in MotionMark/resources/statistics.js [244:390]
_calculateRegression: function(samples, getComplexity, getFrameLength, startIndex, endIndex, options)
{
if (startIndex == endIndex) {
// Only one sample point; we can't calculate any regression.
var x = getComplexity(samples, startIndex);
return {
complexity: x,
s1: x,
t1: 0,
s2: x,
t2: 0,
error1: 0,
error2: 0
};
}
// x is expected to increase in complexity
var iterationDirection = endIndex > startIndex ? 1 : -1;
var lowComplexity = getComplexity(samples, startIndex);
var highComplexity = getComplexity(samples, endIndex);
var a1 = 0, b1 = 0, c1 = 0, d1 = 0, h1 = 0, k1 = 0;
var a2 = 0, b2 = 0, c2 = 0, d2 = 0, h2 = 0, k2 = 0;
// Iterate from low to high complexity
for (var i = startIndex; iterationDirection * (endIndex - i) > -1; i += iterationDirection) {
var x = getComplexity(samples, i);
var y = getFrameLength(samples, i);
a2 += 1;
b2 += x;
c2 += x * x;
d2 += y;
h2 += y * x;
k2 += y * y;
}
var s1_best, t1_best, s2_best, t2_best, n1_best, n2_best, error1_best, error2_best, x_best, x_prime;
function setBest(s1, t1, error1, s2, t2, error2, splitIndex, x_prime, x)
{
s1_best = s1;
t1_best = t1;
error1_best = error1;
s2_best = s2;
t2_best = t2;
error2_best = error2;
// Number of samples included in the first segment, inclusive of splitIndex
n1_best = iterationDirection * (splitIndex - startIndex) + 1;
// Number of samples included in the second segment
n2_best = iterationDirection * (endIndex - splitIndex);
if (!options.shouldClip || (x_prime >= lowComplexity && x_prime <= highComplexity))
x_best = x_prime;
else {
// Discontinuous piecewise regression
x_best = x;
}
}
// Iterate from startIndex to endIndex - 1, inclusive
for (var i = startIndex; iterationDirection * (endIndex - i) > 0; i += iterationDirection) {
var x = getComplexity(samples, i);
var y = getFrameLength(samples, i);
var xx = x * x;
var yx = y * x;
var yy = y * y;
// a1, b1, etc. is sum from startIndex to i, inclusive
a1 += 1;
b1 += x;
c1 += xx;
d1 += y;
h1 += yx;
k1 += yy;
// a2, b2, etc. is sum from i+1 to endIndex, inclusive
a2 -= 1;
b2 -= x;
c2 -= xx;
d2 -= y;
h2 -= yx;
k2 -= yy;
var A = c1*d1 - b1*h1;
var B = a1*h1 - b1*d1;
var C = a1*c1 - b1*b1;
var D = c2*d2 - b2*h2;
var E = a2*h2 - b2*d2;
var F = a2*c2 - b2*b2;
var s1 = options.s1 !== undefined ? options.s1 : (A / C);
var t1 = options.t1 !== undefined ? options.t1 : (B / C);
var s2 = options.s2 !== undefined ? options.s2 : (D / F);
var t2 = options.t2 !== undefined ? options.t2 : (E / F);
// Assumes that the two segments meet
var x_prime = (s1 - s2) / (t2 - t1);
var error1 = (k1 + a1*s1*s1 + c1*t1*t1 - 2*d1*s1 - 2*h1*t1 + 2*b1*s1*t1) || Number.MAX_VALUE;
var error2 = (k2 + a2*s2*s2 + c2*t2*t2 - 2*d2*s2 - 2*h2*t2 + 2*b2*s2*t2) || Number.MAX_VALUE;
if (i == startIndex) {
setBest(s1, t1, error1, s2, t2, error2, i, x_prime, x);
continue;
}
if (C == 0 || F == 0)
continue;
// Projected point is not between this and the next sample
if (x_prime > getComplexity(samples, i + iterationDirection) || x_prime < x) {
// Calculate lambda, which divides the weight of this sample between the two lines
// These values remove the influence of this sample
var I = c1 - 2*b1*x + a1*xx;
var H = C - I;
var G = A + B*x - C*y;
var J = D + E*x - F*y;
var K = c2 - 2*b2*x + a2*xx;
var lambda = (G*F + G*K - H*J) / (I*J + G*K);
if (lambda > 0 && lambda < 1) {
var lambda1 = 1 - lambda;
s1 = options.s1 !== undefined ? options.s1 : ((A - lambda1*(-h1*x + d1*xx + c1*y - b1*yx)) / (C - lambda1*I));
t1 = options.t1 !== undefined ? options.t1 : ((B - lambda1*(h1 - d1*x - b1*y + a1*yx)) / (C - lambda1*I));
s2 = options.s2 !== undefined ? options.s2 : ((D + lambda1*(-h2*x + d2*xx + c2*y - b2*yx)) / (F + lambda1*K));
t2 = options.t2 !== undefined ? options.t2 : ((E + lambda1*(h2 - d2*x - b2*y + a2*yx)) / (F + lambda1*K));
x_prime = (s1 - s2) / (t2 - t1);
error1 = ((k1 + a1*s1*s1 + c1*t1*t1 - 2*d1*s1 - 2*h1*t1 + 2*b1*s1*t1) - lambda1 * Math.pow(y - (s1 + t1*x), 2)) || Number.MAX_VALUE;
error2 = ((k2 + a2*s2*s2 + c2*t2*t2 - 2*d2*s2 - 2*h2*t2 + 2*b2*s2*t2) + lambda1 * Math.pow(y - (s2 + t2*x), 2)) || Number.MAX_VALUE;
} else if (t1 != t2)
continue;
}
if (error1 + error2 < error1_best + error2_best)
setBest(s1, t1, error1, s2, t2, error2, i, x_prime, x);
}
return {
complexity: x_best,
s1: s1_best,
t1: t1_best,
stdev1: Math.sqrt(error1_best / n1_best),
s2: s2_best,
t2: t2_best,
stdev2: Math.sqrt(error2_best / n2_best),
error: error1_best + error2_best,
n1: n1_best,
n2: n2_best
};
}