vega-statistics - npm Package Compare versions

Comparing version 1.3.1 to 1.4.0

build/vega-statistics.js

@@ -62,19 +62,19 @@ (function (global, factory) {
 
-  function numbers(array, f) {
-    var numbers = [],
-        n = array.length,
-        i = -1, a;
-
-    if (f == null) {
-      while (++i < n) if (!isNaN(a = number(array[i]))) numbers.push(a);
+  function* numbers(values, valueof) {
+    if (valueof === undefined) {
+      for (let value of values) {
+        if (value != null && (value = +value) >= value) {
+          yield value;
+        }
+      }
     } else {
-      while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) numbers.push(a);
+      let index = -1;
+      for (let value of values) {
+        if ((value = valueof(value, ++index, values)) != null && (value = +value) >= value) {
+          yield value;
+        }
+      }
     }
-    return numbers;
   }
 
-  function number(x) {
-    return x === null ? NaN : +x;
-  }
-
   exports.random = Math.random;
@@ -89,3 +89,3 @@
 
-    var values = numbers(array, f),
+    var values = Float64Array.from(numbers(array, f)),
         n = values.length,
@@ -109,3 +109,3 @@ m = samples,
   function quartiles(array, f) {
-    var values = numbers(array, f);
+    var values = Float64Array.from(numbers(array, f));
 
@@ -449,12 +449,474 @@ return [
 
+  // Ordinary Least Squares
+  function ols(uX, uY, uXY, uX2) {
+    const delta = uX2 - uX * uX,
+          slope = Math.abs(delta) < 1e-24 ? 0 : (uXY - uX * uY) / delta,
+          intercept = uY - slope * uX;
+
+    return [intercept, slope];
+  }
+
+  function points(data, x, y, sort) {
+    data = data.filter(d => {
+      let u = x(d), v = y(d);
+      return u != null && (u = +u) >= u && v != null && (v = +v) >= v;
+    });
+
+    if (sort) {
+      data.sort((a, b) => x(a) - x(b));
+    }
+
+    const X = new Float64Array(data.length),
+          Y = new Float64Array(data.length);
+
+    let i = 0;
+    for (let d of data) {
+      X[i] = x(d);
+      Y[i] = y(d);
+      ++i;
+    }
+
+    return [X, Y];
+  }
+
+  function visitPoints(data, x, y, callback) {
+    let index = -1, i = -1, u, v;
+
+    for (let d of data) {
+      u = x(d, ++index, data);
+      v = y(d, index, data);
+      if (u != null && (u = +u) >= u && v != null && (v = +v) >= v) {
+        callback(u, v, ++i);
+      }
+    }
+  }
+
+  // Adapted from d3-regression by Harry Stevens
+  // License: https://github.com/HarryStevens/d3-regression/blob/master/LICENSE
+  function rSquared(data, x, y, uY, predict) {
+    let SSE = 0, SST = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      const sse = dy - predict(dx),
+            sst = dy - uY;
+
+      SSE += sse * sse;
+      SST += sst * sst;
+    });
+
+    return 1 - SSE / SST;
+  }
+
+  // Adapted from d3-regression by Harry Stevens
+  // License: https://github.com/HarryStevens/d3-regression/blob/master/LICENSE
+  function linear(data, x, y) {
+    let X = 0, Y = 0, XY = 0, X2 = 0, n = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      X += dx;
+      Y += dy;
+      XY += dx * dy;
+      X2 += dx * dx;
+      ++n;
+    });
+
+    const coef = ols(X / n, Y / n, XY / n, X2 / n),
+          predict = x => coef[0] + coef[1] * x;
+
+    return {
+      coef: coef,
+      predict: predict,
+      rSquared: rSquared(data, x, y, Y / n, predict)
+    };
+  }
+
+  // Adapted from d3-regression by Harry Stevens
+  // License: https://github.com/HarryStevens/d3-regression/blob/master/LICENSE
+  function log(data, x, y) {
+    let X = 0, Y = 0, XY = 0, X2 = 0, n = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      dx = Math.log(dx);
+      X += dx;
+      Y += dy;
+      XY += dx * dy;
+      X2 += dx * dx;
+      ++n;
+    });
+
+    const coef = ols(X / n, Y / n, XY / n, X2 / n),
+          predict = x => coef[0] + coef[1] * Math.log(x);
+
+    return {
+      coef: coef,
+      predict: predict,
+      rSquared: rSquared(data, x, y, Y / n, predict)
+    };
+  }
+
+  function exp(data, x, y) {
+    let Y = 0, YL = 0, XY = 0, XYL = 0, X2Y = 0, n = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      const ly = Math.log(dy),
+            xy = dx * dy;
+      Y += dy;
+      XY += xy;
+      X2Y += dx * xy;
+      YL += dy * ly;
+      XYL += xy * ly;
+      ++n;
+    });
+
+    const coef = ols(XY / Y, YL / Y, XYL / Y, X2Y / Y),
+          predict = x => coef[0] * Math.exp(coef[1] * x);
+
+    coef[0] = Math.exp(coef[0]);
+
+    return {
+      coef: coef,
+      predict: predict,
+      rSquared: rSquared(data, x, y, Y / n, predict)
+    };
+  }
+
+  // Adapted from d3-regression by Harry Stevens
+  // License: https://github.com/HarryStevens/d3-regression/blob/master/LICENSE
+  function pow(data, x, y) {
+    let X = 0, Y = 0, XY = 0, X2 = 0, YS = 0, n = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      const lx = Math.log(dx),
+            ly = Math.log(dy);
+      X += lx;
+      Y += ly;
+      XY += lx * ly;
+      X2 += lx * lx;
+      YS += dy;
+      ++n;
+    });
+
+    const coef = ols(X / n, Y / n, XY / n, X2 / n),
+          predict = x => coef[0] * Math.pow(x, coef[1]);
+
+    coef[0] = Math.exp(coef[0]);
+
+    return {
+      coef: coef,
+      predict: predict,
+      rSquared: rSquared(data, x, y, YS / n, predict)
+    };
+  }
+
+  function quad(data, x, y) {
+    let X = 0, Y = 0, X2 = 0, X3 = 0, X4 = 0, XY = 0, X2Y = 0, n = 0;
+
+    visitPoints(data, x, y, (dx, dy) => {
+      const x2 = dx * dx;
+      X += dx;
+      Y += dy;
+      X2 += x2;
+      X3 += x2 * dx;
+      X4 += x2 * x2;
+      XY += dx * dy;
+      X2Y += x2 * dy;
+      ++n;
+    });
+
+    Y = Y / n;
+    XY = XY - X * Y;
+    X2Y = X2Y - X2 * Y;
+
+    const XX = X2 - X * X / n,
+          XX2 = X3 - (X2 * X / n),
+          X2X2 = X4 - (X2 * X2 / n),
+          d = (XX * X2X2 - XX2 * XX2),
+          a = (X2Y * XX - XY * XX2) / d,
+          b = (XY * X2X2 - X2Y * XX2) / d,
+          c = Y - (b * (X / n)) - (a * (X2 / n)),
+          predict = x => a * x * x + b * x + c;
+
+    return {
+      coef: [c, b, a],
+      predict: predict,
+      rSquared: rSquared(data, x, y, Y, predict)
+    };
+  }
+
+  // Adapted from d3-regression by Harry Stevens
+  // License: https://github.com/HarryStevens/d3-regression/blob/master/LICENSE
+  // ... which was adapted from regression-js by Tom Alexander
+  // Source: https://github.com/Tom-Alexander/regression-js/blob/master/src/regression.js#L246
+  // License: https://github.com/Tom-Alexander/regression-js/blob/master/LICENSE
+  function poly(data, x, y, order) {
+    // use more efficient methods for lower orders
+    if (order === 1) return linear(data, x, y);
+    if (order === 2) return quad(data, x, y);
+
+    const [xv, yv] = points(data, x, y),
+          n = xv.length,
+          lhs = [],
+          rhs = [],
+          k = order + 1;
+
+    let Y = 0, i, j, l, v, c;
+
+    for (i = 0; i < n; ++i) {
+      Y += yv[i];
+    }
+
+    for (i = 0; i < k; ++i) {
+      for (l = 0, v = 0; l < n; ++l) {
+        v += Math.pow(xv[l], i) * yv[l];
+      }
+      lhs.push(v);
+
+      c = new Float64Array(k);
+      for (j = 0; j < k; ++j) {
+        for (l = 0, v = 0; l < n; ++l) {
+          v += Math.pow(xv[l], i + j);
+        }
+        c[j] = v;
+      }
+      rhs.push(c);
+    }
+    rhs.push(lhs);
+
+    const coef = gaussianElimination(rhs),
+          predict = x => {
+            let y = 0, i = 0, n = coef.length;
+            for (; i < n; ++i) y += coef[i] * Math.pow(x, i);
+            return y;
+          };
+
+    return {
+      coef: coef,
+      predict: predict,
+      rSquared: rSquared(data, x, y, Y / n, predict)
+    };
+  }
+
+  // Given an array for a two-dimensional matrix and the polynomial order,
+  // solve A * x = b using Gaussian elimination.
+  function gaussianElimination(matrix) {
+    const n = matrix.length - 1,
+          coef = [];
+
+    let i, j, k, r, t;
+
+    for (i = 0; i < n; ++i) {
+      r = i; // max row
+      for (j = i + 1; j < n; ++j) {
+        if (Math.abs(matrix[i][j]) > Math.abs(matrix[i][r])) {
+          r = j;
+        }
+      }
+
+      for (k = i; k < n + 1; ++k) {
+        t = matrix[k][i];
+        matrix[k][i] = matrix[k][r];
+        matrix[k][r] = t;
+      }
+
+      for (j = i + 1; j < n; ++j) {
+        for (k = n; k >= i; k--) {
+          matrix[k][j] -= (matrix[k][i] * matrix[i][j]) / matrix[i][i];
+        }
+      }
+    }
+
+    for (j = n - 1; j >= 0; --j) {
+      t = 0;
+      for (k = j + 1; k < n; ++k) {
+        t += matrix[k][j] * coef[k];
+      }
+      coef[j] = (matrix[n][j] - t) / matrix[j][j];
+    }
+
+    return coef;
+  }
+
+  const maxiters = 2,
+        epsilon = 1e-12;
+
+  // Adapted from science.js by Jason Davies
+  // Source: https://github.com/jasondavies/science.js/blob/master/src/stats/loess.js
+  // License: https://github.com/jasondavies/science.js/blob/master/LICENSE
+  function loess(data, x, y, bandwidth) {
+    const [xv, yv] = points(data, x, y, true),
+          n = xv.length,
+          bw = Math.max(2, ~~(bandwidth * n)), // # nearest neighbors
+          yhat = new Float64Array(n),
+          residuals = new Float64Array(n),
+          robustWeights = new Float64Array(n).fill(1);
+
+    for (let iter = -1; ++iter <= maxiters; ) {
+      const interval = [0, bw - 1];
+
+      for (let i = 0; i < n; ++i) {
+        const dx = xv[i],
+              i0 = interval[0],
+              i1 = interval[1],
+              edge = (dx - xv[i0]) > (xv[i1] - dx) ? i0 : i1;
+
+        let W = 0, X = 0, Y = 0, XY = 0, X2 = 0,
+            denom = 1 / Math.abs(xv[edge] - dx || 1); // avoid singularity!
+
+        for (let k = i0; k <= i1; ++k) {
+          const xk = xv[k],
+                yk = yv[k],
+                w = tricube(Math.abs(dx - xk) * denom) * robustWeights[k],
+                xkw = xk * w;
+
+          W += w;
+          X += xkw;
+          Y += yk * w;
+          XY += yk * xkw;
+          X2 += xk * xkw;
+        }
+
+        // linear regression fit
+        const [a, b] = ols(X / W, Y / W, XY / W, X2 / W);
+        yhat[i] = a + b * dx;
+        residuals[i] = Math.abs(yv[i] - yhat[i]);
+
+        updateInterval(xv, i + 1, interval);
+      }
+
+      if (iter === maxiters) {
+        break;
+      }
+
+      const medianResidual = d3Array.median(residuals);
+      if (Math.abs(medianResidual) < epsilon) break;
+
+      for (let i = 0, arg, w; i < n; ++i){
+        arg = residuals[i] / (6 * medianResidual);
+        // default to epsilon (rather than zero) for large deviations
+        // keeping weights tiny but non-zero prevents singularites
+        robustWeights[i] = (arg >= 1) ? epsilon : ((w = 1 - arg * arg) * w);
+      }
+    }
+
+    return output(xv, yhat);
+  }
+
+  // weighting kernel for local regression
+  function tricube(x) {
+    return (x = 1 - x * x * x) * x * x;
+  }
+
+  // advance sliding window interval of nearest neighbors
+  function updateInterval(xv, i, interval) {
+    let val = xv[i],
+        left = interval[0],
+        right = interval[1] + 1;
+
+    if (right >= xv.length) return;
+
+    // step right if distance to new right edge is <= distance to old left edge
+    // step when distance is equal to ensure movement over duplicate x values
+    while (i > left && (xv[right] - val) <= (val - xv[left])) {
+      interval[0] = ++left;
+      interval[1] = right;
+      ++right;
+    }
+  }
+
+  // generate smoothed output points
+  // average points with repeated x values
+  function output(xv, yhat) {
+    const n = xv.length,
+          out = [];
+
+    for (let i=0, cnt=0, prev=[], v; i<n; ++i) {
+      v = xv[i];
+      if (prev[0] === v) {
+        // average output values via online update
+        prev[1] += (yhat[i] - prev[1]) / (++cnt);
+      } else {
+        // add new output point
+        cnt = 0;
+        prev = [v, yhat[i]];
+        out.push(prev);
+      }
+    }
+    return out;
+  }
+
+  // subdivide up to accuracy of 0.1 degrees
+  const MIN_RADIANS = 0.1 * Math.PI / 180;
+
+  // Adaptively sample an interpolated function over a domain extent
+  function sampleCurve(f, extent, minSteps, maxSteps) {
+    minSteps = minSteps || 25;
+    maxSteps = Math.max(minSteps, maxSteps || 200);
+
+    const point = x => [x, f(x)],
+          minX = extent[0],
+          maxX = extent[1],
+          span = maxX - minX,
+          stop = span / maxSteps,
+          prev = [point(minX)],
+          next = [];
+
+    if (minSteps === maxSteps) {
+      // no adaptation, sample uniform grid directly and return
+      for (let i = 1; i < maxSteps; ++i) {
+        prev.push(point(minX + (i / minSteps) * span));
+      }
+      prev.push(point(maxX));
+      return prev;
+    } else {
+      // sample minimum points on uniform grid
+      // then move on to perform adaptive refinement
+      next.push(point(maxX));
+      for (let i = minSteps; --i > 0;) {
+        next.push(point(minX + (i / minSteps) * span));
+      }
+    }
+
+    let p0 = prev[0],
+        p1 = next[next.length - 1];
+
+    while (p1) {
+      const pm = point((p0[0] + p1[0]) / 2);
+
+      if (pm[0] - p0[0] >= stop && angleDelta(p0, pm, p1) > MIN_RADIANS) {
+        next.push(pm);
+      } else {
+        p0 = p1;
+        prev.push(p1);
+        next.pop();
+      }
+      p1 = next[next.length - 1];
+    }
+
+    return prev;
+  }
+
+  function angleDelta(p, q, r) {
+    const a0 = Math.atan2(r[1] - p[1], r[0] - p[0]),
+          a1 = Math.atan2(q[1] - p[1], q[0] - p[0]);
+    return Math.abs(a0 - a1);
+  }
+
   exports.bin = bin;
   exports.bootstrapCI = bootstrapCI;
   exports.quartiles = quartiles;
-  exports.setRandom = setRandom;
-  exports.randomLCG = lcg;
   exports.randomInteger = integer;
   exports.randomKDE = kde;
+  exports.randomLCG = lcg;
   exports.randomMixture = mixture;
   exports.randomNormal = gaussian;
   exports.randomUniform = uniform;
+  exports.regressionExp = exp;
+  exports.regressionLinear = linear;
+  exports.regressionLoess = loess;
+  exports.regressionLog = log;
+  exports.regressionPoly = poly;
+  exports.regressionPow = pow;
+  exports.regressionQuad = quad;
+  exports.sampleCurve = sampleCurve;
+  exports.setRandom = setRandom;
 
@@ -461,0 +923,0 @@ Object.defineProperty(exports, '__esModule', { value: true });

build/vega-statistics.min.js

@@ -1,1 +0,1 @@
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u=0;for(let e of t)o[u]=n(e),a[u]=r(e),++u;return[o,a]}function f(t,n,r,e){let o,a,u=-1,f=-1;for(let i of t)o=n(i,++u,t),a=r(i,u,t),null!=o&&(o=+o)>=o&&null!=a&&(a=+a)>=a&&e(o,a,++f)}function i(t,n,r,e,o){let a=0,u=0;return f(t,n,r,(t,n)=>{const r=n-o(t),f=n-e;a+=r*r,u+=f*f}),1-a/u}function l(t,n,r){let e=0,o=0,u=0,l=0,c=0;f(t,n,r,(t,n)=>{e+=t,o+=n,u+=t*n,l+=t*t,++c});const s=a(e/c,o/c,u/c,l/c),h=t=>s[0]+s[1]*t;return{coef:s,predict:h,rSquared:i(t,n,r,o/c,h)}}function c(t,n,r){let e=0,o=0,a=0,u=0,l=0,c=0,s=0,h=0;f(t,n,r,(t,n)=>{const r=t*t;e+=t,o+=n,a+=r,u+=r*t,l+=r*r,c+=t*n,s+=r*n,++h});const d=a-e*e/h,p=u-a*e/h,M=l-a*a/h,g=d*M-p*p,m=((s-=a*(o/=h))*d-(c-=e*o)*p)/g,v=(c*M-s*p)/g,w=o-v*(e/h)-m*(a/h),b=t=>m*t*t+v*t+w;return{coef:[w,v,m],predict:b,rSquared:i(t,n,r,o,b)}}t.random=Math.random;const s=2,h=1e-12;function d(t){return(t=1-t*t*t)*t*t}function p(t,n,r){let e=t[n],o=r[0],a=r[1]+1;if(!(a>=t.length))for(;n>o&&t[a]-e<=e-t[o];)r[0]=++o,r[1]=a,++a}const M=.1*Math.PI/180;function g(t,n,r){const e=Math.atan2(r[1]-t[1],r[0]-t[0]),o=Math.atan2(n[1]-t[1],n[0]-t[0]);return Math.abs(e-o)}t.bin=function(t){var n,r,e,o,a,u,f,i,l=t.maxbins||20,c=t.base||10,s=Math.log(c),h=t.divide||[5,2],d=t.extent[0],p=t.extent[1],M=p-d||Math.abs(d)||1;if(t.step)n=t.step;else if(t.steps){for(a=M/l,u=0,f=t.steps.length;u<f&&t.steps[u]<a;++u);n=t.steps[Math.max(0,u-1)]}else{for(r=Math.ceil(Math.log(l)/s),e=t.minstep||0,n=Math.max(e,Math.pow(c,Math.round(Math.log(M)/s)-r));Math.ceil(M/n)>l;)n*=c;for(u=0,f=h.length;u<f;++u)(a=n/h[u])>=e&&M/a<=l&&(n=a)}return o=(a=Math.log(n))>=0?0:1+~~(-a/s),i=Math.pow(c,-o-1),(t.nice||void 0===t.nice)&&(d=d<(a=Math.floor(d/n+i)*n)?a-n:a,p=Math.ceil(p/n)*n),{start:d,stop:p===d?d+n:p,step:n}},t.bootstrapCI=function(e,o,a,u){if(!e.length)return[void 0,void 0];var f,i,l,c,s=Float64Array.from(r(e,u)),h=s.length,d=o;for(l=0,c=Array(d);l<d;++l){for(f=0,i=0;i<h;++i)f+=s[~~(t.random()*h)];c[l]=f/h}return[n.quantile(c.sort(n.ascending),a/2),n.quantile(c,1-a/2)]},t.quartiles=e,t.randomInteger=function(n,r){null==r&&(r=n,n=0);var e,o,a,u={};return u.min=function(t){return arguments.length?(a=o-(e=t||0),u):e},u.max=function(t){return arguments.length?(a=(o=t||0)-e,u):o},u.sample=function(){return e+Math.floor(a*t.random())},u.pdf=function(t){return t===Math.floor(t)&&t>=e&&t<o?1/a:0},u.cdf=function(t){var n=Math.floor(t);return n<e?0:n>=o?1:(n-e+1)/a},u.icdf=function(t){return t>=0&&t<=1?e-1+Math.floor(t*a):NaN},u.min(n).max(r)},t.randomKDE=function(r,a){var u=o(),f={},i=0;return f.data=function(t){return arguments.length?(r=t,i=t?t.length:0,f.bandwidth(a)):r},f.bandwidth=function(t){return arguments.length?(!(a=t)&&r&&(u=(o=r).length,i=e(o),l=(i[2]-i[0])/1.34,a=1.06*Math.min(Math.sqrt(n.variance(o)),l)*Math.pow(u,-.2)),f):a;var o,u,i,l},f.sample=function(){return r[~~(t.random()*i)]+a*u.sample()},f.pdf=function(t){for(var n=0,e=0;e<i;++e)n+=u.pdf((t-r[e])/a);return n/a/i},f.cdf=function(t){for(var n=0,e=0;e<i;++e)n+=u.cdf((t-r[e])/a);return n/i},f.icdf=function(){throw Error("KDE icdf not supported.")},f.data(r)},t.randomLCG=function(t){return function(){return(t=(1103515245*t+12345)%2147483647)/2147483647}},t.randomMixture=function(n,r){var e,o={},a=0;return o.weights=function(t){return arguments.length?(e=function(t){var n,r=[],e=0;for(n=0;n<a;++n)e+=r[n]=null==t[n]?1:+t[n];for(n=0;n<a;++n)r[n]/=e;return r}(r=t||[]),o):r},o.distributions=function(t){return arguments.length?(t?(a=t.length,n=t):(a=0,n=[]),o.weights(r)):n},o.sample=function(){for(var r=t.random(),o=n[a-1],u=e[0],f=0;f<a-1;u+=e[++f])if(r<u){o=n[f];break}return o.sample()},o.pdf=function(t){for(var r=0,o=0;o<a;++o)r+=e[o]*n[o].pdf(t);return r},o.cdf=function(t){for(var r=0,o=0;o<a;++o)r+=e[o]*n[o].cdf(t);return r},o.icdf=function(){throw Error("Mixture icdf not supported.")},o.distributions(n).weights(r)},t.randomNormal=o,t.randomUniform=function(n,r){null==r&&(r=null==n?1:n,n=0);var e,o,a,u={};return u.min=function(t){return arguments.length?(a=o-(e=t||0),u):e},u.max=function(t){return arguments.length?(a=(o=t||0)-e,u):o},u.sample=function(){return e+a*t.random()},u.pdf=function(t){return t>=e&&t<=o?1/a:0},u.cdf=function(t){return t<e?0:t>o?1:(t-e)/a},u.icdf=function(t){return t>=0&&t<=1?e+t*a:NaN},u.min(n).max(r)},t.regressionExp=function(t,n,r){let e=0,o=0,u=0,l=0,c=0,s=0;f(t,n,r,(t,n)=>{const r=Math.log(n),a=t*n;e+=n,u+=a,c+=t*a,o+=n*r,l+=a*r,++s});const h=a(u/e,o/e,l/e,c/e),d=t=>h[0]*Math.exp(h[1]*t);return h[0]=Math.exp(h[0]),{coef:h,predict:d,rSquared:i(t,n,r,e/s,d)}},t.regressionLinear=l,t.regressionLoess=function(t,r,e,o){const[f,i]=u(t,r,e,!0),l=f.length,c=Math.max(2,~~(o*l)),M=new Float64Array(l),g=new Float64Array(l),m=new Float64Array(l).fill(1);for(let t=-1;++t<=s;){const r=[0,c-1];for(let t=0;t<l;++t){const n=f[t],e=r[0],o=r[1],u=n-f[e]>f[o]-n?e:o;let l=0,c=0,s=0,h=0,v=0,w=1/Math.abs(f[u]-n||1);for(let t=e;t<=o;++t){const r=f[t],e=i[t],o=d(Math.abs(n-r)*w)*m[t],a=r*o;l+=o,c+=a,s+=e*o,h+=e*a,v+=r*a}const[b,x]=a(c/l,s/l,h/l,v/l);M[t]=b+x*n,g[t]=Math.abs(i[t]-M[t]),p(f,t+1,r)}if(t===s)break;const e=n.median(g);if(Math.abs(e)<h)break;for(let t,n,r=0;r<l;++r)t=g[r]/(6*e),m[r]=t>=1?h:(n=1-t*t)*n}return function(t,n){const r=t.length,e=[];for(let o,a=0,u=0,f=[];a<r;++a)o=t[a],f[0]===o?f[1]+=(n[a]-f[1])/++u:(u=0,f=[o,n[a]],e.push(f));return e}(f,M)},t.regressionLog=function(t,n,r){let e=0,o=0,u=0,l=0,c=0;f(t,n,r,(t,n)=>{t=Math.log(t),e+=t,o+=n,u+=t*n,l+=t*t,++c});const s=a(e/c,o/c,u/c,l/c),h=t=>s[0]+s[1]*Math.log(t);return{coef:s,predict:h,rSquared:i(t,n,r,o/c,h)}},t.regressionPoly=function(t,n,r,e){if(1===e)return l(t,n,r);if(2===e)return c(t,n,r);const[o,a]=u(t,n,r),f=o.length,s=[],h=[],d=e+1;let p,M,g,m,v,w=0;for(p=0;p<f;++p)w+=a[p];for(p=0;p<d;++p){for(g=0,m=0;g<f;++g)m+=Math.pow(o[g],p)*a[g];for(s.push(m),v=new Float64Array(d),M=0;M<d;++M){for(g=0,m=0;g<f;++g)m+=Math.pow(o[g],p+M);v[M]=m}h.push(v)}h.push(s);const b=function(t){const n=t.length-1,r=[];let e,o,a,u,f;for(e=0;e<n;++e){for(u=e,o=e+1;o<n;++o)Math.abs(t[e][o])>Math.abs(t[e][u])&&(u=o);for(a=e;a<n+1;++a)f=t[a][e],t[a][e]=t[a][u],t[a][u]=f;for(o=e+1;o<n;++o)for(a=n;a>=e;a--)t[a][o]-=t[a][e]*t[e][o]/t[e][e]}for(o=n-1;o>=0;--o){for(f=0,a=o+1;a<n;++a)f+=t[a][o]*r[a];r[o]=(t[n][o]-f)/t[o][o]}return r}(h),x=t=>{let n=0,r=0,e=b.length;for(;r<e;++r)n+=b[r]*Math.pow(t,r);return n};return{coef:b,predict:x,rSquared:i(t,n,r,w/f,x)}},t.regressionPow=function(t,n,r){let e=0,o=0,u=0,l=0,c=0,s=0;f(t,n,r,(t,n)=>{const r=Math.log(t),a=Math.log(n);e+=r,o+=a,u+=r*a,l+=r*r,c+=n,++s});const h=a(e/s,o/s,u/s,l/s),d=t=>h[0]*Math.pow(t,h[1]);return h[0]=Math.exp(h[0]),{coef:h,predict:d,rSquared:i(t,n,r,c/s,d)}},t.regressionQuad=c,t.sampleCurve=function(t,n,r,e){r=r||25,e=Math.max(r,e||200);const o=n=>[n,t(n)],a=n[0],u=n[1],f=u-a,i=f/e,l=[o(a)],c=[];if(r===e){for(let t=1;t<e;++t)l.push(o(a+t/r*f));return l.push(o(u)),l}c.push(o(u));for(let t=r;--t>0;)c.push(o(a+t/r*f));let s=l[0],h=c[c.length-1];for(;h;){const t=o((s[0]+h[0])/2);t[0]-s[0]>=i&&g(s,t,h)>M?c.push(t):(s=h,l.push(h),c.pop()),h=c[c.length-1]}return l},t.setRandom=function(n){t.random=n},Object.defineProperty(t,"__esModule",{value:!0})});

index.js

@@ -11,1 +11,9 @@ export {default as bin} from './src/bin';
 export {default as randomUniform} from './src/uniform';
+export {default as regressionLinear} from './src/regression/linear';
+export {default as regressionLog} from './src/regression/log';
+export {default as regressionExp} from './src/regression/exp';
+export {default as regressionPow} from './src/regression/pow';
+export {default as regressionQuad} from './src/regression/quad';
+export {default as regressionPoly} from './src/regression/poly';
+export {default as regressionLoess} from './src/regression/loess';
+export {default as sampleCurve} from './src/sampleCurve';

package.json

 {
   "name": "vega-statistics",
-  "version": "1.3.1",
+  "version": "1.4.0",
   "description": "Statistical routines and probability distributions.",
@@ -29,3 +29,3 @@ "keywords": [
   },
-  "gitHead": "8e012f8b7b5a520bb60a2b5ebb0764991048e16a"
+  "gitHead": "d2576ca617d8165211ffe6c23582b9dc1b88db7d"
 }

README.md

@@ -9,2 +9,3 @@ # vega-statistics
 - [Distributions](#distributions)
+- [Regression](#regression)
 - [Statistics](#statistics)
@@ -83,2 +84,80 @@
 
+### Regression
+
+Two-dimensional regression methods to predict one variable given another.
+
+<a name="regressionLinear" href="#regressionLinear">#</a>
+vega.<b>regressionLinear</b>(<i>data</i>, <i>x</i>, <i>y</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/linear.js "Source")
+
+Fit a linear regression model with functional form _y = a + b * x_ for the input *data* array and corresponding *x* and *y* accessor functions. Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An array of fitted coefficients of the form _[a, b]_.
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionLog" href="#regressionLog">#</a>
+vega.<b>regressionLog</b>(<i>data</i>, <i>x</i>, <i>y</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/log.js "Source")
+
+Fit a logarithmic regression model with functional form _y = a + b * log(x)_ for the input input *data* array and corresponding *x* and *y* accessor functions.
+
+Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An array of fitted coefficients of the form _[a, b]_.
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionExp" href="#regressionExp">#</a>
+vega.<b>regressionExp</b>(<i>data</i>, <i>x</i>, <i>y</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/exp.js "Source")
+
+Fit an exponential regression model with functional form _y = a + e<sup>b * x</sup>_ for the input *data* array and corresponding *x* and *y* accessor functions. Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An array of fitted coefficients of the form _[a, b]_.
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionPow" href="#regressionPow">#</a>
+vega.<b>regressionPow</b>(<i>data</i>, <i>x</i>, <i>y</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/pow.js "Source")
+
+Fit a power law regression model with functional form _y = a * x<sup>b</sup>_ for the input *data* array and corresponding *x* and *y* accessor functions. Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An array of fitted coefficients of the form _[a, b]_.
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionQuad" href="#regressionQuad">#</a>
+vega.<b>regressionLinear</b>(<i>data</i>, <i>x</i>, <i>y</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/quad.js "Source")
+
+Fit a quadratic regression model with functional form _y = a + b * x + c * x<sup>2</sup>_ for the input *data* array and corresponding *x* and *y* accessor functions. Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An array of fitted coefficients of the form _[a, b, c]_,
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionPoly" href="#regressionPoly">#</a>
+vega.<b>regressionPoly</b>(<i>data</i>, <i>x</i>, <i>y</i>, <i>order</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/poly.js "Source")
+
+Fit a polynomial regression model of specified _order_ with functional form _y = a + b * x + ... + k * x<sup>order</sup>_ for the input *data* array and corresponding *x* and *y* accessor functions. Returns an object for the fit model parameters with the following properties:
+
+- _coef_: An _(order + 1)_-length array of polynomial coefficients of the form _[a, b, c, d, ...]_.
+- _predict_: A function that returns a regression prediction for an input _x_ value.
+- _rSquared_: The R<sup>2</sup> [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), indicating the amount of total variance of _y_ accounted for by the model.
+
+<a name="regressionLoess" href="#regressionLoess">#</a>
+vega.<b>regressionLoess/b>(<i>data</i>, <i>x</i>, <i>y</i>, <i>bandwidth</i>)
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/regression/loess.js "Source")
+
+Fit a smoothed, non-parametric trend line the input *data* array and corresponding *x* and *y* accessor functions using _loess_ (locally-estimated scatterplot smoothing). Loess performs a sequence of local weighted regressions over a sliding window of nearest-neighbor points. The _bandwidth_ argument determines the size of the sliding window, expressed as a [0, 1] fraction of the total number of data points included.
+
+<a name="sampleCurve" href="#sampleCurve">#</a>
+vega.<b>sampleCurve</b>(<i>f</i>, <i>extent</i>[, <i>minSteps</i>, <i>maxSteps</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/sampleCurve.js "Source")
+
+Generate sample points from an interpolation function _f_ for the provided domain _extent_ and return an array of _[x, y]_ points. Performs adaptive subdivision to dynamically sample more points in regions of higher curvature. Subdivision stops when the difference in angles between the current samples and a proposed subdivision falls below one-quarter of a degree. The optional _minSteps_ argument (default 25), determines the minimal number of initial, uniformly-spaced sample points to draw. The optional _maxSteps_ argument (default 200), indicates the maximum resolution at which adaptive sampling will stop, defined relative to a uniform grid of size _maxSteps_. If _minSteps_ and _maxSteps_ are identical, no adaptive sampling will be performed and only the initial, uniformly-spaced samples will be returned.
+
 ### Statistics
@@ -85,0 +164,0 @@

src/bootstrapCI.js

@@ -8,3 +8,3 @@ import numbers from './numbers';
 
-  var values = numbers(array, f),
+  var values = Float64Array.from(numbers(array, f)),
       n = values.length,
@@ -11,0 +11,0 @@ m = samples,

src/numbers.js

@@ -1,16 +0,16 @@
-export default function(array, f) {
-  var numbers = [],
-      n = array.length,
-      i = -1, a;
-
-  if (f == null) {
-    while (++i < n) if (!isNaN(a = number(array[i]))) numbers.push(a);
+export default function*(values, valueof) {
+  if (valueof === undefined) {
+    for (let value of values) {
+      if (value != null && (value = +value) >= value) {
+        yield value;
+      }
+    }
   } else {
-    while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) numbers.push(a);
+    let index = -1;
+    for (let value of values) {
+      if ((value = valueof(value, ++index, values)) != null && (value = +value) >= value) {
+        yield value;
+      }
+    }
   }
-  return numbers;
 }
-
-function number(x) {
-  return x === null ? NaN : +x;
-}

src/quartiles.js

@@ -5,3 +5,3 @@ import numbers from './numbers';
 export default function(array, f) {
-  var values = numbers(array, f);
+  var values = Float64Array.from(numbers(array, f));
 
@@ -8,0 +8,0 @@ return [

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