improve pod ex figures and result summary

"""

Proper Orthogonal Decomposition method implementations

Proper Orthogonal Decomposition method with interpolation

Author: William Gurecky.  wll@ornl.gov.  May 2023

"""

import numpy as np

from scipy.stats import norm

        return np.matmul(self.pod_modes, pod_weights_hat)

def pod_example_a():

def pod_example_a(n_pod_modes=14):

    """

    Example using POD with interpolation to create model

    of 1D pressure field data as a fn on vane angle.

    Uses simple, synthetic data for testing.

    Args:

        n_pod_modes: Number of eigen modes to retain in the pod model.

            A truncated SVD is done to find the dominate modes.

            A larger number of retained modes is more accurate but slower.

    """

    # Construct synthetic data

    n_avail_snapshots = 20

        p_profile = norm(loc=p_center, scale=p_wave_sd * (1. + u)).pdf(grid_x) * p_scale

        test_p_snaps.append(p_profile)

        test_p_t.append(u)

        plt.plot(grid_x, p_profile, label="vane: %0.2f" % u)

        plt.plot(grid_x, p_profile, label="vane u: %0.2f" % u)

    plt.ylabel("Pressure [arbitrary scale]")

    plt.xlabel("Space [m]")

    plt.grid(ls="--")

    plt.legend(bbox_to_anchor=(1.1, 1.1))

    plt.legend(bbox_to_anchor=(1.05, 1.1))

    plt.tight_layout()

    plt.savefig("pod_example_a_p_snaps.png")

    plt.close()

    test_p_t = np.asarray(test_p_t)

    # POD model fitting

    pod_model = PODInterpModel(max_modes=14, pod_method="svd")

    pod_model = PODInterpModel(max_modes=n_pod_modes, pod_method="svd")

    pod_model.fit(test_p_snaps, test_p_t)

    # Check POD model modes at known snapshot points

    # predict at known vane angle point

    pred_p = pod_model.predict(grid_u[0])

    # predict at unknown vane angle

    u_test = (grid_u[0] + grid_u[1]) / 2.

    u_test = (grid_u[3] + grid_u[4]) / 2.

    known_p_test = gen_p_profile(u_test)

    pred_p_test = pod_model.predict(u_test)

    plt.plot(grid_x, known_p, label="train, u=%0.2f" % grid_u[0])

    plt.ylabel("Pressure [arbitrary scale]")

    plt.xlabel("Space [m]")

    plt.grid(ls="--")

    plt.legend(bbox_to_anchor=(1.1, 1.1))

    plt.legend(bbox_to_anchor=(1.05, 1.1))

    plt.title("POD N-Modes: %d \n POD L2 error at train u: %0.2e \n POD L2 error at test u: %0.2e" % \

            (pod_model.max_modes, np.linalg.norm(known_p - pred_p), np.linalg.norm(known_p_test - pred_p_test)))

    plt.tight_layout()

    plt.savefig("pod_example_a_p_check.png")

    plt.savefig("pod_" + str(n_pod_modes) + "_example_a_p_check.png")

    train_l2_err = np.linalg.norm(known_p - pred_p)

    test_l2_err = np.linalg.norm(known_p_test - pred_p_test)

    # Make more predictions at unknown vane angles

    for u_test in np.linspace(0.2, 0.8, 5):

        pred_p_test = pod_model.predict(u_test)

        plt.plot(grid_x, pred_p_test, ls='', marker=".", label="POD, u=%0.2f" % u_test)

    plt.legend(bbox_to_anchor=(1.1, 1.1))

    plt.legend(bbox_to_anchor=(1.05, 1.1))

    plt.tight_layout()

    plt.savefig("pod_example_a_p_check_many.png")

    plt.savefig("pod_" + str(n_pod_modes) + "_example_a_p_check_many.png")

    plt.close()

    return train_l2_err, test_l2_err

if __name__ == "__main__":

    pod_example_a()

    print("N Modes, Train L2, Test L2 error")

    errs = []

    for n_modes in [1, 2, 3, 4, 6, 8, 10, 12, 14]:

        train_l2_err, test_l2_err = pod_example_a(n_modes)

        errs.append([n_modes, train_l2_err, test_l2_err])

    for n_modes, train_l2_err, test_l2_err in errs:

        print("%d, %0.8e, %0.8e" % (n_modes, train_l2_err, test_l2_err))