摘要：
"usestrict";//requires:ccv.js,numeric.jsvarclm={tracker:function(params){if(!
"use strict";
//requires: ccv.js, numeric.js
var clm = {
tracker : function(params) {
if (!params) params = {};
if (params.constantVelocity === undefined) params.constantVelocity = true;
if (params.searchWindow === undefined) params.searchWindow = 11;
if (params.useWebGL === undefined) params.useWebGL = true;
if (params.scoreThreshold === undefined) params.scoreThreshold = 0.5;
if (params.stopOnConvergence === undefined) params.stopOnConvergence = false;
if (params.weightPoints === undefined) params.weightPoints = undefined;
if (params.sharpenResponse === undefined) params.sharpenResponse = false;
var numPatches, patchSize, numParameters, patchType;
var gaussianPD;
var eigenVectors, eigenValues;
var sketchCC, sketchW, sketchH, sketchCanvas;
var candidate;
var weights, model, biases;
var sobelInit = false;
var lbpInit = false;
var currentParameters = [];
var currentPositions = [];
var previousParameters = [];
var previousPositions = [];
var patches = [];
var responses = [];
var meanShape = [];
var responseMode = 'single';
var responseList = ['raw'];
var responseIndex = 0;
/*
It's possible to experiment with the sequence of variances used for the finding the maximum in the KDE.
This sequence is pretty arbitrary, but was found to be okay using some manual testing.
*/
var varianceSeq = [10,5,1];
//var varianceSeq = [3,1.5,0.75];
//var varianceSeq = [6,3,0.75];
var PDMVariance = 0.7;
var relaxation = 0.1;
var first = true;
var convergenceLimit = 0.01;
var learningRate = [];
var stepParameter = 1.25;
var prevCostFunc = []
var searchWindow;
var modelWidth, modelHeight;
var halfSearchWindow, vecProbs, responsePixels;
if(typeof Float64Array !== 'undefined') {
var updatePosition = new Float64Array(2);
var vecpos = new Float64Array(2);
} else {
var updatePosition = new Array(2);
var vecpos = new Array(2);
}
var pw, pl, pdataLength;
var facecheck_count = 0;
var webglFi, svmFi, mosseCalc;
var scoringCanvas = document.createElement('canvas');
//document.body.appendChild(scoringCanvas);
var scoringContext = scoringCanvas.getContext('2d');
var msxmin, msymin, msxmax, msymax;
var msmodelwidth, msmodelheight;
var scoringWeights, scoringBias;
var scoringHistory = [];
var meanscore = 0;
var mossef_lefteye, mossef_righteye, mossef_nose;
var right_eye_position = [0.0,0.0];
var left_eye_position = [0.0,0.0];
var nose_position = [0.0,0.0];
var lep, rep, mep;
var runnerTimeout, runnerElement, runnerBox;
var pointWeights;
var halfPI = Math.PI/2;
/*
* load model data, initialize filters, etc.
*
* @param <Object> pdm model object
*/
this.init = function(pdmmodel) {
model = pdmmodel;
// load from model
patchType = model.patchModel.patchType;
numPatches = model.patchModel.numPatches;
patchSize = model.patchModel.patchSize[0];
if (patchType == "MOSSE") {
searchWindow = patchSize;
} else {
searchWindow = params.searchWindow;
}
numParameters = model.shapeModel.numEvalues;
modelWidth = model.patchModel.canvasSize[0];
modelHeight = model.patchModel.canvasSize[1];
// set up canvas to work on
sketchCanvas = document.createElement('canvas');
sketchCC = sketchCanvas.getContext('2d');
sketchW = sketchCanvas.width = modelWidth + (searchWindow-1) + patchSize-1;
sketchH = sketchCanvas.height = modelHeight + (searchWindow-1) + patchSize-1;
if (model.hints && mosseFilter && left_eye_filter && right_eye_filter && nose_filter) {
//var mossef_lefteye = new mosseFilter({drawResponse : document.getElementById('overlay2')});
mossef_lefteye = new mosseFilter();
mossef_lefteye.load(left_eye_filter);
//var mossef_righteye = new mosseFilter({drawResponse : document.getElementById('overlay2')});
mossef_righteye = new mosseFilter();
mossef_righteye.load(right_eye_filter);
//var mossef_nose = new mosseFilter({drawResponse : document.getElementById('overlay2')});
mossef_nose = new mosseFilter();
mossef_nose.load(nose_filter);
} else {
console.log("MOSSE filters not found, using rough approximation for initialization.");
}
// load eigenvectors
eigenVectors = numeric.rep([numPatches*2,numParameters],0.0);
for (var i = 0;i < numPatches*2;i++) {
for (var j = 0;j < numParameters;j++) {
eigenVectors[i][j] = model.shapeModel.eigenVectors[i][j];
}
}
// load mean shape
for (var i = 0; i < numPatches;i++) {
meanShape[i] = [model.shapeModel.meanShape[i][0], model.shapeModel.meanShape[i][1]];
}
// get max and mins, width and height of meanshape
msxmax = msymax = 0;
msxmin = msymin = 1000000;
for (var i = 0;i < numPatches;i++) {
if (meanShape[i][0] < msxmin) msxmin = meanShape[i][0];
if (meanShape[i][1] < msymin) msymin = meanShape[i][1];
if (meanShape[i][0] > msxmax) msxmax = meanShape[i][0];
if (meanShape[i][1] > msymax) msymax = meanShape[i][1];
}
msmodelwidth = msxmax-msxmin;
msmodelheight = msymax-msymin;
// get scoringweights if they exist
if (model.scoring) {
scoringWeights = new Float64Array(model.scoring.coef);
scoringBias = model.scoring.bias;
scoringCanvas.width = model.scoring.size[0];
scoringCanvas.height = model.scoring.size[1];
}
// load eigenvalues
eigenValues = model.shapeModel.eigenValues;
weights = model.patchModel.weights;
biases = model.patchModel.bias;
// precalculate gaussianPriorDiagonal
gaussianPD = numeric.rep([numParameters+4, numParameters+4],0);
// set values and append manual inverse
for (var i = 0;i < numParameters;i++) {
if (model.shapeModel.nonRegularizedVectors.indexOf(i) >= 0) {
gaussianPD[i+4][i+4] = 1/10000000;
} else {
gaussianPD[i+4][i+4] = 1/eigenValues[i];
}
}
for (var i = 0;i < numParameters+4;i++) {
currentParameters[i] = 0;
}
if (patchType == "SVM") {
var webGLContext;
var webGLTestCanvas = document.createElement('canvas');
if (window.WebGLRenderingContext) {
webGLContext = webGLTestCanvas.getContext('webgl') || webGLTestCanvas.getContext('experimental-webgl');
if (!webGLContext || !webGLContext.getExtension('OES_texture_float')) {
webGLContext = null;
}
}
if (webGLContext && params.useWebGL && (typeof(webglFilter) !== "undefined")) {
webglFi = new webglFilter();
try {
webglFi.init(weights, biases, numPatches, searchWindow+patchSize-1, searchWindow+patchSize-1, patchSize, patchSize);
if ('lbp' in weights) lbpInit = true;
if ('sobel' in weights) sobelInit = true;
}
catch(err) {
alert("There was a problem setting up webGL programs, falling back to slightly slower javascript version. :(");
webglFi = undefined;
svmFi = new svmFilter();
svmFi.init(weights['raw'], biases['raw'], numPatches, patchSize, searchWindow);
}
} else if (typeof(svmFilter) !== "undefined") {
// use fft convolution if no webGL is available
svmFi = new svmFilter();
svmFi.init(weights['raw'], biases['raw'], numPatches, patchSize, searchWindow);
} else {
throw "Could not initiate filters, please make sure that svmfilter.js or svmfilter_conv_js.js is loaded."
}
} else if (patchType == "MOSSE") {
mosseCalc = new mosseFilterResponses();
mosseCalc.init(weights, numPatches, patchSize, patchSize);
}
if (patchType == "SVM") {
pw = pl = patchSize+searchWindow-1;
} else {
pw = pl = searchWindow;
}
pdataLength = pw*pl;
halfSearchWindow = (searchWindow-1)/2;
responsePixels = searchWindow*searchWindow;
if(typeof Float64Array !== 'undefined') {
vecProbs = new Float64Array(responsePixels);
for (var i = 0;i < numPatches;i++) {
patches[i] = new Float64Array(pdataLength);
}
} else {
vecProbs = new Array(responsePixels);
for (var i = 0;i < numPatches;i++) {
patches[i] = new Array(pdataLength);
}
}
for (var i = 0;i < numPatches;i++) {
learningRate[i] = 1.0;
prevCostFunc[i] = 0.0;
}
if (params.weightPoints) {
// weighting of points
pointWeights = [];
for (var i = 0;i < numPatches;i++) {
if (i in params.weightPoints) {
pointWeights[(i*2)] = params.weightPoints[i];
pointWeights[(i*2)+1] = params.weightPoints[i];
} else {
pointWeights[(i*2)] = 1;
pointWeights[(i*2)+1] = 1;
}
}
pointWeights = numeric.diag(pointWeights);
}
}
/*
* starts the tracker to run on a regular interval
*/
this.start = function(element, box) {
// check if model is initalized, else return false
if (typeof(model) === "undefined") {
console.log("tracker needs to be initalized before starting to track.");
return false;
}
//check if a runnerelement already exists, if not, use passed parameters
if (typeof(runnerElement) === "undefined") {
runnerElement = element;
runnerBox = box;
}
// start named timeout function
runnerTimeout = requestAnimFrame(runnerFunction);
}
/*
* stop the running tracker
*/
this.stop = function() {
// stop the running tracker if any exists
cancelRequestAnimFrame(runnerTimeout);
}
/*
* element : canvas or video element
* TODO: should be able to take img element as well
*/
this.track = function(element, box) {
var scaling, translateX, translateY, rotation;
var croppedPatches = [];
var ptch, px, py;
if (first) {
// do viola-jones on canvas to get initial guess, if we don't have any points
var gi = getInitialPosition(element, box);
if (!gi) {
// send an event on no face found
var evt = document.createEvent("Event");
evt.initEvent("clmtrackrNotFound", true, true);
document.dispatchEvent(evt)
return false;
}
scaling = gi[0];
rotation = gi[1];
translateX = gi[2];
translateY = gi[3];
first = false;
} else {
facecheck_count += 1;
if (params.constantVelocity) {
// calculate where to get patches via constant velocity prediction
if (previousParameters.length >= 2) {
for (var i = 0;i < currentParameters.length;i++) {
currentParameters[i] = (relaxation)*previousParameters[1][i] + (1-relaxation)*((2*previousParameters[1][i]) - previousParameters[0][i]);
//currentParameters[i] = (3*previousParameters[2][i]) - (3*previousParameters[1][i]) + previousParameters[0][i];
}
}
}
// change translation, rotation and scale parameters
rotation = halfPI - Math.atan((currentParameters[0]+1)/currentParameters[1]);
if (rotation > halfPI) {
rotation -= Math.PI;
}
scaling = currentParameters[1] / Math.sin(rotation);
translateX = currentParameters[2];
translateY = currentParameters[3];
}
// copy canvas to a new dirty canvas
sketchCC.save();
// clear canvas
sketchCC.clearRect(0, 0, sketchW, sketchH);
sketchCC.scale(1/scaling, 1/scaling);
sketchCC.rotate(-rotation);
sketchCC.translate(-translateX, -translateY);
sketchCC.drawImage(element, 0, 0, element.width, element.height);
sketchCC.restore();
// get cropped images around new points based on model parameters (not scaled and translated)
var patchPositions = calculatePositions(currentParameters, false);
// check whether tracking is ok
if (scoringWeights && (facecheck_count % 10 == 0)) {
if (!checkTracking()) {
// reset all parameters
first = true;
scoringHistory = [];
for (var i = 0;i < currentParameters.length;i++) {
currentParameters[i] = 0;
previousParameters = [];
}
// send event to signal that tracking was lost
var evt = document.createEvent("Event");
evt.initEvent("clmtrackrLost", true, true);
document.dispatchEvent(evt)
return false;
}
}
var pdata, pmatrix, grayscaleColor;
for (var i = 0; i < numPatches; i++) {
px = patchPositions[i][0]-(pw/2);
py = patchPositions[i][1]-(pl/2);
ptch = sketchCC.getImageData(Math.round(px), Math.round(py), pw, pl);
pdata = ptch.data;
// convert to grayscale
pmatrix = patches[i];
for (var j = 0;j < pdataLength;j++) {
grayscaleColor = pdata[j*4]*0.3 + pdata[(j*4)+1]*0.59 + pdata[(j*4)+2]*0.11;
pmatrix[j] = grayscaleColor;
}
}
/*print weights*/
/*sketchCC.clearRect(0, 0, sketchW, sketchH);
var nuWeights;
for (var i = 0;i < numPatches;i++) {
nuWeights = weights[i].map(function(x) {return x*2000+127;});
drawData(sketchCC, nuWeights, patchSize, patchSize, false, patchPositions[i][0]-(patchSize/2), patchPositions[i][1]-(patchSize/2));
}*/
// print patches
/*sketchCC.clearRect(0, 0, sketchW, sketchH);
for (var i = 0;i < numPatches;i++) {
if ([27,32,44,50].indexOf(i) > -1) {
drawData(sketchCC, patches[i], pw, pl, false, patchPositions[i][0]-(pw/2), patchPositions[i][1]-(pl/2));
}
}*/
if (patchType == "SVM") {
if (typeof(webglFi) !== "undefined") {
responses = getWebGLResponses(patches);
} else if (typeof(svmFi) !== "undefined"){
responses = svmFi.getResponses(patches);
} else {
throw "SVM-filters do not seem to be initiated properly."
}
} else if (patchType == "MOSSE") {
responses = mosseCalc.getResponses(patches);
}
// option to increase sharpness of responses
if (params.sharpenResponse) {
for (var i = 0;i < numPatches;i++) {
for (var j = 0;j < responses[i].length;j++) {
responses[i][j] = Math.pow(responses[i][j], params.sharpenResponse);
}
}
}
// print responses
/*sketchCC.clearRect(0, 0, sketchW, sketchH);
var nuWeights;
for (var i = 0;i < numPatches;i++) {
nuWeights = [];
for (var j = 0;j < responses[i].length;j++) {
nuWeights.push(responses[i][j]*255);
}
//if ([27,32,44,50].indexOf(i) > -1) {
// drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[i][0]-((searchWindow-1)/2), patchPositions[i][1]-((searchWindow-1)/2));
//}
drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[i][0]-((searchWindow-1)/2), patchPositions[i][1]-((searchWindow-1)/2));
}*/
// iterate until convergence or max 10, 20 iterations?:
var originalPositions = currentPositions;
var jac;
var meanshiftVectors = [];
for (var i = 0; i < varianceSeq.length; i++) {
// calculate jacobian
jac = createJacobian(currentParameters, eigenVectors);
// for debugging
//var debugMVs = [];
//
var opj0, opj1;
for (var j = 0;j < numPatches;j++) {
opj0 = originalPositions[j][0]-((searchWindow-1)*scaling/2);
opj1 = originalPositions[j][1]-((searchWindow-1)*scaling/2);
// calculate PI x gaussians
var vpsum = gpopt(searchWindow, currentPositions[j], updatePosition, vecProbs, responses, opj0, opj1, j, varianceSeq[i], scaling);
// calculate meanshift-vector
gpopt2(searchWindow, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1, scaling);
// for debugging
//var debugMatrixMV = gpopt2(searchWindow, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1);
// evaluate here whether to increase/decrease stepSize
/*if (vpsum >= prevCostFunc[j]) {
learningRate[j] *= stepParameter;
} else {
learningRate[j] = 1.0;
}
prevCostFunc[j] = vpsum;*/
// compute mean shift vectors
// extrapolate meanshiftvectors
/*var msv = [];
msv[0] = learningRate[j]*(vecpos[0] - currentPositions[j][0]);
msv[1] = learningRate[j]*(vecpos[1] - currentPositions[j][1]);
meanshiftVectors[j] = msv;*/
meanshiftVectors[j] = [vecpos[0] - currentPositions[j][0], vecpos[1] - currentPositions[j][1]];
//if (isNaN(msv[0]) || isNaN(msv[1])) debugger;
//for debugging
//debugMVs[j] = debugMatrixMV;
//
}
// draw meanshiftVector
/*sketchCC.clearRect(0, 0, sketchW, sketchH);
var nuWeights;
for (var npidx = 0;npidx < numPatches;npidx++) {
nuWeights = debugMVs[npidx].map(function(x) {return x*255*500;});
drawData(sketchCC, nuWeights, searchWindow, searchWindow, false, patchPositions[npidx][0]-((searchWindow-1)/2), patchPositions[npidx][1]-((searchWindow-1)/2));
}*/
var meanShiftVector = numeric.rep([numPatches*2, 1],0.0);
for (var k = 0;k < numPatches;k++) {
meanShiftVector[k*2][0] = meanshiftVectors[k][0];
meanShiftVector[(k*2)+1][0] = meanshiftVectors[k][1];
}
// compute pdm parameter update
//var prior = numeric.mul(gaussianPD, PDMVariance);
var prior = numeric.mul(gaussianPD, varianceSeq[i]);
if (params.weightPoints) {
var jtj = numeric.dot(numeric.transpose(jac), numeric.dot(pointWeights, jac));
} else {
var jtj = numeric.dot(numeric.transpose(jac), jac);
}
var cpMatrix = numeric.rep([numParameters+4, 1],0.0);
for (var l = 0;l < (numParameters+4);l++) {
cpMatrix[l][0] = currentParameters[l];
}
var priorP = numeric.dot(prior, cpMatrix);
if (params.weightPoints) {
var jtv = numeric.dot(numeric.transpose(jac), numeric.dot(pointWeights, meanShiftVector));
} else {
var jtv = numeric.dot(numeric.transpose(jac), meanShiftVector);
}
var paramUpdateLeft = numeric.add(prior, jtj);
var paramUpdateRight = numeric.sub(priorP, jtv);
var paramUpdate = numeric.dot(numeric.inv(paramUpdateLeft), paramUpdateRight);
//var paramUpdate = numeric.solve(paramUpdateLeft, paramUpdateRight, true);
var oldPositions = currentPositions;
// update estimated parameters
for (var k = 0;k < numParameters+4;k++) {
currentParameters[k] -= paramUpdate[k];
}
// clipping of parameters if they're too high
var clip;
for (var k = 0;k < numParameters;k++) {
clip = Math.abs(3*Math.sqrt(eigenValues[k]));
if (Math.abs(currentParameters[k+4]) > clip) {
if (currentParameters[k+4] > 0) {
currentParameters[k+4] = clip;
} else {
currentParameters[k+4] = -clip;
}
}
}
// update current coordinates
currentPositions = calculatePositions(currentParameters, true);
// check if converged
// calculate norm of parameterdifference
var positionNorm = 0;
var pnsq_x, pnsq_y;
for (var k = 0;k < currentPositions.length;k++) {
pnsq_x = (currentPositions[k][0]-oldPositions[k][0]);
pnsq_y = (currentPositions[k][1]-oldPositions[k][1]);
positionNorm += ((pnsq_x*pnsq_x) + (pnsq_y*pnsq_y));
}
//console.log("positionnorm:"+positionNorm);
// if norm < limit, then break
if (positionNorm < convergenceLimit) {
break;
}
}
if (params.constantVelocity) {
// add current parameter to array of previous parameters
previousParameters.push(currentParameters.slice());
previousParameters.splice(0, previousParameters.length == 3 ? 1 : 0);
}
// store positions, for checking convergence
previousPositions.splice(0, previousPositions.length == 10 ? 1 : 0);
previousPositions.push(currentPositions.slice(0));
// send an event on each iteration
var evt = document.createEvent("Event");
evt.initEvent("clmtrackrIteration", true, true);
document.dispatchEvent(evt)
if (this.getConvergence() < 0.5) {
// we must get a score before we can say we've converged
if (scoringHistory.length >= 5) {
if (params.stopOnConvergence) {
this.stop();
}
var evt = document.createEvent("Event");
evt.initEvent("clmtrackrConverged", true, true);
document.dispatchEvent(evt)
}
}
// return new points
return currentPositions;
}
/*
* reset tracking, so that track() will start a new detection
*/
this.reset = function() {
first = true;
scoringHistory = [];
for (var i = 0;i < currentParameters.length;i++) {
currentParameters[i] = 0;
previousParameters = [];
}
runnerElement = undefined;
runnerBox = undefined;
}
/*
* draw model on given canvas
*/
this.draw = function(canvas, pv, path) {
// if no previous points, just draw in the middle of canvas
var params;
if (pv === undefined) {
params = currentParameters.slice(0);
} else {
params = pv.slice(0);
}
var cc = canvas.getContext('2d');
cc.fillStyle = "rgb(200,200,200)";
cc.strokeStyle = "rgb(130,255,50)";
//cc.lineWidth = 1;
var paths;
if (path === undefined) {
paths = model.path.normal;
} else {
paths = model.path[path];
}
for (var i = 0;i < paths.length;i++) {
if (typeof(paths[i]) == 'number') {
drawPoint(cc, paths[i], params);
} else {
drawPath(cc, paths[i], params);
}
}
}
/*
* get the score of the current model fit
* (based on svm of face according to current model)
*/
this.getScore = function() {
return meanscore;
}
/*
* calculate positions based on parameters
*/
this.calculatePositions = function(parameters) {
return calculatePositions(parameters, true);
}
/*
* get coordinates of current model fit
*/
this.getCurrentPosition = function() {
if (first) {
return false;
} else {
return currentPositions;
}
}
/*
* get parameters of current model fit
*/
this.getCurrentParameters = function() {
return currentParameters;
}
/*
* Get the average of recent model movements
* Used for checking whether model fit has converged
*/
this.getConvergence = function() {
if (previousPositions.length < 10) return 999999;
var prevX = 0.0;
var prevY = 0.0;
var currX = 0.0;
var currY = 0.0;
// average 5 previous positions
for (var i = 0;i < 5;i++) {
for (var j = 0;j < numPatches;j++) {
prevX += previousPositions[i][j][0];
prevY += previousPositions[i][j][1];
}
}
prevX /= 5;
prevY /= 5;
// average 5 positions before that
for (var i = 5;i < 10;i++) {
for (var j = 0;j < numPatches;j++) {
currX += previousPositions[i][j][0];
currY += previousPositions[i][j][1];
}
}
currX /= 5;
currY /= 5;
// calculate difference
var diffX = currX-prevX;
var diffY = currY-prevY;
var msavg = ((diffX*diffX) + (diffY*diffY));
msavg /= previousPositions.length
return msavg;
}
/*
* Set response mode (only useful if webGL is available)
* mode : either "single", "blend" or "cycle"
* list : array of values "raw", "sobel", "lbp"
*/
this.setResponseMode = function(mode, list) {
// clmtrackr must be initialized with model first
if (typeof(model) === "undefined") {
console.log("Clmtrackr has not been initialized with a model yet. No changes made.");
return;
}
// must check whether webGL or not
if (typeof(webglFi) === "undefined") {
console.log("Responsemodes are only allowed when using webGL. In pure JS, only 'raw' mode is available.");
return;
}
if (['single', 'blend', 'cycle'].indexOf(mode) < 0) {
console.log("Tried to set an unknown responsemode : '"+mode+"'. No changes made.");
return;
}
if (!(list instanceof Array)) {
console.log("List in setResponseMode must be an array of strings! No changes made.");
return;
} else {
for (var i = 0;i < list.length;i++) {
if (['raw', 'sobel', 'lbp'].indexOf(list[i]) < 0) {
console.log("Unknown element in responsemode list : '"+list[i]+"'. No changes made.");
}
// check whether filters are initialized
if (list[i] == 'sobel' && sobelInit == false) {
console.log("The sobel filters have not been initialized! No changes made.");
}
if (list[i] == 'lbp' && lbpInit == false) {
console.log("The LBP filters have not been initialized! No changes made.");
}
}
}
// reset index
responseIndex = 0;
responseMode = mode;
responseList = list;
}
var runnerFunction = function() {
runnerTimeout = requestAnimFrame(runnerFunction);
// schedule as many iterations as we can during each request
var startTime = (new Date()).getTime();
while (((new Date()).getTime() - startTime) < 16) {
var tracking = this.track(runnerElement, runnerBox);
if (!tracking) continue;
}
}.bind(this);
var getWebGLResponsesType = function(type, patches) {
if (type == 'lbp') {
return webglFi.getLBPResponses(patches);
} else if (type == 'raw') {
return webglFi.getRawResponses(patches);
} else if (type == 'sobel') {
return webglFi.getSobelResponses(patches);
}
}
var getWebGLResponses = function(patches) {
if (responseMode == 'single') {
return getWebGLResponsesType(responseList[0], patches);
} else if (responseMode == 'cycle') {
var response = getWebGLResponsesType(responseList[responseIndex], patches);
responseIndex++;
if (responseIndex >= responseList.length) responseIndex = 0;
return response;
} else {
// blend
var responses = [];
for (var i = 0;i < responseList.length;i++) {
responses[i] = getWebGLResponsesType(responseList[i], patches);
}
var blendedResponses = [];
for (var i = 0;i < numPatches;i++) {
var response = Array(searchWindow*searchWindow);
for (var k = 0;k < searchWindow*searchWindow;k++) response[k] = 0;
for (var j = 0;j < responseList.length;j++) {
for (var k = 0;k < searchWindow*searchWindow;k++) {
response[k] += (responses[j][i][k]/responseList.length);
}
}
blendedResponses[i] = response;
}
return blendedResponses;
}
}
// generates the jacobian matrix used for optimization calculations
var createJacobian = function(parameters, eigenVectors) {
var jacobian = numeric.rep([2*numPatches, numParameters+4],0.0);
var j0,j1;
for (var i = 0;i < numPatches;i ++) {
// 1
j0 = meanShape[i][0];
j1 = meanShape[i][1];
for (var p = 0;p < numParameters;p++) {
j0 += parameters[p+4]*eigenVectors[i*2][p];
j1 += parameters[p+4]*eigenVectors[(i*2)+1][p];
}
jacobian[i*2][0] = j0;
jacobian[(i*2)+1][0] = j1;
// 2
j0 = meanShape[i][1];
j1 = meanShape[i][0];
for (var p = 0;p < numParameters;p++) {
j0 += parameters[p+4]*eigenVectors[(i*2)+1][p];
j1 += parameters[p+4]*eigenVectors[i*2][p];
}
jacobian[i*2][1] = -j0;
jacobian[(i*2)+1][1] = j1;
// 3
jacobian[i*2][2] = 1;
jacobian[(i*2)+1][2] = 0;
// 4
jacobian[i*2][3] = 0;
jacobian[(i*2)+1][3] = 1;
// the rest
for (var j = 0;j < numParameters;j++) {
j0 = parameters[0]*eigenVectors[i*2][j] - parameters[1]*eigenVectors[(i*2)+1][j] + eigenVectors[i*2][j];
j1 = parameters[0]*eigenVectors[(i*2)+1][j] + parameters[1]*eigenVectors[i*2][j] + eigenVectors[(i*2)+1][j];
jacobian[i*2][j+4] = j0;
jacobian[(i*2)+1][j+4] = j1;
}
}
return jacobian;
}
// calculate positions from parameters
var calculatePositions = function(parameters, useTransforms) {
var x, y, a, b;
var numParameters = parameters.length;
var positions = [];
for (var i = 0;i < numPatches;i++) {
x = meanShape[i][0];
y = meanShape[i][1];
for (var j = 0;j < numParameters-4;j++) {
x += model.shapeModel.eigenVectors[(i*2)][j]*parameters[j+4];
y += model.shapeModel.eigenVectors[(i*2)+1][j]*parameters[j+4];
}
if (useTransforms) {
a = parameters[0]*x - parameters[1]*y + parameters[2];
b = parameters[0]*y + parameters[1]*x + parameters[3];
x += a;
y += b;
}
positions[i] = [x,y];
}
return positions;
}
// detect position of face on canvas/video element
var detectPosition = function(el) {
var canvas = document.createElement('canvas');
canvas.width = el.width;
canvas.height = el.height;
var cc = canvas.getContext('2d');
cc.drawImage(el, 0, 0, el.width, el.height);
// do viola-jones on canvas to get initial guess, if we don't have any points
/*var comp = ccv.detect_objects(
ccv.grayscale(canvas), ccv.cascade, 5, 1
);*/
var jf = new jsfeat_face(canvas);
var comp = jf.findFace();
if (comp.length > 0) {
candidate = comp[0];
} else {
return false;
}
for (var i = 1; i < comp.length; i++) {
if (comp[i].confidence > candidate.confidence) {
candidate = comp[i];
}
}
return candidate;
}
// part one of meanshift calculation
var gpopt = function(responseWidth, currentPositionsj, updatePosition, vecProbs, responses, opj0, opj1, j, variance, scaling) {
var pos_idx = 0;
var vpsum = 0;
var dx, dy;
for (var k = 0;k < responseWidth;k++) {
updatePosition[1] = opj1+(k*scaling);
for (var l = 0;l < responseWidth;l++) {
updatePosition[0] = opj0+(l*scaling);
dx = currentPositionsj[0] - updatePosition[0];
dy = currentPositionsj[1] - updatePosition[1];
vecProbs[pos_idx] = responses[j][pos_idx] * Math.exp(-0.5*((dx*dx)+(dy*dy))/(variance*scaling));
vpsum += vecProbs[pos_idx];
pos_idx++;
}
}
return vpsum;
}
// part two of meanshift calculation
var gpopt2 = function(responseWidth, vecpos, updatePosition, vecProbs, vpsum, opj0, opj1, scaling) {
//for debugging
//var vecmatrix = [];
var pos_idx = 0;
var vecsum = 0;
vecpos[0] = 0;
vecpos[1] = 0;
for (var k = 0;k < responseWidth;k++) {
updatePosition[1] = opj1+(k*scaling);
for (var l = 0;l < responseWidth;l++) {
updatePosition[0] = opj0+(l*scaling);
vecsum = vecProbs[pos_idx]/vpsum;
//for debugging
//vecmatrix[k*responseWidth + l] = vecsum;
vecpos[0] += vecsum*updatePosition[0];
vecpos[1] += vecsum*updatePosition[1];
pos_idx++;
}
}
// for debugging
//return vecmatrix;
}
// calculate score of current fit
var checkTracking = function() {
scoringContext.drawImage(sketchCanvas, Math.round(msxmin+(msmodelwidth/4.5)), Math.round(msymin-(msmodelheight/12)), Math.round(msmodelwidth-(msmodelwidth*2/4.5)), Math.round(msmodelheight-(msmodelheight/12)), 0, 0, 20, 22);
// getImageData of canvas
var imgData = scoringContext.getImageData(0,0,20,22);
// convert data to grayscale
var scoringData = new Array(20*22);
var scdata = imgData.data;
var scmax = 0;
for (var i = 0;i < 20*22;i++) {
scoringData[i] = scdata[i*4]*0.3 + scdata[(i*4)+1]*0.59 + scdata[(i*4)+2]*0.11;
scoringData[i] = Math.log(scoringData[i]+1);
if (scoringData[i] > scmax) scmax = scoringData[i];
}
if (scmax > 0) {
// normalize & multiply by svmFilter
var mean = 0;
for (var i = 0;i < 20*22;i++) {
mean += scoringData[i];
}
mean /= (20*22);
var sd = 0;
for (var i = 0;i < 20*22;i++) {
sd += (scoringData[i]-mean)*(scoringData[i]-mean);
}
sd /= (20*22 - 1)
sd = Math.sqrt(sd);
var score = 0;
for (var i = 0;i < 20*22;i++) {
scoringData[i] = (scoringData[i]-mean)/sd;
score += (scoringData[i])*scoringWeights[i];
}
score += scoringBias;
score = 1/(1+Math.exp(-score));
scoringHistory.splice(0, scoringHistory.length == 5 ? 1 : 0);
scoringHistory.push(score);
if (scoringHistory.length > 4) {
// get average
meanscore = 0;
for (var i = 0;i < 5;i++) {
meanscore += scoringHistory[i];
}
meanscore /= 5;
// if below threshold, then reset (return false)
if (meanscore < params.scoreThreshold) return false;
}
}
return true;
}
// get initial starting point for model
var getInitialPosition = function(element, box) {
var translateX, translateY, scaling, rotation;
if (box) {
candidate = {x : box[0], y : box[1], width : box[2], height : box[3]};
} else {
var det = detectPosition(element);
if (!det) {
// if no face found, stop.
return false;
}
}
if (model.hints && mosseFilter && left_eye_filter && right_eye_filter && nose_filter) {
var noseFilterWidth = candidate.width * 4.5/10;
var eyeFilterWidth = candidate.width * 6/10;
// detect position of eyes and nose via mosse filter
//
/*element.pause();
var canvasContext = document.getElementById('overlay2').getContext('2d')
canvasContext.clearRect(0,0,500,375);
canvasContext.strokeRect(candidate.x, candidate.y, candidate.width, candidate.height);*/
//
var nose_result = mossef_nose.track(element, Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth, false);
var right_result = mossef_righteye.track(element, Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth, false);
var left_result = mossef_lefteye.track(element, Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth, false);
right_eye_position[0] = Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2))+right_result[0];
right_eye_position[1] = Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2))+right_result[1];
left_eye_position[0] = Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2))+left_result[0];
left_eye_position[1] = Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2))+left_result[1];
nose_position[0] = Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2))+nose_result[0];
nose_position[1] = Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2))+nose_result[1];
//
/*canvasContext.strokeRect(Math.round(candidate.x+(candidate.width*3/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth);
canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/4)-(eyeFilterWidth/2)), Math.round(candidate.y+candidate.height*(2/5)-(eyeFilterWidth/2)), eyeFilterWidth, eyeFilterWidth);
//canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(3/4)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth);
canvasContext.strokeRect(Math.round(candidate.x+(candidate.width/2)-(noseFilterWidth/2)), Math.round(candidate.y+candidate.height*(5/8)-(noseFilterWidth/2)), noseFilterWidth, noseFilterWidth);
canvasContext.fillStyle = "rgb(0,0,250)";
canvasContext.beginPath();
canvasContext.arc(left_eye_position[0], left_eye_position[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
canvasContext.beginPath();
canvasContext.arc(right_eye_position[0], right_eye_position[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
canvasContext.beginPath();
canvasContext.arc(nose_position[0], nose_position[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
debugger;
element.play()
canvasContext.clearRect(0,0,element.width,element.height);*/
//
// get eye and nose positions of model
var lep = model.hints.leftEye;
var rep = model.hints.rightEye;
var mep = model.hints.nose;
// get scaling, rotation, etc. via procrustes analysis
var procrustes_params = procrustes([left_eye_position, right_eye_position, nose_position], [lep, rep, mep]);
translateX = procrustes_params[0];
translateY = procrustes_params[1];
scaling = procrustes_params[2];
rotation = procrustes_params[3];
//element.play();
//var maxscale = 1.10;
//if ((scaling*modelHeight)/candidate.height < maxscale*0.7) scaling = (maxscale*0.7*candidate.height)/modelHeight;
//if ((scaling*modelHeight)/candidate.height > maxscale*1.2) scaling = (maxscale*1.2*candidate.height)/modelHeight;
/*var smean = [0,0];
smean[0] += lep[0];
smean[1] += lep[1];
smean[0] += rep[0];
smean[1] += rep[1];
smean[0] += mep[0];
smean[1] += mep[1];
smean[0] /= 3;
smean[1] /= 3;
var nulep = [(lep[0]*scaling*Math.cos(-rotation)+lep[1]*scaling*Math.sin(-rotation))+translateX, (lep[0]*scaling*(-Math.sin(-rotation)) + lep[1]*scaling*Math.cos(-rotation))+translateY];
var nurep = [(rep[0]*scaling*Math.cos(-rotation)+rep[1]*scaling*Math.sin(-rotation))+translateX, (rep[0]*scaling*(-Math.sin(-rotation)) + rep[1]*scaling*Math.cos(-rotation))+translateY];
var numep = [(mep[0]*scaling*Math.cos(-rotation)+mep[1]*scaling*Math.sin(-rotation))+translateX, (mep[0]*scaling*(-Math.sin(-rotation)) + mep[1]*scaling*Math.cos(-rotation))+translateY];
canvasContext.fillStyle = "rgb(200,10,100)";
canvasContext.beginPath();
canvasContext.arc(nulep[0], nulep[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
canvasContext.beginPath();
canvasContext.arc(nurep[0], nurep[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
canvasContext.beginPath();
canvasContext.arc(numep[0], numep[1], 3, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();*/
currentParameters[0] = (scaling*Math.cos(rotation))-1;
currentParameters[1] = (scaling*Math.sin(rotation));
currentParameters[2] = translateX;
currentParameters[3] = translateY;
//this.draw(document.getElementById('overlay'), currentParameters);
} else {
scaling = candidate.width/modelheight;
//var ccc = document.getElementById('overlay').getContext('2d');
//ccc.strokeRect(candidate.x,candidate.y,candidate.width,candidate.height);
translateX = candidate.x-(xmin*scaling)+0.1*candidate.width;
translateY = candidate.y-(ymin*scaling)+0.25*candidate.height;
currentParameters[0] = scaling-1;
currentParameters[2] = translateX;
currentParameters[3] = translateY;
}
currentPositions = calculatePositions(currentParameters, true);
return [scaling, rotation, translateX, translateY];
}
// draw a parametrized line on a canvas
var drawPath = function(canvasContext, path, dp) {
canvasContext.beginPath();
var i, x, y, a, b;
for (var p = 0;p < path.length;p++) {
i = path[p]*2;
x = meanShape[i/2][0];
y = meanShape[i/2][1];
for (var j = 0;j < numParameters;j++) {
x += model.shapeModel.eigenVectors[i][j]*dp[j+4];
y += model.shapeModel.eigenVectors[i+1][j]*dp[j+4];
}
a = dp[0]*x - dp[1]*y + dp[2];
b = dp[0]*y + dp[1]*x + dp[3];
x += a;
y += b;
if (i == 0) {
canvasContext.moveTo(x,y);
} else {
canvasContext.lineTo(x,y);
}
}
canvasContext.moveTo(0,0);
canvasContext.closePath();
canvasContext.stroke();
}
// draw a point on a canvas
function drawPoint(canvasContext, point, dp) {
var i, x, y, a, b;
i = point*2;
x = meanShape[i/2][0];
y = meanShape[i/2][1];
for (var j = 0;j < numParameters;j++) {
x += model.shapeModel.eigenVectors[i][j]*dp[j+4];
y += model.shapeModel.eigenVectors[i+1][j]*dp[j+4];
}
a = dp[0]*x - dp[1]*y + dp[2];
b = dp[0]*y + dp[1]*x + dp[3];
x += a;
y += b;
canvasContext.beginPath();
canvasContext.arc(x, y, 1, 0, Math.PI*2, true);
canvasContext.closePath();
canvasContext.fill();
}
// procrustes analysis
function procrustes(template, shape) {
// assume template and shape is a vector of x,y-coordinates
//i.e. template = [[x1,y1], [x2,y2], [x3,y3]];
var templateClone = [];
var shapeClone = [];
for (var i = 0;i < template.length;i++) {
templateClone[i] = [template[i][0], template[i][1]];
}
for (var i = 0;i < shape.length;i++) {
shapeClone[i] = [shape[i][0], shape[i][1]];
}
shape = shapeClone;
template = templateClone;
// calculate translation
var templateMean = [0.0, 0.0];
for (var i = 0;i < template.length;i++) {
templateMean[0] += template[i][0];
templateMean[1] += template[i][1];
}
templateMean[0] /= template.length;
templateMean[1] /= template.length;
var shapeMean = [0.0, 0.0];
for (var i = 0;i < shape.length;i++) {
shapeMean[0] += shape[i][0];
shapeMean[1] += shape[i][1];
}
shapeMean[0] /= shape.length;
shapeMean[1] /= shape.length;
var translationX = templateMean[0] - shapeMean[0];
var translationY = templateMean[1] - shapeMean[1];
// centralize
for (var i = 0;i < shape.length;i++) {
shape[i][0] -= shapeMean[0];
shape[i][1] -= shapeMean[1];
}
for (var i = 0;i < template.length;i++) {
template[i][0] -= templateMean[0];
template[i][1] -= templateMean[1];
}
// scaling
var scaleS = 0.0;
for (var i = 0;i < shape.length;i++) {
scaleS += ((shape[i][0])*(shape[i][0]));
scaleS += ((shape[i][1])*(shape[i][1]));
}
scaleS = Math.sqrt(scaleS/shape.length);
var scaleT = 0.0;
for (var i = 0;i < template.length;i++) {
scaleT += ((template[i][0])*(template[i][0]));
scaleT += ((template[i][1])*(template[i][1]));
}
scaleT = Math.sqrt(scaleT/template.length);
var scaling = scaleT/scaleS;
for (var i = 0;i < shape.length;i++) {
shape[i][0] *= scaling;
shape[i][1] *= scaling;
}
// rotation
var top = 0.0;
var bottom = 0.0;
for (var i = 0;i < shape.length;i++) {
top += (shape[i][0]*template[i][1] - shape[i][1]*template[i][0]);
bottom += (shape[i][0]*template[i][0] + shape[i][1]*template[i][1]);
}
var rotation = Math.atan(top/bottom);
translationX += (shapeMean[0]-(scaling*Math.cos(-rotation)*shapeMean[0])-(scaling*shapeMean[1]*Math.sin(-rotation)));
translationY += (shapeMean[1]+(scaling*Math.sin(-rotation)*shapeMean[0])-(scaling*shapeMean[1]*Math.cos(-rotation)));
//returns rotation, scaling, transformx and transformx
return [translationX, translationY, scaling, rotation];
}
// function to draw pixeldata on some canvas, only used for debugging
var drawData = function(canvasContext, data, width, height, transposed, drawX, drawY) {
var psci = canvasContext.createImageData(width, height);
var pscidata = psci.data;
for (var j = 0;j < width*height;j++) {
if (!transposed) {
var val = data[(j%width)+((j/width) >> 0)*width];
} else {
var val = data[(j%height)*height+((j/height) >> 0)];
}
val = val > 255 ? 255 : val;
val = val < 0 ? 0 : val;
pscidata[j*4] = val;
pscidata[(j*4)+1] = val;
pscidata[(j*4)+2] = val;
pscidata[(j*4)+3] = 255;
}
canvasContext.putImageData(psci, drawX, drawY);
}
var requestAnimFrame = (function() {
return window.requestAnimationFrame ||
window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame ||
window.oRequestAnimationFrame ||
window.msRequestAnimationFrame ||
function(/* function FrameRequestCallback */ callback, /* DOMElement Element */ element) {
return window.setTimeout(callback, 1000/60);
};
})();
var cancelRequestAnimFrame = (function() {
return window.cancelAnimationFrame ||
window.webkitCancelRequestAnimationFrame ||
window.mozCancelRequestAnimationFrame ||
window.oCancelRequestAnimationFrame ||
window.msCancelRequestAnimationFrame ||
window.clearTimeout;
})();
return true;
}
}
"use strict";
var webglFilter = function() {
/*
* Textures:
* 0 : raw filter
* 1 : patches
* 2 : finished response
* 3 : grad/lbp treated patches
* 4 : sobel filter
* 5 : lbp filter
*
* Routing:
* ( ) 0/4/5 --
* ( ) _|
* 1 ----> ( ---------->3 ) ----------> 2
* lbpResponse/ patchResponse
* gradientResponse
*/
var gl, canvas;
var filterWidth, filterHeight, patchWidth, patchHeight, numPatches, canvasWidth, canvasHeight;
var patchResponseProgram, patchDrawProgram;
var fbo, numBlocks, patchTex;
var drawRectBuffer, drawLayerBuffer, drawImageBuffer, rttTexture;
var texCoordBuffer, texCoordLocation, apositionBuffer;
var newCanvasWidth, newCanvasBlockHeight, newCanvasHeight;
var drawOutRectangles, drawOutImages, drawOutLayer;
var patchCells, textureWidth, textureHeight, patchSize, patchArray;
var biases;
var lbpResponseProgram;
var lbo, lbpTexCoordLocation, lbpTexCoordBuffer, lbpPositionLocation, lbpAPositionBuffer;
var gradientResponseProgram;
var gbo, gradTexCoordLocation, gradTexCoordBuffer, gradPositionLocation, gradAPositionBuffer;
var lbpInit = false;
var sobelInit = false;
var rawInit = false;
var lbpResponseVS = [
"attribute vec2 a_texCoord;",
"attribute vec2 a_position;",
"",
"varying vec2 v_texCoord;",
"",
"void main() {",
" // transform coordinates to regular coordinates",
" gl_Position = vec4(a_position,0.0,1.0);",
" ",
" // pass the texCoord to the fragment shader",
" v_texCoord = a_texCoord;",
"}"
].join('
');
var lbpResponseFS;
var gradientResponseVS = [
"attribute vec2 a_texCoord;",
"attribute vec2 a_position;",
"",
"varying vec2 v_texCoord;",
"",
"void main() {",
" // transform coordinates to regular coordinates",
" gl_Position = vec4(a_position,0.0,1.0);",
" ",
" // pass the texCoord to the fragment shader",
" v_texCoord = a_texCoord;",
"}"
].join('
');
var gradientResponseFS;
var patchResponseVS;
var patchResponseFS;
var drawResponsesVS = [
"attribute vec2 a_texCoord_draw;",
"attribute vec2 a_position_draw;",
"attribute float a_patchChoice_draw;",
"",
"uniform vec2 u_resolutiondraw;",
"",
"varying vec2 v_texCoord;",
"varying float v_select;",
"",
"void main() {",
" // convert the rectangle from pixels to 0.0 to 1.0",
" vec2 zeroToOne = a_position_draw / u_resolutiondraw;",
"",
" // convert from 0->1 to 0->2",
" vec2 zeroToTwo = zeroToOne * 2.0;",
"",
" // convert from 0->2 to -1->+1 (clipspace)",
" vec2 clipSpace = zeroToTwo - 1.0;",
" ",
" // transform coordinates to regular coordinates",
" gl_Position = vec4(clipSpace * vec2(1.0, 1.0), 0, 1);",
"",
" // pass the texCoord to the fragment shader",
" v_texCoord = a_texCoord_draw;",
" ",
" v_select = a_patchChoice_draw;",
"}"
].join('
');
var drawResponsesFS = [
"precision mediump float;",
"",
"// our responses",
"uniform sampler2D u_responses;",
"",
"// the texCoords passed in from the vertex shader.",
"varying vec2 v_texCoord;",
"varying float v_select;",
"",
"const vec4 bit_shift = vec4(256.0*256.0*256.0, 256.0*256.0, 256.0, 1.0);",
"const vec4 bit_mask = vec4(0.0, 1.0/256.0, 1.0/256.0, 1.0/256.0);",
"",
"// packing code from here http://stackoverflow.com/questions/9882716/packing-float-into-vec4-how-does-this-code-work",
"void main() {",
" vec4 colorSum = texture2D(u_responses, v_texCoord);",
" float value = 0.0;",
" if (v_select < 0.1) {",
" value = colorSum[0];",
" } else if (v_select > 0.9 && v_select < 1.1) {",
" value = colorSum[1];",
" } else if (v_select > 1.9 && v_select < 2.1) {",
" value = colorSum[2];",
" } else if (v_select > 2.9 && v_select < 3.1) {",
" value = colorSum[3];",
" } else {",
" value = 1.0;",
" }",
" ",
" vec4 res = fract(value * bit_shift);",
" res -= res.xxyz * bit_mask;",
" ",
" //gl_FragColor = vec4(value, value, value, value);",
" //gl_FragColor = vec4(1.0, value, 1.0, 1.0);",
" gl_FragColor = res;",
"}"
].join('
');
this.init = function(filters, bias, nP, pW, pH, fW, fH) {
// we assume filterVector goes from left to right, rowwise, i.e. row-major order
if (fW != fH) {
alert("filter width and height must be same size!");
return;
}
// if filter width is not odd, alert
if (fW % 2 == 0 || fH % 2 == 0) {
alert("filters used in svm must be of odd dimensions!");
return;
}
// setup variables
biases = bias;
filterWidth = fW;
filterHeight = fH;
patchWidth = pW;
patchHeight = pH;
numPatches = nP;
numBlocks = Math.floor(numPatches / 4) + Math.ceil((numPatches % 4)/4);
canvasWidth = patchWidth;
canvasHeight = patchHeight*numBlocks;
newCanvasWidth = patchWidth-filterWidth+1;
newCanvasBlockHeight = patchHeight-filterWidth+1;
newCanvasHeight = newCanvasBlockHeight*numPatches;
patchCells = (Math.floor(numPatches / 4) + Math.ceil((numPatches % 4)/4));
textureWidth = patchWidth;
textureHeight = patchHeight*patchCells;
patchSize = patchWidth*patchHeight;
patchArray = new Float32Array(patchSize*patchCells*4);
var opp = [1/patchWidth, 1/(patchHeight*numBlocks)];
// write out shaders
patchResponseFS = [
"precision mediump float;",
"",
"const vec2 u_onePixelPatches = vec2("+(1/patchWidth).toFixed(10)+","+(1/(patchHeight*numBlocks)).toFixed(10)+");",
"const vec2 u_onePixelFilters = vec2("+(1/filterWidth).toFixed(10)+","+(1/(filterHeight*numBlocks)).toFixed(10)+");",
"const float u_halffilterwidth = "+((filterWidth-1.0)/2).toFixed(1)+";",
"const float u_halffilterheight = "+((filterHeight-1.0)/2).toFixed(1)+";",
"",
"// our patches",
"uniform sampler2D u_patches;",
"// our filters",
"uniform sampler2D u_filters;",
"",
"// the texCoords passed in from the vertex shader.",
"varying vec2 v_texCoord;",
"varying vec2 v_texCoordFilters; // this should give us correct filter",
"",
"void main() {",
" vec4 colorSum = vec4(0.0, 0.0, 0.0, 0.0);",
" vec4 maxn = vec4(0.0, 0.0, 0.0, 0.0);",
" vec4 minn = vec4(256.0, 256.0, 256.0, 256.0);",
" vec4 scale = vec4(0.0, 0.0, 0.0, 0.0);",
" vec4 patchValue = vec4(0.0, 0.0, 0.0, 0.0);",
" vec4 filterValue = vec4(0.0, 0.0, 0.0, 0.0);",
" vec4 filterTemp = vec4(0.0, 0.0, 0.0, 0.0);",
" for (int w = 0;w < "+filterWidth+";w++) {",
" for (int h = 0;h < "+filterHeight+";h++) {",
" patchValue = texture2D(u_patches, v_texCoord + u_onePixelPatches * vec2(float(w)-u_halffilterwidth, float(h)-u_halffilterheight));",
" filterValue = texture2D(u_filters, v_texCoordFilters + u_onePixelFilters * vec2(float(w)-u_halffilterwidth, float(h)-u_halffilterheight));",
" maxn = max(patchValue, maxn);",
" minn = min(patchValue, minn);",
" colorSum += patchValue*filterValue;",
" filterTemp += filterValue;",
" } ",
" }",
" scale = maxn-minn;",
" colorSum = (colorSum-(minn*filterTemp))/scale;",
" // logistic transformation",
" colorSum = 1.0/(1.0 + exp(- (colorSum) ));",
" gl_FragColor = colorSum;",
"}"
].join('
');
patchResponseVS = [
"attribute vec2 a_texCoord;",
"attribute vec2 a_position;",
"",
"const vec2 u_resolution = vec2("+canvasWidth.toFixed(1)+","+canvasHeight.toFixed(1)+");",
"const float u_patchHeight = "+(1/numBlocks).toFixed(10)+";",
"const float u_filterHeight = "+(1/numBlocks).toFixed(10)+";",
"const vec2 u_midpoint = vec2(0.5 ,"+(1/(numBlocks*2)).toFixed(10)+");",
"",
"varying vec2 v_texCoord;",
"varying vec2 v_texCoordFilters;",
"",
"void main() {",
" // convert the rectangle from pixels to 0.0 to 1.0",
" vec2 zeroToOne = a_position / u_resolution;",
"",
" // convert from 0->1 to 0->2",
" vec2 zeroToTwo = zeroToOne * 2.0;",
"",
" // convert from 0->2 to -1->+1 (clipspace)",
" vec2 clipSpace = zeroToTwo - 1.0;",
" ",
" // transform coordinates to regular coordinates",
" gl_Position = vec4(clipSpace * vec2(1.0, 1.0), 0, 1);",
" ",
" // pass the texCoord to the fragment shader",
" v_texCoord = a_texCoord;",
" ",
" // set the filtertexture coordinate based on number filter to use",
" v_texCoordFilters = u_midpoint + vec2(0.0, u_filterHeight * floor(a_texCoord[1]/u_patchHeight));",
"}"
].join('
');
if ('lbp' in filters) {
// lbpResponseFragment
lbpResponseFS = [
"precision mediump float;",
"",
"uniform vec2 u_onePixelPatches;",
"",
"// our patches",
"uniform sampler2D u_patches;",
"",
"// the texCoords passed in from the vertex shader.",
"varying vec2 v_texCoord;",
"",
"void main() {",
" vec4 topLeft = texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", -"+opp[1].toFixed(5)+"));",
" vec4 topMid = texture2D(u_patches, v_texCoord + vec2(0.0, -"+opp[1].toFixed(5)+"));",
" vec4 topRight = texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", -"+opp[1].toFixed(5)+"));",
" vec4 midLeft = texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", 0.0));",
" vec4 midMid = texture2D(u_patches, v_texCoord);",
" vec4 midRight = texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", 0.0));",
" vec4 bottomLeft = texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", "+opp[1].toFixed(5)+"));",
" vec4 bottomMid = texture2D(u_patches, v_texCoord + vec2(0.0, "+opp[1].toFixed(5)+"));",
" vec4 bottomRight = texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", "+opp[1].toFixed(5)+"));",
" vec4 lbp = step(midMid, midRight)*1.0 + step(midMid, topRight)*2.0 + step(midMid, topMid)*4.0;",
" lbp = lbp + step(midMid, topLeft)*8.0 + step(midMid, midLeft)*16.0 + step(midMid, bottomLeft)*32.0;",
" lbp = lbp + step(midMid, bottomMid)*64.0 + step(midMid, bottomRight)*128.0;",
" gl_FragColor = lbp;",
"}"
].join('
');
}
if ('sobel' in filters) {
// gradResponseFragment
gradientResponseFS = [
"precision mediump float;",
"",
"uniform vec2 u_onePixelPatches;",
"",
"// our patches",
"uniform sampler2D u_patches;",
"",
"// the texCoords passed in from the vertex shader.",
"varying vec2 v_texCoord;",
"",
"void main() {",
" vec4 bottomLeft = texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", "+opp[1].toFixed(5)+"));",
" vec4 bottomRight = texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", "+opp[1].toFixed(5)+"));",
" vec4 topLeft = texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", -"+opp[1].toFixed(5)+"));",
" vec4 topRight = texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", -"+opp[1].toFixed(5)+"));",
" vec4 dx = (",
" bottomLeft +",
" (texture2D(u_patches, v_texCoord + vec2(-"+opp[0].toFixed(5)+", 0.0))*vec4(2.0,2.0,2.0,2.0)) +",
" topLeft -",
" bottomRight -",
" (texture2D(u_patches, v_texCoord + vec2("+opp[0].toFixed(5)+", 0.0))*vec4(2.0,2.0,2.0,2.0)) -",
" topRight)/4.0;",
" vec4 dy = (",
" bottomLeft +",
" (texture2D(u_patches, v_texCoord + vec2(0.0, "+opp[1].toFixed(5)+"))*vec4(2.0,2.0,2.0,2.0)) +",
" bottomRight -",
" topLeft -",
" (texture2D(u_patches, v_texCoord + vec2(0.0, -"+opp[1].toFixed(5)+"))*vec4(2.0,2.0,2.0,2.0)) -",
" topRight)/4.0;",
" vec4 gradient = sqrt((dx*dx) + (dy*dy));",
" gl_FragColor = gradient;",
"}"
].join('
');
}
//create webglcanvas
canvas = document.createElement('canvas')
canvas.setAttribute('width', (patchWidth-filterWidth+1)+"px");
canvas.setAttribute('height', ((patchHeight-filterHeight+1)*numPatches)+"px");
canvas.setAttribute('id', 'renderCanvas');
canvas.setAttribute('style', 'display:none;');
document.body.appendChild(canvas);
// TODO : isolate this library from webgl-util.js
gl = setupWebGL(canvas, {premultipliedAlpha: false, preserveDrawingBuffer : true, antialias : false});
// check for float textures support and fail if not
if (!gl.getExtension("OES_texture_float")) {
alert("Your graphics card does not support floating point textures! :(");
return;
}
/** insert filters into textures **/
if ('raw' in filters) {
insertFilter(filters['raw'], gl.TEXTURE0)
rawInit = true;
}
if ('sobel' in filters) {
insertFilter(filters['sobel'], gl.TEXTURE4)
sobelInit = true;
}
if ('lbp' in filters) {
insertFilter(filters['lbp'], gl.TEXTURE5)
lbpInit = true;
}
/** calculate vertices for calculating responses **/
// vertex rectangles to draw out
var rectangles = [];
var halfFilter = (filterWidth-1)/2;
var yOffset;
for (var i = 0;i < numBlocks;i++) {
yOffset = i*patchHeight;
//first triangle
rectangles = rectangles.concat(
[halfFilter, yOffset+halfFilter,
patchWidth-halfFilter, yOffset+halfFilter,
halfFilter, yOffset+patchHeight-halfFilter]
);
//second triangle
rectangles = rectangles.concat(
[halfFilter, yOffset+patchHeight-halfFilter,
patchWidth-halfFilter, yOffset+halfFilter,
patchWidth-halfFilter, yOffset+patchHeight-halfFilter]
);
}
rectangles = new Float32Array(rectangles);
// image rectangles to draw out
var irectangles = [];
for (var i = 0;i < rectangles.length;i++) {
if (i % 2 == 0) {
irectangles[i] = rectangles[i]/canvasWidth;
} else {
irectangles[i] = rectangles[i]/canvasHeight;
}
}
irectangles = new Float32Array(irectangles);
if ('lbp' in filters || 'sobel' in filters) {
var topCoord = 1.0 - 2/(patchHeight*numBlocks);
var bottomCoord = 1.0 - 2/numBlocks + 2/(patchHeight*numBlocks);
var yOffset;
// calculate position of vertex rectangles for gradient/lbp program
var gradRectangles = [];
for (var i = 0;i < numBlocks;i++) {
yOffset = i * (2/numBlocks);
//first triangle
gradRectangles = gradRectangles.concat(
[-1.0, topCoord - yOffset,
1.0, topCoord - yOffset,
-1.0, bottomCoord - yOffset]
);
//second triangle
gradRectangles = gradRectangles.concat(
[-1.0, bottomCoord - yOffset,
1.0, topCoord - yOffset,
1.0, bottomCoord - yOffset]
);
}
gradRectangles = new Float32Array(gradRectangles);
topCoord = 1.0 - 1/(patchHeight*numBlocks);
bottomCoord = 1.0 - 1/numBlocks + 1/(patchHeight*numBlocks);
// calculate position of image rectangles to draw out
var gradIRectangles = [];
for (var i = 0;i < numBlocks;i++) {
yOffset = i * (1/numBlocks);
//first triangle
gradIRectangles = gradIRectangles.concat(
[0.0, topCoord - yOffset,
1.0, topCoord - yOffset,
0.0, bottomCoord - yOffset]
);
//second triangle
gradIRectangles = gradIRectangles.concat(
[0.0, bottomCoord - yOffset,
1.0, topCoord - yOffset,
1.0, bottomCoord - yOffset]
);
}
gradIRectangles = new Float32Array(gradIRectangles);
}
// vertices for drawing out responses
// drawOutRectangles
drawOutRectangles = new Float32Array(12*numPatches);
var yOffset, indexOffset;
for (var i = 0;i < numPatches;i++) {
yOffset = i*newCanvasBlockHeight;
indexOffset = i*12;
//first triangle
drawOutRectangles[indexOffset] = 0.0;
drawOutRectangles[indexOffset+1] = yOffset;
drawOutRectangles[indexOffset+2] = newCanvasWidth;
drawOutRectangles[indexOffset+3] = yOffset;
drawOutRectangles[indexOffset+4] = 0.0;
drawOutRectangles[indexOffset+5] = yOffset+newCanvasBlockHeight;
//second triangle
drawOutRectangles[indexOffset+6] = 0.0;
drawOutRectangles[indexOffset+7] = yOffset+newCanvasBlockHeight;
drawOutRectangles[indexOffset+8] = newCanvasWidth;
drawOutRectangles[indexOffset+9] = yOffset;
drawOutRectangles[indexOffset+10] = newCanvasWidth;
drawOutRectangles[indexOffset+11] = yOffset+newCanvasBlockHeight;
}
// images
drawOutImages = new Float32Array(numPatches*12);
var halfFilterWidth = ((filterWidth-1)/2)/patchWidth;
var halfFilterHeight = ((filterWidth-1)/2)/(patchHeight*patchCells);
var patchHeightT = patchHeight / (patchHeight*patchCells);
for (var i = 0;i < numPatches;i++) {
yOffset = Math.floor(i / 4)*patchHeightT;
indexOffset = i*12;
//first triangle
drawOutImages[indexOffset] = halfFilterWidth;
drawOutImages[indexOffset+1] = yOffset+halfFilterHeight;
drawOutImages[indexOffset+2] = 1.0-halfFilterWidth;
drawOutImages[indexOffset+3] = yOffset+halfFilterHeight;
drawOutImages[indexOffset+4] = halfFilterWidth;
drawOutImages[indexOffset+5] = yOffset+patchHeightT-halfFilterHeight;
//second triangle
drawOutImages[indexOffset+6] = halfFilterWidth;
drawOutImages[indexOffset+7] = yOffset+patchHeightT-halfFilterHeight;
drawOutImages[indexOffset+8] = 1.0-halfFilterWidth;
drawOutImages[indexOffset+9] = yOffset+halfFilterHeight;
drawOutImages[indexOffset+10] = 1.0-halfFilterWidth;
drawOutImages[indexOffset+11] = yOffset+patchHeightT-halfFilterHeight;
}
// layer
drawOutLayer = new Float32Array(numPatches*6);
var layernum;
for (var i = 0;i < numPatches;i++) {
layernum = i % 4;
indexOffset = i*6;
drawOutLayer[indexOffset] = layernum;
drawOutLayer[indexOffset+1] = layernum;
drawOutLayer[indexOffset+2] = layernum;
drawOutLayer[indexOffset+3] = layernum;
drawOutLayer[indexOffset+4] = layernum;
drawOutLayer[indexOffset+5] = layernum;
}
/** set up programs and load attributes etc **/
if ('sobel' in filters) {
var grVertexShader = loadShader(gl, gradientResponseVS, gl.VERTEX_SHADER);
var grFragmentShader = loadShader(gl, gradientResponseFS, gl.FRAGMENT_SHADER);
gradientResponseProgram = createProgram(gl, [grVertexShader, grFragmentShader]);
gl.useProgram(gradientResponseProgram);
// set up vertices with rectangles
gradPositionLocation = gl.getAttribLocation(gradientResponseProgram, "a_position");
gradAPositionBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, gradAPositionBuffer);
gl.bufferData(gl.ARRAY_BUFFER, gradRectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(gradPositionLocation);
gl.vertexAttribPointer(gradPositionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
gradTexCoordLocation = gl.getAttribLocation(gradientResponseProgram, "a_texCoord");
gradTexCoordBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, gradTexCoordBuffer);
gl.bufferData(gl.ARRAY_BUFFER, gradIRectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(gradTexCoordLocation);
gl.vertexAttribPointer(gradTexCoordLocation, 2, gl.FLOAT, false, 0, 0);
// set up patches texture in gradientResponseProgram
gl.uniform1i(gl.getUniformLocation(gradientResponseProgram, "u_patches"), 1);
}
if ('lbp' in filters) {
var lbpVertexShader = loadShader(gl, lbpResponseVS, gl.VERTEX_SHADER);
var lbpFragmentShader = loadShader(gl, lbpResponseFS, gl.FRAGMENT_SHADER);
lbpResponseProgram = createProgram(gl, [lbpVertexShader, lbpFragmentShader]);
gl.useProgram(lbpResponseProgram);
// set up vertices with rectangles
lbpPositionLocation = gl.getAttribLocation(lbpResponseProgram, "a_position");
lbpAPositionBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, lbpAPositionBuffer);
gl.bufferData(gl.ARRAY_BUFFER, gradRectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(lbpPositionLocation);
gl.vertexAttribPointer(lbpPositionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
gradTexCoordLocation = gl.getAttribLocation(lbpResponseProgram, "a_texCoord");
lbpTexCoordBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, lbpTexCoordBuffer);
gl.bufferData(gl.ARRAY_BUFFER, gradIRectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(lbpTexCoordLocation);
gl.vertexAttribPointer(lbpTexCoordLocation, 2, gl.FLOAT, false, 0, 0);
// set up patches texture in lbpResponseProgram
gl.uniform1i(gl.getUniformLocation(lbpResponseProgram, "u_patches"), 1);
}
// setup patchdraw program
var drVertexShader = loadShader(gl, drawResponsesVS, gl.VERTEX_SHADER);
var drFragmentShader = loadShader(gl, drawResponsesFS, gl.FRAGMENT_SHADER);
patchDrawProgram = createProgram(gl, [drVertexShader, drFragmentShader]);
gl.useProgram(patchDrawProgram);
// set the resolution/dimension of the canvas
var resolutionLocation = gl.getUniformLocation(patchDrawProgram, "u_resolutiondraw");
gl.uniform2f(resolutionLocation, newCanvasWidth, newCanvasHeight);
// set u_responses
var responsesLocation = gl.getUniformLocation(patchDrawProgram, "u_responses");
gl.uniform1i(responsesLocation, 2);
// setup patchresponse program
var prVertexShader = loadShader(gl, patchResponseVS, gl.VERTEX_SHADER);
var prFragmentShader = loadShader(gl, patchResponseFS, gl.FRAGMENT_SHADER);
patchResponseProgram = createProgram(gl, [prVertexShader, prFragmentShader]);
gl.useProgram(patchResponseProgram);
// set up vertices with rectangles
var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
apositionBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
gl.bufferData(gl.ARRAY_BUFFER, rectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(positionLocation);
gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
texCoordBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
gl.bufferData(gl.ARRAY_BUFFER, irectangles, gl.STATIC_DRAW);
gl.enableVertexAttribArray(texCoordLocation);
gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
if ('lbp' in filters || 'sobel' in filters) {
// set up gradient/lbp buffer (also used for lbp)
gl.activeTexture(gl.TEXTURE3);
var gradients = gl.createTexture();
gl.bindTexture(gl.TEXTURE_2D, gradients);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, patchWidth, patchHeight*numBlocks, 0, gl.RGBA, gl.FLOAT, null);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
// set up gradient/lbp framebuffer
gbo = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, gbo);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, gradients, 0);
}
// set up buffer to draw to
gl.activeTexture(gl.TEXTURE2);
rttTexture = gl.createTexture();
gl.bindTexture(gl.TEXTURE_2D, rttTexture);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, patchWidth, patchHeight*numBlocks, 0, gl.RGBA, gl.FLOAT, null);
// set up response framebuffer
fbo = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, rttTexture, 0);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
/* initialize some textures and buffers used later on */
patchTex = gl.createTexture();
drawRectBuffer = gl.createBuffer();
drawImageBuffer = gl.createBuffer();
drawLayerBuffer = gl.createBuffer();
}
this.getRawResponses = function(patches) {
// TODO: check patches correct length/dimension
insertPatches(patches);
// switch to correct program
gl.useProgram(patchResponseProgram);
// set u_patches to point to texture 1
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_patches"), 1);
// set u_filters to point to correct filter
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_filters"), 0);
// set up vertices with rectangles
var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
gl.enableVertexAttribArray(positionLocation);
gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
var texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
gl.enableVertexAttribArray(texCoordLocation);
gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
// set framebuffer to the original one if not already using it
gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
// draw to framebuffer
gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
//gl.finish();
var responses = drawOut('raw');
return responses;
}
this.getSobelResponses = function(patches) {
// check that it is initialized
if (!sobelInit) return;
insertPatches(patches);
/* do sobel filter on patches */
// switch to correct program
gl.useProgram(gradientResponseProgram);
// set up vertices with rectangles
var gradPositionLocation = gl.getAttribLocation(gradientResponseProgram, "a_position");
gl.bindBuffer(gl.ARRAY_BUFFER, gradAPositionBuffer);
gl.enableVertexAttribArray(gradPositionLocation);
gl.vertexAttribPointer(gradPositionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
var gradTexCoordLocation = gl.getAttribLocation(gradientResponseProgram, "a_texCoord");
gl.bindBuffer(gl.ARRAY_BUFFER, gradTexCoordBuffer);
gl.enableVertexAttribArray(gradTexCoordLocation);
gl.vertexAttribPointer(gradTexCoordLocation, 2, gl.FLOAT, false, 0, 0);
// set framebuffer to the original one if not already using it
gl.bindFramebuffer(gl.FRAMEBUFFER, gbo);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
// draw to framebuffer
gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
/* calculate responses */
gl.useProgram(patchResponseProgram);
// set patches and filters to point to correct textures
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_filters"), 4);
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_patches"), 3);
var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
gl.enableVertexAttribArray(positionLocation);
gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
var texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
gl.enableVertexAttribArray(texCoordLocation);
gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
// draw to framebuffer
gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
/* get the responses */
var responses = drawOut('sobel');
return responses;
}
this.getLBPResponses = function(patches) {
// check that it is initialized
if (!lbpInit) return;
insertPatches(patches);
/* do sobel filter on patches */
// switch to correct program
gl.useProgram(lbpResponseProgram);
// set up vertices with rectangles
var lbpPositionLocation = gl.getAttribLocation(lbpResponseProgram, "a_position");
gl.bindBuffer(gl.ARRAY_BUFFER, lbpAPositionBuffer);
gl.enableVertexAttribArray(lbpPositionLocation);
gl.vertexAttribPointer(lbpPositionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
var lbpTexCoordLocation = gl.getAttribLocation(lbpResponseProgram, "a_texCoord");
gl.bindBuffer(gl.ARRAY_BUFFER, lbpTexCoordBuffer);
gl.enableVertexAttribArray(lbpTexCoordLocation);
gl.vertexAttribPointer(lbpTexCoordLocation, 2, gl.FLOAT, false, 0, 0);
// set framebuffer to the original one if not already using it
gl.bindFramebuffer(gl.FRAMEBUFFER, gbo);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
// draw to framebuffer
gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
/* calculate responses */
gl.useProgram(patchResponseProgram);
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_filters"), 5);
gl.uniform1i(gl.getUniformLocation(patchResponseProgram, "u_patches"), 3);
var positionLocation = gl.getAttribLocation(patchResponseProgram, "a_position");
gl.bindBuffer(gl.ARRAY_BUFFER, apositionBuffer);
gl.enableVertexAttribArray(positionLocation);
gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
// set up texture positions
var texCoordLocation = gl.getAttribLocation(patchResponseProgram, "a_texCoord");
gl.bindBuffer(gl.ARRAY_BUFFER, texCoordBuffer);
gl.enableVertexAttribArray(texCoordLocation);
gl.vertexAttribPointer(texCoordLocation, 2, gl.FLOAT, false, 0, 0);
gl.bindFramebuffer(gl.FRAMEBUFFER, fbo);
gl.viewport(0, 0, patchWidth, patchHeight*numBlocks);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
// draw to framebuffer
gl.drawArrays(gl.TRIANGLES, 0, patchCells*6);
/* get the responses */
var responses = drawOut('lbp');
return responses;
}
var insertPatches = function(patches) {
// pass patches into texture, each patch in either r, g, b or a
var patchArrayIndex = 0;
var patchesIndex1 = 0;
var patchesIndex2 = 0;
for (var i = 0;i < patchCells;i++) {
for (var j = 0;j < patchHeight;j++) {
for (var k = 0;k < patchWidth;k++) {
patchesIndex1 = i*4;
patchesIndex2 = (j*patchWidth) + k;
patchArrayIndex = ((patchSize*i) + patchesIndex2)*4;
//set r with first patch
if (patchesIndex1 < numPatches) {
patchArray[patchArrayIndex] = patches[patchesIndex1][patchesIndex2];
} else {
patchArray[patchArrayIndex] = 0;
}
//set g with 2nd patch
if (patchesIndex1+1 < numPatches) {
patchArray[patchArrayIndex + 1] = patches[patchesIndex1+1][patchesIndex2];
} else {
patchArray[patchArrayIndex + 1] = 0;
}
//set b with 3rd patch
if (patchesIndex1+2 < numPatches) {
patchArray[patchArrayIndex + 2] = patches[patchesIndex1+2][patchesIndex2];
} else {
patchArray[patchArrayIndex + 2] = 0;
}
//set a with 4th patch
if (patchesIndex1+3 < numPatches) {
patchArray[patchArrayIndex + 3] = patches[patchesIndex1+3][patchesIndex2];
} else {
patchArray[patchArrayIndex + 3] = 0;
}
}
}
}
// pass texture into an uniform
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, patchTex);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, textureWidth, textureHeight, 0, gl.RGBA, gl.FLOAT, patchArray);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
}
var insertFilter = function(filter, textureNum) {
var filterSize = filterWidth*filterHeight;
var filterArray = new Float32Array(filterSize*(numBlocks)*4);
for (var i = 0;i < numBlocks;i++) {
for (var j = 0;j < filterHeight;j++) {
for (var k = 0;k < filterWidth;k++) {
//set r with first filter
if (i*4 < filter.length) {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4] = filter[i*4][(j*filterWidth) + k];
} else {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4] = 0;
}
//set g with 2nd filter
if ((i*4 + 1) < filter.length) {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 1] = filter[(i*4)+1][(j*filterWidth) + k];
} else {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 1] = 0;
}
//set b with 3rd filter
if ((i*4 + 2) < filter.length) {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 2] = filter[(i*4)+2][(j*filterWidth) + k];
} else {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 2] = 0;
}
//set a with 4th filter
if ((i*4 + 3) < filter.length) {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 3] = filter[(i*4)+3][(j*filterWidth) + k];
} else {
filterArray[((filterSize*i) + (j*filterWidth) + k)*4 + 3] = 0;
}
}
}
}
gl.activeTexture(textureNum);
var filterTexture = gl.createTexture();
gl.bindTexture(gl.TEXTURE_2D, filterTexture);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, filterWidth, filterHeight*numBlocks, 0, gl.RGBA, gl.FLOAT, filterArray);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
}
var drawOut = function(type) {
// switch programs
gl.useProgram(patchDrawProgram);
// bind canvas buffer
gl.bindFramebuffer(gl.FRAMEBUFFER, null);
gl.viewport(0, 0, newCanvasWidth, newCanvasHeight);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER)
gl.bindBuffer(gl.ARRAY_BUFFER, drawRectBuffer);
gl.bufferData(
gl.ARRAY_BUFFER,
drawOutRectangles,
gl.STATIC_DRAW);
var positionLocation = gl.getAttribLocation(patchDrawProgram, "a_position_draw");
gl.enableVertexAttribArray(positionLocation);
gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
gl.bindBuffer(gl.ARRAY_BUFFER, drawImageBuffer);
gl.bufferData(
gl.ARRAY_BUFFER,
drawOutImages,
gl.STATIC_DRAW);
var textureLocation = gl.getAttribLocation(patchDrawProgram, "a_texCoord_draw");
gl.enableVertexAttribArray(textureLocation);
gl.vertexAttribPointer(textureLocation, 2, gl.FLOAT, false, 0, 0);
gl.bindBuffer(gl.ARRAY_BUFFER, drawLayerBuffer);
gl.bufferData(
gl.ARRAY_BUFFER,
drawOutLayer,
gl.STATIC_DRAW);
var layerLocation = gl.getAttribLocation(patchDrawProgram, "a_patchChoice_draw");
gl.enableVertexAttribArray(layerLocation);
gl.vertexAttribPointer(layerLocation, 1, gl.FLOAT, false, 0, 0);
// draw out
gl.drawArrays(gl.TRIANGLES, 0, numPatches*6);
var responses = getOutput();
responses = unpackToFloat(responses);
// split
responses = splitArray(responses, numPatches);
// add bias
responses = addBias(responses, biases[type]);
// normalize responses to lie within [0,1]
var rl = responses.length;
for (var i = 0;i < rl;i++) {
responses[i] = normalizeFilterMatrix(responses[i]);
}
return responses;
}
var addBias = function(responses, bias) {
// do a little trick to add bias in the logit function
var biasMult;
for (var i = 0;i < responses.length;i++) {
biasMult = Math.exp(bias[i]);
for (var j = 0;j < responses[i].length;j++) {
responses[i][j] = 1/(1+((1-responses[i][j])/(responses[i][j]*biasMult)));
}
}
return responses;
}
var splitArray = function(array, parts) {
var sp = [];
var al = array.length;
var splitlength = al/parts;
var ta = [];
for (var i = 0;i < al;i++) {
if (i % splitlength == 0) {
if (i != 0) {
sp.push(ta);
}
ta = [];
}
ta.push(array[i]);
}
sp.push(ta);
return sp;
}
var getOutput = function() {
// get data
var pixelValues = new Uint8Array(4*canvas.width*canvas.height);
var data = gl.readPixels(0, 0, canvas.width, canvas.height, gl.RGBA, gl.UNSIGNED_BYTE, pixelValues);
// return
return pixelValues;
}
var unpackToFloat = function(array) {
// convert packed floats to proper floats : see http://stackoverflow.com/questions/9882716/packing-float-into-vec4-how-does-this-code-work
var newArray = [];
var al = array.length;
for (var i = 0;i < al;i+=4) {
newArray[(i / 4) >> 0] = ((array[i]/(256*256*256*256))+(array[i+1]/(256*256*256))+(array[i+2]/(256*256))+(array[i+3]/256));
}
return newArray;
}
var normalizeFilterMatrix = function(response) {
// normalize responses to lie within [0,1]
var msize = response.length;
var max = 0;
var min = 1;
for (var i = 0;i < msize;i++) {
max = response[i] > max ? response[i] : max;
min = response[i] < min ? response[i] : min;
}
var dist = max-min;
if (dist == 0) {
console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
response = response.map(function() {return 1});
} else {
for (var i = 0;i < msize;i++) {
response[i] = (response[i]-min)/dist;
}
}
return response
}
};
// The rest of the code is based on webgl-utils.js authored by Gregg Tavares, license below:
/*
* Copyright (c) 2011, Gregg Tavares
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * 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.
*
* * Neither the name of greggman.com 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 HOLDER 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.
*/
(function() {
/**
* Wrapped logging function.
* @param {string} msg The message to log.
*/
var log = function(msg) {
if (window.console && window.console.log) {
window.console.log(msg);
}
};
/**
* Wrapped logging function.
* @param {string} msg The message to log.
*/
var error = function(msg) {
if (window.console) {
if (window.console.error) {
window.console.error(msg);
}
else if (window.console.log) {
window.console.log(msg);
}
}
throw msg;
};
/**
* Turn off all logging.
*/
var loggingOff = function() {
log = function() {};
error = function() {};
};
/**
* Check if the page is embedded.
* @return {boolean} True of we are in an iframe
*/
var isInIFrame = function() {
return window != window.top;
};
/**
* Converts a WebGL enum to a string
* @param {!WebGLContext} gl The WebGLContext to use.
* @param {number} value The enum value.
* @return {string} The enum as a string.
*/
var glEnumToString = function(gl, value) {
for (var p in gl) {
if (gl[p] == value) {
return p;
}
}
return "0x" + value.toString(16);
};
/**
* Creates the HTLM for a failure message
* @param {string} canvasContainerId id of container of th
* canvas.
* @return {string} The html.
*/
var makeFailHTML = function(msg) {
return '' +
'<table style="background-color: #8CE; 100%; height: 100%;"><tr>' +
'<td align="center">' +
'<div style="display: table-cell; vertical-align: middle;">' +
'<div style="">' + msg + '</div>' +
'</div>' +
'</td></tr></table>';
};
/**
* Mesasge for getting a webgl browser
* @type {string}
*/
var GET_A_WEBGL_BROWSER = '' +
'This page requires a browser that supports WebGL.<br/>' +
'<a href="http://get.webgl.org">Click here to upgrade your browser.</a>';
/**
* Mesasge for need better hardware
* @type {string}
*/
var OTHER_PROBLEM = '' +
"It doesn't appear your computer can support WebGL.<br/>" +
'<a href="http://get.webgl.org/troubleshooting/">Click here for more information.</a>';
/**
* Creates a webgl context. If creation fails it will
* change the contents of the container of the <canvas>
* tag to an error message with the correct links for WebGL.
* @param {Element} canvas. The canvas element to create a
* context from.
* @param {WebGLContextCreationAttirbutes} opt_attribs Any
* creation attributes you want to pass in.
* @return {WebGLRenderingContext} The created context.
*/
var setupWebGL = function(canvas, opt_attribs) {
function showLink(str) {
var container = canvas.parentNode;
if (container) {
container.innerHTML = makeFailHTML(str);
}
};
if (!window.WebGLRenderingContext) {
//showLink(GET_A_WEBGL_BROWSER);
return null;
}
var context = create3DContext(canvas, opt_attribs);
if (!context) {
//showLink(OTHER_PROBLEM);
return null;
}
return context;
};
/**
* Creates a webgl context.
* @param {!Canvas} canvas The canvas tag to get context
* from. If one is not passed in one will be created.
* @return {!WebGLContext} The created context.
*/
var create3DContext = function(canvas, opt_attribs) {
var names = ["webgl", "experimental-webgl"];
var context = null;
for (var ii = 0; ii < names.length; ++ii) {
try {
context = canvas.getContext(names[ii], opt_attribs);
} catch(e) {}
if (context) {
break;
}
}
return context;
}
var updateCSSIfInIFrame = function() {
if (isInIFrame()) {
document.body.className = "iframe";
}
};
/**
* Gets a WebGL context.
* makes its backing store the size it is displayed.
*/
var getWebGLContext = function(canvas) {
if (isInIFrame()) {
updateCSSIfInIFrame();
// make the canvas backing store the size it's displayed.
canvas.width = canvas.clientWidth;
canvas.height = canvas.clientHeight;
}
var gl = setupWebGL(canvas);
return gl;
};
/**
* Loads a shader.
* @param {!WebGLContext} gl The WebGLContext to use.
* @param {string} shaderSource The shader source.
* @param {number} shaderType The type of shader.
* @param {function(string): void) opt_errorCallback callback for errors.
* @return {!WebGLShader} The created shader.
*/
var loadShader = function(gl, shaderSource, shaderType, opt_errorCallback) {
var errFn = opt_errorCallback || error;
// Create the shader object
var shader = gl.createShader(shaderType);
// Load the shader source
gl.shaderSource(shader, shaderSource);
// Compile the shader
gl.compileShader(shader);
// Check the compile status
var compiled = gl.getShaderParameter(shader, gl.COMPILE_STATUS);
if (!compiled) {
// Something went wrong during compilation; get the error
var lastError = gl.getShaderInfoLog(shader);
errFn("*** Error compiling shader '" + shader + "':" + lastError);
gl.deleteShader(shader);
return null;
}
return shader;
}
/**
* Creates a program, attaches shaders, binds attrib locations, links the
* program and calls useProgram.
* @param {!Array.<!WebGLShader>} shaders The shaders to attach
* @param {!Array.<string>} opt_attribs The attribs names.
* @param {!Array.<number>} opt_locations The locations for the attribs.
*/
var loadProgram = function(gl, shaders, opt_attribs, opt_locations) {
var program = gl.createProgram();
for (var ii = 0; ii < shaders.length; ++ii) {
gl.attachShader(program, shaders[ii]);
}
if (opt_attribs) {
for (var ii = 0; ii < opt_attribs.length; ++ii) {
gl.bindAttribLocation(
program,
opt_locations ? opt_locations[ii] : ii,
opt_attribs[ii]);
}
}
gl.linkProgram(program);
// Check the link status
var linked = gl.getProgramParameter(program, gl.LINK_STATUS);
if (!linked) {
// something went wrong with the link
var lastError = gl.getProgramInfoLog (program);
error("Error in program linking:" + lastError);
gl.deleteProgram(program);
return null;
}
return program;
};
/**
* Loads a shader from a script tag.
* @param {!WebGLContext} gl The WebGLContext to use.
* @param {string} scriptId The id of the script tag.
* @param {number} opt_shaderType The type of shader. If not passed in it will
* be derived from the type of the script tag.
* @param {function(string): void) opt_errorCallback callback for errors.
* @return {!WebGLShader} The created shader.
*/
var createShaderFromScript = function(
gl, scriptId, opt_shaderType, opt_errorCallback) {
var shaderSource = "";
var shaderType;
var shaderScript = document.getElementById(scriptId);
if (!shaderScript) {
throw("*** Error: unknown script element" + scriptId);
}
shaderSource = shaderScript.text;
if (!opt_shaderType) {
if (shaderScript.type == "x-shader/x-vertex") {
shaderType = gl.VERTEX_SHADER;
} else if (shaderScript.type == "x-shader/x-fragment") {
shaderType = gl.FRAGMENT_SHADER;
} else if (shaderType != gl.VERTEX_SHADER && shaderType != gl.FRAGMENT_SHADER) {
throw("*** Error: unknown shader type");
return null;
}
}
return loadShader(
gl, shaderSource, opt_shaderType ? opt_shaderType : shaderType,
opt_errorCallback);
};
/* export functions */
window.setupWebGL = setupWebGL;
window.createProgram = loadProgram;
window.createShaderFromScriptElement = createShaderFromScript;
window.getWebGLContext = getWebGLContext;
window.updateCSSIfInIFrame = updateCSSIfInIFrame;
window.loadShader = loadShader;
}());
"use strict";
var svmFilter = function() {
var _fft, fft_filters, responses, biases;
var fft_size, filterLength, filter_width, search_width, num_patches;
var temp_imag_part, temp_real_part;
// fft function
this.fft_inplace = function(array, _im_part) {
// in-place
if (typeof _im_part == "undefined") {
_im_part = temp_imag_part;
}
for (var i = 0;i < filterLength;i++) {
_im_part[i] = 0.0;
}
_fft.real_fft2d(array,_im_part);
return [array, _im_part];
}
this.ifft = function(rn, cn) {
// in-place
_fft.real_ifft2d(rn, cn);
return rn;
}
var complex_mult_inplace = function(cn1, cn2) {
// in-place, cn1 is the one modified
var temp1, temp2;
for (var r = 0;r < filterLength;r++) {
temp1 = (cn1[0][r]*cn2[0][r]) - (cn1[1][r]*cn2[1][r]);
temp2 = (cn1[0][r]*cn2[1][r]) + (cn1[1][r]*cn2[0][r]);
cn1[0][r] = temp1;
cn1[1][r] = temp2;
}
}
this.init = function(filter_input, bias_input, numPatches, filterWidth, searchWidth) {
var temp, fft, offset;
// calculate needed size of fft (has to be power of two)
fft_size = upperPowerOfTwo(filterWidth-1+searchWidth);
filterLength = fft_size*fft_size;
_fft = new FFT();
_fft.init(fft_size);
fft_filters = Array(numPatches);
var fft_filter;
var edge = (filterWidth-1)/2;
for (var i = 0;i < numPatches;i++) {
var flar_fi0 = new Float64Array(filterLength);
var flar_fi1 = new Float64Array(filterLength);
// load filter
var xOffset, yOffset;
for (var j = 0;j < filterWidth;j++) {
for (var k = 0;k < filterWidth;k++) {
// TODO : rotate filter
xOffset = k < edge ? (fft_size-edge) : (-edge);
yOffset = j < edge ? (fft_size-edge) : (-edge);
flar_fi0[k+xOffset+((j+yOffset)*fft_size)] = filter_input[i][(filterWidth-1-j)+((filterWidth-1-k)*filterWidth)];
/*xOffset = k < edge ? (fft_size-edge) : (-edge);
yOffset = j < edge ? (fft_size-edge) : (-edge);
flar_fi0[k+xOffset+((j+yOffset)*fft_size)] = filter_input[i][k+(j*filterWidth)];*/
//console.log(k + ","+ j+":" + (k+xOffset+((j+yOffset)*fft_size)))
}
}
// fft it and store
fft_filter = this.fft_inplace(flar_fi0, flar_fi1);
fft_filters[i] = fft_filter;
}
// set up biases
biases = new Float64Array(numPatches);
for (var i = 0;i < numPatches;i++) {
biases[i] = bias_input[i];
}
responses = Array(numPatches);
temp_imag_part = Array(numPatches);
for (var i = 0;i < numPatches;i++) {
responses[i] = new Float64Array(searchWidth*searchWidth);
temp_imag_part[i] = new Float64Array(searchWidth*searchWidth);
}
temp_real_part = new Float64Array(filterLength);
num_patches = numPatches;
filter_width = filterWidth;
search_width = searchWidth;
}
this.getResponses = function(patches) {
var response, temp, edge;
var patch_width = filter_width-1+search_width;
for (var i = 0;i < num_patches;i++) {
// reset zeroes in temp_real_part
for (var j = 0;j < fft_size*fft_size;j++) {
temp_real_part[j] = 0.0;
}
// normalize patches to 0-1
patches[i] = normalizePatches(patches[i]);
// patch must be padded (with zeroes) to match fft size
for (var j = 0;j < patch_width;j++) {
for (var k = 0;k < patch_width;k++) {
temp_real_part[j + (fft_size*k)] = patches[i][k + (patch_width*j)];
}
}
//drawData(document.getElementById('sketch').getContext('2d'), temp_real_part, 32, 32, false, 0, 0);
// fft it
response = this.fft_inplace(temp_real_part);
// multiply pointwise with filter
complex_mult_inplace(response, fft_filters[i]);
// inverse fft it
response = this.ifft(response[0], response[1]);
// crop out edges
edge = (filter_width-1)/2;
for (var j = 0;j < search_width;j++) {
for (var k = 0;k < search_width;k++) {
responses[i][j + (k*search_width)] = response[edge + k + ((j+edge)*(fft_size))];
}
}
// add bias
for (var j = 0;j < search_width*search_width;j++) {
responses[i][j] += biases[i];
}
// logistic transformation
responses[i] = logisticResponse(responses[i]);
/*responses[i] = new Float64Array(32*32)
for (var j = 0;j < 32;j++) {
for (var k = 0;k < 32;k++) {
responses[i][k + (j*(32))] = response[k + (j*(32))]
}
}*/
// normalization?
inplaceNormalizeFilterMatrix(responses[i]);
}
return responses;
}
var normalizePatches = function(patch) {
var patch_width = filter_width-1+search_width;
var max = 0;
var min = 1000;
var value;
for (var j = 0;j < patch_width;j++) {
for (var k = 0;k < patch_width;k++) {
value = patch[k + (patch_width*j)]
if (value < min) {
min = value;
}
if (value > max) {
max = value;
}
}
}
var scale = max-min;
for (var j = 0;j < patch_width;j++) {
for (var k = 0;k < patch_width;k++) {
patch[k + (patch_width*j)] = (patch[k + (patch_width*j)]-min)/scale;
}
}
return patch;
}
var logisticResponse = function(response) {
// create probability by doing logistic transformation
for (var j = 0;j < search_width;j++) {
for (var k = 0;k < search_width;k++) {
response[j + (k*search_width)] = 1.0/(1.0 + Math.exp(- (response[j + (k*search_width)] - 1.0 )));
}
}
return response
}
var upperPowerOfTwo = function(x) {
x--;
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x++;
return x;
}
var inplaceNormalizeFilterMatrix = function(response) {
// normalize responses to lie within [0,1]
var msize = response.length;
var max = 0;
var min = 1;
for (var i = 0;i < msize;i++) {
max = response[i] > max ? response[i] : max;
min = response[i] < min ? response[i] : min;
}
var dist = max-min;
if (dist == 0) {
console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
} else {
for (var i = 0;i < msize;i++) {
response[i] = (response[i]-min)/dist;
}
}
}
/**
* Fast Fourier Transform
* 1D-FFT/IFFT, 2D-FFT/IFFT (radix-2)
*
* @author ryo / github.com/wellflat
* Based on https://github.com/wellflat/javascript-labs with some tiny optimizations
*/
function FFT() {
var _n = 0, // order
_bitrev = null, // bit reversal table
_cstb = null; // sin/cos table
var _tre, _tim;
this.init = function (n) {
if(n !== 0 && (n & (n - 1)) === 0) {
_n = n;
_setVariables();
_makeBitReversal();
_makeCosSinTable();
} else {
throw new Error("init: radix-2 required");
}
}
// 1D-FFT
this.fft1d = function (re, im) {
fft(re, im, 1);
}
// 1D-IFFT
this.ifft1d = function (re, im) {
var n = 1/_n;
fft(re, im, -1);
for(var i=0; i<_n; i++) {
re[i] *= n;
im[i] *= n;
}
}
// 2D-FFT
this.fft2d = function (re, im) {
var i = 0;
// x-axis
for(var y=0; y<_n; y++) {
i = y*_n;
for(var x1=0; x1<_n; x1++) {
_tre[x1] = re[x1 + i];
_tim[x1] = im[x1 + i];
}
this.fft1d(_tre, _tim);
for(var x2=0; x2<_n; x2++) {
re[x2 + i] = _tre[x2];
im[x2 + i] = _tim[x2];
}
}
// y-axis
for(var x=0; x<_n; x++) {
for(var y1=0; y1<_n; y1++) {
i = x + y1*_n;
_tre[y1] = re[i];
_tim[y1] = im[i];
}
this.fft1d(_tre, _tim);
for(var y2=0; y2<_n; y2++) {
i = x + y2*_n;
re[i] = _tre[y2];
im[i] = _tim[y2];
}
}
}
// 2D-IFFT
this.ifft2d = function (re, im) {
var i = 0;
// x-axis
for(var y=0; y<_n; y++) {
i = y*_n;
for(var x1=0; x1<_n; x1++) {
_tre[x1] = re[x1 + i];
_tim[x1] = im[x1 + i];
}
this.ifft1d(_tre, _tim);
for(var x2=0; x2<_n; x2++) {
re[x2 + i] = _tre[x2];
im[x2 + i] = _tim[x2];
}
}
// y-axis
for(var x=0; x<_n; x++) {
for(var y1=0; y1<_n; y1++) {
i = x + y1*_n;
_tre[y1] = re[i];
_tim[y1] = im[i];
}
this.ifft1d(_tre, _tim);
for(var y2=0; y2<_n; y2++) {
i = x + y2*_n;
re[i] = _tre[y2];
im[i] = _tim[y2];
}
}
}
// 2D-IFFT, real-valued
// only outputs the real valued part
this.real_ifft2d = function (re, im) {
var i2;
var i = 0;
// x-axis
for(var y=0; y<_n; y++) {
i = y*_n;
for(var x1=0; x1<_n; x1++) {
_tre[x1] = re[x1 + i];
_tim[x1] = im[x1 + i];
}
this.ifft1d(_tre, _tim);
for(var x2=0; x2<_n; x2++) {
re[x2 + i] = _tre[x2];
im[x2 + i] = _tim[x2];
}
}
// y-axis
var halfn = _n/2;
var rowIdx = 0;
for(var x=0; x<_n; x+=2) {
//untangle
i = x;
i2 = x+1;
_tre[0] = re[0 + i];
_tim[0] = re[0 + i2];
_tre[_n/2] = re[(halfn*_n) + i];
_tim[_n/2] = re[(halfn*_n) + i2];
for (var x2=1;x2<halfn;x2++) {
rowIdx = x2*_n
_tre[x2] = re[rowIdx+i] - im[rowIdx + i2];
_tre[_n - x2] = re[rowIdx+i] + im[rowIdx + i2];
_tim[x2] = im[rowIdx+i] + re[rowIdx+i2];
_tim[_n - x2] = re[rowIdx+i2] - im[rowIdx+i];
}
this.ifft1d(_tre, _tim);
for(var y2=0; y2<_n; y2++) {
i = x + y2*_n;
i2 = (x + 1) + y2*_n;
re[i] = _tre[y2];
re[i2] = _tim[y2];
}
}
}
// 2D-FFT, real-valued only
// ignores the imaginary input
// see:
// http://www.inf.fu-berlin.de/lehre/SS12/SP-Par/download/fft1.pdf
// http://cnx.org/content/m12021/latest/
// http://images.apple.com/acg/pdf/g4fft.pdf
// http://www.ti.com/lit/an/spra291/spra291.pdf
this.real_fft2d = function (re, im) {
var i = 0, i2 = 0;
var fftlen = (_n*_n)-1;
// x-axis
for(var y=0; y<_n; y += 2) {
i = y*_n;
i2 = (y+1)*_n;
// tangle
for(var x1=0; x1<_n; x1++) {
_tre[x1] = re[x1 + i];
_tim[x1] = re[x1 + i2];
}
this.fft1d(_tre, _tim);
// untangle
re[0 + i] = _tre[0];
re[0 + i2] = _tim[0];
im[0 + i] = 0;
im[0 + i2] = 0;
re[_n/2 + i] = _tre[_n/2];
re[_n/2 + i2] = _tim[_n/2];
im[_n/2 + i] = 0;
im[_n/2 + i2] = 0;
for(var x2=1;x2<(_n/2);x2++) {
re[x2 + i] = 0.5 * (_tre[x2] + _tre[_n - x2]);
im[x2 + i] = 0.5 * (_tim[x2] - _tim[_n - x2]);
re[x2 + i2] = 0.5 * (_tim[x2] + _tim[_n - x2]);
im[x2 + i2] = -0.5 * (_tre[x2] - _tre[_n - x2]);
re[(_n-x2) + i] = re[x2 + i];
im[(_n-x2) + i] = -im[x2 + i];
re[(_n-x2) + i2] = re[x2 + i2];
im[(_n-x2) + i2] = -im[x2 + i2];
}
}
// y-axis
for(var x=0; x<_n; x++) {
for(var y1=0; y1<_n; y1++) {
i = x + y1*_n;
_tre[y1] = re[i];
_tim[y1] = im[i];
}
this.fft1d(_tre, _tim);
for(var y2=0; y2<_n; y2++) {
i = x + y2*_n;
re[i] = _tre[y2];
im[i] = _tim[y2];
}
}
}
// core operation of FFT
function fft(re, im, inv) {
var d, h, ik, m, tmp, wr, wi, xr, xi,
n4 = _n >> 2;
// bit reversal
for(var l=0; l<_n; l++) {
m = _bitrev[l];
if(l < m) {
tmp = re[l];
re[l] = re[m];
re[m] = tmp;
tmp = im[l];
im[l] = im[m];
im[m] = tmp;
}
}
// butterfly operation
//butfly(re,im,inv,n4);
for(var k=1; k<_n; k<<=1) {
h = 0;
d = _n/(k << 1);
for(var j=0; j<k; j++) {
wr = _cstb[h + n4];
wi = inv*_cstb[h];
for(var i=j; i<_n; i+=(k<<1)) {
ik = i + k;
xr = wr*re[ik] + wi*im[ik];
xi = wr*im[ik] - wi*re[ik];
re[ik] = re[i] - xr;
re[i] += xr;
im[ik] = im[i] - xi;
im[i] += xi;
}
h += d;
}
}
}
function butfly(re, im, inv, n4) {
var h,d,wr,wi,ik,xr,xi;
for(var k=1; k<_n; k<<=1) {
h = 0;
d = _n/(k << 1);
for(var j=0; j<k; j++) {
wr = _cstb[h + n4];
wi = inv*_cstb[h];
for(var i=j; i<_n; i+=(k<<1)) {
ik = i + k;
xr = wr*re[ik] + wi*im[ik];
xi = wr*im[ik] - wi*re[ik];
re[ik] = re[i] - xr;
re[i] += xr;
im[ik] = im[i] - xi;
im[i] += xi;
}
h += d;
}
}
}
// set variables
function _setVariables() {
if(typeof Uint8Array !== 'undefined') {
_bitrev = new Uint8Array(_n);
} else {
_bitrev = new Array(_n);
}
if(typeof Float64Array !== 'undefined') {
_cstb = new Float64Array(_n*1.25);
_tre = new Float64Array(_n);
_tim = new Float64Array(_n);
} else {
_cstb = new Array(_n*1.25);
_tre = new Array(_n);
_tim = new Array(_n);
}
}
// make bit reversal table
function _makeBitReversal() {
var i = 0,
j = 0,
k = 0;
_bitrev[0] = 0;
while(++i < _n) {
k = _n >> 1;
while(k <= j) {
j -= k;
k >>= 1;
}
j += k;
_bitrev[i] = j;
}
}
// make trigonometric function table
function _makeCosSinTable() {
var n2 = _n >> 1,
n4 = _n >> 2,
n8 = _n >> 3,
n2p4 = n2 + n4,
t = Math.sin(Math.PI/_n),
dc = 2*t*t,
ds = Math.sqrt(dc*(2 - dc)),
c = _cstb[n4] = 1,
s = _cstb[0] = 0;
t = 2*dc;
for(var i=1; i<n8; i++) {
c -= dc;
dc += t*c;
s += ds;
ds -= t*s;
_cstb[i] = s;
_cstb[n4 - i] = c;
}
if(n8 !== 0) {
_cstb[n8] = Math.sqrt(0.5);
}
for(var j=0; j<n4; j++) {
_cstb[n2 - j] = _cstb[j];
}
for(var k=0; k<n2p4; k++) {
_cstb[k + n2] = -_cstb[k];
}
}
}
}
// requires mosse.js
var mosseFilterResponses = function() {
var filters = [];
var responses = [];
var num_Patches = 0;
this.init = function(filter_input, numPatches, filterWidth, filterHeight) {
// load filters, make fft ready
for (var i = 0;i < numPatches;i++) {
var temp = {};
temp.width = filterWidth;
temp.height = filterHeight;
var filterLength = filterWidth*filterHeight
var flar_fi0 = new Float64Array(filterLength);
var flar_fi1 = new Float64Array(filterLength);
for (var j = 0;j < filterLength;j++) {
flar_fi0[j] = filter_input[i][0][j];
flar_fi1[j] = filter_input[i][1][j];
}
temp.real = flar_fi0;
temp.imag = flar_fi1;
filters[i] = new mosseFilter();
filters[i].load(temp);
}
num_Patches = numPatches;
}
this.getResponses = function(patches) {
for (var i = 0;i < num_Patches;i++) {
responses[i] = filters[i].getResponse(patches[i]);
//responses[i] = logisticResponse(responses[i]);
responses[i] = normalizeFilterMatrix(responses[i]);
}
return responses;
}
var logisticResponse = function(response) {
// create probability by doing logistic transformation
var filter_size = response.length;
for (var j = 0;j < filter_size;j++) {
response[j] = 1.0/(1.0 + Math.exp(- (response[j]-1.0) ));
}
return response;
}
var normalizeFilterMatrix = function(response) {
// normalize responses to lie within [0,1]
var msize = response.length;
var max = 0;
var min = 1;
for (var i = 0;i < msize;i++) {
max = response[i] > max ? response[i] : max;
min = response[i] < min ? response[i] : min;
}
var dist = max-min;
if (dist == 0) {
console.log("a patchresponse was monotone, causing normalization to fail. Leaving it unchanged.")
response = response.map(function() {return 1});
} else {
for (var i = 0;i < msize;i++) {
response[i] = (response[i]-min)/dist;
}
}
return response
}
}
var left_eye_filter = {"real": [1.5419219943717721, 0.40010880110578706, -0.79043641265342957, -1.2685464969238938, 0.39878117336167285, -1.0673489992245377, -0.079880838229404019, -0.45374680224191505, -0.043474097938900787, -0.31125662385352687, 0.17092430376098702, -0.29613086164846153, 0.5616469648110296, -1.559786848789493, 0.64513037997492662, -1.2899747976234162, 1.1761667998175334, -1.2899747976233551, 0.64513037997490474, -1.5597868487894897, 0.56164696481102505, -0.29613086164845964, 0.17092430376099094, -0.31125662385352959, -0.043474097938900787, -0.45374680224191177, -0.079880838229404658, -1.0673489992245357, 0.39878117336167307, -1.2685464969238942, -0.79043641265343012, 0.40010880110578717, -1.3820969331049027, 0.069560471269205768, -1.9786339579213206, -1.9807415717551982, -0.78667274410450883, -1.2217002325587256, -0.19150029104902774, -0.35131617290773243, -0.17646388464205803, -0.16672095020503441, -0.092298612924566523, -0.028899376452253527, -0.1314555696102146, -0.32892265898101813, -0.40987148655061206, 0.11741827111366547, -0.67254330182605138, -0.46007833291519956, -0.67215259521101001, -0.44871907432473013, -0.034749316729184583, 0.0055639281302433969, -0.17675902360981591, -0.26196208085032191, -0.36301254306387037, -0.33546767337818123, -0.6458889740799838, -1.1981932989987978, 0.12372650763830917, -1.4996172161865935, -2.4084298023013888, -2.0505291279591722, -1.7249706159518585, -2.277646289702639, -3.1259631743419591, -2.9656385065342015, -2.8480835086962011, -1.4260964500310189, -0.61792590829173544, -0.2611655301498782, -0.38519889843539723, -0.17511899827006483, -0.32808050503227176, 0.0076800871037463036, -0.18710828510427668, 0.1976534820339281, -0.55444453100465052, 0.14583567590328381, -0.69844971117515287, -0.90188577233526623, -0.53500016384583371, -0.044420751861669799, 0.014727914354086128, -0.28084584584371913, -0.29890408748685848, -0.39431380149336548, -0.39569215798819307, -0.74351999988258299, -0.82502198370631752, -1.851491897104155, -0.74302378668934244, 0.21156442062863762, -3.3061472495599986, -1.7990472945779568, -2.2193764251732282, -2.3438802466919251, -3.3615971067123311, -3.5383249085863708, -2.2639673745086588, -2.0271757806780748, -0.75242583405872232, -0.30143411016839378, -0.3625272253546275, -0.25489431004647689, -0.18928491561467081, -0.1179891518538482, 0.027920290231533224, -0.035472107498143821, -0.29008721857562259, -0.3604588674139817, -0.39156143807433802, -0.82222257402876564, -0.44979914971695928, -0.098136330355476253, 0.065628582466229365, -0.33607304327303128, -0.32161201323497779, -0.41856090178723965, -0.64028425429629054, -0.7766428172010218, -1.3946448661671447, -2.2603422126144683, -0.38769722219534525, -0.95341593939478653, -1.412952994959813, -2.3602336858020432, -1.2756392437278019, -2.0983496132652038, -2.5682454610054268, -2.8791053946930378, -2.1809972632688095, -0.84281293847776861, -0.75998936793718697, -0.18584599820380068, -0.30105748355308259, -0.16098142942852958, -0.13792125740417191, -0.089790022871128708, -0.12321821342876504, -0.1128661923016878, -0.3924098378001975, -0.5780902167586397, -0.48685989567066695, -0.53565359443296234, -0.051036689850526382, -0.0068547033925117689, -0.18963405157839419, -0.22514761090777807, -0.35555823460888908, -0.46670603976585517, -0.56179541485257889, -0.7495095888115163, -1.4772075422260349, -1.5836466114968029, -2.3846549454186694, -1.4884613952536236, -1.8237453905245253, -1.6712324532934877, -1.5169157844507295, -1.6930052820597281, -2.1023566589276004, -2.2062031109308458, -1.7945281756942255, -0.26457398838912649, 0.22038139379151148, -0.43479836723775234, -0.19830827357221226, -0.18018565146479498, -0.097060879184795737, -0.10088329756370379, -0.063069709957272527, -0.17970932516041177, -0.1943040732581543, -0.37970560392277619, -0.47302301606251812, -0.30366967948052181, -0.064732391018915397, -0.08902516330269715, -0.082000200083027344, -0.22965854401457736, 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-0.55610134656922283, 0.40792084439497267, 1.0440547633891391, -0.23916839371037832, 0.2750333919575636, 0.62135646441400449, -0.21110858701983135, -0.81615985313544015, 0.14589390394899499, 0.32406742573949032, 0.74952192547288177, -0.32511669967392071, -0.48825453192442569, 0.36648156701751228, 1.0443697855595189, -0.22841081726546683, -1.4950174056034862, 6.4644843028741308, 2.9904131431626397, -13.820343051841599, 1.9854594697574315, -13.304182061875386, -6.3352095159572039, 0.3195679261341049, 0.22665765093840967, 0.19533791786523994, 0.21778449617622839, 0.69288180199640803, 0.084400039832664031, -0.31425797573231284, -0.31479155143425158, 0.078939183973069621, -0.58294801786464789, 0.46161406526582016, 0.41846754429722727, 0.79801858694486438, 0.43858849762191948, 0.23788459440435036, -1.2725586605629382, -0.75720231383362191, -0.29841298969258917, 0.14587335963051393, -0.16753374785242225, -0.21612918483653495, 0.53597221218340851, 0.69495683349647419, -1.0539667118389073, 0.87617222540110107, 4.3629732153958827, -8.0952123464619206, -7.414834109374171, 7.5311386138631651, -44.041788084316849, 22.050605310259897, 5.1510032561702142, -5.6601916863792514, 8.4367427775736488, 1.5703737430868991, -0.83895281997413862, 0.19212817740850727, 0.39792121836056477, -0.14922819541222082, -0.047770712409500753, -0.2908510034609289, -0.015061212014133111, 0.32646574432385927, 0.77395352504545112, -0.16614591312540627, 0.36806371804963284, -0.097634295479077288, 0.091330331747514912, -0.24450075339721231, -0.029095718259234932, 0.16613612027343472, 0.28240974426972948, -0.18044316667269469, -0.48074766055651602, -0.36626836712779753, 3.4507560855810189, -1.9317197634824488, -11.789513877445398, 17.692027714058376, 32.190550839656112, -28.446155418037584, 65.634374404237818, -24.878800155519698, -2.0570987009734387, -3.2997425925449106, -11.516126179313863, 12.372184270457085, 4.9611285532463585, 0.86391702025516592, 0.16530865667454706, -0.46079094226119116, -0.1732663636027687, -0.25470104821282824, -0.43031399471588622, -0.041501479859297648, -0.54386217024143224, 0.81683568275167029, 0.097089152898783726, -0.13744024889929929, -0.095619359707603865, 0.098626184449285684, -0.63036999033225893, -0.18311714867083492, -0.07372642556981146, -0.19104942819406445, 0.075862266735016198, 3.0325028906240856, -9.0326984830007238, -11.815798616251362, 36.620593610799446, 10.636065931319884, -38.68839724466217, 45.716174186409333, -314.74785574475044, 197.27075321520152, 337.61540934331566, 21.930976284520245, -28.837963587037731, -13.475211488788421, 9.5917712473092944, 1.5250850436867665, -1.5545017016282761, -0.64667209976974838, 0.44513357712322837, 0.056507066939540815, -0.23461588343644407, -0.26011219704759359, 0.8042712968338912, 0.30779007494077798, 0.77483290182744469, -0.65133332546861145, -0.18908937081392915, -0.50446476014305819, -0.0074294169071514489, -0.43833208591156614, 0.3383874374890965, 1.0227323524080993, -0.18896973496668346, -8.9206630611282982, -3.6862817789376785, 19.35920062861366, -44.579795546563581, 57.025448777424586, 360.31891091191056, 8.8001261891013822, 1526.2181503116453, 45.053807917762221, -140.68826246910882, 254.89688572081207, -61.967816961200398, -4.5083476182968329, 11.964107143689583, 3.7790359077733431, -1.9045345605049631, -1.7624207728132955, -0.01261576384946491, 0.19558932994062728, -0.30219131214854072, 0.4699644624025669, -0.91230383136372128, 0.36883118795348824, -0.13682839189736087, 0.66713893962058779, -0.25989055470659439, -0.44968314290067052, -1.2882353738829488, -0.76755040332110314, 0.21593130161202181, 1.7124190510555817, 0.6346191100738432, -2.3593378023079388, -10.295701682078779, -39.603849315110132, 54.052681314235315, 182.3786468306393, -282.18880697804133, 735.50774046161428, -423.76919790180091, 46.72930747865378, 744.09540667092074, 65.421023262373566, -26.998515460375824, -110.68919188818332, 1.7026644231740455, 8.6847068298461902, -3.6812627646537122, 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/**
* Numeric Javascript
* Copyright (C) 2011 by Sébastien Loisel
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
"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(',
');
else ret.push('
{');
flag = true;
ret.push(k);
ret.push(':
');
foo(x[k]);
} }
if(flag) ret.push('}
');
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('
'); } 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(',
'); flag = true; ret.push(k); ret.push(':
'); 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('
');
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('
')+'
';
}
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+';
'+
'if(typeof x === "number") { var xi = x; '+body+'; return accum; }
'+
'if(typeof _s === "undefined") _s = numeric.dim(x);
'+
'if(typeof _k === "undefined") _k = 0;
'+
'var _n = _s[_k];
'+
'var i,xi;
'+
'if(_k < _s.length-1) {
'+
' for(i=_n-1;i>=0;i--) {
'+
' accum = arguments.callee(x[i],accum,_s,_k+1);
'+
' }'+
' return accum;
'+
'}
'+
'for(i=_n-1;i>=1;i-=2) {
'+
' xi = x[i];
'+
' '+body+';
'+
' xi = x[i-1];
'+
' '+body+';
'+
'}
'+
'if(i === 0) {
'+
' xi = x[i];
'+
' '+body+'
'+
'}
'+
'return accum;'
);
}
numeric.mapreduce2 = function mapreduce2(body,setup) {
return Function('x',
'var n = x.length;
'+
'var i,xi;
'+setup+';
'+
'for(i=n-1;i!==-1;--i) {
'+
' xi = x[i];
'+
' '+body+';
'+
'}
'+
'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+');
'+
'if(typeof _k === "undefined") _k = 0;
'+
'var _n = _s[_k];
'+
'var i'+(haveret?'':', ret = Array(_n)')+';
'+
'if(_k < _s.length-1) {
'+
' for(i=_n-1;i>=0;i--) ret[i] = arguments.callee('+params.join(',')+',_s,_k+1);
'+
' return ret;
'+
'}
'+
setup+'
'+
'for(i=_n-1;i!==-1;--i) {
'+
' '+body+'
'+
'}
'+
'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;
'+
'var i'+(haveret?'':', ret = Array(_n)')+';
'+
setup+'
'+
'for(i=_n-1;i!==-1;--i) {
'+
body+'
'+
'}
'+
'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+';
';
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;
'+
'var VV = numeric.'+i+'VV, VS = numeric.'+i+'VS, SV = numeric.'+i+'SV;
'+
'var dim = numeric.dim;
'+
'for(i=1;i!==n;++i) {
'+
' y = arguments[i];
'+
' if(typeof x === "object") {
'+
' if(typeof y === "object") x = numeric._biforeach2(x,y,dim(x),0,VV);
'+
' else x = numeric._biforeach2(x,y,dim(x),0,VS);
'+
' } else if(typeof y === "object") x = numeric._biforeach2(x,y,dim(y),0,SV);
'+
' else '+codeeq('x','y')+'
'+
'}
return x;
');
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;
'+
'var V = numeric.'+i+'eqV, S = numeric.'+i+'eqS
'+
'var s = numeric.dim(x);
'+
'for(i=1;i!==n;++i) {
'+
' y = arguments[i];
'+
' if(typeof y === "object") numeric._biforeach(x,y,s,0,V);
'+
' else numeric._biforeach(x,y,s,0,S);
'+
'}
return x;
');
}
}
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+';
';
}
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
'+
'var i;
'+
'var V = numeric.'+i+'eqV;
'+
'var s = numeric.dim(x);
'+
'numeric._foreach(x,s,0,V);
'+
'return x;
');
numeric[i+'V'] = numeric.pointwise2(['x[i]'],'ret[i] = '+o+'(x[i]);',setup);
numeric[i] = Function('x',
'if(typeof x !== "object") return '+o+'(x)
'+
'var i;
'+
'var V = numeric.'+i+'V;
'+
'var s = numeric.dim(x);
'+
'return numeric._foreach2(x,s,0,V);
');
}
}
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;
'+
o[0]+';
'+
' return accum;
'+
'}'+
'if(typeof s === "undefined") s = numeric.dim(x);
'+
'if(typeof k === "undefined") k = 0;
'+
'if(k === s.length-1) return numeric.'+i+'V(x);
'+
'var xi;
'+
'var n = x.length, i;
'+
'for(i=n-1;i!==-1;--i) {
'+
' xi = arguments.callee(x[i]);
'+
o[0]+';
'+
'}
'+
'return accum;
');
}
}
}());
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+';
';
}
}
}
return Function(['y'],
'var x = this;
'+
'if(!(y instanceof numeric.T)) { y = new numeric.T(y); }
'+
setup+'
'+
'if(x.y) {'+
' if(y.y) {'+
' return new numeric.T('+cc+');
'+
' }
'+
' return new numeric.T('+cr+');
'+
'}
'+
'if(y.y) {
'+
' return new numeric.T('+rc+');
'+
'}
'+
'return new numeric.T('+rr+');
'
);
}
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;
'+
s+'
'+
'if(x.y) {'+
' '+c+';
'+
'}
'+
r+';
'
);
}
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();
'+
'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;
'+
'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];
'+
'var Yi = Y[0], Yj = Y[1], Yv = Y[2];
'+
'var n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;
'+
'var Zi = numeric.rep([n+1],0), Zj = [], Zv = [];
'+
'var x = numeric.rep([m],0),y = numeric.rep([m],0);
'+
'var xk,yk,zk;
'+
'var i,j,j0,j1,k,p=0;
'+
setup+
'for(i=0;i<n;++i) {
'+
' j0 = Xi[i]; j1 = Xi[i+1];
'+
' for(j=j0;j!==j1;++j) {
'+
' k = Xj[j];
'+
' x[k] = 1;
'+
' Zj[p] = k;
'+
' ++p;
'+
' }
'+
' j0 = Yi[i]; j1 = Yi[i+1];
'+
' for(j=j0;j!==j1;++j) {
'+
' k = Yj[j];
'+
' y[k] = Yv[j];
'+
' if(x[k] === 0) {
'+
' Zj[p] = k;
'+
' ++p;
'+
' }
'+
' }
'+
' Zi[i+1] = p;
'+
' j0 = Xi[i]; j1 = Xi[i+1];
'+
' for(j=j0;j!==j1;++j) x[Xj[j]] = Xv[j];
'+
' j0 = Zi[i]; j1 = Zi[i+1];
'+
' for(j=j0;j!==j1;++j) {
'+
' k = Zj[j];
'+
' xk = x[k];
'+
' yk = y[k];
'+
body+'
'+
' Zv[j] = zk;
'+
' }
'+
' j0 = Xi[i]; j1 = Xi[i+1];
'+
' for(j=j0;j!==j1;++j) x[Xj[j]] = 0;
'+
' j0 = Yi[i]; j1 = Yi[i+1];
'+
' for(j=j0;j!==j1;++j) y[Yj[j]] = 0;
'+
'}
'+
'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+';
'+
'if(typeof Y === "number") return '+B+';
'+
'return '+C+';
'
);
}
}());
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('
'); }
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+'
Line '+i+': '+MPS[i]+'
Current state: '+states[state]+'
'); }
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' ? '