--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/toolkit/javascript/d3/lib/science/science.js Thu Apr 10 14:20:23 2014 +0200
@@ -0,0 +1,225 @@
+(function(){science = {version: "1.7.0"}; // semver
+science.ascending = function(a, b) {
+ return a - b;
+};
+// Euler's constant.
+science.EULER = .5772156649015329;
+// Compute exp(x) - 1 accurately for small x.
+science.expm1 = function(x) {
+ return (x < 1e-5 && x > -1e-5) ? x + .5 * x * x : Math.exp(x) - 1;
+};
+science.functor = function(v) {
+ return typeof v === "function" ? v : function() { return v; };
+};
+// Based on:
+// http://www.johndcook.com/blog/2010/06/02/whats-so-hard-about-finding-a-hypotenuse/
+science.hypot = function(x, y) {
+ x = Math.abs(x);
+ y = Math.abs(y);
+ var max,
+ min;
+ if (x > y) { max = x; min = y; }
+ else { max = y; min = x; }
+ var r = min / max;
+ return max * Math.sqrt(1 + r * r);
+};
+science.quadratic = function() {
+ var complex = false;
+
+ function quadratic(a, b, c) {
+ var d = b * b - 4 * a * c;
+ if (d > 0) {
+ d = Math.sqrt(d) / (2 * a);
+ return complex
+ ? [{r: -b - d, i: 0}, {r: -b + d, i: 0}]
+ : [-b - d, -b + d];
+ } else if (d === 0) {
+ d = -b / (2 * a);
+ return complex ? [{r: d, i: 0}] : [d];
+ } else {
+ if (complex) {
+ d = Math.sqrt(-d) / (2 * a);
+ return [
+ {r: -b, i: -d},
+ {r: -b, i: d}
+ ];
+ }
+ return [];
+ }
+ }
+
+ quadratic.complex = function(x) {
+ if (!arguments.length) return complex;
+ complex = x;
+ return quadratic;
+ };
+
+ return quadratic;
+};
+// Constructs a multi-dimensional array filled with zeroes.
+science.zeroes = function(n) {
+ var i = -1,
+ a = [];
+ if (arguments.length === 1)
+ while (++i < n)
+ a[i] = 0;
+ else
+ while (++i < n)
+ a[i] = science.zeroes.apply(
+ this, Array.prototype.slice.call(arguments, 1));
+ return a;
+};
+science.vector = {};
+science.vector.cross = function(a, b) {
+ // TODO how to handle non-3D vectors?
+ // TODO handle 7D vectors?
+ return [
+ a[1] * b[2] - a[2] * b[1],
+ a[2] * b[0] - a[0] * b[2],
+ a[0] * b[1] - a[1] * b[0]
+ ];
+};
+science.vector.dot = function(a, b) {
+ var s = 0,
+ i = -1,
+ n = Math.min(a.length, b.length);
+ while (++i < n) s += a[i] * b[i];
+ return s;
+};
+science.vector.length = function(p) {
+ return Math.sqrt(science.vector.dot(p, p));
+};
+science.vector.normalize = function(p) {
+ var length = science.vector.length(p);
+ return p.map(function(d) { return d / length; });
+};
+// 4x4 matrix determinant.
+science.vector.determinant = function(matrix) {
+ var m = matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);
+ return (
+ m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] -
+ m[12] * m[5] * m[10] * m[3] + m[4] * m[13] * m[10] * m[3] +
+ m[8] * m[5] * m[14] * m[3] - m[4] * m[9] * m[14] * m[3] -
+ m[12] * m[9] * m[2] * m[7] + m[8] * m[13] * m[2] * m[7] +
+ m[12] * m[1] * m[10] * m[7] - m[0] * m[13] * m[10] * m[7] -
+ m[8] * m[1] * m[14] * m[7] + m[0] * m[9] * m[14] * m[7] +
+ m[12] * m[5] * m[2] * m[11] - m[4] * m[13] * m[2] * m[11] -
+ m[12] * m[1] * m[6] * m[11] + m[0] * m[13] * m[6] * m[11] +
+ m[4] * m[1] * m[14] * m[11] - m[0] * m[5] * m[14] * m[11] -
+ m[8] * m[5] * m[2] * m[15] + m[4] * m[9] * m[2] * m[15] +
+ m[8] * m[1] * m[6] * m[15] - m[0] * m[9] * m[6] * m[15] -
+ m[4] * m[1] * m[10] * m[15] + m[0] * m[5] * m[10] * m[15]);
+};
+// Performs in-place Gauss-Jordan elimination.
+//
+// Based on Jarno Elonen's Python version (public domain):
+// http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html
+science.vector.gaussjordan = function(m, eps) {
+ if (!eps) eps = 1e-10;
+
+ var h = m.length,
+ w = m[0].length,
+ y = -1,
+ y2,
+ x;
+
+ while (++y < h) {
+ var maxrow = y;
+
+ // Find max pivot.
+ y2 = y; while (++y2 < h) {
+ if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
+ maxrow = y2;
+ }
+
+ // Swap.
+ var tmp = m[y];
+ m[y] = m[maxrow];
+ m[maxrow] = tmp;
+
+ // Singular?
+ if (Math.abs(m[y][y]) <= eps) return false;
+
+ // Eliminate column y.
+ y2 = y; while (++y2 < h) {
+ var c = m[y2][y] / m[y][y];
+ x = y - 1; while (++x < w) {
+ m[y2][x] -= m[y][x] * c;
+ }
+ }
+ }
+
+ // Backsubstitute.
+ y = h; while (--y >= 0) {
+ var c = m[y][y];
+ y2 = -1; while (++y2 < y) {
+ x = w; while (--x >= y) {
+ m[y2][x] -= m[y][x] * m[y2][y] / c;
+ }
+ }
+ m[y][y] /= c;
+ // Normalize row y.
+ x = h - 1; while (++x < w) {
+ m[y][x] /= c;
+ }
+ }
+ return true;
+};
+// Find matrix inverse using Gauss-Jordan.
+science.vector.inverse = function(m) {
+ var n = m.length
+ i = -1;
+
+ // Check if the matrix is square.
+ if (n !== m[0].length) return;
+
+ // Augment with identity matrix I to get AI.
+ m = m.map(function(row, i) {
+ var identity = new Array(n),
+ j = -1;
+ while (++j < n) identity[j] = i === j ? 1 : 0;
+ return row.concat(identity);
+ });
+
+ // Compute IA^-1.
+ science.vector.gaussjordan(m);
+
+ // Remove identity matrix I to get A^-1.
+ while (++i < n) {
+ m[i] = m[i].slice(n);
+ }
+
+ return m;
+};
+science.vector.multiply = function(a, b) {
+ var m = a.length,
+ n = b[0].length,
+ p = b.length,
+ i = -1,
+ j,
+ k;
+ if (p !== a[0].length) throw {"error": "columns(a) != rows(b); " + a[0].length + " != " + p};
+ var ab = new Array(m);
+ while (++i < m) {
+ ab[i] = new Array(n);
+ j = -1; while(++j < n) {
+ var s = 0;
+ k = -1; while (++k < p) s += a[i][k] * b[k][j];
+ ab[i][j] = s;
+ }
+ }
+ return ab;
+};
+science.vector.transpose = function(a) {
+ var m = a.length,
+ n = a[0].length,
+ i = -1,
+ j,
+ b = new Array(n);
+ while (++i < n) {
+ b[i] = new Array(m);
+ j = -1; while (++j < m) b[i][j] = a[j][i];
+ }
+ return b;
+};
+})()
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