
+ t = -b[k];
+ //~ daxpy(k - 1, t, a[1][k], 1, b[1], 1);
+ for (i = 1; i < k; i = i + 1) {
+ b[i] = b[i] + (t * a[i][k]);
+ }
+ }
+}
+
+function dpofa(a, lda, n, info) {
+ var i, j, jm1, k, t, s;
+
+ for (j = 1; j <= n; j = j + 1) {
+ info[1] = j;
+ s = 0;
+ jm1 = j - 1;
+ if (jm1 < 1) {
+ s = a[j][j] - s;
+ if (s <= 0) {
+ break;
+ }
+ a[j][j] = Math.sqrt(s);
+ } else {
+ for (k = 1; k <= jm1; k = k + 1) {
+ //~ t = a[k][j] - ddot(k - 1, a[1][k], 1, a[1][j], 1);
+ t = a[k][j];
+ for (i = 1; i < k; i = i + 1) {
+ t = t - (a[i][j] * a[i][k]);
+ }
+ t = t / a[k][k];
+ a[k][j] = t;
+ s = s + t * t;
+ }
+ s = a[j][j] - s;
+ if (s <= 0) {
+ break;
+ }
+ a[j][j] = Math.sqrt(s);
+ }
+ info[1] = 0;
+ }
+}
+
+function qpgen2(dmat, dvec, fddmat, n, sol, crval, amat,
+ bvec, fdamat, q, meq, iact, nact, iter, work, ierr) {
+
+ var i, j, l, l1, info, it1, iwzv, iwrv, iwrm, iwsv, iwuv, nvl, r, iwnbv,
+ temp, sum, t1, tt, gc, gs, nu,
+ t1inf, t2min,
+ vsmall, tmpa, tmpb,
+ go;
+
+ r = Math.min(n, q);
+ l = 2 * n + (r * (r + 5)) / 2 + 2 * q + 1;
+
+ vsmall = 1.0e-60;
+ do {
+ vsmall = vsmall + vsmall;
+ tmpa = 1 + 0.1 * vsmall;
+ tmpb = 1 + 0.2 * vsmall;
+ } while (tmpa <= 1 || tmpb <= 1);
+
+ for (i = 1; i <= n; i = i + 1) {
+ work[i] = dvec[i];
+ }
+ for (i = n + 1; i <= l; i = i + 1) {
+ work[i] = 0;
+ }
+ for (i = 1; i <= q; i = i + 1) {
+ iact[i] = 0;
+ }
+
+ info = [];
+
+ if (ierr[1] === 0) {
+ dpofa(dmat, fddmat, n, info);
+ if (info[1] !== 0) {
+ ierr[1] = 2;
+ return;
+ }
+ dposl(dmat, fddmat, n, dvec);
+ dpori(dmat, fddmat, n);
+ } else {
+ for (j = 1; j <= n; j = j + 1) {
+ sol[j] = 0;
+ for (i = 1; i <= j; i = i + 1) {
+ sol[j] = sol[j] + dmat[i][j] * dvec[i];
+ }
+ }
+ for (j = 1; j <= n; j = j + 1) {
+ dvec[j] = 0;
+ for (i = j; i <= n; i = i + 1) {
+ dvec[j] = dvec[j] + dmat[j][i] * sol[i];
+ }
+ }
+ }
+
+ crval[1] = 0;
+ for (j = 1; j <= n; j = j + 1) {
+ sol[j] = dvec[j];
+ crval[1] = crval[1] + work[j] * sol[j];
+ work[j] = 0;
+ for (i = j + 1; i <= n; i = i + 1) {
+ dmat[i][j] = 0;
+ }
+ }
+ crval[1] = -crval[1] / 2;
+ ierr[1] = 0;
+
+ iwzv = n;
+ iwrv = iwzv + n;
+ iwuv = iwrv + r;
+ iwrm = iwuv + r + 1;
+ iwsv = iwrm + (r * (r + 1)) / 2;
+ iwnbv = iwsv + q;
+
+ for (i = 1; i <= q; i = i + 1) {
+ sum = 0;
+ for (j = 1; j <= n; j = j + 1) {
+ sum = sum + amat[j][i] * amat[j][i];
+ }
+ work[iwnbv + i] = Math.sqrt(sum);
+ }
+ nact = 0;
+ iter[1] = 0;
+ iter[2] = 0;
+
+ function fn_goto_50() {
+ iter[1] = iter[1] + 1;
+
+ l = iwsv;
+ for (i = 1; i <= q; i = i + 1) {
+ l = l + 1;
+ sum = -bvec[i];
+ for (j = 1; j <= n; j = j + 1) {
+ sum = sum + amat[j][i] * sol[j];
+ }
+ if (Math.abs(sum) < vsmall) {
+ sum = 0;
+ }
+ if (i > meq) {
+ work[l] = sum;
+ } else {
+ work[l] = -Math.abs(sum);
+ if (sum > 0) {
+ for (j = 1; j <= n; j = j + 1) {
+ amat[j][i] = -amat[j][i];
+ }
+ bvec[i] = -bvec[i];
+ }
+ }
+ }
+
+ for (i = 1; i <= nact; i = i + 1) {
+ work[iwsv + iact[i]] = 0;
+ }
+
+ nvl = 0;
+ temp = 0;
+ for (i = 1; i <= q; i = i + 1) {
+ if (work[iwsv + i] < temp * work[iwnbv + i]) {
+ nvl = i;
+ temp = work[iwsv + i] / work[iwnbv + i];
+ }
+ }
+ if (nvl === 0) {
+ return 999;
+ }
+
+ return 0;
+ }
+
+ function fn_goto_55() {
+ for (i = 1; i <= n; i = i + 1) {
+ sum = 0;
+ for (j = 1; j <= n; j = j + 1) {
+ sum = sum + dmat[j][i] * amat[j][nvl];
+ }
+ work[i] = sum;
+ }
+
+ l1 = iwzv;
+ for (i = 1; i <= n; i = i + 1) {
+ work[l1 + i] = 0;
+ }
+ for (j = nact + 1; j <= n; j = j + 1) {
+ for (i = 1; i <= n; i = i + 1) {
+ work[l1 + i] = work[l1 + i] + dmat[i][j] * work[j];
+ }
+ }
+
+ t1inf = true;
+ for (i = nact; i >= 1; i = i - 1) {
+ sum = work[i];
+ l = iwrm + (i * (i + 3)) / 2;
+ l1 = l - i;
+ for (j = i + 1; j <= nact; j = j + 1) {
+ sum = sum - work[l] * work[iwrv + j];
+ l = l + j;
+ }
+ sum = sum / work[l1];
+ work[iwrv + i] = sum;
+ if (iact[i] < meq) {
+ // continue;
+ break;
+ }
+ if (sum < 0) {
+ // continue;
+ break;
+ }
+ t1inf = false;
+ it1 = i;
+ }
+
+ if (!t1inf) {
+ t1 = work[iwuv + it1] / work[iwrv + it1];
+ for (i = 1; i <= nact; i = i + 1) {
+ if (iact[i] < meq) {
+ // continue;
+ break;
+ }
+ if (work[iwrv + i] < 0) {
+ // continue;
+ break;
+ }
+ temp = work[iwuv + i] / work[iwrv + i];
+ if (temp < t1) {
+ t1 = temp;
+ it1 = i;
+ }
+ }
+ }
+
+ sum = 0;
+ for (i = iwzv + 1; i <= iwzv + n; i = i + 1) {
+ sum = sum + work[i] * work[i];
+ }
+ if (Math.abs(sum) <= vsmall) {
+ if (t1inf) {
+ ierr[1] = 1;
+ // GOTO 999
+ return 999;
+ } else {
+ for (i = 1; i <= nact; i = i + 1) {
+ work[iwuv + i] = work[iwuv + i] - t1 * work[iwrv + i];
+ }
+ work[iwuv + nact + 1] = work[iwuv + nact + 1] + t1;
+ // GOTO 700
+ return 700;
+ }
+ } else {
+ sum = 0;
+ for (i = 1; i <= n; i = i + 1) {
+ sum = sum + work[iwzv + i] * amat[i][nvl];
+ }
+ tt = -work[iwsv + nvl] / sum;
+ t2min = true;
+ if (!t1inf) {
+ if (t1 < tt) {
+ tt = t1;
+ t2min = false;
+ }
+ }
+
+ for (i = 1; i <= n; i = i + 1) {
+ sol[i] = sol[i] + tt * work[iwzv + i];
+ if (Math.abs(sol[i]) < vsmall) {
+ sol[i] = 0;
+ }
+ }
+
+ crval[1] = crval[1] + tt * sum * (tt / 2 + work[iwuv + nact + 1]);
+ for (i = 1; i <= nact; i = i + 1) {
+ work[iwuv + i] = work[iwuv + i] - tt * work[iwrv + i];
+ }
+ work[iwuv + nact + 1] = work[iwuv + nact + 1] + tt;
+
+ if (t2min) {
+ nact = nact + 1;
+ iact[nact] = nvl;
+
+ l = iwrm + ((nact - 1) * nact) / 2 + 1;
+ for (i = 1; i <= nact - 1; i = i + 1) {
+ work[l] = work[i];
+ l = l + 1;
+ }
+
+ if (nact === n) {
+ work[l] = work[n];
+ } else {
+ for (i = n; i >= nact + 1; i = i - 1) {
+ if (work[i] === 0) {
+ // continue;
+ break;
+ }
+ gc = Math.max(Math.abs(work[i - 1]), Math.abs(work[i]));
+ gs = Math.min(Math.abs(work[i - 1]), Math.abs(work[i]));
+ if (work[i - 1] >= 0) {
+ temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
+ } else {
+ temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
+ }
+ gc = work[i - 1] / temp;
+ gs = work[i] / temp;
+
+ if (gc === 1) {
+ // continue;
+ break;
+ }
+ if (gc === 0) {
+ work[i - 1] = gs * temp;
+ for (j = 1; j <= n; j = j + 1) {
+ temp = dmat[j][i - 1];
+ dmat[j][i - 1] = dmat[j][i];
+ dmat[j][i] = temp;
+ }
+ } else {
+ work[i - 1] = temp;
+ nu = gs / (1 + gc);
+ for (j = 1; j <= n; j = j + 1) {
+ temp = gc * dmat[j][i - 1] + gs * dmat[j][i];
+ dmat[j][i] = nu * (dmat[j][i - 1] + temp) - dmat[j][i];
+ dmat[j][i - 1] = temp;
+
+ }
+ }
+ }
+ work[l] = work[nact];
+ }
+ } else {
+ sum = -bvec[nvl];
+ for (j = 1; j <= n; j = j + 1) {
+ sum = sum + sol[j] * amat[j][nvl];
+ }
+ if (nvl > meq) {
+ work[iwsv + nvl] = sum;
+ } else {
+ work[iwsv + nvl] = -Math.abs(sum);
+ if (sum > 0) {
+ for (j = 1; j <= n; j = j + 1) {
+ amat[j][nvl] = -amat[j][nvl];
+ }
+ bvec[nvl] = -bvec[nvl];
+ }
+ }
+ // GOTO 700
+ return 700;
+ }
+ }
+
+ return 0;
+ }
+
+ function fn_goto_797() {
+ l = iwrm + (it1 * (it1 + 1)) / 2 + 1;
+ l1 = l + it1;
+ if (work[l1] === 0) {
+ // GOTO 798
+ return 798;
+ }
+ gc = Math.max(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
+ gs = Math.min(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
+ if (work[l1 - 1] >= 0) {
+ temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
+ } else {
+ temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
+ }
+ gc = work[l1 - 1] / temp;
+ gs = work[l1] / temp;
+
+ if (gc === 1) {
+ // GOTO 798
+ return 798;
+ }
+ if (gc === 0) {
+ for (i = it1 + 1; i <= nact; i = i + 1) {
+ temp = work[l1 - 1];
+ work[l1 - 1] = work[l1];
+ work[l1] = temp;
+ l1 = l1 + i;
+ }
+ for (i = 1; i <= n; i = i + 1) {
+ temp = dmat[i][it1];
+ dmat[i][it1] = dmat[i][it1 + 1];
+ dmat[i][it1 + 1] = temp;
+ }
+ } else {
+ nu = gs / (1 + gc);
+ for (i = it1 + 1; i <= nact; i = i + 1) {
+ temp = gc * work[l1 - 1] + gs * work[l1];
+ work[l1] = nu * (work[l1 - 1] + temp) - work[l1];
+ work[l1 - 1] = temp;
+ l1 = l1 + i;
+ }
+ for (i = 1; i <= n; i = i + 1) {
+ temp = gc * dmat[i][it1] + gs * dmat[i][it1 + 1];
+ dmat[i][it1 + 1] = nu * (dmat[i][it1] + temp) - dmat[i][it1 + 1];
+ dmat[i][it1] = temp;
+ }
+ }
+
+ return 0;
+ }
+
+ function fn_goto_798() {
+ l1 = l - it1;
+ for (i = 1; i <= it1; i = i + 1) {
+ work[l1] = work[l];
+ l = l + 1;
+ l1 = l1 + 1;
+ }
+
+ work[iwuv + it1] = work[iwuv + it1 + 1];
+ iact[it1] = iact[it1 + 1];
+ it1 = it1 + 1;
+ if (it1 < nact) {
+ // GOTO 797
+ return 797;
+ }
+
+ return 0;
+ }
+
+ function fn_goto_799() {
+ work[iwuv + nact] = work[iwuv + nact + 1];
+ work[iwuv + nact + 1] = 0;
+ iact[nact] = 0;
+ nact = nact - 1;
+ iter[2] = iter[2] + 1;
+
+ return 0;
+ }
+
+ go = 0;
+ while (true) {
+ go = fn_goto_50();
+ if (go === 999) {
+ return;
+ }
+ while (true) {
+ go = fn_goto_55();
+ if (go === 0) {
+ break;
+ }
+ if (go === 999) {
+ return;
+ }
+ if (go === 700) {
+ if (it1 === nact) {
+ fn_goto_799();
+ } else {
+ while (true) {
+ fn_goto_797();
+ go = fn_goto_798();
+ if (go !== 797) {
+ break;
+ }
+ }
+ fn_goto_799();
+ }
+ }
+ }
+ }
+
+}
+
+function solveQP(Dmat, dvec, Amat, bvec, meq, factorized) {
+ Dmat = base0to1(Dmat);
+ dvec = base0to1(dvec);
+ Amat = base0to1(Amat);
+ var i, n, q,
+ nact, r,
+ crval = [], iact = [], sol = [], work = [], iter = [],
+ message;
+
+ meq = meq || 0;
+ factorized = factorized ? base0to1(factorized) : [undefined, 0];
+ bvec = bvec ? base0to1(bvec) : [];
+
+ // In Fortran the array index starts from 1
+ n = Dmat.length - 1;
+ q = Amat[1].length - 1;
+
+ if (!bvec) {
+ for (i = 1; i <= q; i = i + 1) {
+ bvec[i] = 0;
+ }
+ }
+ for (i = 1; i <= q; i = i + 1) {
+ iact[i] = 0;
+ }
+ nact = 0;
+ r = Math.min(n, q);
+ for (i = 1; i <= n; i = i + 1) {
+ sol[i] = 0;
+ }
+ crval[1] = 0;
+ for (i = 1; i <= (2 * n + (r * (r + 5)) / 2 + 2 * q + 1); i = i + 1) {
+ work[i] = 0;
+ }
+ for (i = 1; i <= 2; i = i + 1) {
+ iter[i] = 0;
+ }
+
+ qpgen2(Dmat, dvec, n, n, sol, crval, Amat,
+ bvec, n, q, meq, iact, nact, iter, work, factorized);
+
+ message = "";
+ if (factorized[1] === 1) {
+ message = "constraints are inconsistent, no solution!";
+ }
+ if (factorized[1] === 2) {
+ message = "matrix D in quadratic function is not positive definite!";
+ }
+
+ return {
+ solution: base1to0(sol),
+ value: base1to0(crval),
+ unconstrained_solution: base1to0(dvec),
+ iterations: base1to0(iter),
+ iact: base1to0(iact),
+ message: message
+ };
+}
+exports.solveQP = solveQP;
+}(numeric));
+/*
+Shanti Rao sent me this routine by private email. I had to modify it
+slightly to work on Arrays instead of using a Matrix object.
+It is apparently translated from http://stitchpanorama.sourceforge.net/Python/svd.py
+*/
+
+numeric.svd= function svd(A) {
+ var temp;
+//Compute the thin SVD from G. H. Golub and C. Reinsch, Numer. Math. 14, 403-420 (1970)
+ var prec= numeric.epsilon; //Math.pow(2,-52) // assumes double prec
+ var tolerance= 1.e-64/prec;
+ var itmax= 50;
+ var c=0;
+ var i=0;
+ var j=0;
+ var k=0;
+ var l=0;
+
+ var u= numeric.clone(A);
+ var m= u.length;
+
+ var n= u[0].length;
+
+ if (m < n) throw "Need more rows than columns"
+
+ var e = new Array(n);
+ var q = new Array(n);
+ for (i=0; i<n; i++) e[i] = q[i] = 0.0;
+ var v = numeric.rep([n,n],0);
+// v.zero();
+
+ function pythag(a,b)
+ {
+ a = Math.abs(a)
+ b = Math.abs(b)
+ if (a > b)
+ return a*Math.sqrt(1.0+(b*b/a/a))
+ else if (b == 0.0)
+ return a
+ return b*Math.sqrt(1.0+(a*a/b/b))
+ }
+
+ //Householder's reduction to bidiagonal form
+
+ var f= 0.0;
+ var g= 0.0;
+ var h= 0.0;
+ var x= 0.0;
+ var y= 0.0;
+ var z= 0.0;
+ var s= 0.0;
+
+ for (i=0; i < n; i++)
+ {
+ e[i]= g;
+ s= 0.0;
+ l= i+1;
+ for (j=i; j < m; j++)
+ s += (u[j][i]*u[j][i]);
+ if (s <= tolerance)
+ g= 0.0;
+ else
+ {
+ f= u[i][i];
+ g= Math.sqrt(s);
+ if (f >= 0.0) g= -g;
+ h= f*g-s
+ u[i][i]=f-g;
+ for (j=l; j < n; j++)
+ {
+ s= 0.0
+ for (k=i; k < m; k++)
+ s += u[k][i]*u[k][j]
+ f= s/h
+ for (k=i; k < m; k++)
+ u[k][j]+=f*u[k][i]
+ }
+ }
+ q[i]= g
+ s= 0.0
+ for (j=l; j < n; j++)
+ s= s + u[i][j]*u[i][j]
+ if (s <= tolerance)
+ g= 0.0
+ else
+ {
+ f= u[i][i+1]
+ g= Math.sqrt(s)
+ if (f >= 0.0) g= -g
+ h= f*g - s
+ u[i][i+1] = f-g;
+ for (j=l; j < n; j++) e[j]= u[i][j]/h
+ for (j=l; j < m; j++)
+ {
+ s=0.0
+ for (k=l; k < n; k++)
+ s += (u[j][k]*u[i][k])
+ for (k=l; k < n; k++)
+ u[j][k]+=s*e[k]
+ }
+ }
+ y= Math.abs(q[i])+Math.abs(e[i])
+ if (y>x)
+ x=y
+ }
+
+ // accumulation of right hand gtransformations
+ for (i=n-1; i != -1; i+= -1)
+ {
+ if (g != 0.0)
+ {
+ h= g*u[i][i+1]
+ for (j=l; j < n; j++)
+ v[j][i]=u[i][j]/h
+ for (j=l; j < n; j++)
+ {
+ s=0.0
+ for (k=l; k < n; k++)
+ s += u[i][k]*v[k][j]
+ for (k=l; k < n; k++)
+ v[k][j]+=(s*v[k][i])
+ }
+ }
+ for (j=l; j < n; j++)
+ {
+ v[i][j] = 0;
+ v[j][i] = 0;
+ }
+ v[i][i] = 1;
+ g= e[i]
+ l= i
+ }
+
+ // accumulation of left hand transformations
+ for (i=n-1; i != -1; i+= -1)
+ {
+ l= i+1
+ g= q[i]
+ for (j=l; j < n; j++)
+ u[i][j] = 0;
+ if (g != 0.0)
+ {
+ h= u[i][i]*g
+ for (j=l; j < n; j++)
+ {
+ s=0.0
+ for (k=l; k < m; k++) s += u[k][i]*u[k][j];
+ f= s/h
+ for (k=i; k < m; k++) u[k][j]+=f*u[k][i];
+ }
+ for (j=i; j < m; j++) u[j][i] = u[j][i]/g;
+ }
+ else
+ for (j=i; j < m; j++) u[j][i] = 0;
+ u[i][i] += 1;
+ }
+
+ // diagonalization of the bidiagonal form
+ prec= prec*x
+ for (k=n-1; k != -1; k+= -1)
+ {
+ for (var iteration=0; iteration < itmax; iteration++)
+ { // test f splitting
+ var test_convergence = false
+ for (l=k; l != -1; l+= -1)
+ {
+ if (Math.abs(e[l]) <= prec)
+ { test_convergence= true
+ break
+ }
+ if (Math.abs(q[l-1]) <= prec)
+ break
+ }
+ if (!test_convergence)
+ { // cancellation of e[l] if l>0
+ c= 0.0
+ s= 1.0
+ var l1= l-1
+ for (i =l; i<k+1; i++)
+ {
+ f= s*e[i]
+ e[i]= c*e[i]
+ if (Math.abs(f) <= prec)
+ break
+ g= q[i]
+ h= pythag(f,g)
+ q[i]= h
+ c= g/h
+ s= -f/h
+ for (j=0; j < m; j++)
+ {
+ y= u[j][l1]
+ z= u[j][i]
+ u[j][l1] = y*c+(z*s)
+ u[j][i] = -y*s+(z*c)
+ }
+ }
+ }
+ // test f convergence
+ z= q[k]
+ if (l== k)
+ { //convergence
+ if (z<0.0)
+ { //q[k] is made non-negative
+ q[k]= -z
+ for (j=0; j < n; j++)
+ v[j][k] = -v[j][k]
+ }
+ break //break out of iteration loop and move on to next k value
+ }
+ if (iteration >= itmax-1)
+ throw 'Error: no convergence.'
+ // shift from bottom 2x2 minor
+ x= q[l]
+ y= q[k-1]
+ g= e[k-1]
+ h= e[k]
+ f= ((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y)
+ g= pythag(f,1.0)
+ if (f < 0.0)
+ f= ((x-z)*(x+z)+h*(y/(f-g)-h))/x
+ else
+ f= ((x-z)*(x+z)+h*(y/(f+g)-h))/x
+ // next QR transformation
+ c= 1.0
+ s= 1.0
+ for (i=l+1; i< k+1; i++)
+ {
+ g= e[i]
+ y= q[i]
+ h= s*g
+ g= c*g
+ z= pythag(f,h)
+ e[i-1]= z
+ c= f/z
+ s= h/z
+ f= x*c+g*s
+ g= -x*s+g*c
+ h= y*s
+ y= y*c
+ for (j=0; j < n; j++)
+ {
+ x= v[j][i-1]
+ z= v[j][i]
+ v[j][i-1] = x*c+z*s
+ v[j][i] = -x*s+z*c
+ }
+ z= pythag(f,h)
+ q[i-1]= z
+ c= f/z
+ s= h/z
+ f= c*g+s*y
+ x= -s*g+c*y
+ for (j=0; j < m; j++)
+ {
+ y= u[j][i-1]
+ z= u[j][i]
+ u[j][i-1] = y*c+z*s
+ u[j][i] = -y*s+z*c
+ }
+ }
+ e[l]= 0.0
+ e[k]= f
+ q[k]= x
+ }
+ }
+
+ //vt= transpose(v)
+ //return (u,q,vt)
+ for (i=0;i<q.length; i++)
+ if (q[i] < prec) q[i] = 0
+
+ //sort eigenvalues
+ for (i=0; i< n; i++)
+ {
+ //writeln(q)
+ for (j=i-1; j >= 0; j--)
+ {
+ if (q[j] < q[i])
+ {
+ // writeln(i,'-',j)
+ c = q[j]
+ q[j] = q[i]
+ q[i] = c
+ for(k=0;k<u.length;k++) { temp = u[k][i]; u[k][i] = u[k][j]; u[k][j] = temp; }
+ for(k=0;k<v.length;k++) { temp = v[k][i]; v[k][i] = v[k][j]; v[k][j] = temp; }
+// u.swapCols(i,j)
+// v.swapCols(i,j)
+ i = j
+ }
+ }
+ }
+
+ return {U:u,S:q,V:v}
+};
+
diff --git a/dependencies/numeric-1.2.6.min.js b/dependencies/numeric-1.2.6.min.js
new file mode 100644
index 00000000..9262d4ec
--- /dev/null
+++ b/dependencies/numeric-1.2.6.min.js
@@ -0,0 +1,3 @@
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parseFloat(i)===10&&(t++,r=1,i=r.toPrecision(numeric.precision)),parseFloat(i).toString()+"e"+t.toString()}return"Infinity"}function i(e){var t;if(typeof e=="undefined")return r.push(Array(numeric.precision+8).join(" ")),!1;if(typeof e=="string")return r.push('"'+e+'"'),!1;if(typeof e=="boolean")return r.push(e.toString()),!1;if(typeof e=="number"){var s=n(e),o=e.toPrecision(numeric.precision),u=parseFloat(e.toString()).toString(),a=[s,o,u,parseFloat(o).toString(),parseFloat(u).toString()];for(t=1;t<a.length;t++)a[t].length<s.length&&(s=a[t]);return r.push(Array(numeric.precision+8-s.length).join(" ")+s),!1}if(e===null)return r.push("null"),!1;if(typeof e=="function"){r.push(e.toString());var f=!1;for(t in e)e.hasOwnProperty(t)&&(f?r.push(",\n"):r.push("\n{"),f=!0,r.push(t),r.push(": \n"),i(e[t]));return f&&r.push("}\n"),!0}if(e instanceof Array){if(e.length>numeric.largeArray)return r.push("...Large Array..."),!0;var 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x;\n")}for(e=0;e<numeric.mathfuns2.length;++e)t=numeric.mathfuns2[e],delete numeric.ops2[t];for(e=0;e<numeric.mathfuns.length;++e)t=numeric.mathfuns[e],numeric.ops1[t]=t;for(e in numeric.ops1)numeric.ops1.hasOwnProperty(e)&&(i="",t=numeric.ops1[e],numeric.myIndexOf.call(numeric.mathfuns,e)!==-1&&Math.hasOwnProperty(t)&&(i="var "+t+" = Math."+t+";\n"),numeric[e+"eqV"]=numeric.pointwise2(["ret[i]"],"ret[i] = "+t+"(ret[i]);",i),numeric[e+"eq"]=Function("x",'if(typeof x !== "object") return '+t+"x\n"+"var i;\n"+"var V = numeric."+e+"eqV;\n"+"var s = numeric.dim(x);\n"+"numeric._foreach(x,s,0,V);\n"+"return x;\n"),numeric[e+"V"]=numeric.pointwise2(["x[i]"],"ret[i] = "+t+"(x[i]);",i),numeric[e]=Function("x",'if(typeof x !== "object") return '+t+"(x)\n"+"var i;\n"+"var V = numeric."+e+"V;\n"+"var s = numeric.dim(x);\n"+"return numeric._foreach2(x,s,0,V);\n"));for(e=0;e<numeric.mathfuns.length;++e)t=numeric.mathfuns[e],delete numeric.ops1[t];for(e in numeric.mapreducers)numeric.mapreducers.hasOwnProperty(e)&&(t=numeric.mapreducers[e],numeric[e+"V"]=numeric.mapreduce2(t[0],t[1]),numeric[e]=Function("x","s","k",t[1]+'if(typeof x !== "object") {'+" xi = x;\n"+t[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."+e+"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"+t[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(t,n){return typeof t=="object"?typeof n=="object"?numeric.truncVV(t,n):numeric.truncVS(t,n):typeof n=="object"?numeric.truncSV(t,n):Math.round(t/n)*n},numeric.inv=function(t){var n=numeric.dim(t),r=Math.abs,i=n[0],s=n[1],o=numeric.clone(t),u,a,f=numeric.identity(i),l,c,h,p,d,t;for(p=0;p<s;++p){var v=-1,m=-1;for(h=p;h!==i;++h)d=r(o[h][p]),d>m&&(v=h,m=d);a=o[v],o[v]=o[p],o[p]=a,c=f[v],f[v]=f[p],f[p]=c,t=a[p];for(d=p;d!==s;++d)a[d]/=t;for(d=s-1;d!==-1;--d)c[d]/=t;for(h=i-1;h!==-1;--h)if(h!==p){u=o[h],l=f[h],t=u[p];for(d=p+1;d!==s;++d)u[d]-=a[d]*t;for(d=s-1;d>0;--d)l[d]-=c[d]*t,--d,l[d]-=c[d]*t;d===0&&(l[0]-=c[0]*t)}}return f},numeric.det=function(t){var n=numeric.dim(t);if(n.length!==2||n[0]!==n[1])throw new Error("numeric: det() only works on square matrices");var r=n[0],i=1,s,o,u,a=numeric.clone(t),f,l,c,h,p,d,v;for(o=0;o<r-1;o++){u=o;for(s=o+1;s<r;s++)Math.abs(a[s][o])>Math.abs(a[u][o])&&(u=s);u!==o&&(h=a[u],a[u]=a[o],a[o]=h,i*=-1),f=a[o];for(s=o+1;s<r;s++){l=a[s],c=l[o]/f[o];for(u=o+1;u<r-1;u+=2)p=u+1,l[u]-=f[u]*c,l[p]-=f[p]*c;u!==r&&(l[u]-=f[u]*c)}if(f[o]===0)return 0;i*=f[o]}return i*a[o][o]},numeric.transpose=function(t){var n,r,i=t.length,s=t[0].length,o=Array(s),u,a,f;for(r=0;r<s;r++)o[r]=Array(i);for(n=i-1;n>=1;n-=2){a=t[n],u=t[n-1];for(r=s-1;r>=1;--r)f=o[r],f[n]=a[r],f[n-1]=u[r],--r,f=o[r],f[n]=a[r],f[n-1]=u[r];r===0&&(f=o[0],f[n]=a[0],f[n-1]=u[0])}if(n===0){u=t[0];for(r=s-1;r>=1;--r)o[r][0]=u[r],--r,o[r][0]=u[r];r===0&&(o[0][0]=u[0])}return o},numeric.negtranspose=function(t){var n,r,i=t.length,s=t[0].length,o=Array(s),u,a,f;for(r=0;r<s;r++)o[r]=Array(i);for(n=i-1;n>=1;n-=2){a=t[n],u=t[n-1];for(r=s-1;r>=1;--r)f=o[r],f[n]=-a[r],f[n-1]=-u[r],--r,f=o[r],f[n]=-a[r],f[n-1]=-u[r];r===0&&(f=o[0],f[n]=-a[0],f[n-1]=-u[0])}if(n===0){u=t[0];for(r=s-1;r>=1;--r)o[r][0]=-u[r],--r,o[r][0]=-u[r];r===0&&(o[0][0]=-u[0])}return o},numeric._random=function _random(e,t){var n,r=e[t],i=Array(r),s;if(t===e.length-1){s=Math.random;for(n=r-1;n>=1;n-=2)i[n]=s(),i[n-1]=s();return n===0&&(i[0]=s()),i}for(n=r-1;n>=0;n--)i[n]=_random(e,t+1);return i},numeric.random=function(t){return numeric._random(t,0)},numeric.norm2=function(t){return Math.sqrt(numeric.norm2Squared(t))},numeric.linspace=function(t,n,r){typeof r=="undefined"&&(r=Math.max(Math.round(n-t)+1,1));if(r<2)return r===1?[t]:[];var i,s=Array(r);r--;for(i=r;i>=0;i--)s[i]=(i*n+(r-i)*t)/r;return s},numeric.getBlock=function(t,n,r){function s(e,t){var o,u=n[t],a=r[t]-u,f=Array(a);if(t===i.length-1){for(o=a;o>=0;o--)f[o]=e[o+u];return f}for(o=a;o>=0;o--)f[o]=s(e[o+u],t+1);return f}var i=numeric.dim(t);return s(t,0)},numeric.setBlock=function(t,n,r,i){function o(e,t,i){var u,a=n[i],f=r[i]-a;if(i===s.length-1)for(u=f;u>=0;u--)e[u+a]=t[u];for(u=f;u>=0;u--)o(e[u+a],t[u],i+1)}var s=numeric.dim(t);return o(t,i,0),t},numeric.getRange=function(t,n,r){var i=n.length,s=r.length,o,u,a=Array(i),f,l;for(o=i-1;o!==-1;--o){a[o]=Array(s),f=a[o],l=t[n[o]];for(u=s-1;u!==-1;--u)f[u]=l[r[u]]}return a},numeric.blockMatrix=function(t){var n=numeric.dim(t);if(n.length<4)return numeric.blockMatrix([t]);var r=n[0],i=n[1],s,o,u,a,f;s=0,o=0;for(u=0;u<r;++u)s+=t[u][0].length;for(a=0;a<i;++a)o+=t[0][a][0].length;var l=Array(s);for(u=0;u<s;++u)l[u]=Array(o);var c=0,h,p,d,v,m;for(u=0;u<r;++u){h=o;for(a=i-1;a!==-1;--a){f=t[u][a],h-=f[0].length;for(d=f.length-1;d!==-1;--d){m=f[d],p=l[c+d];for(v=m.length-1;v!==-1;--v)p[h+v]=m[v]}}c+=t[u][0].length}return l},numeric.tensor=function(t,n){if(typeof t=="number"||typeof n=="number")return numeric.mul(t,n);var r=numeric.dim(t),i=numeric.dim(n);if(r.length!==1||i.length!==1)throw new Error("numeric: tensor product is only defined for vectors");var s=r[0],o=i[0],u=Array(s),a,f,l,c;for(f=s-1;f>=0;f--){a=Array(o),c=t[f];for(l=o-1;l>=3;--l)a[l]=c*n[l],--l,a[l]=c*n[l],--l,a[l]=c*n[l],--l,a[l]=c*n[l];while(l>=0)a[l]=c*n[l],--l;u[f]=a}return u},numeric.T=function(t,n){this.x=t,this.y=n},numeric.t=function(t,n){return new numeric.T(t,n)},numeric.Tbinop=function(t,n,r,i,s){var o=numeric.indexOf;if(typeof s!="string"){var u;s="";for(u in numeric)numeric.hasOwnProperty(u)&&(t.indexOf(u)>=0||n.indexOf(u)>=0||r.indexOf(u)>=0||i.indexOf(u)>=0)&&u.length>1&&(s+="var "+u+" = numeric."+u+";\n")}return Function(["y"],"var x = this;\nif(!(y instanceof numeric.T)) { y = new numeric.T(y); }\n"+s+"\n"+"if(x.y) {"+" if(y.y) {"+" return new numeric.T("+i+");\n"+" }\n"+" return new numeric.T("+r+");\n"+"}\n"+"if(y.y) {\n"+" return new numeric.T("+n+");\n"+"}\n"+"return new numeric.T("+t+");\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(){var t=numeric.mul,n=numeric.div;if(this.y){var r=numeric.add(t(this.x,this.x),t(this.y,this.y));return new numeric.T(n(this.x,r),n(numeric.neg(this.y),r))}return new T(n(1,this.x))},numeric.T.prototype.div=function div(e){e instanceof numeric.T||(e=new numeric.T(e));if(e.y)return this.mul(e.reciprocal());var div=numeric.div;return this.y?new numeric.T(div(this.x,e.x),div(this.y,e.x)):new numeric.T(div(this.x,e.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(){var t=numeric.transpose,n=this.x,r=this.y;return r?new numeric.T(t(n),t(r)):new numeric.T(t(n))},numeric.T.prototype.transjugate=function(){var t=numeric.transpose,n=this.x,r=this.y;return r?new numeric.T(t(n),numeric.negtranspose(r)):new numeric.T(t(n))},numeric.Tunop=function(t,n,r){return typeof r!="string"&&(r=""),Function("var x = this;\n"+r+"\n"+"if(x.y) {"+" "+n+";\n"+"}\n"+t+";\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();\nreturn new numeric.T(numeric.log(r.x),theta.x);"),numeric.T.prototype.norm2=numeric.Tunop("return numeric.norm2(x.x);","var f = numeric.norm2Squared;\nreturn Math.sqrt(f(x.x)+f(x.y));"),numeric.T.prototype.inv=function(){var t=this;if(typeof t.y=="undefined")return new numeric.T(numeric.inv(t.x));var n=t.x.length,r,i,s,o=numeric.identity(n),u=numeric.rep([n,n],0),a=numeric.clone(t.x),f=numeric.clone(t.y),l,c,h,p,d,v,m,g,r,i,s,y,b,w,E,S,x,T;for(r=0;r<n;r++){w=a[r][r],E=f[r][r],y=w*w+E*E,s=r;for(i=r+1;i<n;i++)w=a[i][r],E=f[i][r],b=w*w+E*E,b>y&&(s=i,y=b);s!==r&&(T=a[r],a[r]=a[s],a[s]=T,T=f[r],f[r]=f[s],f[s]=T,T=o[r],o[r]=o[s],o[s]=T,T=u[r],u[r]=u[s],u[s]=T),l=a[r],c=f[r],d=o[r],v=u[r],w=l[r],E=c[r];for(i=r+1;i<n;i++)S=l[i],x=c[i],l[i]=(S*w+x*E)/y,c[i]=(x*w-S*E)/y;for(i=0;i<n;i++)S=d[i],x=v[i],d[i]=(S*w+x*E)/y,v[i]=(x*w-S*E)/y;for(i=r+1;i<n;i++){h=a[i],p=f[i],m=o[i],g=u[i],w=h[r],E=p[r];for(s=r+1;s<n;s++)S=l[s],x=c[s],h[s]-=S*w-x*E,p[s]-=x*w+S*E;for(s=0;s<n;s++)S=d[s],x=v[s],m[s]-=S*w-x*E,g[s]-=x*w+S*E}}for(r=n-1;r>0;r--){d=o[r],v=u[r];for(i=r-1;i>=0;i--){m=o[i],g=u[i],w=a[i][r],E=f[i][r];for(s=n-1;s>=0;s--)S=d[s],x=v[s],m[s]-=w*S-E*x,g[s]-=w*x+E*S}}return new numeric.T(o,u)},numeric.T.prototype.get=function(t){var n=this.x,r=this.y,i=0,s,o=t.length;if(r){while(i<o)s=t[i],n=n[s],r=r[s],i++;return new numeric.T(n,r)}while(i<o)s=t[i],n=n[s],i++;return new numeric.T(n)},numeric.T.prototype.set=function(t,n){var r=this.x,i=this.y,s=0,o,u=t.length,a=n.x,f=n.y;if(u===0)return f?this.y=f:i&&(this.y=undefined),this.x=r,this;if(f){i||(i=numeric.rep(numeric.dim(r),0),this.y=i);while(s<u-1)o=t[s],r=r[o],i=i[o],s++;return o=t[s],r[o]=a,i[o]=f,this}if(i){while(s<u-1)o=t[s],r=r[o],i=i[o],s++;return o=t[s],r[o]=a,a instanceof Array?i[o]=numeric.rep(numeric.dim(a),0):i[o]=0,this}while(s<u-1)o=t[s],r=r[o],s++;return o=t[s],r[o]=a,this},numeric.T.prototype.getRows=function(t,n){var r=n-t+1,i,s=Array(r),o,u=this.x,a=this.y;for(i=t;i<=n;i++)s[i-t]=u[i];if(a){o=Array(r);for(i=t;i<=n;i++)o[i-t]=a[i];return new numeric.T(s,o)}return new numeric.T(s)},numeric.T.prototype.setRows=function(t,n,r){var i,s=this.x,o=this.y,u=r.x,a=r.y;for(i=t;i<=n;i++)s[i]=u[i-t];if(a){o||(o=numeric.rep(numeric.dim(s),0),this.y=o);for(i=t;i<=n;i++)o[i]=a[i-t]}else if(o)for(i=t;i<=n;i++)o[i]=numeric.rep([u[i-t].length],0);return this},numeric.T.prototype.getRow=function(t){var n=this.x,r=this.y;return r?new numeric.T(n[t],r[t]):new numeric.T(n[t])},numeric.T.prototype.setRow=function(t,n){var r=this.x,i=this.y,s=n.x,o=n.y;return r[t]=s,o?(i||(i=numeric.rep(numeric.dim(r),0),this.y=i),i[t]=o):i&&(i=numeric.rep([s.length],0)),this},numeric.T.prototype.getBlock=function(t,n){var r=this.x,i=this.y,s=numeric.getBlock;return i?new numeric.T(s(r,t,n),s(i,t,n)):new numeric.T(s(r,t,n))},numeric.T.prototype.setBlock=function(t,n,r){r instanceof numeric.T||(r=new numeric.T(r));var i=this.x,s=this.y,o=numeric.setBlock,u=r.x,a=r.y;if(a)return s||(this.y=numeric.rep(numeric.dim(this),0),s=this.y),o(i,t,n,u),o(s,t,n,a),this;o(i,t,n,u),s&&o(s,t,n,numeric.rep(numeric.dim(u),0))},numeric.T.rep=function(t,n){var r=numeric.T;n instanceof r||(n=new r(n));var i=n.x,s=n.y,o=numeric.rep;return s?new r(o(t,i),o(t,s)):new r(o(t,i))},numeric.T.diag=function diag(e){e instanceof numeric.T||(e=new numeric.T(e));var t=e.x,n=e.y,diag=numeric.diag;return n?new numeric.T(diag(t),diag(n)):new numeric.T(diag(t))},numeric.T.eig=function(){if(this.y)throw new Error("eig: not implemented for complex matrices.");return numeric.eig(this.x)},numeric.T.identity=function(t){return new numeric.T(numeric.identity(t))},numeric.T.prototype.getDiag=function(){var t=numeric,n=this.x,r=this.y;return r?new t.T(t.getDiag(n),t.getDiag(r)):new t.T(t.getDiag(n))},numeric.house=function(t){var n=numeric.clone(t),r=t[0]>=0?1:-1,i=r*numeric.norm2(t);n[0]+=i;var s=numeric.norm2(n);if(s===0)throw new Error("eig: internal error");return numeric.div(n,s)},numeric.toUpperHessenberg=function(t){var n=numeric.dim(t);if(n.length!==2||n[0]!==n[1])throw new Error("numeric: toUpperHessenberg() only works on square matrices");var r=n[0],i,s,o,u,a,f=numeric.clone(t),l,c,h,p,d=numeric.identity(r),v;for(s=0;s<r-2;s++){u=Array(r-s-1);for(i=s+1;i<r;i++)u[i-s-1]=f[i][s];if(numeric.norm2(u)>0){a=numeric.house(u),l=numeric.getBlock(f,[s+1,s],[r-1,r-1]),c=numeric.tensor(a,numeric.dot(a,l));for(i=s+1;i<r;i++){h=f[i],p=c[i-s-1];for(o=s;o<r;o++)h[o]-=2*p[o-s]}l=numeric.getBlock(f,[0,s+1],[r-1,r-1]),c=numeric.tensor(numeric.dot(l,a),a);for(i=0;i<r;i++){h=f[i],p=c[i];for(o=s+1;o<r;o++)h[o]-=2*p[o-s-1]}l=Array(r-s-1);for(i=s+1;i<r;i++)l[i-s-1]=d[i];c=numeric.tensor(a,numeric.dot(a,l));for(i=s+1;i<r;i++){v=d[i],p=c[i-s-1];for(o=0;o<r;o++)v[o]-=2*p[o]}}}return{H:f,Q:d}},numeric.epsilon=2.220446049250313e-16,numeric.QRFrancis=function(e,t){typeof t=="undefined"&&(t=1e4),e=numeric.clone(e);var n=numeric.clone(e),r=numeric.dim(e),i=r[0],s,o,u,a,f,l,c,h,p,d=numeric.identity(i),v,m,g,y,b,w,E,S,x;if(i<3)return{Q:d,B:[[0,i-1]]};var T=numeric.epsilon;for(x=0;x<t;x++){for(E=0;E<i-1;E++)if(Math.abs(e[E+1][E])<T*(Math.abs(e[E][E])+Math.abs(e[E+1][E+1]))){var N=numeric.QRFrancis(numeric.getBlock(e,[0,0],[E,E]),t),C=numeric.QRFrancis(numeric.getBlock(e,[E+1,E+1],[i-1,i-1]),t);g=Array(E+1);for(w=0;w<=E;w++)g[w]=d[w];y=numeric.dot(N.Q,g);for(w=0;w<=E;w++)d[w]=y[w];g=Array(i-E-1);for(w=E+1;w<i;w++)g[w-E-1]=d[w];y=numeric.dot(C.Q,g);for(w=E+1;w<i;w++)d[w]=y[w-E-1];return{Q:d,B:N.B.concat(numeric.add(C.B,E+1))}}u=e[i-2][i-2],a=e[i-2][i-1],f=e[i-1][i-2],l=e[i-1][i-1],h=u+l,c=u*l-a*f,p=numeric.getBlock(e,[0,0],[2,2]);if(h*h>=4*c){var k,L;k=.5*(h+Math.sqrt(h*h-4*c)),L=.5*(h-Math.sqrt(h*h-4*c)),p=numeric.add(numeric.sub(numeric.dot(p,p),numeric.mul(p,k+L)),numeric.diag(numeric.rep([3],k*L)))}else p=numeric.add(numeric.sub(numeric.dot(p,p),numeric.mul(p,h)),numeric.diag(numeric.rep([3],c)));s=[p[0][0],p[1][0],p[2][0]],o=numeric.house(s),g=[e[0],e[1],e[2]],y=numeric.tensor(o,numeric.dot(o,g));for(w=0;w<3;w++){m=e[w],b=y[w];for(S=0;S<i;S++)m[S]-=2*b[S]}g=numeric.getBlock(e,[0,0],[i-1,2]),y=numeric.tensor(numeric.dot(g,o),o);for(w=0;w<i;w++){m=e[w],b=y[w];for(S=0;S<3;S++)m[S]-=2*b[S]}g=[d[0],d[1],d[2]],y=numeric.tensor(o,numeric.dot(o,g));for(w=0;w<3;w++){v=d[w],b=y[w];for(S=0;S<i;S++)v[S]-=2*b[S]}var A;for(E=0;E<i-2;E++){for(S=E;S<=E+1;S++)if(Math.abs(e[S+1][S])<T*(Math.abs(e[S][S])+Math.abs(e[S+1][S+1]))){var N=numeric.QRFrancis(numeric.getBlock(e,[0,0],[S,S]),t),C=numeric.QRFrancis(numeric.getBlock(e,[S+1,S+1],[i-1,i-1]),t);g=Array(S+1);for(w=0;w<=S;w++)g[w]=d[w];y=numeric.dot(N.Q,g);for(w=0;w<=S;w++)d[w]=y[w];g=Array(i-S-1);for(w=S+1;w<i;w++)g[w-S-1]=d[w];y=numeric.dot(C.Q,g);for(w=S+1;w<i;w++)d[w]=y[w-S-1];return{Q:d,B:N.B.concat(numeric.add(C.B,S+1))}}A=Math.min(i-1,E+3),s=Array(A-E);for(w=E+1;w<=A;w++)s[w-E-1]=e[w][E];o=numeric.house(s),g=numeric.getBlock(e,[E+1,E],[A,i-1]),y=numeric.tensor(o,numeric.dot(o,g));for(w=E+1;w<=A;w++){m=e[w],b=y[w-E-1];for(S=E;S<i;S++)m[S]-=2*b[S-E]}g=numeric.getBlock(e,[0,E+1],[i-1,A]),y=numeric.tensor(numeric.dot(g,o),o);for(w=0;w<i;w++){m=e[w],b=y[w];for(S=E+1;S<=A;S++)m[S]-=2*b[S-E-1]}g=Array(A-E);for(w=E+1;w<=A;w++)g[w-E-1]=d[w];y=numeric.tensor(o,numeric.dot(o,g));for(w=E+1;w<=A;w++){v=d[w],b=y[w-E-1];for(S=0;S<i;S++)v[S]-=2*b[S]}}}throw new Error("numeric: eigenvalue iteration does not converge -- increase maxiter?")},numeric.eig=function(t,n){var r=numeric.toUpperHessenberg(t),i=numeric.QRFrancis(r.H,n),s=numeric.T,o=t.length,u,a,f=!1,l=i.B,c=numeric.dot(i.Q,numeric.dot(r.H,numeric.transpose(i.Q))),h=new s(numeric.dot(i.Q,r.Q)),p,d=l.length,v,m,g,y,b,w,E,S,x,T,N,C,k,L,A=Math.sqrt;for(a=0;a<d;a++){u=l[a][0];if(u!==l[a][1]){v=u+1,m=c[u][u],g=c[u][v],y=c[v][u],b=c[v][v];if(g===0&&y===0)continue;w=-m-b,E=m*b-g*y,S=w*w-4*E,S>=0?(w<0?x=-0.5*(w-A(S)):x=-0.5*(w+A(S)),k=(m-x)*(m-x)+g*g,L=y*y+(b-x)*(b-x),k>L?(k=A(k),N=(m-x)/k,C=g/k):(L=A(L),N=y/L,C=(b-x)/L),p=new s([[C,-N],[N,C]]),h.setRows(u,v,p.dot(h.getRows(u,v)))):(x=-0.5*w,T=.5*A(-S),k=(m-x)*(m-x)+g*g,L=y*y+(b-x)*(b-x),k>L?(k=A(k+T*T),N=(m-x)/k,C=g/k,x=0,T/=k):(L=A(L+T*T),N=y/L,C=(b-x)/L,x=T/L,T=0),p=new s([[C,-N],[N,C]],[[x,
+T],[T,-x]]),h.setRows(u,v,p.dot(h.getRows(u,v))))}}var O=h.dot(t).dot(h.transjugate()),o=t.length,M=numeric.T.identity(o);for(v=0;v<o;v++)if(v>0)for(a=v-1;a>=0;a--){var _=O.get([a,a]),D=O.get([v,v]);if(!numeric.neq(_.x,D.x)&&!numeric.neq(_.y,D.y)){M.setRow(v,M.getRow(a));continue}x=O.getRow(a).getBlock([a],[v-1]),T=M.getRow(v).getBlock([a],[v-1]),M.set([v,a],O.get([a,v]).neg().sub(x.dot(T)).div(_.sub(D)))}for(v=0;v<o;v++)x=M.getRow(v),M.setRow(v,x.div(x.norm2()));return M=M.transpose(),M=h.transjugate().dot(M),{lambda:O.getDiag(),E:M}},numeric.ccsSparse=function(t){var n=t.length,r,i,s,o,u=[];for(s=n-1;s!==-1;--s){i=t[s];for(o in i){o=parseInt(o);while(o>=u.length)u[u.length]=0;i[o]!==0&&u[o]++}}var r=u.length,a=Array(r+1);a[0]=0;for(s=0;s<r;++s)a[s+1]=a[s]+u[s];var f=Array(a[r]),l=Array(a[r]);for(s=n-1;s!==-1;--s){i=t[s];for(o in i)i[o]!==0&&(u[o]--,f[a[o]+u[o]]=s,l[a[o]+u[o]]=i[o])}return[a,f,l]},numeric.ccsFull=function(t){var n=t[0],r=t[1],i=t[2],s=numeric.ccsDim(t),o=s[0],u=s[1],a,f,l,c,h,p=numeric.rep([o,u],0);for(a=0;a<u;a++){l=n[a],c=n[a+1];for(f=l;f<c;++f)p[r[f]][a]=i[f]}return p},numeric.ccsTSolve=function(t,n,r,i,s){function h(e){var t;if(r[e]!==0)return;r[e]=1;for(t=o[e];t<o[e+1];++t)h(u[t]);s[c]=e,++c}var o=t[0],u=t[1],a=t[2],f=o.length-1,l=Math.max,c=0;typeof i=="undefined"&&(r=numeric.rep([f],0)),typeof i=="undefined"&&(i=numeric.linspace(0,r.length-1)),typeof s=="undefined"&&(s=[]);var p,d,v,m,g,y,b,w,E;for(p=i.length-1;p!==-1;--p)h(i[p]);s.length=c;for(p=s.length-1;p!==-1;--p)r[s[p]]=0;for(p=i.length-1;p!==-1;--p)d=i[p],r[d]=n[d];for(p=s.length-1;p!==-1;--p){d=s[p],v=o[d],m=l(o[d+1],v);for(g=v;g!==m;++g)if(u[g]===d){r[d]/=a[g];break}E=r[d];for(g=v;g!==m;++g)y=u[g],y!==d&&(r[y]-=E*a[g])}return r},numeric.ccsDFS=function(t){this.k=Array(t),this.k1=Array(t),this.j=Array(t)},numeric.ccsDFS.prototype.dfs=function(t,n,r,i,s,o){var u=0,a,f=s.length,l=this.k,c=this.k1,h=this.j,p,d;if(i[t]!==0)return;i[t]=1,h[0]=t,l[0]=p=n[t],c[0]=d=n[t+1];for(;;)if(p>=d){s[f]=h[u];if(u===0)return;++f,--u,p=l[u],d=c[u]}else a=o[r[p]],i[a]===0?(i[a]=1,l[u]=p,++u,h[u]=a,p=n[a],c[u]=d=n[a+1]):++p},numeric.ccsLPSolve=function(t,n,r,i,s,o,u){var a=t[0],f=t[1],l=t[2],c=a.length-1,h=0,p=n[0],d=n[1],v=n[2],m,g,y,b,w,E,S,x,T,N,C,k;g=p[s],y=p[s+1],i.length=0;for(m=g;m<y;++m)u.dfs(o[d[m]],a,f,r,i,o);for(m=i.length-1;m!==-1;--m)r[i[m]]=0;for(m=g;m!==y;++m)b=o[d[m]],r[b]=v[m];for(m=i.length-1;m!==-1;--m){b=i[m],E=a[b],S=a[b+1];for(x=E;x<S;++x)if(o[f[x]]===b){r[b]/=l[x];break}k=r[b];for(x=E;x<S;++x)T=o[f[x]],T!==b&&(r[T]-=k*l[x])}return r},numeric.ccsLUP1=function(t,n){var r=t[0].length-1,i=[numeric.rep([r+1],0),[],[]],s=[numeric.rep([r+1],0),[],[]],o=i[0],u=i[1],a=i[2],f=s[0],l=s[1],c=s[2],h=numeric.rep([r],0),p=numeric.rep([r],0),d,v,m,g,y,b,w,E,S,x,T=numeric.ccsLPSolve,N=Math.max,C=Math.abs,k=numeric.linspace(0,r-1),L=numeric.linspace(0,r-1),A=new numeric.ccsDFS(r);typeof n=="undefined"&&(n=1);for(d=0;d<r;++d){T(i,t,h,p,d,L,A),b=-1,w=-1;for(v=p.length-1;v!==-1;--v){m=p[v];if(m<=d)continue;E=C(h[m]),E>b&&(w=m,b=E)}C(h[d])<n*b&&(v=k[d],b=k[w],k[d]=b,L[b]=d,k[w]=v,L[v]=w,b=h[d],h[d]=h[w],h[w]=b),b=o[d],w=f[d],S=h[d],u[b]=k[d],a[b]=1,++b;for(v=p.length-1;v!==-1;--v)m=p[v],E=h[m],p[v]=0,h[m]=0,m<=d?(l[w]=m,c[w]=E,++w):(u[b]=k[m],a[b]=E/S,++b);o[d+1]=b,f[d+1]=w}for(v=u.length-1;v!==-1;--v)u[v]=L[u[v]];return{L:i,U:s,P:k,Pinv:L}},numeric.ccsDFS0=function(t){this.k=Array(t),this.k1=Array(t),this.j=Array(t)},numeric.ccsDFS0.prototype.dfs=function(t,n,r,i,s,o,u){var a=0,f,l=s.length,c=this.k,h=this.k1,p=this.j,d,v;if(i[t]!==0)return;i[t]=1,p[0]=t,c[0]=d=n[o[t]],h[0]=v=n[o[t]+1];for(;;){if(isNaN(d))throw new Error("Ow!");if(d>=v){s[l]=o[p[a]];if(a===0)return;++l,--a,d=c[a],v=h[a]}else f=r[d],i[f]===0?(i[f]=1,c[a]=d,++a,p[a]=f,f=o[f],d=n[f],h[a]=v=n[f+1]):++d}},numeric.ccsLPSolve0=function(t,n,r,i,s,o,u,a){var f=t[0],l=t[1],c=t[2],h=f.length-1,p=0,d=n[0],v=n[1],m=n[2],g,y,b,w,E,S,x,T,N,C,k,L;y=d[s],b=d[s+1],i.length=0;for(g=y;g<b;++g)a.dfs(v[g],f,l,r,i,o,u);for(g=i.length-1;g!==-1;--g)w=i[g],r[u[w]]=0;for(g=y;g!==b;++g)w=v[g],r[w]=m[g];for(g=i.length-1;g!==-1;--g){w=i[g],N=u[w],S=f[w],x=f[w+1];for(T=S;T<x;++T)if(l[T]===N){r[N]/=c[T];break}L=r[N];for(T=S;T<x;++T)r[l[T]]-=L*c[T];r[N]=L}},numeric.ccsLUP0=function(t,n){var r=t[0].length-1,i=[numeric.rep([r+1],0),[],[]],s=[numeric.rep([r+1],0),[],[]],o=i[0],u=i[1],a=i[2],f=s[0],l=s[1],c=s[2],h=numeric.rep([r],0),p=numeric.rep([r],0),d,v,m,g,y,b,w,E,S,x,T=numeric.ccsLPSolve0,N=Math.max,C=Math.abs,k=numeric.linspace(0,r-1),L=numeric.linspace(0,r-1),A=new numeric.ccsDFS0(r);typeof n=="undefined"&&(n=1);for(d=0;d<r;++d){T(i,t,h,p,d,L,k,A),b=-1,w=-1;for(v=p.length-1;v!==-1;--v){m=p[v];if(m<=d)continue;E=C(h[k[m]]),E>b&&(w=m,b=E)}C(h[k[d]])<n*b&&(v=k[d],b=k[w],k[d]=b,L[b]=d,k[w]=v,L[v]=w),b=o[d],w=f[d],S=h[k[d]],u[b]=k[d],a[b]=1,++b;for(v=p.length-1;v!==-1;--v)m=p[v],E=h[k[m]],p[v]=0,h[k[m]]=0,m<=d?(l[w]=m,c[w]=E,++w):(u[b]=k[m],a[b]=E/S,++b);o[d+1]=b,f[d+1]=w}for(v=u.length-1;v!==-1;--v)u[v]=L[u[v]];return{L:i,U:s,P:k,Pinv:L}},numeric.ccsLUP=numeric.ccsLUP0,numeric.ccsDim=function(t){return[numeric.sup(t[1])+1,t[0].length-1]},numeric.ccsGetBlock=function(t,n,r){var i=numeric.ccsDim(t),s=i[0],o=i[1];typeof n=="undefined"?n=numeric.linspace(0,s-1):typeof n=="number"&&(n=[n]),typeof r=="undefined"?r=numeric.linspace(0,o-1):typeof r=="number"&&(r=[r]);var u,a,f,l=n.length,c,h=r.length,p,d,v,m=numeric.rep([o],0),g=[],y=[],b=[m,g,y],w=t[0],E=t[1],S=t[2],x=numeric.rep([s],0),T=0,N=numeric.rep([s],0);for(c=0;c<h;++c){d=r[c];var C=w[d],k=w[d+1];for(u=C;u<k;++u)p=E[u],N[p]=1,x[p]=S[u];for(u=0;u<l;++u)v=n[u],N[v]&&(g[T]=u,y[T]=x[n[u]],++T);for(u=C;u<k;++u)p=E[u],N[p]=0;m[c+1]=T}return b},numeric.ccsDot=function(t,n){var r=t[0],i=t[1],s=t[2],o=n[0],u=n[1],a=n[2],f=numeric.ccsDim(t),l=numeric.ccsDim(n),c=f[0],h=f[1],p=l[1],d=numeric.rep([c],0),v=numeric.rep([c],0),m=Array(c),g=numeric.rep([p],0),y=[],b=[],w=[g,y,b],E,S,x,T,N,C,k,L,A,O,M;for(x=0;x!==p;++x){T=o[x],N=o[x+1],A=0;for(S=T;S<N;++S){O=u[S],M=a[S],C=r[O],k=r[O+1];for(E=C;E<k;++E)L=i[E],v[L]===0&&(m[A]=L,v[L]=1,A+=1),d[L]=d[L]+s[E]*M}T=g[x],N=T+A,g[x+1]=N;for(S=A-1;S!==-1;--S)M=T+S,E=m[S],y[M]=E,b[M]=d[E],v[E]=0,d[E]=0;g[x+1]=g[x]+A}return w},numeric.ccsLUPSolve=function(t,n){var r=t.L,i=t.U,s=t.P,o=n[0],u=!1;typeof o!="object"&&(n=[[0,n.length],numeric.linspace(0,n.length-1),n],o=n[0],u=!0);var a=n[1],f=n[2],l=r[0].length-1,c=o.length-1,h=numeric.rep([l],0),p=Array(l),d=numeric.rep([l],0),v=Array(l),m=numeric.rep([c+1],0),g=[],y=[],b=numeric.ccsTSolve,w,E,S,x,T,N,C=0;for(w=0;w<c;++w){T=0,S=o[w],x=o[w+1];for(E=S;E<x;++E)N=t.Pinv[a[E]],v[T]=N,d[N]=f[E],++T;v.length=T,b(r,d,h,v,p);for(E=v.length-1;E!==-1;--E)d[v[E]]=0;b(i,h,d,p,v);if(u)return d;for(E=p.length-1;E!==-1;--E)h[p[E]]=0;for(E=v.length-1;E!==-1;--E)N=v[E],g[C]=N,y[C]=d[N],d[N]=0,++C;m[w+1]=C}return[m,g,y]},numeric.ccsbinop=function(t,n){return typeof n=="undefined"&&(n=""),Function("X","Y","var Xi = X[0], Xj = X[1], Xv = X[2];\nvar Yi = Y[0], Yj = Y[1], Yv = Y[2];\nvar n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;\nvar Zi = numeric.rep([n+1],0), Zj = [], Zv = [];\nvar x = numeric.rep([m],0),y = numeric.rep([m],0);\nvar xk,yk,zk;\nvar i,j,j0,j1,k,p=0;\n"+n+"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"+t+"\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)isFinite(eval("1"+numeric.ops2[k]+"0"))?A="[Y[0],Y[1],numeric."+k+"(X,Y[2])]":A="NaN",isFinite(eval("0"+numeric.ops2[k]+"1"))?B="[X[0],X[1],numeric."+k+"(X[2],Y)]":B="NaN",isFinite(eval("1"+numeric.ops2[k]+"0"))&&isFinite(eval("0"+numeric.ops2[k]+"1"))?C="numeric.ccs"+k+"MM(X,Y)":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(t){var n=t[0],r=t[1],i=t[2],s=numeric.sup(r)+1,o=n.length,u=numeric.rep([s],0),a=Array(o),f=Array(o),l=numeric.rep([s],0),c;for(c=0;c<o;++c)l[r[c]]++;for(c=0;c<s;++c)u[c+1]=u[c]+l[c];var h=u.slice(0),p,d;for(c=0;c<o;++c)d=r[c],p=h[d],a[p]=n[c],f[p]=i[c],h[d]=h[d]+1;return[u,a,f]},numeric.ccsGather=function(t){var n=t[0],r=t[1],i=t[2],s=n.length-1,o=r.length,u=Array(o),a=Array(o),f=Array(o),l,c,h,p,d;d=0;for(l=0;l<s;++l){h=n[l],p=n[l+1];for(c=h;c!==p;++c)a[d]=l,u[d]=r[c],f[d]=i[c],++d}return[u,a,f]},numeric.sdim=function dim(e,t,n){typeof t=="undefined"&&(t=[]);if(typeof e!="object")return t;typeof n=="undefined"&&(n=0),n in t||(t[n]=0),e.length>t[n]&&(t[n]=e.length);var r;for(r in e)e.hasOwnProperty(r)&&dim(e[r],t,n+1);return t},numeric.sclone=function clone(e,t,n){typeof t=="undefined"&&(t=0),typeof n=="undefined"&&(n=numeric.sdim(e).length);var r,i=Array(e.length);if(t===n-1){for(r in e)e.hasOwnProperty(r)&&(i[r]=e[r]);return i}for(r in e)e.hasOwnProperty(r)&&(i[r]=clone(e[r],t+1,n));return i},numeric.sdiag=function(t){var n=t.length,r,i=Array(n),s,o,u;for(r=n-1;r>=1;r-=2)s=r-1,i[r]=[],i[r][r]=t[r],i[s]=[],i[s][s]=t[s];return r===0&&(i[0]=[],i[0][0]=t[r]),i},numeric.sidentity=function(t){return numeric.sdiag(numeric.rep([t],1))},numeric.stranspose=function(t){var n=[],r=t.length,i,s,o;for(i in t){if(!t.hasOwnProperty(i))continue;o=t[i];for(s in o){if(!o.hasOwnProperty(s))continue;typeof n[s]!="object"&&(n[s]=[]),n[s][i]=o[s]}}return n},numeric.sLUP=function(t,n){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(t,n){var r=t.length,i=n.length,s=numeric.stranspose(n),o=s.length,u,a,f,l,c,h,p=Array(r),d;for(f=r-1;f>=0;f--){d=[],u=t[f];for(c=o-1;c>=0;c--){h=0,a=s[c];for(l in u){if(!u.hasOwnProperty(l))continue;l in a&&(h+=u[l]*a[l])}h&&(d[c]=h)}p[f]=d}return p},numeric.sdotMV=function(t,n){var r=t.length,i,s,o,u=Array(r),a;for(s=r-1;s>=0;s--){i=t[s],a=0;for(o in i){if(!i.hasOwnProperty(o))continue;n[o]&&(a+=i[o]*n[o])}a&&(u[s]=a)}return u},numeric.sdotVM=function(t,n){var r,i,s,o,u=[],a;for(r in t){if(!t.hasOwnProperty(r))continue;s=n[r],o=t[r];for(i in s){if(!s.hasOwnProperty(i))continue;u[i]||(u[i]=0),u[i]+=o*s[i]}}return u},numeric.sdotVV=function(t,n){var r,i=0;for(r in t)t[r]&&n[r]&&(i+=t[r]*n[r]);return i},numeric.sdot=function(t,n){var r=numeric.sdim(t).length,i=numeric.sdim(n).length,s=r*1e3+i;switch(s){case 0:return t*n;case 1001:return numeric.sdotVV(t,n);case 2001:return numeric.sdotMV(t,n);case 1002:return numeric.sdotVM(t,n);case 2002:return numeric.sdotMM(t,n);default:throw new Error("numeric.sdot not implemented for tensors of order "+r+" and "+i)}},numeric.sscatter=function(t){var n=t[0].length,r,i,s,o=t.length,u=[],a;for(i=n-1;i>=0;--i){if(!t[o-1][i])continue;a=u;for(s=0;s<o-2;s++)r=t[s][i],a[r]||(a[r]=[]),a=a[r];a[t[s][i]]=t[s+1][i]}return u},numeric.sgather=function gather(e,t,n){typeof t=="undefined"&&(t=[]),typeof n=="undefined"&&(n=[]);var r,i,s;r=n.length;for(i in e)if(e.hasOwnProperty(i)){n[r]=parseInt(i),s=e[i];if(typeof s=="number"){if(s){if(t.length===0)for(i=r+1;i>=0;--i)t[i]=[];for(i=r;i>=0;--i)t[i].push(n[i]);t[r+1].push(s)}}else gather(s,t,n)}return n.length>r&&n.pop(),t},numeric.cLU=function(t){var n=t[0],r=t[1],i=t[2],s=n.length,o=0,u,a,f,l,c,h;for(u=0;u<s;u++)n[u]>o&&(o=n[u]);o++;var p=Array(o),d=Array(o),v=numeric.rep([o],Infinity),m=numeric.rep([o],-Infinity),g,y,b;for(f=0;f<s;f++)u=n[f],a=r[f],a<v[u]&&(v[u]=a),a>m[u]&&(m[u]=a);for(u=0;u<o-1;u++)m[u]>m[u+1]&&(m[u+1]=m[u]);for(u=o-1;u>=1;u--)v[u]<v[u-1]&&(v[u-1]=v[u]);var w=0,E=0;for(u=0;u<o;u++)d[u]=numeric.rep([m[u]-v[u]+1],0),p[u]=numeric.rep([u-v[u]],0),w+=u-v[u]+1,E+=m[u]-u+1;for(f=0;f<s;f++)u=n[f],d[u][r[f]-v[u]]=i[f];for(u=0;u<o-1;u++){l=u-v[u],g=d[u];for(a=u+1;v[a]<=u&&a<o;a++){c=u-v[a],h=m[u]-u,y=d[a],b=y[c]/g[l];if(b){for(f=1;f<=h;f++)y[f+c]-=b*g[f+l];p[a][u-v[a]]=b}}}var g=[],y=[],S=[],x=[],T=[],N=[],s,C,k;s=0,C=0;for(u=0;u<o;u++){l=v[u],c=m[u],k=d[u];for(a=u;a<=c;a++)k[a-l]&&(g[s]=u,y[s]=a,S[s]=k[a-l],s++);k=p[u];for(a=l;a<u;a++)k[a-l]&&(x[C]=u,T[C]=a,N[C]=k[a-l],C++);x[C]=u,T[C]=u,N[C]=1,C++}return{U:[g,y,S],L:[x,T,N]}},numeric.cLUsolve=function(t,n){var r=t.L,i=t.U,s=numeric.clone(n),o=r[0],u=r[1],a=r[2],f=i[0],l=i[1],c=i[2],h=f.length,p=o.length,d=s.length,v,m,g;g=0;for(v=0;v<d;v++){while(u[g]<v)s[v]-=a[g]*s[u[g]],g++;g++}g=h-1;for(v=d-1;v>=0;v--){while(l[g]>v)s[v]-=c[g]*s[l[g]],g--;s[v]/=c[g],g--}return s},numeric.cgrid=function(t,n){typeof t=="number"&&(t=[t,t]);var r=numeric.rep(t,-1),i,s,o;if(typeof n!="function")switch(n){case"L":n=function(e,n){return e>=t[0]/2||n<t[1]/2};break;default:n=function(e,t){return!0}}o=0;for(i=1;i<t[0]-1;i++)for(s=1;s<t[1]-1;s++)n(i,s)&&(r[i][s]=o,o++);return r},numeric.cdelsq=function(t){var n=[[-1,0],[0,-1],[0,1],[1,0]],r=numeric.dim(t),i=r[0],s=r[1],o,u,a,f,l,c=[],h=[],p=[];for(o=1;o<i-1;o++)for(u=1;u<s-1;u++){if(t[o][u]<0)continue;for(a=0;a<4;a++){f=o+n[a][0],l=u+n[a][1];if(t[f][l]<0)continue;c.push(t[o][u]),h.push(t[f][l]),p.push(-1)}c.push(t[o][u]),h.push(t[o][u]),p.push(4)}return[c,h,p]},numeric.cdotMV=function(t,n){var r,i=t[0],s=t[1],o=t[2],u,a=i.length,f;f=0;for(u=0;u<a;u++)i[u]>f&&(f=i[u]);f++,r=numeric.rep([f],0);for(u=0;u<a;u++)r[i[u]]+=o[u]*n[s[u]];return r},numeric.Spline=function(t,n,r,i,s){this.x=t,this.yl=n,this.yr=r,this.kl=i,this.kr=s},numeric.Spline.prototype._at=function(t,n){var r=this.x,i=this.yl,s=this.yr,o=this.kl,u=this.kr,t,a,f,l,c=numeric.add,h=numeric.sub,p=numeric.mul;a=h(p(o[n],r[n+1]-r[n]),h(s[n+1],i[n])),f=c(p(u[n+1],r[n]-r[n+1]),h(s[n+1],i[n])),l=(t-r[n])/(r[n+1]-r[n]);var d=l*(1-l);return c(c(c(p(1-l,i[n]),p(l,s[n+1])),p(a,d*(1-l))),p(f,d*l))},numeric.Spline.prototype.at=function(t){if(typeof t=="number"){var n=this.x,r=n.length,i,s,o,u=Math.floor,a,f,l;i=0,s=r-1;while(s-i>1)o=u((i+s)/2),n[o]<=t?i=o:s=o;return this._at(t,i)}var r=t.length,c,h=Array(r);for(c=r-1;c!==-1;--c)h[c]=this.at(t[c]);return h},numeric.Spline.prototype.diff=function(){var t=this.x,n=this.yl,r=this.yr,i=this.kl,s=this.kr,o=n.length,u,a,f,l=i,c=s,h=Array(o),p=Array(o),d=numeric.add,v=numeric.mul,m=numeric.div,g=numeric.sub;for(u=o-1;u!==-1;--u)a=t[u+1]-t[u],f=g(r[u+1],n[u]),h[u]=m(d(v(f,6),v(i[u],-4*a),v(s[u+1],-2*a)),a*a),p[u+1]=m(d(v(f,-6),v(i[u],2*a),v(s[u+1],4*a)),a*a);return new numeric.Spline(t,l,c,h,p)},numeric.Spline.prototype.roots=function(){function t(e){return e*e}function n(e,t,n,r,i){var s=n*2-(t-e),o=-r*2+(t-e),u=(i+1)*.5,a=u*(1-u);return(1-u)*e+u*t+s*a*(1-u)+o*a*u}var r=[],i=this.x,s=this.yl,o=this.yr,u=this.kl,a=this.kr;typeof s[0]=="number"&&(s=[s],o=[o],u=[u],a=[a]);var 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s=t.length,o=[],u=[],a=[],f,l=numeric.sub,c=numeric.mul,h=numeric.add;for(f=s-2;f>=0;f--)u[f]=t[f+1]-t[f],a[f]=l(n[f+1],n[f]);if(typeof r=="string"||typeof i=="string")r=i="periodic";var p=[[],[],[]];switch(typeof r){case"undefined":o[0]=c(3/(u[0]*u[0]),a[0]),p[0].push(0,0),p[1].push(0,1),p[2].push(2/u[0],1/u[0]);break;case"string":o[0]=h(c(3/(u[s-2]*u[s-2]),a[s-2]),c(3/(u[0]*u[0]),a[0])),p[0].push(0,0,0),p[1].push(s-2,0,1),p[2].push(1/u[s-2],2/u[s-2]+2/u[0],1/u[0]);break;default:o[0]=r,p[0].push(0),p[1].push(0),p[2].push(1)}for(f=1;f<s-1;f++)o[f]=h(c(3/(u[f-1]*u[f-1]),a[f-1]),c(3/(u[f]*u[f]),a[f])),p[0].push(f,f,f),p[1].push(f-1,f,f+1),p[2].push(1/u[f-1],2/u[f-1]+2/u[f],1/u[f]);switch(typeof i){case"undefined":o[s-1]=c(3/(u[s-2]*u[s-2]),a[s-2]),p[0].push(s-1,s-1),p[1].push(s-2,s-1),p[2].push(1/u[s-2],2/u[s-2]);break;case"string":p[1][p[1].length-1]=0;break;default:o[s-1]=i,p[0].push(s-1),p[1].push(s-1),p[2].push(1)}typeof o[0]!="number"?o=numeric.transpose(o):o=[o];var 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N=s(1e-6*i,1e-8);for(;;){++E;if(E>20)throw new Error("Numerical gradient fails");u[o]=n[o]+N,a=t(u),u[o]=n[o]-N,f=t(u),u[o]=n[o];if(isNaN(a)||isNaN(f)){N/=16;continue}l[o]=(a-f)/(2*N),y=n[o]-N,b=n[o],w=n[o]+N,S=(a-i)/N,x=(i-f)/N,T=s(m(l[o]),m(i),m(a),m(f),m(y),m(b),m(w),1e-8),p=g(s(m(S-l[o]),m(x-l[o]),m(S-x))/T,N/T);if(!(p>v))break;N/=16}}return l},numeric.uncmin=function(t,n,r,i,s,o,u){var a=numeric.gradient;typeof u=="undefined"&&(u={}),typeof r=="undefined"&&(r=1e-8),typeof i=="undefined"&&(i=function(e){return a(t,e)}),typeof s=="undefined"&&(s=1e3),n=numeric.clone(n);var f=n.length,l=t(n),c,h;if(isNaN(l))throw new Error("uncmin: f(x0) is a NaN!");var p=Math.max,d=numeric.norm2;r=p(r,numeric.epsilon);var v,m,g,y=u.Hinv||numeric.identity(f),b=numeric.dot,w=numeric.inv,E=numeric.sub,S=numeric.add,x=numeric.tensor,T=numeric.div,N=numeric.mul,C=numeric.all,k=numeric.isFinite,L=numeric.neg,A=0,O,M,_,D,P,H,B,j,F,I,q,R,U="";m=i(n);while(A<s){if(typeof o=="function"&&o(A,n,l,m,y)){U="Callback returned true";break}if(!C(k(m))){U="Gradient has Infinity or NaN";break}v=L(b(y,m));if(!C(k(v))){U="Search direction has Infinity or NaN";break}I=d(v);if(I<r){U="Newton step smaller than tol";break}F=1,h=b(m,v),_=n;while(A<s){if(F*I<r)break;M=N(v,F),_=S(n,M),c=t(_);if(c-l>=.1*F*h||isNaN(c)){F*=.5,++A;continue}break}if(F*I<r){U="Line search step size smaller than tol";break}if(A===s){U="maxit reached during line search";break}g=i(_),D=E(g,m),B=b(D,M),P=b(y,D),y=E(S(y,N((B+b(D,P))/(B*B),x(M,M))),T(S(x(P,M),x(M,P)),B)),n=_,l=c,m=g,++A}return{solution:n,f:l,gradient:m,invHessian:y,iterations:A,message:U}},numeric.Dopri=function(t,n,r,i,s,o,u){this.x=t,this.y=n,this.f=r,this.ymid=i,this.iterations=s,this.events=u,this.message=o},numeric.Dopri.prototype._at=function(t,n){function r(e){return e*e}var i=this,s=i.x,o=i.y,u=i.f,a=i.ymid,f=s.length,l,c,h,p,d,v,t,m=Math.floor,g,y=.5,b=numeric.add,w=numeric.mul,E=numeric.sub,S,x,T;return 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a=[t],f=[r],l=[i(t,r)],c,h,p,d,v,m,g=[],y=.2,b=[.075,.225],w=[44/45,-56/15,32/9],E=[19372/6561,-25360/2187,64448/6561,-212/729],S=[9017/3168,-355/33,46732/5247,49/176,-5103/18656],x=[35/384,0,500/1113,125/192,-2187/6784,11/84],T=[.10013431883002395,0,.3918321794184259,-0.02982460176594817,.05893268337240795,-0.04497888809104361,.023904308236133973],N=[.2,.3,.8,8/9,1,1],C=[-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,.025],k=0,L,A,O=(n-t)/10,M=0,_=numeric.add,D=numeric.mul,P,H,B=Math.max,j=Math.min,F=Math.abs,I=numeric.norminf,q=Math.pow,R=numeric.any,U=numeric.lt,z=numeric.and,W=numeric.sub,X,V,$,J=new numeric.Dopri(a,f,l,g,-1,"");typeof u=="function"&&(X=u(t,r));while(t<n&&M<o){++M,t+O>n&&(O=n-t),c=i(t+N[0]*O,_(r,D(y*O,l[k]))),h=i(t+N[1]*O,_(_(r,D(b[0]*O,l[k])),D(b[1]*O,c))),p=i(t+N[2]*O,_(_(_(r,D(w[0]*O,l[k])),D(w[1]*O,c)),D(w[2]*O,h))),d=i(t+N[3]*O,_(_(_(_(r,D(E[0]*O,l[k])),D(E[1]*O,c)),D(E[2]*O,h)),D(E[3]*O,p))),v=i(t+N[4]*O,_(_(_(_(_(r,D(S[0]*O,l[k])),D(S[1]*O,c)),D(S[2]*O,h)),D(S[3]*O,p)),D(S[4]*O,d))),P=_(_(_(_(_(r,D(l[k],O*x[0])),D(h,O*x[2])),D(p,O*x[3])),D(d,O*x[4])),D(v,O*x[5])),m=i(t+O,P),L=_(_(_(_(_(D(l[k],O*C[0]),D(h,O*C[2])),D(p,O*C[3])),D(d,O*C[4])),D(v,O*C[5])),D(m,O*C[6])),typeof L=="number"?H=F(L):H=I(L);if(H>s){O=.2*O*q(s/H,.25);if(t+O===t){J.msg="Step size became too small";break}continue}g[k]=_(_(_(_(_(_(r,D(l[k],O*T[0])),D(h,O*T[2])),D(p,O*T[3])),D(d,O*T[4])),D(v,O*T[5])),D(m,O*T[6])),++k,a[k]=t+O,f[k]=P,l[k]=m;if(typeof u=="function"){var K,Q=t,G=t+.5*O,Y;V=u(G,g[k-1]),$=z(U(X,0),U(0,V)),R($)||(Q=G,G=t+O,X=V,V=u(G,P),$=z(U(X,0),U(0,V)));if(R($)){var Z,et,tt,nt,rt=0,it=1,st=1;for(;;){if(typeof X=="number")Y=(st*V*Q-it*X*G)/(st*V-it*X);else{Y=G;for(A=X.length-1;A!==-1;--A)X[A]<0&&V[A]>0&&(Y=j(Y,(st*V[A]*Q-it*X[A]*G)/(st*V[A]-it*X[A])))}if(Y<=Q||Y>=G)break;K=J._at(Y,k-1),nt=u(Y,K),tt=z(U(X,0),U(0,nt)),R(tt)?(G=Y,V=nt,$=tt,st=1,rt===-1?it*=.5:it=1,rt=-1):(Q=Y,X=nt,it=1,rt===1?st*=.5:st=1,rt=1)}return P=J._at(.5*(t+Y),k-1),J.f[k]=i(Y,K),J.x[k]=Y,J.y[k]=K,J.ymid[k-1]=P,J.events=$,J.iterations=M,J}}t+=O,r=P,X=V,O=j(.8*O*q(s/H,.25),4*O)}return J.iterations=M,J},numeric.LU=function(e,t){t=t||!1;var n=Math.abs,r,i,s,o,u,a,f,l,c,h=e.length,p=h-1,d=new Array(h);t||(e=numeric.clone(e));for(s=0;s<h;++s){f=s,a=e[s],c=n(a[s]);for(i=s+1;i<h;++i)o=n(e[i][s]),c<o&&(c=o,f=i);d[s]=f,f!=s&&(e[s]=e[f],e[f]=a,a=e[s]),u=a[s];for(r=s+1;r<h;++r)e[r][s]/=u;for(r=s+1;r<h;++r){l=e[r];for(i=s+1;i<p;++i)l[i]-=l[s]*a[i],++i,l[i]-=l[s]*a[i];i===p&&(l[i]-=l[s]*a[i])}}return{LU:e,P:d}},numeric.LUsolve=function(t,n){var r,i,s=t.LU,o=s.length,u=numeric.clone(n),a=t.P,f,l,c,h;for(r=o-1;r!==-1;--r)u[r]=n[r];for(r=0;r<o;++r){f=a[r],a[r]!==r&&(h=u[r],u[r]=u[f],u[f]=h),l=s[r];for(i=0;i<r;++i)u[r]-=u[i]*l[i]}for(r=o-1;r>=0;--r){l=s[r];for(i=r+1;i<o;++i)u[r]-=u[i]*l[i];u[r]/=l[r]}return u},numeric.solve=function(t,n,r){return numeric.LUsolve(numeric.LU(t,r),n)},numeric.echelonize=function(t){var n=numeric.dim(t),r=n[0],i=n[1],s=numeric.identity(r),o=Array(r),u,a,f,l,c,h,p,d,v=Math.abs,m=numeric.diveq;t=numeric.clone(t);for(u=0;u<r;++u){f=0,c=t[u],h=s[u];for(a=1;a<i;++a)v(c[f])<v(c[a])&&(f=a);o[u]=f,m(h,c[f]),m(c,c[f]);for(a=0;a<r;++a)if(a!==u){p=t[a],d=p[f];for(l=i-1;l!==-1;--l)p[l]-=c[l]*d;p=s[a];for(l=r-1;l!==-1;--l)p[l]-=h[l]*d}}return{I:s,A:t,P:o}},numeric.__solveLP=function(t,n,r,i,s,o,u){var a=numeric.sum,f=numeric.log,l=numeric.mul,c=numeric.sub,h=numeric.dot,p=numeric.div,d=numeric.add,v=t.length,m=r.length,g,y=!1,b,w=0,E=1,S,x,T=numeric.transpose(n),N=numeric.svd,C=numeric.transpose,k=numeric.leq,L=Math.sqrt,A=Math.abs,O=numeric.muleq,M=numeric.norminf,_=numeric.any,D=Math.min,P=numeric.all,H=numeric.gt,B=Array(v),j=Array(m),F=numeric.rep([m],1),I,q=numeric.solve,R=c(r,h(n,o)),U,z=h(t,t),W;for(U=w;U<s;++U){var X,V,$;for(X=m-1;X!==-1;--X)j[X]=p(n[X],R[X]);var J=C(j);for(X=v-1;X!==-1;--X)B[X]=a(J[X]);E=.25*A(z/h(t,B));var K=100*L(z/h(B,B));if(!isFinite(E)||E>K)E=K;W=d(t,l(E,B)),I=h(J,j);for(X=v-1;X!==-1;--X)I[X][X]+=1;$=q(I,p(W,E),!0);var Q=p(R,h(n,$)),G=1;for(X=m-1;X!==-1;--X)Q[X]<0&&(G=D(G,-0.999*Q[X]));g=c(o,l($,G)),R=c(r,h(n,g));if(!P(H(R,0)))return{solution:o,message:"",iterations:U};o=g;if(E<i)return{solution:g,message:"",iterations:U};if(u){var Y=h(t,W),Z=h(n,W);y=!0;for(X=m-1;X!==-1;--X)if(Y*Z[X]<0){y=!1;break}}else 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i,s,o,u,a,f;for(s=1;s<=n;s+=1){r[1]=s,f=0,o=s-1;if(o<1){f=e[s][s]-f;if(f<=0)break;e[s][s]=Math.sqrt(f)}else{for(u=1;u<=o;u+=1){a=e[u][s];for(i=1;i<u;i+=1)a-=e[i][s]*e[i][u];a/=e[u][u],e[u][s]=a,f+=a*a}f=e[s][s]-f;if(f<=0)break;e[s][s]=Math.sqrt(f)}r[1]=0}}function o(e,t,n,o,u,a,f,l,c,h,p,d,v,m,g,y){function V(){m[1]=m[1]+1,E=L;for(b=1;b<=h;b+=1){E+=1,P=-l[b];for(w=1;w<=o;w+=1)P+=f[w][b]*u[w];Math.abs(P)<U&&(P=0);if(b>p)g[E]=P;else{g[E]=-Math.abs(P);if(P>0){for(w=1;w<=o;w+=1)f[w][b]=-f[w][b];l[b]=-l[b]}}}for(b=1;b<=v;b+=1)g[L+d[b]]=0;O=0,D=0;for(b=1;b<=h;b+=1)g[L+b]<D*g[_+b]&&(O=b,D=g[L+b]/g[_+b]);return O===0?999:0}function $(){for(b=1;b<=o;b+=1){P=0;for(w=1;w<=o;w+=1)P+=e[w][b]*f[w][O];g[b]=P}S=N;for(b=1;b<=o;b+=1)g[S+b]=0;for(w=v+1;w<=o;w+=1)for(b=1;b<=o;b+=1)g[S+b]=g[S+b]+e[b][w]*g[w];q=!0;for(b=v;b>=1;b-=1){P=g[b],E=k+b*(b+3)/2,S=E-b;for(w=b+1;w<=v;w+=1)P-=g[E]*g[C+w],E+=w;P/=g[S],g[C+b]=P;if(d[b]<p)break;if(P<0)break;q=!1,T=b}if(!q){H=g[A+T]/g[C+T];for(b=1;b<=v;b+=1){if(d[b]<p)break;if(g[C+b]<0)break;D=g[A+b]/g[C+b],D<
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700}v+=1,d[v]=O,E=k+(v-1)*v/2+1;for(b=1;b<=v-1;b+=1)g[E]=g[b],E+=1;if(v===o)g[E]=g[o];else{for(b=o;b>=v+1;b-=1){if(g[b]===0)break;j=Math.max(Math.abs(g[b-1]),Math.abs(g[b])),F=Math.min(Math.abs(g[b-1]),Math.abs(g[b])),g[b-1]>=0?D=Math.abs(j*Math.sqrt(1+F*F/(j*j))):D=-Math.abs(j*Math.sqrt(1+F*F/(j*j))),j=g[b-1]/D,F=g[b]/D;if(j===1)break;if(j===0){g[b-1]=F*D;for(w=1;w<=o;w+=1)D=e[w][b-1],e[w][b-1]=e[w][b],e[w][b]=D}else{g[b-1]=D,I=F/(1+j);for(w=1;w<=o;w+=1)D=j*e[w][b-1]+F*e[w][b],e[w][b]=I*(e[w][b-1]+D)-e[w][b],e[w][b-1]=D}}g[E]=g[v]}return 0}function J(){E=k+T*(T+1)/2+1,S=E+T;if(g[S]===0)return 798;j=Math.max(Math.abs(g[S-1]),Math.abs(g[S])),F=Math.min(Math.abs(g[S-1]),Math.abs(g[S])),g[S-1]>=0?D=Math.abs(j*Math.sqrt(1+F*F/(j*j))):D=-Math.abs(j*Math.sqrt(1+F*F/(j*j))),j=g[S-1]/D,F=g[S]/D;if(j===1)return 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f,l,c,h,p,d=[],v=[],m=[],g=[],y=[],b;u=u||0,a=a?t(a):[undefined,0],s=s?t(s):[],l=e.length-1,c=i[1].length-1;if(!s)for(f=1;f<=c;f+=1)s[f]=0;for(f=1;f<=c;f+=1)v[f]=0;h=0,p=Math.min(l,c);for(f=1;f<=l;f+=1)m[f]=0;d[1]=0;for(f=1;f<=2*l+p*(p+5)/2+2*c+1;f+=1)g[f]=0;for(f=1;f<=2;f+=1)y[f]=0;return o(e,r,l,l,m,d,i,s,l,c,u,v,h,y,g,a),b="",a[1]===1&&(b="constraints are inconsistent, no solution!"),a[1]===2&&(b="matrix D in quadratic function is not positive definite!"),{solution:n(m),value:n(d),unconstrained_solution:n(r),iterations:n(y),iact:n(v),message:b}}e.solveQP=u}(numeric),numeric.svd=function(t){function g(e,t){return e=Math.abs(e),t=Math.abs(t),e>t?e*Math.sqrt(1+t*t/e/e):t==0?e:t*Math.sqrt(1+e*e/t/t)}var n,r=numeric.epsilon,i=1e-64/r,s=50,o=0,u=0,a=0,f=0,l=0,c=numeric.clone(t),h=c.length,p=c[0].length;if(h<p)throw"Need more rows than columns";var d=new Array(p),v=new Array(p);for(u=0;u<p;u++)d[u]=v[u]=0;var m=numeric.rep([p,p],0),y=0,b=0,w=0,E=0,S=0,x=0,T=0;for(u=0;u<p;u++){d[u]=b,T=0,l=u+1;for(a=u;a<h;a++)T+=c[a][u]*c[a][u];if(T<=i)b=0;else{y=c[u][u],b=Math.sqrt(T),y>=0&&(b=-b),w=y*b-T,c[u][u]=y-b;for(a=l;a<p;a++){T=0;for(f=u;f<h;f++)T+=c[f][u]*c[f][a];y=T/w;for(f=u;f<h;f++)c[f][a]+=y*c[f][u]}}v[u]=b,T=0;for(a=l;a<p;a++)T+=c[u][a]*c[u][a];if(T<=i)b=0;else{y=c[u][u+1],b=Math.sqrt(T),y>=0&&(b=-b),w=y*b-T,c[u][u+1]=y-b;for(a=l;a<p;a++)d[a]=c[u][a]/w;for(a=l;a<h;a++){T=0;for(f=l;f<p;f++)T+=c[a][f]*c[u][f];for(f=l;f<p;f++)c[a][f]+=T*d[f]}}S=Math.abs(v[u])+Math.abs(d[u]),S>E&&(E=S)}for(u=p-1;u!=-1;u+=-1){if(b!=0){w=b*c[u][u+1];for(a=l;a<p;a++)m[a][u]=c[u][a]/w;for(a=l;a<p;a++){T=0;for(f=l;f<p;f++)T+=c[u][f]*m[f][a];for(f=l;f<p;f++)m[f][a]+=T*m[f][u]}}for(a=l;a<p;a++)m[u][a]=0,m[a][u]=0;m[u][u]=1,b=d[u],l=u}for(u=p-1;u!=-1;u+=-1){l=u+1,b=v[u];for(a=l;a<p;a++)c[u][a]=0;if(b!=0){w=c[u][u]*b;for(a=l;a<p;a++){T=0;for(f=l;f<h;f++)T+=c[f][u]*c[f][a];y=T/w;for(f=u;f<h;f++)c[f][a]+=y*c[f][u]}for(a=u;a<h;a++)c[a][u]=c[a][u]/b}else for(a=u;a<h;a++)c[a][u]=0;c[u][u]+=1}r*=E;for(f=p-1;f!=-1;f+=-1)for(var N=0;N<s;N++){var C=!1;for(l=f;l!=-1;l+=-1){if(Math.abs(d[l])<=r){C=!0;break}if(Math.abs(v[l-1])<=r)break}if(!C){o=0,T=1;var k=l-1;for(u=l;u<f+1;u++){y=T*d[u],d[u]=o*d[u];if(Math.abs(y)<=r)break;b=v[u],w=g(y,b),v[u]=w,o=b/w,T=-y/w;for(a=0;a<h;a++)S=c[a][k],x=c[a][u],c[a][k]=S*o+x*T,c[a][u]=-S*T+x*o}}x=v[f];if(l==f){if(x<0){v[f]=-x;for(a=0;a<p;a++)m[a][f]=-m[a][f]}break}if(N>=s-1)throw"Error: no convergence.";E=v[l],S=v[f-1],b=d[f-1],w=d[f],y=((S-x)*(S+x)+(b-w)*(b+w))/(2*w*S),b=g(y,1),y<0?y=((E-x)*(E+x)+w*(S/(y-b)-w))/E:y=((E-x)*(E+x)+w*(S/(y+b)-w))/E,o=1,T=1;for(u=l+1;u<f+1;u++){b=d[u],S=v[u],w=T*b,b=o*b,x=g(y,w),d[u-1]=x,o=y/x,T=w/x,y=E*o+b*T,b=-E*T+b*o,w=S*T,S*=o;for(a=0;a<p;a++)E=m[a][u-1],x=m[a][u],m[a][u-1]=E*o+x*T,m[a][u]=-E*T+x*o;x=g(y,w),v[u-1]=x,o=y/x,T=w/x,y=o*b+T*S,E=-T*b+o*S;for(a=0;a<h;a++)S=c[a][u-1],x=c[a][u],c[a][u-1]=S*o+x*T,c[a][u]=-S*T+x*o}d[l]=0,d[f]=y,v[f]=E}for(u=0;u<v.length;u++)v[u]<r&&(v[u]=0);for(u=0;u<p;u++)for(a=u-1;a>=0;a--)if(v[a]<v[u]){o=v[a],v[a]=v[u],v[u]=o;for(f=0;f<c.length;f++)n=c[f][u],c[f][u]=c[f][a],c[f][a]=n;for(f=0;f<m.length;f++)n=m[f][u],m[f][u]=m[f][a],m[f][a]=n;u=a}return{U:c,S:v,V:m}};
\ No newline at end of file
diff --git a/js/models/dmaBeam.js b/js/models/dmaBeam.js
new file mode 100644
index 00000000..1e2bdd17
--- /dev/null
+++ b/js/models/dmaBeam.js
@@ -0,0 +1,57 @@
+/Math.pow(,
+ * Created by aghassaei on 1/13/15.
+ */
+
+
+//a single beam
+
+function Beam(node1, node2) {
+ this.nodes = [node1, node2];
+ var self = this;
+ _.each(nodes, function(node){
+ node.addBeam(self);
+ });
+}
+
+Beam.prototype.render = function(scene){
+
+};
+
+
+BeamNode.prototype.translate = function(dx, dy, dz){
+};
+
+Beam.prototype.rotate = function(rx, ry, rz){
+};
+
+Beam.prototype.setStiffness = function(scene){
+
+};
+
+Beam.prototype.calcStiffnessMatrix = function(){
+
+ var L = 0;
+ var A = 0;
+ var Iy = 0;
+ var Iz = 0;
+ var E = 0;
+ var G = 0;
+
+ var K = [
+ [A*E/L , 0 , 0 , 0 , 0 , 0 , -A*E/L , 0 , 0 , 0 , 0 , 0] ,//d1x
+ [0 , 12*E*Iz/Math.pow(L, 3) , 0 , 0 , 0 , 6*E*Iz/Math.pow(L, 2) , 0 , -12*E*Iz/Math.pow(L, 3) , 0 , 0 , 0 , 6*E*Iz/Math.pow(L, 2)] ,//d1y
+ [0 , 0 , 12*E*Iy/Math.pow(L, 3) , 0 , -6*E*Iy/Math.pow(L, 2) , 0 , 0 , 0 , -12*E*Iy/Math.pow(L, 3) , 0 , -6*E*Iy/Math.pow(L, 2) , 0] ,//d1z
+ [0 , 0 , 0 , G*J/L , 0 , 0 , 0 , 0 , 0 , -G*J/L , 0 , 0] , //r1x
+ [0 , 0 , -6*E*Iy/Math.pow(L, 2) , 0 , 4*E*Iy/L , 0 , 0 , 0 , 6*E*Iy/Math.pow(L, 2) , 0 , 2*E*Iy/L , 0] ,//r1y
+ [0 , 6*E*Iz/Math.pow(L, 2) , 0 , 0 , 0 , 4*E*Iz/L , 0 , -6*E*Iz/Math.pow(L, 2) , 0 , 0 , 0 , 2*E*Iz/L] ,//r1z
+ [-A*E/L , 0 , 0 , 0 , 0 , 0 , A*E/L , 0 , 0 , 0 , 0 , 0] , //d2x
+ [0 , -12*E*Iz/Math.pow(L, 3) , 0 , 0 , 0 , -6*E*Iz/Math.pow(L, 2) , 0 , 12*E*Iz/Math.pow(L, 3) , 0 , 0 , 0 , -6*E*Iz/Math.pow(L, 2)] ,//d2y
+ [0 , 0 , -12*E*Iy/Math.pow(L, 3) , 0 , 6*E*Iy/Math.pow(L, 2) , 0 , 0 , 0 , 12*E*Iy/Math.pow(L, 3) , 0 , 6*E*Iy/Math.pow(L, 2) , 0] ,//d2z
+ [0 , 0 , 0 , -G*J/L , 0 , 0 , 0 , 0 , 0 , G*J/L , 0 , 0] ,//r2x
+ [0 , 0 , -6*E*Iy/Math.pow(L, 2) , 0 , 2*E*Iy/L , 0 , 0 , 0 , 6*E*Iy/Math.pow(L, 2) , 0 , 4*E*Iy/L , 0] ,//r2y
+ [0 , 6*E*Iz/Math.pow(L, 2) , 0 , 0 , 0 , 2*E*Iz/L , 0 , -6*E*Iz/Math.pow(L, 2) , 0 , 0 , 0 , 4*E*Iz/L]//r2z
+ ];
+
+};
+
+
diff --git a/js/models/dmaCell.js b/js/models/dmaCell.js
new file mode 100644
index 00000000..9d70eac2
--- /dev/null
+++ b/js/models/dmaCell.js
@@ -0,0 +1,3 @@
+/**
+ * Created by aghassaei on 1/14/15.
+ */
diff --git a/js/models/dmaNode.js b/js/models/dmaNode.js
new file mode 100644
index 00000000..90823453
--- /dev/null
+++ b/js/models/dmaNode.js
@@ -0,0 +1,27 @@
+//a node, two for each dmaBeam, not to be confused with node.js
+
+function BeamNode() {
+ this._beams = [];//store all beams attached to this node, eventually this will be used to calc global stiffness K
+}
+
+BeamNode.prototype.addBeam = function(beam){
+ this._beams.push(beam);
+};
+
+BeamNode.prototype.render = function(scene){
+};
+
+
+BeamNode.prototype.deflect = function(dx, dy, dz){
+};
+
+BeamNode.prototype.translate = function(dx, dy, dz){
+};
+
+BeamNode.prototype.rotate = function(rx, ry, rz){
+};
+
+BeamNode.prototype.destroy = function(){
+ this._beam = null;//be sure to remove cyclic reference
+ this = null;
+};
diff --git a/js/models/dmaPart.js b/js/models/dmaPart.js
new file mode 100644
index 00000000..06523c01
--- /dev/null
+++ b/js/models/dmaPart.js
@@ -0,0 +1,27 @@
+/**
+ * Created by aghassaei on 1/14/15.
+ */
+
+
+function Part(nodes, config) {//list of nodes, config tells how nodes are connected
+ self.nodes = nodes;
+ self.beams = self._createBeams(nodes, config);
+};
+
+Part.prototype._createBeams = function(nodes, config){
+ var beams = [];
+ _.each(config, function(pair){
+ beams.push(new Beam(nodes[pair[0]], nodes[pair[2]]));
+ });
+ return beams;
+};
+
+Part.prototype.render = function(scene){
+};
+
+
+Part.prototype.translate = function(dx, dy, dz){
+};
+
+Part.prototype.rotate = function(rx, ry, rz){
+};
diff --git a/js/models/element.js b/js/models/element.js
deleted file mode 100644
index 723469e4..00000000
--- a/js/models/element.js
+++ /dev/null
@@ -1,7 +0,0 @@
-/**
- * Created by aghassaei on 1/13/15.
- */
-
-
-//element model, do not put anything to do with views in here
-
diff --git a/js/views/importMenu.js b/js/views/importMenu.js
index aad65a7f..3713ff3d 100644
--- a/js/views/importMenu.js
+++ b/js/views/importMenu.js
@@ -2,7 +2,6 @@
* Created by aghassaei on 1/8/15.
*/
-//todo - put stl loading in background thread
$(function(){
diff --git a/js/worker.js b/js/worker.js
index ea96e3b1..4b708de0 100644
--- a/js/worker.js
+++ b/js/worker.js
@@ -21,7 +21,7 @@ function myWorker(){
}
//load all scripts
importScripts(url + 'dependencies/three.js');
- // importScripts(url + 'js/element.js');
+ // importScripts(url + 'js/models/dmaBeam.js');
}
//
if (data.model){
diff --git a/main.html b/main.html
index c186605a..1094f829 100644
--- a/main.html
+++ b/main.html
@@ -30,6 +30,9 @@
<!--stl export-->
<script src="dependencies/THREE2STL.js"></script>
+ <!--numerical javascript-->
+ <script src="dependencies/numeric-1.2.6.js"></script>
+
<!--multi-threading-->
<script src="js/worker.js"></script>
<script src="js/persistentWorkers.js"></script><!--global workers-->
--
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