import marimo

__generated_with = "0.6.21-dev3"
app = marimo.App()


@app.cell
def __():
    import cvxpy as cp
    import numpy as np
    import matplotlib.pyplot as plt
    return cp, np, plt


@app.cell
def __(np):
    n = 2
    m = 50
    # U is a 2 x m matrix. Each column is a single sample u_i from the problem statement.
    U = np.array(
        [
            [
                1.824183228637652032e00,
                1.349093690455489103e00,
                6.966316403935147727e-01,
                7.599387854623529392e-01,
                2.388321695850912363e00,
                8.651370608981923116e-01,
                1.863922545015865406e00,
                7.099743941474848663e-01,
                6.005484882320809570e-01,
                4.561429569892232472e-01,
                5.328296545713475663e-01,
                2.138547819234526415e00,
                1.906676474276197464e00,
                1.015547309536922516e00,
                8.765948388006337133e-01,
                1.648147347399247842e00,
                1.027902202451572045e00,
                2.145586297520478691e00,
                1.793440421753045744e00,
                1.020535583041398908e00,
                8.977911075271942654e-01,
                1.530480229262339398e00,
                2.478088034137528872e-01,
                2.617415807793897820e00,
                2.081978553098443374e00,
                1.891226687205936452e00,
                8.222497927065576251e-01,
                5.803514604868882376e-01,
                1.158670193449639063e00,
                6.016685032455900695e-01,
                5.605410828151705660e-01,
                2.508815467550573164e00,
                2.230201413385580977e00,
                1.170848897912992514e00,
                2.256355929901105561e00,
                6.686991510936428629e-01,
                2.040269595792217672e00,
                3.634166812924328749e-01,
                5.418647611079159265e-01,
                6.631470058399455692e-01,
                4.286142597532469622e-01,
                2.155925078996823618e00,
                2.379380016960549682e00,
                6.343212414048013947e-01,
                1.469076407947448981e00,
                1.225322035289937439e00,
                1.467602887401966871e00,
                9.345319187253748883e-01,
                1.985592768641736505e00,
                2.106896115090134636e00,
            ],
            [
                -9.644136284187876385e-01,
                1.069547315003422927e00,
                6.733229334437943470e-01,
                7.788072961810316164e-01,
                -9.467465278344706636e-01,
                -8.591303443863639311e-01,
                1.279527420871080956e00,
                5.314829019311283487e-01,
                6.975676079749143499e-02,
                -4.641873429414754559e-01,
                -2.094571396598311763e-01,
                -8.003479827938377866e-01,
                6.135280782546607137e-01,
                -9.961307468791747999e-01,
                -8.765215480412106297e-01,
                9.655406812422813179e-01,
                1.011230180540185541e00,
                6.105416770440197372e-01,
                9.486552370654932620e-01,
                -9.863592657836954825e-01,
                7.695327845100754516e-01,
                -1.060072365810699413e00,
                -4.041043465424410952e-01,
                -2.352952920283236105e-01,
                7.560391050507236921e-01,
                -9.454246095204003053e-01,
                -5.303145312191936966e-01,
                5.979590038743245461e-01,
                -1.154309511133019717e00,
                -6.123184171955468047e-01,
                -1.464683782538583889e-01,
                -1.839128688968104386e-01,
                4.250070477845909744e-01,
                8.861864983476224200e-01,
                3.927648421593328276e-01,
                -6.726102374256350824e-01,
                -1.047252884197514833e00,
                1.825096825995130845e-01,
                -4.482373962742914886e-01,
                5.115625649313135792e-01,
                7.846201103116770548e-02,
                6.006325432819290544e-01,
                -5.710733714464664157e-01,
                4.725559971890586075e-01,
                -8.440290321502940118e-01,
                -1.003920890712479475e00,
                -1.067089412136528637e00,
                7.909281966910661765e-01,
                -1.059509163675931065e00,
                -7.136351632325785843e-01,
            ],
        ]
    )
    return U, m, n


@app.cell
def __(cp):
    c = cp.Variable(2)
    t = cp.Variable()
    return c, t


@app.cell
def __(cp):
    # Fill in the `...`!

    prob = cp.Problem(...)

    prob.solve()
    return prob,


@app.cell
def __(U, c, np, plt, t):
    r = np.sqrt(t.value + np.linalg.norm(c.value) ** 2)
    print("The center is", c.value, "and the radius is", r)

    fig, ax = plt.subplots()
    ax.scatter(U[0, :], U[1, :], edgecolor="k", color="w")
    cir = plt.Circle(
        c.value, r, color="k", fill=False, linestyle="dashed", alpha=0.5
    )
    ax.set_aspect("equal", adjustable="box")
    ax.add_patch(cir)
    plt.savefig("fitted_sphere.eps", dpi=300)
    plt.show()
    return ax, cir, fig, r


@app.cell
def __():
    import marimo as mo
    return mo,


if __name__ == "__main__":
    app.run()