private boolean getNextPosition( final Function1D<DoubleMatrix1D, Double> function, final Function1D<DoubleMatrix1D, DoubleMatrix1D> grad, final DataBundle data) { final DoubleMatrix1D p = getDirection(data); if (data.getLambda0() < 1.0) { data.setLambda0(1.0); } else { data.setLambda0(data.getLambda0() * BETA); } updatePosition(p, function, data); final double g1 = data.getG1(); // the function is invalid at the new position, try to recover if (Double.isInfinite(g1) || Double.isNaN(g1)) { bisectBacktrack(p, function, data); } if (data.getG1() > data.getG0() / (1 + ALPHA * data.getLambda0())) { quadraticBacktrack(p, function, data); int count = 0; while (data.getG1() > data.getG0() / (1 + ALPHA * data.getLambda0())) { if (count > 5) { return false; } cubicBacktrack(p, function, data); count++; } } final DoubleMatrix1D deltaX = data.getDeltaX(); data.setX((DoubleMatrix1D) MA.add(data.getX(), deltaX)); data.setG0(data.getG1()); final DoubleMatrix1D gradNew = grad.evaluate(data.getX()); data.setDeltaGrad((DoubleMatrix1D) MA.subtract(gradNew, data.getGrad())); data.setGrad(gradNew); return true; }
private void quadraticBacktrack( final DoubleMatrix1D p, final Function1D<DoubleMatrix1D, Double> function, final DataBundle data) { final double lambda0 = data.getLambda0(); final double g0 = data.getG0(); final double lambda = Math.max(0.01 * lambda0, g0 * lambda0 * lambda0 / (data.getG1() + g0 * (2 * lambda0 - 1))); data.swapLambdaAndReplace(lambda); updatePosition(p, function, data); }
private void bisectBacktrack( final DoubleMatrix1D p, final Function1D<DoubleMatrix1D, Double> function, final DataBundle data) { do { data.setLambda0(data.getLambda0() * 0.1); updatePosition(p, function, data); } while (Double.isNaN(data.getG1()) || Double.isInfinite(data.getG1()) || Double.isNaN(data.getG2()) || Double.isInfinite(data.getG2())); }
protected void updatePosition( final DoubleMatrix1D p, final Function1D<DoubleMatrix1D, Double> function, final DataBundle data) { final double lambda0 = data.getLambda0(); final DoubleMatrix1D deltaX = (DoubleMatrix1D) MA.scale(p, lambda0); final DoubleMatrix1D xNew = (DoubleMatrix1D) MA.add(data.getX(), deltaX); data.setDeltaX(deltaX); data.setG2(data.getG1()); final double y = function.evaluate(xNew); data.setG1(y * y); }
private void cubicBacktrack( final DoubleMatrix1D p, final Function1D<DoubleMatrix1D, Double> function, final DataBundle data) { double temp1, temp2, temp3, temp4, temp5; final double lambda0 = data.getLambda0(); final double lambda1 = data.getLambda1(); final double g0 = data.getG0(); temp1 = 1.0 / lambda0 / lambda0; temp2 = 1.0 / lambda1 / lambda1; temp3 = data.getG1() + g0 * (2 * lambda0 - 1.0); temp4 = data.getG2() + g0 * (2 * lambda1 - 1.0); temp5 = 1.0 / (lambda0 - lambda1); final double a = temp5 * (temp1 * temp3 - temp2 * temp4); final double b = temp5 * (-lambda1 * temp1 * temp3 + lambda0 * temp2 * temp4); double lambda = (-b + Math.sqrt(b * b + 6 * a * g0)) / 3 / a; lambda = Math.min( Math.max(lambda, 0.01 * lambda0), 0.75 * lambda1); // make sure new lambda is between 1% & 75% of old value data.swapLambdaAndReplace(lambda); updatePosition(p, function, data); }