clmtrackr
Version:
Javascript library for precise tracking of facial features via Constrained Local Models
1,418 lines (1,355 loc) • 2.39 MB
JavaScript
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
typeof define === 'function' && define.amd ? define(factory) :
(global.clm = factory());
}(this, (function () { 'use strict';
var commonjsGlobal = typeof window !== 'undefined' ? window : typeof global !== 'undefined' ? global : typeof self !== 'undefined' ? self : {};
function createCommonjsModule(fn, module) {
return module = { exports: {} }, fn(module, module.exports), module.exports;
}
var numeric1_2_6 = createCommonjsModule(function (module, exports) {
"use strict";
var numeric = exports;
if(typeof commonjsGlobal !== "undefined") { commonjsGlobal.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.QR