.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/misc/plot_hartmann.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_misc_plot_hartmann.py: Hartmann functions ================== Hello world .. GENERATED FROM PYTHON SOURCE LINES 8-18 .. code-block:: default import tensorflow as tf import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns from scipy.optimize import minimize from etudes.decorators import value_and_gradient, numpy_io .. GENERATED FROM PYTHON SOURCE LINES 20-26 .. code-block:: default num_iterations = 50000 num_runs = 100 seed = 886 # set random seed for reproducibility random_state = np.random.RandomState(seed) .. GENERATED FROM PYTHON SOURCE LINES 27-70 .. code-block:: default alpha = np.array([1.0, 1.2, 3.0, 3.2]) A = {} A[3] = np.array([[3.0, 10.0, 30.0], [0.1, 10.0, 35.0], [3.0, 10.0, 30.0], [0.1, 10.0, 35.0]]) A[6] = np.array([[10.0, 3.0, 17.0, 3.5, 1.7, 8.0], [0.05, 10.0, 17.0, 0.1, 8.0, 14.0], [3.0, 3.5, 1.7, 10.0, 17.0, 8.0], [17.0, 8.0, 0.05, 10.0, 0.1, 14.0]]) A[4] = A[6].T P = {} P[3] = 1e-4 * np.array([[3689, 1170, 2673], [4699, 4387, 7470], [1091, 8732, 5547], [381, 5743, 8828]]) P[6] = 1e-4 * np.array([[1312, 1696, 5569, 124, 8283, 5886], [2329, 4135, 8307, 3736, 1004, 9991], [2348, 1451, 3522, 2883, 3047, 6650], [4047, 8828, 8732, 5743, 1091, 381]]) P[4] = P[6].T x_min = {} x_min[3] = np.array([0.114614, 0.555649, 0.852547]) x_min[6] = np.array([0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573]) axis = {} axis[3] = -1 axis[6] = -1 axis[4] = -2 a = {} a[3] = 0.0 a[4] = 1.1 a[6] = 0.0 b = {} b[3] = 1.0 b[4] = 0.839 b[6] = 1.0 .. GENERATED FROM PYTHON SOURCE LINES 71-83 .. code-block:: default def make_hartmann_tf(alpha, A, P, a=0.0, b=1.0, axis=-1): @numpy_io @value_and_gradient def hartmann(x): r = tf.reduce_sum(A * tf.square(x - P), axis=axis) return (a - tf.reduce_sum(alpha * tf.exp(-r), axis=-1)) / b return hartmann .. GENERATED FROM PYTHON SOURCE LINES 84-87 .. code-block:: default hartmann4d = make_hartmann_tf(alpha, A[4], P[4], a[4], b[4], axis[4]) .. GENERATED FROM PYTHON SOURCE LINES 88-89 Starting point .. GENERATED FROM PYTHON SOURCE LINES 89-92 .. code-block:: default x_init = random_state.rand(4) x_init .. rst-class:: sphx-glr-script-out Out: .. code-block:: none array([0.00140876, 0.75240707, 0.10057118, 0.4699249 ]) .. GENERATED FROM PYTHON SOURCE LINES 93-95 .. code-block:: default res = minimize(hartmann4d, x0=x_init, jac=True, method="L-BFGS-B", tol=1e-8) res .. rst-class:: sphx-glr-script-out Out: .. code-block:: none fun: -0.1182632861801847 hess_inv: <4x4 LbfgsInvHessProduct with dtype=float64> jac: array([-2.38112332e-07, 6.28465891e-07, 1.22074520e-05, 1.61916050e-06]) message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH' nfev: 42 nit: 27 status: 0 success: True x: array([0.40389835, 0.67337835, 0.35171053, 0.41247776]) .. GENERATED FROM PYTHON SOURCE LINES 96-97 .. code-block:: default x_min[4] = res.x .. GENERATED FROM PYTHON SOURCE LINES 98-107 .. code-block:: default def make_hartmann(alpha, A, P, a=0.0, b=1.0, axis=-1): def hartmann(x): r = np.sum(A * np.square(x - P), axis=axis) return (a - np.dot(np.exp(-r), alpha)) / b return hartmann .. GENERATED FROM PYTHON SOURCE LINES 108-129 .. code-block:: default frames = [] for dim in [3, 4, 6]: hartmann = make_hartmann(alpha, A[dim], P[dim], a[dim], b[dim], axis[dim]) xs = random_state.rand(num_runs, num_iterations, 1, dim) ys = hartmann(xs) y_min = hartmann(x_min[dim]) df = pd.DataFrame(np.minimum.accumulate(np.abs(y_min - ys), axis=1)) df.index.name = "run" df.columns.name = "iteration" s = df.stack() s.name = "regret" frame = s.reset_index() frames.append(frame.assign(name=f"Hartmann {dim}D")) .. GENERATED FROM PYTHON SOURCE LINES 130-132 .. code-block:: default data = pd.concat(frames, axis="index", sort=True) .. GENERATED FROM PYTHON SOURCE LINES 133-142 .. code-block:: default fig, ax = plt.subplots() sns.lineplot(x="iteration", y="regret", hue="name", # units="run", estimator=None, ci="sd", palette="deep", data=data, ax=ax) ax.set_xscale("log") ax.set_yscale("log") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_hartmann_001.png :alt: plot hartmann :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 27.213 seconds) .. _sphx_glr_download_auto_examples_misc_plot_hartmann.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_hartmann.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_hartmann.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_