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: 2.843917885588297
loss: {'stopping_criterion': [np.float64(4.936424991369895), np.float64(3.1120231938542977), np.float64(2.8852594148178747), np.float64(2.8529760102986677), np.float64(2.8490581667577874), np.float64(2.847220993521691), np.float64(2.84603194859164), np.float64(2.845232096852182), np.float64(2.844710356872045), np.float64(2.844382959911563), np.float64(2.844182839395289), np.float64(2.8440618969857256), np.float64(2.8439889115754537), np.float64(2.843944735280049), np.float64(2.843917885588297)]}
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)]

        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 21 iterations
X: [[ 2.68842412e+00  1.09599981e+00]
 [ 1.55912805e+00  2.38647009e+00]
 [ 2.29417463e+00 -1.62025545e+00]
 [ 8.73881960e-01 -4.21363885e-01]
 [-9.37262661e-01  5.52608389e-01]
 [-5.87261319e-01  2.79238265e+00]
 [ 7.78685207e-01  6.82302685e-01]
 [-2.79962446e-02  1.05594435e+00]
 [ 2.82942989e+00 -6.30715130e-04]
 [-9.67824920e-01 -1.13793725e+00]
 [-2.68582634e+00  4.41838874e-03]
 [ 1.19964287e-01 -1.47985916e+00]]
loss: 0.9295969562099679
loss: {'stopping_criterion': [np.float64(1.1111715092817795), np.float64(0.9993291222189953), np.float64(0.9760642927409933), np.float64(0.9680153266106677), np.float64(0.9626324299046127), np.float64(0.9558520953502078), np.float64(0.9467225856503887), np.float64(0.9398129442102338), np.float64(0.9361812921942554), np.float64(0.9342093230908112), np.float64(0.9329927572759469), np.float64(0.9320054919651546), np.float64(0.9311157454966993), np.float64(0.9304046957292161), np.float64(0.9299799494833249), np.float64(0.9297861943888723), np.float64(0.9296981657592907), np.float64(0.9296532984458659), np.float64(0.9296282498772628), np.float64(0.9296132098622316), np.float64(0.9296035560662714), np.float64(0.9295969562099679)]}
marginals OT 1: [0.06618056 0.08875821 0.09146287 0.07037951 0.05774555 0.08107184
 0.08135332 0.06986731] [0.00310181 0.00374822 0.00555563 0.11145393 0.11383835 0.00361137
 0.09462385 0.09166486 0.00586713 0.0812108  0.01050873 0.08163449]
marginals OT 2: [0.06278333 0.06338094 0.03842342 0.04061282 0.03841422 0.0407365
 0.00996723 0.01588222 0.04788771 0.01555663 0.01660503 0.01150615
 0.01638365 0.01139418 0.04205736 0.03625903] [0.06339147 0.07603822 0.07588453 0.00250028 0.01029464 0.07597129
 0.00297987 0.00325317 0.06282094 0.02807196 0.07893083 0.02771321]
-- 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 85 iterations
X: [[ 1.70022474  0.69073093]
 [-0.68589113  1.70240108]
 [ 0.69092405 -1.69820167]
 [ 1.48910469 -1.26930932]
 [-1.99317971  0.20045476]
 [-1.47047184  1.26961356]
 [ 1.27056616  1.47829821]
 [ 0.19628411  1.99078793]
 [ 1.98238004 -0.1872851 ]
 [-1.2683901  -1.48056485]
 [-1.70066579 -0.68601938]
 [-0.19194926 -1.98512645]]
loss: 1.180304277647728
loss: {'stopping_criterion': [np.float64(1.798724802168507), np.float64(1.4305610062423397), np.float64(1.3147277646162947), np.float64(1.252297979110813), np.float64(1.231390567091456), np.float64(1.220902292709011), np.float64(1.2103044401249228), np.float64(1.202402694384619), np.float64(1.198139771654552), np.float64(1.1953168524945126), np.float64(1.1933845923540076), np.float64(1.1920692274131905), np.float64(1.1911734974063395), np.float64(1.1904637273046608), np.float64(1.1898364066599831), np.float64(1.1892417766605128), np.float64(1.1886479791233866), np.float64(1.1880332858632527), np.float64(1.1873877426678243), np.float64(1.186732135238251), np.float64(1.1861491323092554), np.float64(1.1856968265994412), np.float64(1.1853508079606567), np.float64(1.185079440443497), np.float64(1.1848590675478425), np.float64(1.1846740737958013), np.float64(1.1845145170748332), np.float64(1.1843735192890361), np.float64(1.1842459175003215), np.float64(1.184127631930783), np.float64(1.1840153457659564), np.float64(1.1839063577517452), np.float64(1.1837985759055447), np.float64(1.183690650940986), np.float64(1.1835822268718297), np.float64(1.1834742019794717), np.float64(1.1833687576658853), np.float64(1.1832688593423573), np.float64(1.1831772181872369), np.float64(1.1830952728574318), np.float64(1.1830228677728805), np.float64(1.1829586419818323), np.float64(1.1829006353653275), np.float64(1.1828467592401148), np.float64(1.1827950523312691), np.float64(1.1827437696518568), np.float64(1.1826913841062479), np.float64(1.1826365688851634), np.float64(1.1825782028120377), np.float64(1.182515418946104), np.float64(1.182447698819043), np.float64(1.182374991984632), np.float64(1.182297809644938), np.float64(1.1822172163245004), np.float64(1.1821346595631192), np.float64(1.1820516583538088), np.float64(1.181969472663286), np.float64(1.1818888975475659), np.float64(1.1818102337903713), np.float64(1.181733379705666), np.float64(1.1816579594851109), np.float64(1.1815834373720113), np.float64(1.1815092057333791), np.float64(1.1814346542150487), np.float64(1.1813592316952353), np.float64(1.1812825113102368), np.float64(1.1812042648355625), np.float64(1.1811245460463728), np.float64(1.1810437723522083), np.float64(1.180962780480147), np.float64(1.1808828199998473), np.float64(1.1808054487862891), np.float64(1.1807323198442576), np.float64(1.180664900321218), np.float64(1.1806042153182774), np.float64(1.1805507164264233), np.float64(1.180504315763009), np.float64(1.1804645392759026), np.float64(1.1804307086297985), np.float64(1.1804020837065319), np.float64(1.1803779471612978), np.float64(1.1803576438811345), np.float64(1.1803405942401124), np.float64(1.1803262945660689), np.float64(1.1803143120636608), np.float64(1.180304277647728)]}
marginals OT 1: [0.10002298 0.09960635 0.10007487 0.09947066 0.09994939 0.09936447
 0.09988376 0.09949421] [0.06736653 0.06738454 0.06753319 0.06705707 0.06426934 0.06781033
 0.0673816  0.06435004 0.06488032 0.06751196 0.06753346 0.06478831]
marginals OT 2: [0.04622202 0.05230038 0.0471858  0.03942826 0.0460349  0.05227207
 0.0472552  0.03940357 0.04589417 0.05222031 0.04702734 0.03937127
 0.04606573 0.0522423  0.04694669 0.03939887] [0.0527685  0.05280262 0.05274162 0.06477495 0.06827063 0.06373418
 0.06413337 0.06796629 0.06730838 0.06433729 0.05278109 0.06764997]
-- 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'}
BCD converged in 11 iterations
X: [[ 1.8230975   0.62058465]
 [-0.61895968  1.82464784]
 [ 0.62108914 -1.8225415 ]
 [ 1.48488198 -1.28720631]
 [-1.95301123  0.27221545]
 [-1.4827518   1.28749749]
 [ 1.28764671  1.48333508]
 [ 0.27192475  1.95311998]
 [ 1.95324935 -0.27000088]
 [-1.28682245 -1.4847197 ]
 [-1.82455359 -0.61898173]
 [-0.2696589  -1.95318824]]
loss: 1.3112846598690693
loss: {'stopping_criterion': [np.float64(2.8256280235755744), np.float64(1.5953740740922324), np.float64(1.3849313699965542), np.float64(1.3453364290728318), np.float64(1.329475743846162), np.float64(1.3234336963868087), np.float64(1.3186380731014324), np.float64(1.3137330350508067), np.float64(1.3116416571334852), np.float64(1.3113377863594846), np.float64(1.311291662254598), np.float64(1.3112846598690693)]}
marginals OT 1: [0.11875424 0.11664454 0.11876711 0.1166224  0.11875924 0.11661492
 0.11874403 0.11664536] [0.07779922 0.0777859  0.07780846 0.07964171 0.07792436 0.07968067
 0.07965719 0.07791883 0.07793324 0.0796678  0.07779222 0.07794223]
marginals OT 2: [0.05740124 0.06006977 0.05861491 0.0559522  0.05739297 0.06003801
 0.05861695 0.05595194 0.05738893 0.06003462 0.05857785 0.0559329
 0.05740005 0.06007618 0.05858573 0.05593782] [0.07520825 0.07525763 0.07519621 0.07773012 0.07906109 0.07767097
 0.07768143 0.07905839 0.07905569 0.07773409 0.07526075 0.07905745]

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 11.778 seconds)

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