@Override
public Numeric gradient(Var y, Var fx) {
Numeric delta = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
delta.addValue(y.value(i) - fx.value(i));
}
return delta;
}
@Override
public Numeric gradient(Var y, Var fx) {
Numeric gradient = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
gradient.addValue(y.value(i) - fx.value(i) < 0 ? -1. : 1.);
}
return gradient;
}
public BoxPlot(Var x, Var factor, GOpt... opts) {
Map<String, List<Double>> map =
x.stream().collect(groupingBy(s -> factor.label(s.row()), mapping(VSpot::value, toList())));
names = factor.streamLevels().filter(map::containsKey).toArray(String[]::new);
vars = Arrays.stream(names).map(map::get).map(Numeric::copy).toArray(Var[]::new);
this.options.apply(opts);
initialize();
}
@Override
public double findMinimum(Var y, Var fx) {
Numeric values = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
values.addValue(y.value(i) - fx.value(i));
}
double result = Quantiles.from(values, new double[] {0.5}).values()[0];
if (Double.isNaN(result)) {
WS.println();
}
return result;
}
@Override
public Range buildRange() {
Range range = new Range();
range.union(0, Double.NaN);
range.union(vars.length, Double.NaN);
for (Var v : vars) {
for (int i = 0; i < v.rowCount(); i++) {
if (v.missing(i)) continue;
range.union(Double.NaN, v.value(i));
}
}
return range;
}
@Override
public Numeric gradient(Var y, Var fx) {
// compute absolute residuals
Numeric absResidual = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
absResidual.addValue(Math.abs(y.value(i) - fx.value(i)));
}
// compute rho as an alpha-quantile of absolute residuals
double rho = Quantiles.from(absResidual, new double[] {alpha}).values()[0];
// now compute gradient
Numeric gradient = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
if (absResidual.value(i) <= rho) {
gradient.addValue(y.value(i) - fx.value(i));
} else {
gradient.addValue(rho * ((y.value(i) - fx.value(i) <= 0) ? -1 : 1));
}
}
// return gradient
return gradient;
}
private Minimum(Var var) {
this.varName = var.name();
for (int i = 0; i < var.rowCount(); i++) {
if (var.missing(i)) {
missingCount++;
} else {
completeCount++;
}
}
if (var.stream().complete().count() == 0) {
value = Double.NaN;
} else {
value = var.stream().complete().mapToDouble().min().getAsDouble();
}
}
@Override
public double findMinimum(Var y, Var fx) {
// compute residuals
Numeric residual = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
residual.addValue(y.value(i) - fx.value(i));
}
// compute median of residuals
double r_bar = Quantiles.from(residual, new double[] {0.5}).values()[0];
// compute absolute residuals
Numeric absResidual = Numeric.empty();
for (int i = 0; i < y.rowCount(); i++) {
absResidual.addValue(Math.abs(y.value(i) - fx.value(i)));
}
// compute rho as an alpha-quantile of absolute residuals
double rho = Quantiles.from(absResidual, new double[] {alpha}).values()[0];
// compute one-iteration approximation
double gamma = r_bar;
double count = y.rowCount();
for (int i = 0; i < y.rowCount(); i++) {
gamma +=
(residual.value(i) - r_bar <= 0 ? -1 : 1)
* Math.min(rho, Math.abs(residual.value(i) - r_bar))
/ count;
}
return gamma;
}
// compute the FFT of x[], assuming its length is a power of 2
public static Pair<Var, Var> fft(Pair<Var, Var> x) {
int N = x._1.rowCount();
// base case
if (N == 1) return x;
// radix 2 Cooley-Tukey FFT
if (N % 2 != 0) {
throw new RuntimeException("N is not a power of 2");
}
// fft of even terms
Mapping evenMap = Mapping.empty();
for (int k = 0; k < N / 2; k++) {
evenMap.add(2 * k);
}
Pair<Var, Var> even = Pair.from(x._1.mapRows(evenMap), x._2.mapRows(evenMap));
Pair<Var, Var> q = fft(even);
// fft of odd terms
Mapping oddMap = Mapping.empty();
for (int k = 0; k < N / 2; k++) {
oddMap.add(2 * k + 1);
}
Pair<Var, Var> r = fft(Pair.from(x._1.mapRows(oddMap), x._2.mapRows(oddMap)));
// combine
Var rey = Numeric.fill(N, 0.0);
Var imy = Numeric.fill(N, 0.0);
for (int k = 0; k < N / 2; k++) {
double kth = -2 * k * Math.PI / N;
double coskth = Math.cos(kth);
double sinkth = Math.sin(kth);
rey.setValue(k, q._1.value(k) + coskth * r._1.value(k) - sinkth * r._2.value(k));
imy.setValue(k, q._2.value(k) + coskth * r._2.value(k) + sinkth * r._1.value(k));
rey.setValue(k + N / 2, q._1.value(k) - coskth * r._1.value(k) + sinkth * r._2.value(k));
imy.setValue(k + N / 2, q._2.value(k) - coskth * r._2.value(k) - sinkth * r._1.value(k));
}
return Pair.from(rey, imy);
}
@Override
public void paint(Graphics2D g2d, Rectangle rect) {
super.paint(g2d, rect);
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, options.getAlpha()));
for (int i = 0; i < vars.length; i++) {
Var v = vars[i];
if (v.rowCount() == 0) {
continue;
}
double[] p = new double[] {0.25, 0.5, 0.75};
double[] q = Quantiles.from(v, p).values();
double iqr = q[2] - q[0];
double innerFence = 1.5 * iqr;
double outerFence = 3 * iqr;
double x1 = i + 0.5 - 0.3;
double x2 = i + 0.5;
double x3 = i + 0.5 + 0.3;
// first we fill the space
g2d.setColor(options.getColor(i));
g2d.fill(
new Rectangle2D.Double(
xScale(x1), yScale(q[2]), xScale(x3) - xScale(x1), yScale(q[0]) - yScale(q[2])));
g2d.setColor(ColorPalette.STANDARD.getColor(0));
// median
g2d.setStroke(new BasicStroke(options.getLwd() * 2));
g2d.draw(new Line2D.Double(xScale(x1), yScale(q[1]), xScale(x3), yScale(q[1])));
// box
g2d.setStroke(new BasicStroke(options.getLwd()));
g2d.draw(new Line2D.Double(xScale(x1), yScale(q[0]), xScale(x3), yScale(q[0])));
g2d.draw(new Line2D.Double(xScale(x1), yScale(q[2]), xScale(x3), yScale(q[2])));
g2d.draw(new Line2D.Double(xScale(x1), yScale(q[0]), xScale(x1), yScale(q[2])));
g2d.draw(new Line2D.Double(xScale(x3), yScale(q[0]), xScale(x3), yScale(q[2])));
// outliers
double upperwhisker = q[2];
double lowerqhisker = q[0];
for (int j = 0; j < v.rowCount(); j++) {
double point = v.value(j);
if ((point > q[2] + outerFence) || (point < q[0] - outerFence)) {
// big outlier
g2d.setStroke(new BasicStroke(options.getLwd()));
PchPalette.STANDARD.draw(
g2d, xScale(x2), yScale(point), options.getSz(i), options.getPch(1));
continue;
}
if ((point > q[2] + innerFence) || (point < q[0] - innerFence)) {
// outlier
g2d.setStroke(new BasicStroke(options.getLwd()));
PchPalette.STANDARD.draw(
g2d, xScale(x2), yScale(point), options.getSz(i), options.getPch(0));
continue;
}
if ((point > upperwhisker) && (point < q[2] + innerFence)) {
upperwhisker = Math.max(upperwhisker, point);
}
if ((point < lowerqhisker) && (point >= q[0] - innerFence)) {
lowerqhisker = Math.min(lowerqhisker, point);
}
}
// whiskers
g2d.draw(
new Line2D.Double(xScale(x1), yScale(upperwhisker), xScale(x3), yScale(upperwhisker)));
g2d.draw(
new Line2D.Double(xScale(x1), yScale(lowerqhisker), xScale(x3), yScale(lowerqhisker)));
g2d.setStroke(
new BasicStroke(
options.getLwd(),
BasicStroke.CAP_BUTT,
BasicStroke.JOIN_MITER,
1f,
new float[] {8},
0));
g2d.draw(new Line2D.Double(xScale(x2), yScale(q[2]), xScale(x2), yScale(upperwhisker)));
g2d.draw(new Line2D.Double(xScale(x2), yScale(q[0]), xScale(x2), yScale(lowerqhisker)));
}
}
