gauss-2d.juttle

reducer normal(mean, sigma) {
    // return a Box-Muller approximate normal with given mean and stddev.
    // this is written as a custom "reducer" because Box-Muller values come
    // in pairs, and we want to save one for next time. 
    // 
    var leftover = null;
    function update() {}
    function result() {
        if (leftover != null) { 
            var result = mean + sigma * leftover; 
            leftover = null;
            return result;
        } else {
            var u = 2 * Math.random() - 1;
            var v = 2 * Math.random() - 1;
            var r = u*u + v*v;
            if (r == 0 || r > 1) {
                // out of bounds, try again
                return result();
            }
            var c = Math.sqrt(-2*Math.log(r)/r);
            leftover = u * c;
            return mean + sigma * v * c;
        }
    }
}
reducer xdp(y, P) {
    // given a list of data values and corresponding percentiles, return the
    // derivative. This numerically differentiates  the EDF to get an approximate
    // PDF. It can be a bumpy ride.
    var Y = [];
    function update() {
        Y = *y; //P = *pct;
    }
    function iter(X, dPdX, n) { 
        if (X == null || X[n+1] == null) {
            return dPdX;
        } else if (n > 0) {
            dPdX[n] = [(X[n+1]+X[n])/2, (P[n+1] - P[n]) / (X[n+1] - X[n])];
        }
        return iter(X, dPdX, n+1);
    }
    function result() { 
        return iter(Y, [0], 0);
    }
}
export const PCT = [0, .01, .02, .03, .04,.05,.06,.07, .1, .15, .2, .25, .3, .35, .4, .45, .5, .55, .6, .65, .7, .75, .8, .85, .9, .92,.93,.94,.95,.96, .97, .98, .99, 1];
export sub run() {
    emit -limit 100000 -every :.01s:
        | put -acc true x=normal(10,1), y=normal(11, 2)
        | (@scatterchart -controlField 'x' -valueField 'y' -title 'X vs Y' 
           -display.duration :3s: -display.markerOpacity 0.5; merge)
        | reduce -acc true -every :3s: px = percentile(x, PCT), py = percentile(y, PCT)
        | put dpx = xdp(px, PCT), dpy = xdp(py, PCT) 
        | split dpx, dpy
        | put x=value[0], dp=value[1]
        | @scatterchart -controlField 'x' -valueField 'dp' -title 'density' -keyField 'name' 
        -display.duration :3s:
}
run