Optimal Transport Barycenter solvers comparison

This example illustrates solutions returned for different variants of exact, regularized and unbalanced OT barycenter problems with free support using our wrapper ot.solve_bary_sample.

# Author: Cédric Vincent-Cuaz <cedvincentcuaz@gmail.com>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 2

import numpy as np
import matplotlib.pylab as pl
import ot
from ot.plot import plot2D_samples_mat

2D data example

We first generate two sets of samples in 2D of 8 and 16 points uniformly separated on circles. The weights of the samples are uniform.

# Problem size
n1, n2 = 8, 16
nbary = 12

# Generate random data
np.random.seed(0)

r1, r2 = 1, 3
x1 = r1 * np.array(
    [(np.cos(2 * i * np.pi / n1), np.sin(2 * i * np.pi / n1)) for i in range(n1)]
)

x2 = r2 * np.array(
    [(np.cos(2 * i * np.pi / n2), np.sin(2 * i * np.pi / n2)) for i in range(n2)]
)

style = {"markeredgecolor": "k"}

pl.figure(1, (4, 4))
pl.plot(x1[:, 0], x1[:, 1], "ob", **style)
pl.plot(x2[:, 0], x2[:, 1], "or", **style)
pl.title("Source distributions")
pl.show()

Set up parameters for balanced OT barycenter solvers and solve

# balanced OT
lst_balanced_solvers = [  # name, param for ot.solve function
    ("Exact OT", dict()),
    ("Entropic Reg. OT", dict(reg=1.0)),
]

lst_balanced_res = []
for name, param in lst_balanced_solvers:
    print(f"-- name = {name} / param = {param}")
    res = ot.solve_bary_sample(X_a_list=[x1, x2], n=nbary, **param)
    lst_balanced_res.append(res)
    list_P = [res.list_res[k].plan for k in range(2)]
    print("X:", res.X)
    print("loss:", res.value)
    print("loss:", res.log)
    print(
        "marginals OT 1:",
        res.list_res[0].plan.sum(axis=1),
        res.list_res[0].plan.sum(axis=0),
    )
    print(
        "marginals OT 2:",
        res.list_res[1].plan.sum(axis=1),
        res.list_res[1].plan.sum(axis=0),
    )

-- name = Exact OT / param = {}
/home/circleci/project/ot/solvers/_bary.py:162: RuntimeWarning: invalid value encountered in scalar divide
  if abs(new_criterion - prev_criterion) / abs(prev_criterion) < tol_bary:
BCD converged in 4 iterations
X: [[ 1.84114117  0.60729556]
 [ 0.28701257  1.94290965]
 [ 1.49550334 -1.29255481]
 [ 0.60729556 -1.84114117]
 [-1.94290965  0.28701257]
 [-0.60729556  1.84114117]
 [ 1.29255481  1.49550334]
 [-1.49550334  1.29255481]
 [ 1.94290965 -0.28701257]
 [-1.29255481 -1.49550334]
 [-1.84114117 -0.60729556]
 [-0.28701257 -1.94290965]]
loss: 1.1589629991802717
loss: {'stopping_criterion': [np.float64(3.5548104740331845), np.float64(1.2465846410185621), np.float64(1.1650649412388852), np.float64(1.1589629991802715), np.float64(1.1589629991802717)]}
marginals OT 1: [0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125] [0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333
 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333]
marginals OT 2: [0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625
 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625] [0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333
 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333]
-- name = Entropic Reg. OT / param = {'reg': 1.0}
BCD converged in 14 iterations
X: [[ 1.74513458  0.63006858]
 [ 0.32292074  1.82909418]
 [ 1.41519337 -1.20237787]
 [ 0.64094898 -1.74169796]
 [-1.83108912  0.30287904]
 [-0.63325353  1.74362168]
 [ 1.19878558  1.41897616]
 [-1.41333452  1.20660735]
 [ 1.82957495 -0.32101269]
 [-1.17898838 -1.43635404]
 [-1.75427084 -0.60505515]
 [-0.34162181 -1.82474926]]
loss: 2.843917885588441
loss: {'stopping_criterion': [np.float64(4.936424991370039), np.float64(3.1120231938544416), np.float64(2.8852594148180186), np.float64(2.8529760102988124), np.float64(2.8490581667579313), np.float64(2.8472209935218347), np.float64(2.8460319485917838), np.float64(2.8452320968523264), np.float64(2.8447103568721888), np.float64(2.844382959911707), np.float64(2.844182839395433), np.float64(2.8440618969858695), np.float64(2.8439889115755976), np.float64(2.8439447352801928), np.float64(2.843917885588441)]}
marginals OT 1: [0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125] [0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333
 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333]
marginals OT 2: [0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625
 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625] [0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333
 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333]

Plot distributions and plans for balanced OT barycenter solvers

def plot_list_res(
    lst_res,
    lst_solvers,
    fig_num=1,
    n_cols=2,
    show_masses=False,
    show_legend=True,
    s=100,
    fig_width=None,
    fig_height=None,
):
    n_plots = len(lst_res)
    n_rows = int(np.ceil(n_plots / n_cols))

    if fig_width is None:
        fig_width = 8 * n_cols
    if fig_height is None:
        fig_height = 4 * n_rows

    fig, axes = pl.subplots(
        n_rows,
        n_cols,
        figsize=(fig_width, fig_height),
        squeeze=False,
        num=fig_num,
    )
    axes = axes.ravel()

    legend_handles = None
    for i, (name, param) in enumerate(lst_solvers):
        ax = axes[i]
        pl.sca(ax)

        X = lst_res[i].X
        list_P = [lst_res[i].list_res[k].plan for k in range(2)]
        loss = lst_res[i].value

        plot2D_samples_mat(x1, X, list_P[0])
        plot2D_samples_mat(x2, X, list_P[1])

        if show_masses:
            # Marginals induced by transport plans

            a1 = list_P[0].sum(axis=1) * list_P[0].shape[0]
            a2 = list_P[1].sum(axis=1) * list_P[1].shape[0]

            # weighted average barycenter masses
            b = (
                0.5
                * (list_P[0].sum(axis=0) + list_P[1].sum(axis=0))
                * list_P[0].shape[1]
            )

            # background uniform distribution
            ax.scatter(x1[:, 0], x1[:, 1], s=s, color="blue", marker="o", alpha=0.25)
            ax.scatter(x2[:, 0], x2[:, 1], s=s, color="red", marker="o", alpha=0.25)
            ax.scatter(X[:, 0], X[:, 1], s=s, color="green", marker="o", alpha=0.25)

            list_size_1 = s * a1
            list_size_2 = s * a2
            list_size_b = s * b
        else:
            list_size_1 = s
            list_size_2 = s
            list_size_b = s

        if i == 0:  # add labels
            h1 = ax.scatter(
                x1[:, 0],
                x1[:, 1],
                s=list_size_1,
                color="blue",
                marker="o",
                alpha=1,
                label="Source distribution 1",
            )
            h2 = ax.scatter(
                x2[:, 0],
                x2[:, 1],
                s=list_size_2,
                color="red",
                marker="o",
                alpha=1,
                label="Source distribution 2",
            )
            h3 = ax.scatter(
                X[:, 0],
                X[:, 1],
                s=list_size_b,
                color="green",
                marker="o",
                alpha=1,
                label="Barycenter distribution",
            )

        else:
            h1 = ax.scatter(
                x1[:, 0], x1[:, 1], s=list_size_1, color="blue", marker="o", alpha=1
            )
            h2 = ax.scatter(
                x2[:, 0], x2[:, 1], s=list_size_2, color="red", marker="o", alpha=1
            )
            h3 = ax.scatter(
                X[:, 0], X[:, 1], s=list_size_b, color="green", marker="o", alpha=1
            )

        if legend_handles is None:
            legend_handles = [h1, h2, h3]

        ax.set_title(name)

    ############################################################
    # remove unused axes

    for j in range(i + 1, len(axes)):
        fig.delaxes(axes[j])

    ############################################################
    # Single legend above all subplots

    if show_legend:
        labels = [h.get_label() for h in legend_handles]

        fig.legend(
            legend_handles,
            labels,
            loc="upper center",
            bbox_to_anchor=(0.5, 1.02),
            ncol=3,
            frameon=False,
        )
    fig.tight_layout()
    pl.show()


plot_list_res(
    lst_balanced_res,
    lst_balanced_solvers,
    fig_num=2,
    n_cols=2,
    show_masses=False,
    fig_width=8,
    fig_height=4,
    show_legend=True,
)

Set up parameters for unbalanced OT barycenter solvers and solve

lambda_unbalanced_vals = [1, 2.5, 10]

# unbalanced OT KL
lst_unbalanced_solvers = [
    (
        "Unbalanced KL No Reg \n" + r"$\lambda_u$=%s" % lambda_val,
        dict(unbalanced=lambda_val),
    )
    for lambda_val in lambda_unbalanced_vals
] + [
    (
        "Unbalanced KL with KL Reg \n"
        + r"$\lambda_u$=%s, $\lambda_{ent}$=%s" % (lambda_val, 0.1),
        dict(reg=0.1, unbalanced=lambda_val, unbalanced_type="kl", reg_type="kl"),
    )
    for lambda_val in lambda_unbalanced_vals
]

lst_unbalanced_res = []
for name, param in lst_unbalanced_solvers:
    print(f"-- name = {name} / param = {param}")
    res = ot.solve_bary_sample(X_a_list=[x1, x2], n=nbary, **param)
    lst_unbalanced_res.append(res)
    list_P = [res.list_res[k].plan for k in range(2)]
    print("X:", res.X)
    print("loss:", res.value)
    print("loss:", res.log)
    print(
        "marginals OT 1:",
        res.list_res[0].plan.sum(axis=1),
        res.list_res[0].plan.sum(axis=0),
    )
    print(
        "marginals OT 2:",
        res.list_res[1].plan.sum(axis=1),
        res.list_res[1].plan.sum(axis=0),
    )

-- name = Unbalanced KL No Reg
$\lambda_u$=1 / param = {'unbalanced': 1}
BCD converged in 19 iterations
X: [[ 2.73309406e+00  1.13981794e+00]
 [ 1.56554060e+00  2.42446865e+00]
 [ 2.33584421e+00 -1.68611571e+00]
 [ 1.04768727e+00 -3.09021185e-02]
 [-9.21750458e-01  5.41230220e-01]
 [-1.03655713e-01  1.43390903e+00]
 [ 1.04768727e+00 -3.09021185e-02]
 [ 7.46726238e-01  7.46726238e-01]
 [ 2.95773740e+00 -7.24654594e-32]
 [-4.56978745e-01 -1.10324492e+00]
 [-2.76214828e+00  5.95794784e-02]
 [ 7.57192081e-01 -9.41610048e-01]]
loss: 0.8156206216899978
loss: {'stopping_criterion': [np.float64(0.9793293190550253), np.float64(0.8543325708607069), np.float64(0.8288789083180792), np.float64(0.8219574448681899), np.float64(0.8195840664796413), np.float64(0.8182782311927407), np.float64(0.8174360620725586), np.float64(0.8168531793971974), np.float64(0.8163834905610549), np.float64(0.8161073710204839), np.float64(0.8159370905214629), np.float64(0.8158305469634906), np.float64(0.8157621733682839), np.float64(0.815716831647574), np.float64(0.8156857241679643), np.float64(0.8156637260950893), np.float64(0.8156477877700095), np.float64(0.8156360296708335), np.float64(0.8156272440107248), np.float64(0.8156206216899978)]}
marginals OT 1: [0.14488511 0.10386344 0.09239477 0.07553914 0.06029111 0.06466776
 0.06466778 0.10057852] [0.00137193 0.00251392 0.00279821 0.07166427 0.12811452 0.09239477
 0.07166427 0.09997758 0.00155657 0.12933554 0.00771573 0.09778032]
marginals OT 2: [0.07210436 0.07211275 0.04133113 0.04595124 0.01634922 0.01077561
 0.01008633 0.01813995 0.05586022 0.01379789 0.00557438 0.0096174
 0.00557438 0.01252993 0.04916616 0.03852079] [0.07211275 0.08440354 0.0837123  0.00198732 0.01008633 0.02712483
 0.00198732 0.00287882 0.07210436 0.02076615 0.08779807 0.01252993]
-- name = Unbalanced KL No Reg
$\lambda_u$=2.5 / param = {'unbalanced': 2.5}
BCD converged in 147 iterations
X: [[ 1.75916227  0.63536543]
 [-0.43128951  2.03199054]
 [ 0.63260879 -1.75681055]
 [ 1.27809612 -1.27809583]
 [-1.75985069  0.62926878]
 [-1.27447552  1.27447552]
 [ 1.27805247  1.27805247]
 [ 0.43128994  2.03198933]
 [ 2.11695968 -0.32380378]
 [-1.21870014 -1.21870014]
 [-2.1250867  -0.3264692 ]
 [-0.32519775 -2.12106236]]
loss: 1.012521956682006
loss: {'stopping_criterion': [np.float64(1.6543038457215027), np.float64(1.2766733820925698), np.float64(1.1549420397743804), np.float64(1.0796690008698673), np.float64(1.0614359605777381), np.float64(1.056644404426096), np.float64(1.052245676106074), np.float64(1.040404895228308), np.float64(1.0287085917097596), np.float64(1.0261257799524386), np.float64(1.0250441656840636), np.float64(1.0243949446135003), np.float64(1.0239017733211542), np.float64(1.0234337365554402), np.float64(1.0228101549007391), np.float64(1.0221295564725252), np.float64(1.0218482823756463), np.float64(1.0216894392513793), np.float64(1.0215872674950233), np.float64(1.0215162291422692), np.float64(1.0214598164442372), np.float64(1.0214079021469153), np.float64(1.0213551848472826), np.float64(1.021298749492615), np.float64(1.0212365746198167), np.float64(1.0211669704582198), np.float64(1.021088326102815), np.float64(1.0209989683363352), np.float64(1.0208970672363211), np.float64(1.0207805580976839), np.float64(1.020647062438803), np.float64(1.0204937952851503), np.float64(1.0203174452056738), np.float64(1.020114008411319), np.float64(1.0198785472083014), np.float64(1.0196049093456208), np.float64(1.0193242177414579), np.float64(1.0192093387140257), np.float64(1.0191630655023523), np.float64(1.01913712663923), np.float64(1.0191194406283075), np.float64(1.0191051109399434), np.float64(1.0190920219388155), np.float64(1.0190792378488969), np.float64(1.0190663317748392), np.float64(1.019053098367578), np.float64(1.0190394291197475), np.float64(1.0190252572592038), np.float64(1.0190105325423873), np.float64(1.018995208686241), np.float64(1.0189792355603693), np.float64(1.0189625520561378), np.float64(1.0189450766829553), np.float64(1.0189266926243918), np.float64(1.0189072227662967), np.float64(1.0188863891653384), np.float64(1.0188637533384182), np.float64(1.0188386418250182), np.float64(1.0188100736900307), np.float64(1.0187767123586748), np.float64(1.0187368358138469), np.float64(1.0186882719047394), np.float64(1.0186282748189233), np.float64(1.0185533637728519), np.float64(1.0184591311095532), np.float64(1.0183400130337417), np.float64(1.0181890176871877), np.float64(1.0179974092367328), np.float64(1.0177543511138627), np.float64(1.017446601957201), np.float64(1.017045967675591), np.float64(1.0164767583698064), np.float64(1.0158222230713658), np.float64(1.0156085289128036), np.float64(1.0154983154812163), np.float64(1.0154297384493223), np.float64(1.0153823501568355), np.float64(1.0153472490189512), np.float64(1.0153196253215053), np.float64(1.0152964443578698), np.float64(1.015275576616455), np.float64(1.015255397892461), np.float64(1.015234567963896), np.float64(1.015211888339991), np.float64(1.015186199021757), np.float64(1.0151562949124775), np.float64(1.0151208506442315), np.float64(1.0150783460328032), np.float64(1.0150269857195076), np.float64(1.0149646066888853), np.float64(1.014888566501431), np.float64(1.0147956031142111), np.float64(1.0146816536134449), np.float64(1.014541613014629), np.float64(1.0143690201684257), np.float64(1.0141721294587536), np.float64(1.0140500333685747), np.float64(1.0139678067074809), np.float64(1.013897901846465), np.float64(1.0138348946426363), np.float64(1.0137765457239434), np.float64(1.013721632138481), np.float64(1.0136728564886415), np.float64(1.0136475857630862), np.float64(1.013631434504593), np.float64(1.0136175258746798), np.float64(1.0136042970732402), np.float64(1.013591107238666), np.float64(1.0135776610430336), np.float64(1.0135638101701523), np.float64(1.013549471506805), np.float64(1.013534591206511), np.float64(1.0135191284728375), np.float64(1.0135030481409726), np.float64(1.0134863172672317), np.float64(1.013468903577034), np.float64(1.0134507747941273), np.float64(1.0134318984027975), np.float64(1.0134122416364795), np.float64(1.0133917715978282), np.float64(1.0133704554674263), np.float64(1.0133482607827913), np.float64(1.0133251557808776), np.float64(1.0133011098022198), np.float64(1.0132760937577818), np.float64(1.0132500806585205), np.float64(1.0132230462084182), np.float64(1.0131949694594218), np.float64(1.013165833524924), np.float64(1.0131356263456996), np.float64(1.0131043414989689), np.float64(1.0130719790375227), np.float64(1.0130385463416993), np.float64(1.0130040589625504), np.float64(1.0129685414300464), np.float64(1.0129320279958183), np.float64(1.0128945632761657), np.float64(1.0128562027581691), np.float64(1.012817013130272), np.float64(1.0127770723990293), np.float64(1.012736469756368), np.float64(1.0126953051670178), np.float64(1.0126536886540967), np.float64(1.0126117392756038), np.float64(1.0125696071398163), np.float64(1.0125368375022983), np.float64(1.0125263988798812), np.float64(1.012521956682006)]}
marginals OT 1: [0.10519574 0.09978745 0.11238741 0.09958179 0.10535861 0.09191738
 0.10523055 0.09971987] [0.06690896 0.05619368 0.067076   0.08047725 0.06698385 0.08085498
 0.08042594 0.05619373 0.05764828 0.09191738 0.05710157 0.05739717]
marginals OT 2: [0.04370016 0.05578002 0.05430234 0.04785734 0.04668079 0.04785731
 0.05417119 0.05572529 0.04380001 0.04009479 0.05209757 0.04003162
 0.04374992 0.05569528 0.05430393 0.03996487] [0.05578014 0.07119775 0.05569539 0.05430394 0.0557257  0.05417119
 0.05430234 0.07119768 0.08366491 0.05209757 0.08389439 0.08378143]
-- name = Unbalanced KL No Reg
$\lambda_u$=10 / param = {'unbalanced': 10}
BCD converged in 12 iterations
X: [[ 1.82074549  0.6294374 ]
 [-0.62789474  1.82224861]
 [ 0.63003989 -1.8201331 ]
 [ 1.48406534 -1.2881548 ]
 [-1.95725595  0.26789071]
 [-1.4819154   1.28844781]
 [ 1.28858778  1.4824035 ]
 [ 0.26769023  1.95730585]
 [ 1.95735118 -0.26583032]
 [-1.28772028 -1.48407916]
 [-1.82223757 -0.627887  ]
 [-0.26528103 -1.95735837]]
loss: 1.1213900871011715
loss: {'stopping_criterion': [np.float64(2.654720244931114), np.float64(1.3956794887823305), np.float64(1.1932596712223411), np.float64(1.1602759725893586), np.float64(1.144375121053439), np.float64(1.138015263016813), np.float64(1.1327575714801612), np.float64(1.127261599818235), np.float64(1.1224327114664423), np.float64(1.1215530890306828), np.float64(1.121416593731658), np.float64(1.1213938881659422), np.float64(1.1213900871011715)]}
marginals OT 1: [0.11979118 0.11769648 0.11980552 0.11767453 0.11980046 0.11766952
 0.11978194 0.11770166] [0.07813443 0.07812094 0.07814238 0.08055024 0.07876938 0.08059295
 0.08057051 0.07876615 0.07878271 0.08057614 0.07812446 0.07879098]
marginals OT 2: [0.05768233 0.06133303 0.0594347  0.05608432 0.05767285 0.06129702
 0.05943683 0.0560843  0.05767004 0.06129396 0.05938931 0.05606317
 0.05768314 0.06134408 0.05940112 0.05606948] [0.07551875 0.07557258 0.07550106 0.07854535 0.08042855 0.07848045
 0.07848999 0.08042634 0.08042186 0.07855543 0.07557614 0.08042321]
-- name = Unbalanced KL with KL Reg
$\lambda_u$=1, $\lambda_{ent}$=0.1 / param = {'reg': 0.1, 'unbalanced': 1, 'unbalanced_type': 'kl', 'reg_type': 'kl'}
BCD converged in 196 iterations
X: [[ 2.67324047e+00  1.10754552e+00]
 [ 1.61461149e+00  2.28086520e+00]
 [ 2.28144022e+00 -1.61577590e+00]
 [ 8.92292838e-01 -3.74215653e-01]
 [-1.21498913e+00  1.46213009e-01]
 [-5.14172874e-01  2.75409120e+00]
 [ 3.65180887e-01  8.96086079e-01]
 [-9.36592489e-01  9.34378030e-01]
 [ 2.82330825e+00 -6.68814283e-04]
 [-9.68994784e-01 -1.14106159e+00]
 [-2.80146090e+00 -5.34721474e-01]
 [ 1.24492531e-01 -1.48554800e+00]]
loss: -2.6020852139652106e-18
loss: {'stopping_criterion': [np.float64(1.7083748998780734e-10), np.float64(-7.224101421232643e-10), np.float64(-4.5647908369916834e-10), np.float64(-5.689692883503739e-10), np.float64(-5.313356438857442e-10), np.float64(-5.635175243101642e-10), np.float64(-5.553726731971631e-10), np.float64(-3.5403962747593276e-10), np.float64(-3.134207841176684e-10), np.float64(-9.991966802569419e-11), np.float64(1.281478968079286e-10), np.float64(4.882211752932353e-10), np.float64(7.001881565868451e-10), np.float64(3.3612386702089325e-10), np.float64(4.97012027887711e-10), np.float64(1.0373192018894861e-09), np.float64(9.869674236955353e-10), np.float64(1.0741946980356853e-09), np.float64(1.126230317013456e-09), np.float64(1.1827792083425603e-09), np.float64(1.2359004622659875e-09), np.float64(1.5756417702690595e-09), np.float64(1.6387758001740887e-09), np.float64(2.0800180303192153e-09), np.float64(2.163638792218245e-09), np.float64(1.2309275244058726e-09), np.float64(6.835813369347743e-10), 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np.float64(-4.387072302658446e-14), np.float64(-3.6251383839225326e-14), np.float64(-2.9886249724997427e-14), np.float64(-2.482172453688314e-14), np.float64(-2.0474073825216266e-14), np.float64(-1.684850176042474e-14), np.float64(-1.3997483727656856e-14), np.float64(-1.1616575756878689e-14), np.float64(-9.583913523902865e-15), np.float64(-7.848756367057064e-15), np.float64(-6.3547257733720386e-15), np.float64(-5.560656102243655e-15), np.float64(-4.355890648177763e-15), np.float64(-3.5514126361935183e-15), np.float64(-2.955101441326491e-15), np.float64(-2.4273118237605473e-15), np.float64(-2.0660556598883772e-15), np.float64(-1.7525043916055694e-15), np.float64(-1.5469396597023177e-15), np.float64(-1.0586150012148465e-15), np.float64(-6.574601973952099e-16), np.float64(-7.988401606873197e-16), np.float64(-6.218983661376853e-16), np.float64(-5.117434254131581e-16), np.float64(-3.7339922820400773e-16), np.float64(-2.6194324487249787e-16), np.float64(-1.6436504934880247e-16), np.float64(-1.4094628242311558e-16), np.float64(-2.2941717969793274e-16), np.float64(-6.938893903907228e-17), np.float64(-2.5240226575462543e-16), np.float64(-2.6020852139652106e-18), np.float64(-2.6020852139652106e-18)]}
marginals OT 1: [0.06511394 0.06505919 0.06542103 0.08720513 0.09025411 0.08099069
 0.08095141 0.06540024] [0.00342089 0.00621653 0.00616502 0.11591243 0.08729366 0.00595931
 0.11593877 0.08709493 0.00607672 0.08103414 0.0037425  0.08154084]
marginals OT 2: [0.06271858 0.06333169 0.04209957 0.03609597 0.03986905 0.03716368
 0.01643944 0.01272938 0.03964264 0.03782185 0.01666903 0.01156879
 0.01646471 0.01152334 0.04213958 0.03608489] [0.06333856 0.07570326 0.07569847 0.00249822 0.01220803 0.07702018
 0.00249793 0.01696203 0.06275873 0.02820141 0.07746326 0.0280121 ]
-- name = Unbalanced KL with KL Reg
$\lambda_u$=2.5, $\lambda_{ent}$=0.1 / param = {'reg': 0.1, 'unbalanced': 2.5, 'unbalanced_type': 'kl', 'reg_type': 'kl'}
BCD converged in 252 iterations
X: [[ 1.69385367  0.70161716]
 [-0.70161716  1.69385367]
 [ 0.70161716 -1.69385367]
 [ 1.51155693 -1.26936002]
 [-1.96640526  0.17125901]
 [-1.51155693  1.26936002]
 [ 1.26936002  1.51155693]
 [ 0.17125901  1.96640526]
 [ 1.96640526 -0.17125901]
 [-1.26936002 -1.51155693]
 [-1.69385367 -0.70161716]
 [-0.17125901 -1.96640526]]
loss: -4.3298697960381105e-15
loss: {'stopping_criterion': [np.float64(-3.481034072105871e-10), np.float64(-1.74991113266465e-09), np.float64(-1.6117589207720329e-09), np.float64(-1.6956539505841306e-09), np.float64(-8.24356749529187e-10), np.float64(-1.0108024139920957e-09), np.float64(-1.1976257485724062e-09), np.float64(-1.1549109446562511e-09), np.float64(-1.040564689969159e-09), np.float64(-7.64027952016022e-10), np.float64(-8.077332691591721e-10), np.float64(-7.807174073892753e-10), np.float64(-8.983390697991922e-10), np.float64(-7.733769458173612e-10), np.float64(-7.595461204434883e-10), np.float64(-7.427534143289449e-10), np.float64(-6.860461365665316e-10), np.float64(-6.923774886757883e-10), np.float64(-6.484460191025221e-10), np.float64(-6.455297130170123e-10), np.float64(-6.340604430388197e-10), np.float64(-8.673573248518807e-10), np.float64(-7.260561873945193e-10), np.float64(-5.897922428221847e-10), np.float64(-5.074697884133172e-10), np.float64(-4.565651468002585e-10), 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np.float64(-1.0281733797690151e-10), np.float64(-9.715991899916787e-11), np.float64(-9.531331279788446e-11), np.float64(-8.974535004036e-11), np.float64(-8.805409179579726e-11), np.float64(-8.32338087342066e-11), np.float64(-7.838832360995696e-11), np.float64(-7.692668724246232e-11), np.float64(-7.549771918746728e-11), np.float64(-7.138215019075744e-11), np.float64(-6.724271139901816e-11), np.float64(-6.600350821450718e-11), np.float64(-6.479158876082636e-11), np.float64(-5.880645970179899e-11), np.float64(-5.772918254542958e-11), np.float64(-5.6677496029777785e-11), np.float64(-5.5647375596379334e-11), np.float64(-5.051692397728402e-11), np.float64(-4.9598852802645865e-11), np.float64(-4.870465142303715e-11), np.float64(-4.597566771735728e-11), np.float64(-4.342592951900315e-11), np.float64(-4.264588682190151e-11), np.float64(-4.188646651748229e-11), np.float64(-3.955019645118796e-11), np.float64(-3.736475018278895e-11), np.float64(-3.6701613970180347e-11), np.float64(-3.46634942971491e-11), np.float64(-3.405625781383037e-11), np.float64(-3.2190278220767254e-11), np.float64(-3.1628755170487466e-11), np.float64(-2.9888536090538764e-11), np.float64(-2.9378832699933355e-11), np.float64(-2.778613450438172e-11), np.float64(-2.6259605601097746e-11), np.float64(-2.5825369620591232e-11), np.float64(-2.541689081425602e-11), np.float64(-2.3136215165919793e-11), np.float64(-2.2749829797774623e-11), np.float64(-2.2414292644157285e-11), np.float64(-2.0429991032244743e-11), np.float64(-2.0102586262282784e-11), np.float64(-1.983890829393431e-11), np.float64(-1.811822913921901e-11), np.float64(-1.7846862876425007e-11), np.float64(-1.76562930942481e-11), np.float64(-1.6173173911226968e-11), np.float64(-1.59574575775423e-11), np.float64(-1.52268475606121e-11), np.float64(-1.4511974955055962e-11), np.float64(-1.4421019933763546e-11), np.float64(-1.3321954650535872e-11), np.float64(-1.3214096483693538e-11), np.float64(-1.2731787846220755e-11), np.float64(-1.2257583836827735e-11), np.float64(-1.1401102284480658e-11), np.float64(-1.093647394867503e-11), np.float64(-1.0605905043092889e-11), np.float64(-9.639955500517772e-12), np.float64(-8.955530761411978e-12), np.float64(-8.370554249736983e-12), np.float64(-7.5097983387451e-12), np.float64(-6.404266006398984e-12), np.float64(-5.818345805153058e-12), np.float64(-5.017819493247089e-12), np.float64(-4.242384221697648e-12), np.float64(-3.686939642477682e-12), np.float64(-3.24881788138498e-12), np.float64(-2.789185549190165e-12), np.float64(-2.445516011917448e-12), np.float64(-2.0753954110830364e-12), np.float64(-1.7424672815735676e-12), np.float64(-1.5198675651362237e-12), np.float64(-1.3533896225936815e-12), np.float64(-1.16157083951407e-12), np.float64(-9.810763312856352e-13), np.float64(-8.228417947009348e-13), np.float64(-7.439049376500861e-13), np.float64(-6.486755577128633e-13), np.float64(-5.549449788588845e-13), np.float64(-4.689026944504349e-13), np.float64(-3.934630399271555e-13), np.float64(-3.552713678800501e-13), np.float64(-3.118894031928221e-13), np.float64(-2.6836866062751596e-13), np.float64(-2.277067423506196e-13), np.float64(-1.9154122732345513e-13), np.float64(-1.7272294705605873e-13), np.float64(-1.5237811012980274e-13), np.float64(-1.3239409568654992e-13), np.float64(-1.1313172620930345e-13), np.float64(-9.536815781530095e-14), np.float64(-8.587575095475586e-14), np.float64(-7.643885524544203e-14), np.float64(-6.70019595361282e-14), np.float64(-5.800915303666443e-14), np.float64(-4.9432680171435095e-14), np.float64(-4.285460875053104e-14), np.float64(-3.9468428525424315e-14), np.float64(-3.5638159090467525e-14), np.float64(-3.144706717250756e-14), np.float64(-2.7172708527700706e-14), np.float64(-2.2898349882893854e-14), np.float64(-2.0233814623793478e-14), np.float64(-1.8318679906315083e-14), np.float64(-1.6930901125533637e-14), np.float64(-1.529332216421153e-14), np.float64(-1.3433698597964394e-14), np.float64(-1.1268763699945339e-14), np.float64(-1.1102230246251565e-14), np.float64(-9.631184738623233e-15), np.float64(-8.881784197001252e-15), np.float64(-8.18789480661053e-15), np.float64(-7.216449660063518e-15), np.float64(-6.5780714209040525e-15), np.float64(4.163336342344337e-16), np.float64(-8.909539772616881e-15), np.float64(-9.325873406851315e-15), np.float64(-8.604228440844963e-15), np.float64(-7.188694084447889e-15), np.float64(-4.274358644806853e-15), np.float64(-6.855627177060342e-15), np.float64(-6.522560269672795e-15), np.float64(-5.35682609381638e-15), np.float64(-2.7478019859472624e-15), np.float64(-6.217248937900877e-15), np.float64(-6.772360450213455e-15), np.float64(-6.13398221105399e-15), np.float64(-5.662137425588298e-15), np.float64(-4.718447854656915e-15), np.float64(-3.802513859341161e-15), np.float64(-3.969047313034935e-15), np.float64(-1.2490009027033011e-15), np.float64(-5.412337245047638e-15), np.float64(-5.162537064506978e-15), np.float64(-3.552713678800501e-15), np.float64(-5.745404152435185e-15), np.float64(-5.6343818499726694e-15), np.float64(-5.10702591327572e-15), np.float64(-4.9960036108132044e-15), np.float64(-4.773959005888173e-15), np.float64(-4.052314039881821e-15), np.float64(-3.913536161803677e-15), np.float64(-2.3037127760972e-15), np.float64(-4.3298697960381105e-15), np.float64(-4.3298697960381105e-15)]}
marginals OT 1: [0.09973766 0.09973766 0.09973766 0.09973766 0.09973766 0.09973766
 0.09973766 0.09973766] [0.06749926 0.06749926 0.06749926 0.06598803 0.06598803 0.06598803
 0.06598803 0.06598803 0.06598803 0.06598803 0.06749926 0.06598803]
marginals OT 2: [0.04657563 0.05227775 0.04657563 0.03938462 0.04657563 0.05227775
 0.04657563 0.03938462 0.04657563 0.05227775 0.04657563 0.03938462
 0.04657563 0.05227775 0.04657563 0.03938462] [0.05271093 0.05271093 0.05271093 0.06605135 0.06605135 0.06605135
 0.06605135 0.06605135 0.06605135 0.06605135 0.05271093 0.06605135]
-- name = Unbalanced KL with KL Reg
$\lambda_u$=10, $\lambda_{ent}$=0.1 / param = {'reg': 0.1, 'unbalanced': 10, 'unbalanced_type': 'kl', 'reg_type': 'kl'}
X: [[ 1.82295827  0.62071009]
 [-0.62071009  1.82295827]
 [ 0.62071009 -1.82295827]
 [ 1.48472534 -1.28716017]
 [-1.95319153  0.27003949]
 [-1.48472534  1.28716017]
 [ 1.28716017  1.48472534]
 [ 0.27003949  1.95319153]
 [ 1.95319153 -0.27003949]
 [-1.28716017 -1.48472534]
 [-1.82295827 -0.62071009]
 [-0.27003949 -1.95319153]]
loss: -6.777911565336581e-14
loss: {'stopping_criterion': [np.float64(1.91858529063893e-10), np.float64(-1.0895514934716743e-08), np.float64(-8.76812727979015e-09), np.float64(-1.068237809320749e-08), np.float64(-8.524138450649588e-09), np.float64(-7.661017986659857e-09), np.float64(-1.0389622606687965e-08), np.float64(-7.100362464651511e-09), np.float64(-9.001810186148873e-09), np.float64(-4.975917400340535e-09), np.float64(-2.494313089407285e-09), np.float64(-1.5506653738839304e-09), np.float64(-1.2503489910109522e-09), np.float64(-1.0763919755518714e-09), np.float64(-9.63891799710126e-10), np.float64(-8.958868646935514e-10), np.float64(-7.878623309309774e-10), np.float64(-7.440171811978757e-10), np.float64(-6.712680966636242e-10), np.float64(-5.748012621431542e-10), np.float64(-5.494200649991399e-10), np.float64(-4.886551718819021e-10), np.float64(-4.4529674392279617e-10), np.float64(-6.061595114736917e-10), np.float64(-7.976907467899252e-10), np.float64(-8.22540591194354e-10), 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np.float64(9.658940314238862e-15), np.float64(-5.839773109528323e-14), np.float64(-8.587575095475586e-14), np.float64(-8.859579736508749e-14), np.float64(-3.4916514124461173e-14), np.float64(-1.4765966227514582e-14), np.float64(5.184741524999481e-14), np.float64(9.209299989265674e-14), np.float64(9.031664305325648e-14), np.float64(5.551115123125783e-14), np.float64(1.7819079545233762e-14), np.float64(-6.394884621840902e-14), np.float64(-7.388534228880417e-14), np.float64(-7.011058400507864e-14), np.float64(-3.3084646133829665e-14), np.float64(-1.1657341758564144e-14), np.float64(6.111777750561487e-14), np.float64(6.827871601444713e-14), np.float64(5.4067861299245124e-14), np.float64(2.5091040356528538e-14), np.float64(-1.687538997430238e-14), np.float64(-6.777911565336581e-14)]}
marginals OT 1: [0.11874817 0.11664081 0.11874817 0.11664081 0.11874817 0.11664081
 0.11874817 0.11664081] [0.07780397 0.07780397 0.07780397 0.07964714 0.07793787 0.07964714
 0.07964714 0.07793787 0.07793787 0.07964714 0.07780397 0.07793787]
marginals OT 2: [0.05739964 0.06007011 0.05858539 0.05593689 0.05739964 0.06007011
 0.05858539 0.05593689 0.05739964 0.06007011 0.05858539 0.05593689
 0.05739964 0.06007011 0.05858539 0.05593689] [0.07520683 0.07520683 0.07520683 0.07772843 0.07905677 0.07772843
 0.07772843 0.07905677 0.07905677 0.07772843 0.07520683 0.07905677]

Plot distributions and plans for unbalanced OT barycenter solvers

plot_list_res(
    lst_unbalanced_res,
    lst_unbalanced_solvers,
    fig_num=3,
    n_cols=3,
    show_masses=True,
    fig_width=12,
    fig_height=8.5,
    show_legend=False,
)

$Unbalanced KL No Reg $\lambda_u$=1, Unbalanced KL No Reg $\lambda_u$=2.5, Unbalanced KL No Reg $\lambda_u$=10, Unbalanced KL with KL Reg $\lambda_u$=1, $\lambda_{ent}$=0.1, Unbalanced KL with KL Reg $\lambda_u$=2.5, $\lambda_{ent}$=0.1, Unbalanced KL with KL Reg $\lambda_u$=10, $\lambda_{ent}$=0.1$

Total running time of the script: (0 minutes 13.487 seconds)

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