private boolean isConverged(DataBundle data) { DoubleArray deltaX = data.getDeltaX(); DoubleArray x = data.getX(); int n = deltaX.size(); double diff, scale; for (int i = 0; i < n; i++) { diff = Math.abs(deltaX.get(i)); scale = Math.abs(x.get(i)); if (diff > _absoluteTol + scale * _relativeTol) { return false; } } return (Math.sqrt(data.getG0()) < _absoluteTol); }
private void cubicBacktrack(DoubleArray p, Function<DoubleArray, DoubleArray> function, DataBundle data) { double temp1, temp2, temp3, temp4, temp5; double lambda0 = data.getLambda0(); double lambda1 = data.getLambda1(); 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); double a = temp5 * (temp1 * temp3 - temp2 * temp4); 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); }
DataBundle data = new DataBundle(); DoubleArray y = function.apply(startPosition); data.setX(startPosition); data.setY(y); data.setG0(_algebra.getInnerProduct(y, y)); DoubleMatrix estimate = _initializationFunction.getInitializedMatrix(jacobianFunction, startPosition); return data.getX(); // this can happen if the starting position is the root estimate = _initializationFunction.getInitializedMatrix(jacobianFunction, data.getX()); jacReconCount = 1; } else { estimate = _updateFunction.getUpdatedMatrix( jacobianFunction, data.getX(), data.getDeltaX(), data.getDeltaY(), estimate); jacReconCount++; estimate = _initializationFunction.getInitializedMatrix(jacobianFunction, data.getX()); jacReconCount = 1; if (!getNextPosition(function, estimate, data)) { return data.getX(); return data.getX();
DataBundle data) { DoubleArray p = _directionFunction.getDirection(estimate, data.getY()); if (data.getLambda0() < 1.0) { data.setLambda0(1.0); } else { data.setLambda0(data.getLambda0() * BETA); double g1 = data.getG1(); if (!Doubles.isFinite(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; DoubleArray deltaX = data.getDeltaX(); DoubleArray deltaY = data.getDeltaY(); data.setG0(data.getG1()); data.setX((DoubleArray) _algebra.add(data.getX(), deltaX)); data.setY((DoubleArray) _algebra.add(data.getY(), deltaY)); return true;
protected void updatePosition(DoubleArray p, Function<DoubleArray, DoubleArray> function, DataBundle data) { double lambda0 = data.getLambda0(); DoubleArray deltaX = (DoubleArray) _algebra.scale(p, -lambda0); DoubleArray xNew = (DoubleArray) _algebra.add(data.getX(), deltaX); DoubleArray yNew = function.apply(xNew); data.setDeltaX(deltaX); data.setDeltaY((DoubleArray) _algebra.subtract(yNew, data.getY())); data.setG2(data.getG1()); data.setG1(_algebra.getInnerProduct(yNew, yNew)); }
private void quadraticBacktrack( DoubleArray p, Function<DoubleArray, DoubleArray> function, DataBundle data) { double lambda0 = data.getLambda0(); double g0 = data.getG0(); 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(DoubleArray p, Function<DoubleArray, DoubleArray> function, DataBundle data) { do { data.setLambda0(data.getLambda0() * 0.1); updatePosition(p, function, data); if (data.getLambda0() == 0.0) { throw new MathException("Failed to converge"); } } while (Double.isNaN(data.getG1()) || Double.isInfinite(data.getG1()) || Double.isNaN(data.getG2()) || Double.isInfinite(data.getG2())); }