{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0a6dc9b2-d9d0-4fc0-a84e-87ea68ccd9f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "from scipy.integrate import IntegrationWarning\n",
    "\n",
    "# Ignore integration warnings\n",
    "warnings.simplefilter(\"ignore\", IntegrationWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5b591783-a614-4bf3-a99a-56914c10d387",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Physical baryon density parameter (\\Omega_b h^2) from Planck\n",
    "obh2pl = 0.02236\n",
    "\n",
    "# Matter density parameter (\\Omega_m) from Planck\n",
    "ompl = 0.3166\n",
    "\n",
    "# Hubble constant (H_0) in km s^-1 Mpc^-1 from Planck\n",
    "H0pl = 67.27\n",
    "\n",
    "# Dimensionless Hubble parameter (h) from Planck\n",
    "h0pl = H0pl / 100\n",
    "\n",
    "# Dimensionless Hubble parameter (h) from Type Ia Supernovae\n",
    "h0riess = 0.7403\n",
    "\n",
    "# Cosmic Microwave Background (CMB) temperature in Kelvin\n",
    "Tcmb = 2.7255\n",
    "\n",
    "# Speed of light in vacuum in km s^-1\n",
    "c = 299792.458\n",
    "\n",
    "# Hubble distance scale (c / 100) in Mpc\n",
    "cH0 = 2997.92458"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a99a7de3-d5b8-4e30-a760-42b6da099748",
   "metadata": {},
   "outputs": [],
   "source": [
    "import mpmath\n",
    "import numpy as np\n",
    "# w(a) = w_0 + w_a * (1 - a)^n, i.e., nCPL model\n",
    "# For n=1 we get the usual CPL model\n",
    "def w(a, w0, wa, n):\n",
    "    return w0 + wa * (1 - a)**n\n",
    "\n",
    "# f_DE(a) for the nCPL model\n",
    "def f(a, w0, wa, n):\n",
    "    if wa == 0:\n",
    "        return a**(-3 * (1 + w0))\n",
    "    \n",
    "    harmonic_n = mpmath.harmonic(n)\n",
    "    hyper_term = mpmath.hyper([1, 1, 1 - n], [2, 2], a)\n",
    "    term1 = a**(-3 * (1 + w0 + wa))\n",
    "    term2 = mpmath.exp(-3 * wa * harmonic_n + 3 * a * n * wa * hyper_term)\n",
    "    return float(term1 * term2)\n",
    "# Define z_equality and a_equality in order to avoid some problems.\n",
    "# Tcmb is added as a parameter with a default value of 2.725 K.\n",
    "def zeq(om, h, Tcmb=2.725):\n",
    "    return 2.5*10**4 * om * (h**2) * (Tcmb / 2.7)**(-4)\n",
    "\n",
    "def aeq(om, h, Tcmb=2.725):\n",
    "    return 1.0 / (1.0 + zeq(om, h, Tcmb))\n",
    "\n",
    "#humble parameter\n",
    "def H(a, om, w0, wa, n, h):\n",
    "    # matter and radiation term\n",
    "    term_m_r = (a**-3) * om * (1 + aeq(om, h) / a)\n",
    "    # dark energy term\n",
    "    term_de = (1 - om * (1 + aeq(om, h))) * f(a, w0, wa, n)\n",
    "    \n",
    "    return 100 * h * np.sqrt(term_m_r + term_de)\n",
    "\n",
    "#sound speed\n",
    "def cs(a, obh2):\n",
    "    R = 31500 * obh2 * (Tcmb / 2.7)**-4 * a\n",
    "    return c / np.sqrt(3 * (1 + R))\n",
    "\n",
    "#redshift at decoupling\n",
    "def zcmb(om, obh2, h):\n",
    "    omh2 = om * h**2\n",
    "    g1 = (0.0783 * obh2**-0.238) / (1 + 39.5 * obh2**0.763)\n",
    "    g2 = 0.560 / (1 + 21.1 * obh2**1.81)\n",
    "    return 1048 * (1 + 0.00124 * obh2**-0.738) * (1 + g1 * omh2**g2)\n",
    "\n",
    "#drag redshift\n",
    "def zdrag(om, obh2, h):\n",
    "    omh2 = om * h**2\n",
    "    b1 = 0.313 * omh2**-0.419 * (1 + 0.607 * omh2**0.674)\n",
    "    b2 = 0.238 * omh2**0.223\n",
    "    \n",
    "    term1 = 1291 * omh2**0.251 / (1 + 0.659 * omh2**0.828)\n",
    "    term2 = 1 + b1 * obh2**b2\n",
    "    return term1 * term2\n",
    "\n",
    "from scipy.integrate import quad\n",
    "\n",
    "#comoving sound horizon at drag redshift\n",
    "def rs(ze, om, obh2, w0, wa, n, h):\n",
    "    lower_limit = 10**-11\n",
    "    upper_limit = 1.0 / (1.0 + ze)\n",
    "    \n",
    "    def integrand(x):\n",
    "        return cs(x, obh2) / (x**2 * H(x, om, w0, wa, n, h))\n",
    "    \n",
    "    \n",
    "    result, error = quad(integrand, lower_limit, upper_limit)\n",
    "    \n",
    "    return result\n",
    "    \n",
    "#luminosity distance\n",
    "from scipy.integrate import solve_ivp\n",
    "from functools import lru_cache\n",
    "\n",
    "@lru_cache(maxsize=None)\n",
    "def DLsol(om, w0, wa, n, h):\n",
    "    def dy_dz(zz, y):\n",
    "        a = 1.0 / (1.0 + zz)\n",
    "        return 1.0 / (H(a, om, w0, wa, n, h) / (100.0 * h))\n",
    "    sol = solve_ivp(dy_dz, [0, 1300], [0.0], dense_output=True)\n",
    "    return sol.sol\n",
    "\n",
    "def DL(z, om, w0, wa, n, h):\n",
    "    sol_func = DLsol(om, w0, wa, n, h)\n",
    "    y_val = sol_func(z)[0]\n",
    "    dL_val = y_val * (1.0 + z)\n",
    "    return (c / (100.0 * h)) * dL_val\n",
    "    \n",
    "#angular diameter distance\n",
    "def DA(z, om, w0, wa, n, h):\n",
    "    return DL(z, om, w0, wa, n, h) / (1.0 + z)**2\n",
    "    \n",
    "#volume averaged distance\n",
    "def Dv(zbao, om, w0, wa, n, h):\n",
    "    dl_term = DL(zbao, om, w0, wa, n, h) / (1.0 + zbao)\n",
    "    h_val = H(1.0 / (1.0 + zbao), om, w0, wa, n, h)\n",
    "    \n",
    "    return ((dl_term**2) * (c * zbao) / h_val)**(1.0 / 3.0)\n",
    "\n",
    "#BAO dz ratio\n",
    "def dz(zbao, om, obh2, w0, wa, n, h):\n",
    "    term1 = rs(zdrag(om, obh2, h), om, obh2, w0, wa, n, h)\n",
    "    term2 = Dv(zbao, om, w0, wa, n, h)\n",
    "    return term1/term2\n",
    "\n",
    "#DH distance\n",
    "def DH(z, om, w0, wa, n, h):\n",
    "    return c/H(1/(1+z), om, w0, wa, n, h)\n",
    "\n",
    "def hz(z, om, w0, wa, n, h):\n",
    "    return H(1/(1+z), om, w0, wa, n, h)\n",
    "\n",
    "#shift parameter\n",
    "def R(om, obh2, w0, wa, n, h):\n",
    "    term1 = np.sqrt(om*(100*h)**2) * DA(zcmb(om, obh2, h), om, w0, wa, n, h)\n",
    "    term2 = 1 + zcmb(om, obh2, h)\n",
    "    return term1*term2/c\n",
    "\n",
    "#angular scale of sound horizon at recombination\n",
    "def la(om, obh2, w0, wa, n, h):\n",
    "    term1 = np.pi * DA(zcmb(om, obh2, h), om, w0, wa, n, h)\n",
    "    term2 = 1 + zcmb(om, obh2, h)\n",
    "    term3 = rs(zcmb(om, obh2, h), om, obh2, w0, wa, n, h)\n",
    "    return term1*term2/term3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9a5b20d6-d433-4234-9967-f955f17cc8b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Data combination\n",
    "#CMB data\n",
    "datacmb = np.array([1.74963, 301.80845, 0.02237])\n",
    "\n",
    "# Covariance Matrix for {R, l_a, Omega_b h^2}\n",
    "covcmb = 10**-8 * np.array([\n",
    "    [1598.9554,  17112.007,  -36.311179],\n",
    "    [17112.007,  811208.45,  -494.79813],\n",
    "    [-36.311179, -494.79813,  2.1242182]\n",
    "])\n",
    "\n",
    "# Inverse Covariance Matrix\n",
    "invcov = np.linalg.inv(covcmb)\n",
    "\n",
    "# Number of CMB data points\n",
    "ndatCMB = len(datacmb)\n",
    "\n",
    "# Vector of residuals (Model - Data)\n",
    "def vec(om, obh2, w0, wa, n, h):\n",
    "    return np.array([\n",
    "        R(om, obh2, w0, wa, n, h) - datacmb[0],\n",
    "        la(om, obh2, w0, wa, n, h) - datacmb[1],\n",
    "        obh2 - datacmb[2]\n",
    "    ])\n",
    "\n",
    "# chi^2 function for CMB shift parameters\n",
    "def chi2R(om, obh2, w0, wa, n, h):\n",
    "    v = vec(om, obh2, w0, wa, n, h)\n",
    "    return v.T @ invcov @ v\n",
    "\n",
    "#ΒΑΟ data\n",
    "databao = np.array([\n",
    "    [0.106, 0.336, 0.015],\n",
    "    [0.44, 0.073, 0.031],\n",
    "    [0.6, 0.0726, 0.0164],\n",
    "    [0.73, 0.0592, 0.0185]\n",
    "])\n",
    "\n",
    "\n",
    "Cijbaoinv = np.array([\n",
    "    [1 / (databao[0, 2]**2), 0, 0, 0],\n",
    "    [0, 1040.3, -807.5, 336.8],\n",
    "    [0, -807.5, 3720.3, -1551.9],\n",
    "    [0, 336.8, -1551.9, 2914.9]\n",
    "])\n",
    "\n",
    "def vecbao(om, obh2, w0, wa, n, h):\n",
    "    return np.array([\n",
    "        databao[i, 1] - dz(databao[i, 0], om, obh2, w0, wa, n, h)\n",
    "        for i in range(len(databao))\n",
    "    ])\n",
    "\n",
    "#SDSS\n",
    "dataSDSS = np.array([\n",
    "    [0.15, 4.465666824, 0.1681350461],\n",
    "    [0.32, 8.4673, 0.167],\n",
    "    [0.57, 13.7728, 0.134],\n",
    "])\n",
    "\n",
    "#Ly-a\n",
    "dataLya = np.array([\n",
    "    [2.34, 11.2005988024, 0.56],\n",
    "    [2.34, 8.86, 0.29],\n",
    "])\n",
    "\n",
    "CijLyainv = np.array([\n",
    "    [1 / (dataLya[0, 2]**2), 0 ],\n",
    "    [0, 1 / (dataLya[1, 2]**2)]\n",
    "])\n",
    "\n",
    "def vecLya(om, obh2, w0, wa, n, h):\n",
    "    return np.array([\n",
    "        dataLya[0, 1] - DA(dataLya[0, 0], om, w0, wa, n, h) / rs(zdrag(om, obh2, h), om, obh2, w0, wa, n, h),\n",
    "        dataLya[1, 1] - DH(dataLya[1, 0], om, w0, wa, n, h) / rs(zdrag(om, obh2, h), om, obh2, w0, wa, n, h)\n",
    "    ])\n",
    "\n",
    "ndatBAO = len(dataSDSS) + len(databao) + len(dataLya)\n",
    "\n",
    "#total BAO χ^2\n",
    "def chi2bao(om, obh2, w0, wa, n, h):\n",
    "    v_bao = vecbao(om, obh2, w0, wa, n, h)\n",
    "    v_lya = vecLya(om, obh2, w0, wa, n, h)\n",
    "    \n",
    "    term_bao = v_bao.T @ Cijbaoinv @ v_bao\n",
    "    \n",
    "    term_sdss = sum(\n",
    "        ((dataSDSS[i, 1] - 1 / dz(dataSDSS[i, 0], om, obh2, w0, wa, n, h))**2) / (dataSDSS[i, 2]**2)\n",
    "        for i in range(len(dataSDSS))\n",
    "    )\n",
    "    \n",
    "    term_lya = v_lya.T @ CijLyainv @ v_lya\n",
    "    \n",
    "    return term_bao + term_sdss + term_lya"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ed475544-fffb-4877-80d6-3e10c2575be0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#full pantheon data\n",
    "import pandas as pd\n",
    "dataPanth = pd.read_csv(\"lcparam_full_long_zhel.txt\", sep=r'\\s+')\n",
    "ndatPanth = len(dataPanth)\n",
    "Dij0 = np.loadtxt(\"sys_full_long.txt\")\n",
    "Dij = Dij0[1:].reshape((1048,1048))\n",
    "Id = np.ones(ndatPanth)\n",
    "#Construct of the covariance using only the statistical uncertainties\n",
    "Covstat = np.diag(dataPanth.iloc[:, 5]**2)\n",
    "#Construct of the covariance using only the systematic uncertainties\n",
    "Covsys = Dij\n",
    "Cijtot = Covsys + Covstat\n",
    "InvCovTotal = np.linalg.inv(Cijtot)\n",
    "InvCovstat = np.linalg.inv(Covstat)\n",
    "\n",
    "# χ^2 for the pantheon data\n",
    "def chi2Panth(M, om, w0, wa, n, h):\n",
    "    zcmb = dataPanth.iloc[:, 1].values  \n",
    "    zhel = dataPanth.iloc[:, 2].values  \n",
    "    mb = dataPanth.iloc[:, 4].values\n",
    "    dl_vals = DL(zcmb, om, w0, wa, n, h)\n",
    "    delta_m = mb - (M + 5 * np.log10(((1 + zhel) / (1 + zcmb)) * dl_vals) + 25)\n",
    "    chi2 = delta_m.T @ InvCovTotal @ delta_m\n",
    "    return chi2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dcf5402a-9061-45be-9d10-79675dd18b91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Mathematica point in Python: 1032.8152046282435\n",
      "1026.2597302622967\n",
      "0.12038195926556611\n",
      "6.43509240668118\n"
     ]
    }
   ],
   "source": [
    "#total χ^2\n",
    "def chi2total(M, om, w0, wa, h):\n",
    "    return chi2R(om, obh2pl, w0, wa, 1.0, h) + chi2bao(om, obh2pl, w0, wa, 1.0, h) + chi2Panth(M, om, w0, wa, 1.0, h)\n",
    "ndatot = ndatCMB + ndatBAO + ndatPanth\n",
    "test_val = chi2total(-19.4294, 0.316911, -1, 0, 0.672379)\n",
    "print(\"Test Mathematica point in Python:\", test_val)\n",
    "x_val = chi2Panth(-19.4294, 0.316911, -1.0, 0.0, 1.0, 0.672379)\n",
    "print(x_val)\n",
    "y_val = chi2R(0.316911, obh2pl, -1.0, 0.0, 1, 0.672379)\n",
    "print(y_val)\n",
    "z_val = chi2bao(0.316911, obh2pl, -1.0, 0.0, 1, 0.672379)\n",
    "print(z_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4476fe4e-7c3c-4434-b9b1-4392f818f80a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 1032.7906234691416\n",
      "Mlcdm = -19.428583683289137\n",
      "omlcdm = 0.3165893182993782\n",
      "wolcdm = -1\n",
      "walcdm = 0\n",
      "hlcdm = 0.6725515834715047\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import basinhopping\n",
    "\n",
    "def obj_lcdm(params):\n",
    "    M, om, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2total(M, om, -1, 0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess = [-19.05, 0.3205, 0.6705]\n",
    "\n",
    "minimizer_kwargs = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [(None, None), (0.01, 0.99), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minlcdm = basinhopping(\n",
    "    obj_lcdm,\n",
    "    x0=initial_guess,\n",
    "    minimizer_kwargs=minimizer_kwargs,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "Mlcdm = minlcdm.x[0]\n",
    "omlcdm = minlcdm.x[1]\n",
    "wolcdm = -1\n",
    "walcdm = 0\n",
    "hlcdm = minlcdm.x[2]\n",
    "\n",
    "print(\"Minimum chi2:\", minlcdm.fun)\n",
    "print(\"Mlcdm =\", Mlcdm)\n",
    "print(\"omlcdm =\", omlcdm)\n",
    "print(\"wolcdm =\", wolcdm)\n",
    "print(\"walcdm =\", walcdm)\n",
    "print(\"hlcdm =\", hlcdm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8002f6d5-84a2-410a-8a11-a085d61c9ca8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 1032.6923784195612\n",
      "Mwcdm = -19.423397513557912\n",
      "omwcdm = 0.31448390671613147\n",
      "wowcdm = -1.0103536947470049\n",
      "wawcdm = 0\n",
      "hwcdm = 0.6751045370485488\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the wCDM model using all three likelihoods\n",
    "def obj_wcdm(params):\n",
    "    M, om, w0, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or w0 <= -3.0 or w0 >= 1.0 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2total(M, om, w0, 0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_wcdm = [-19.05, 0.3205, -1.0, 0.6705]\n",
    "\n",
    "minimizer_kwargs_wcdm = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [(None, None), (0.01, 0.99), (-3.0, 1.0), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minwcdm = basinhopping(\n",
    "    obj_wcdm,\n",
    "    x0=initial_guess_wcdm,\n",
    "    minimizer_kwargs=minimizer_kwargs_wcdm,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "Mwcdm = minwcdm.x[0]\n",
    "omwcdm = minwcdm.x[1]\n",
    "wowcdm = minwcdm.x[2]\n",
    "wawcdm = 0\n",
    "hwcdm = minwcdm.x[3]\n",
    "\n",
    "print(\"Minimum chi2:\", minwcdm.fun)\n",
    "print(\"Mwcdm =\", Mwcdm)\n",
    "print(\"omwcdm =\", omwcdm)\n",
    "print(\"wowcdm =\", wowcdm)\n",
    "print(\"wawcdm =\", wawcdm)\n",
    "print(\"hwcdm =\", hwcdm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "88c945f8-5e1f-4238-9d55-d0b127785297",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 1031.8200001076264\n",
      "Mcpl = -19.434704769334335\n",
      "omcpl = 0.3145979001968007\n",
      "wocpl = -1.081045814578108\n",
      "wacpl = 0.27987150856828413\n",
      "hcpl = 0.6742663592877898\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the CPL model using all three likelihoods\n",
    "def obj_cpl(params):\n",
    "    M, om, w0, wa, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or w0 <= -3.0 or w0 >= 1.0 or wa <= -3.0 or wa >= 3.0 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2total(M, om, w0, wa, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_cpl = [-19.05, 0.3205, -1.0, 0.0, 0.6705]\n",
    "\n",
    "minimizer_kwargs_cpl = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [(None, None), (0.01, 0.99), (-3.0, 1.0), (-3.0, 3.0), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "mincpl = basinhopping(\n",
    "    obj_cpl,\n",
    "    x0=initial_guess_cpl,\n",
    "    minimizer_kwargs=minimizer_kwargs_cpl,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "Mcpl = mincpl.x[0]\n",
    "omcpl = mincpl.x[1]\n",
    "wocpl = mincpl.x[2]\n",
    "wacpl = mincpl.x[3]\n",
    "hcpl = mincpl.x[4]\n",
    "\n",
    "print(\"Minimum chi2:\", mincpl.fun)\n",
    "print(\"Mcpl =\", Mcpl)\n",
    "print(\"omcpl =\", omcpl)\n",
    "print(\"wocpl =\", wocpl)\n",
    "print(\"wacpl =\", wacpl)\n",
    "print(\"hcpl =\", hcpl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6cb9ebad-1361-40b1-914f-eb3d5c425cb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 0.004707614311938003\n",
      "omlcdmC = 0.3149999481197267\n",
      "wolcdmC = -1.0\n",
      "walcdmC = 0.0\n",
      "hlcdmC = 0.6736130936955896\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the ΛCDM model using only the CMB data\n",
    "import numpy as np\n",
    "from scipy.optimize import basinhopping\n",
    "def obj_lcdmC(params):\n",
    "    om, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2R(om, obh2pl, -1.0, 0.0, 1.0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_lcdmC = [ 0.3205, 0.6705]\n",
    "\n",
    "minimizer_kwargs_lcdmC = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [ (0.01, 0.99), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minlcdmC = basinhopping(\n",
    "    obj_lcdmC,\n",
    "    x0=initial_guess_lcdmC,\n",
    "    minimizer_kwargs=minimizer_kwargs_lcdmC,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "omlcdmC = minlcdmC.x[0]\n",
    "wolcdmC = -1.0\n",
    "walcdmC = 0.0\n",
    "hlcdmC = minlcdmC.x[1]\n",
    "\n",
    "print(\"Minimum chi2:\", minlcdmC.fun)\n",
    "print(\"omlcdmC =\", omlcdmC)\n",
    "print(\"wolcdmC =\", wolcdmC)\n",
    "print(\"walcdmC =\", walcdmC)\n",
    "print(\"hlcdmC =\", hlcdmC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ae5ba0f7-867e-4c4b-9b85-c59acb8483e2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 4.0444549934327805\n",
      "omlcdmB = 0.2874879190981292\n",
      "wolcdmB = -1.0\n",
      "walcdmB = 0.0\n",
      "hlcdmB = 0.6469409306020726\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the ΛCDM model using only the BAO data\n",
    "\n",
    "def obj_lcdmB(params):\n",
    "    om, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2bao(om, obh2pl, -1.0, 0.0, 1.0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_lcdmB = [ 0.3205, 0.6705]\n",
    "\n",
    "minimizer_kwargs_lcdmB = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [ (0.01, 0.99), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minlcdmB = basinhopping(\n",
    "    obj_lcdmB,\n",
    "    x0=initial_guess_lcdmB,\n",
    "    minimizer_kwargs=minimizer_kwargs_lcdmB,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "omlcdmB = minlcdmB.x[0]\n",
    "wolcdmB = -1.0\n",
    "walcdmB = 0.0\n",
    "hlcdmB = minlcdmB.x[1]\n",
    "\n",
    "print(\"Minimum chi2:\", minlcdmB.fun)\n",
    "print(\"omlcdmB =\", omlcdmB)\n",
    "print(\"wolcdmB =\", wolcdmB)\n",
    "print(\"walcdmB =\", walcdmB)\n",
    "print(\"hlcdmB =\", hlcdmB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6e856dbf-118c-4d67-ac0a-248278d29ca5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for BAO and CMB data\n",
    "def chi2cbao(om, w0, wa, h):\n",
    "    return chi2R(om, obh2pl, w0, wa, 1.0, h) + chi2bao(om, obh2pl, w0, wa, 1.0, h) \n",
    "ndatot2 = ndatCMB + ndatBAO\n",
    "print(ndatot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a5639d81-1ca4-4a0a-861f-f33e14d432ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 6.5307922863924555\n",
      "omlcdmCB = 0.3174917143112643\n",
      "wolcdmCB = -1.0\n",
      "walcdmCB = 0.0\n",
      "hlcdmCB = 0.6719608654859085\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the ΛCDM model using BAO and CMB data\n",
    "\n",
    "def obj_lcdmCB(params):\n",
    "    om, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2cbao(om, -1.0, 0.0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_lcdmCB = [ 0.3205, 0.6705]\n",
    "\n",
    "minimizer_kwargs_lcdmCB = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [ (0.01, 0.99), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minlcdmCB = basinhopping(\n",
    "    obj_lcdmCB,\n",
    "    x0=initial_guess_lcdmCB,\n",
    "    minimizer_kwargs=minimizer_kwargs_lcdmCB,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "omlcdmCB = minlcdmCB.x[0]\n",
    "wolcdmCB = -1.0\n",
    "walcdmCB = 0.0\n",
    "hlcdmCB = minlcdmCB.x[1]\n",
    "\n",
    "print(\"Minimum chi2:\", minlcdmCB.fun)\n",
    "print(\"omlcdmCB =\", omlcdmCB)\n",
    "print(\"wolcdmCB =\", wolcdmCB)\n",
    "print(\"walcdmCB =\", walcdmCB)\n",
    "print(\"hlcdmCB =\", hlcdmCB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "58dfbd09-04ee-48eb-a102-aef1c0f75bc8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 5.832808745700806\n",
      "omcplCB = 0.3352260289605499\n",
      "wocplCB = -0.877049712791573\n",
      "wacplCB = -0.19561928707961693\n",
      "hcplCB = 0.6531740559584444\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the cpl model using BAO and CMB data\n",
    "\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def obj_cplCB(params):\n",
    "    om, w0, wa, h = params\n",
    "    try:\n",
    "        val = chi2cbao(om, w0, wa, h)\n",
    "        if np.isnan(val):\n",
    "            return np.inf \n",
    "        return val\n",
    "    except:\n",
    "        return np.inf\n",
    "\n",
    "initial_guess_cplCB = [0.3205, -1.0, 0.0, 0.6705]\n",
    "bounds_cplCB = [(0.01, 0.99), (-3.0, 1.0), (-3.0, 3.0), (0.1, 1.5)]\n",
    "\n",
    "\n",
    "mincplCB = minimize(\n",
    "    obj_cplCB,\n",
    "    x0=initial_guess_cplCB,\n",
    "    method=\"L-BFGS-B\",\n",
    "    bounds=bounds_cplCB,\n",
    "    options={'ftol': 1e-12, 'gtol': 1e-12}\n",
    ")\n",
    "\n",
    "print(\"Minimum chi2:\", mincplCB.fun)\n",
    "print(\"omcplCB =\", mincplCB.x[0])\n",
    "print(\"wocplCB =\", mincplCB.x[1])\n",
    "print(\"wacplCB =\", mincplCB.x[2])\n",
    "print(\"hcplCB =\", mincplCB.x[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2d4de6a1-a171-4d89-b1ec-5975ac5b8d63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1057\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for BAO and SN data\n",
    "def chi2BSN(M, om, w0, wa, h):\n",
    "    return chi2bao(om, obh2pl, w0, wa, 1.0, h) + chi2Panth(M, om, w0, wa, 1.0, h)\n",
    "ndatot3 = ndatPanth + ndatBAO\n",
    "print(ndatot3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2e14f177-d80a-4863-b139-330b671b5634",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum chi2: 1029.685644417206\n",
      "MlcdmBSN = -19.51343579819669\n",
      "omlcdmBSN = 0.29427429983291703\n",
      "wolcdmBSN = -1.0\n",
      "walcdmBSN = 0.0\n",
      "hlcdmBSN = 0.6497696615109092\n"
     ]
    }
   ],
   "source": [
    "#χ^2 for the ΛCDM model using BAO and SN data\n",
    "\n",
    "def obj_lcdmBSN(params):\n",
    "    M, om, h = params\n",
    "    if om <= 0.01 or om >= 0.99 or h <= 0.1 or h >= 1.5:\n",
    "        return 1e10\n",
    "    try:\n",
    "        val = chi2BSN(M, om, -1.0, 0.0, h)\n",
    "        if np.isnan(val):\n",
    "            return 1e10\n",
    "        return val\n",
    "    except:\n",
    "        return 1e10\n",
    "\n",
    "initial_guess_lcdmBSN = [-19.05, 0.3205, 0.6705]\n",
    "\n",
    "minimizer_kwargs_lcdmBSN = {\n",
    "    \"method\": \"Powell\",\n",
    "    \"bounds\": [(None, None), (0.01, 0.99), (0.1, 1.5)],\n",
    "    \"options\": {'ftol': 1e-12, 'xtol': 1e-12}\n",
    "}\n",
    "\n",
    "minlcdmBSN = basinhopping(\n",
    "    obj_lcdmBSN,\n",
    "    x0=initial_guess_lcdmBSN,\n",
    "    minimizer_kwargs=minimizer_kwargs_lcdmBSN,\n",
    "    niter=10,\n",
    "    stepsize=0.05,\n",
    "    T=1.0\n",
    ")\n",
    "\n",
    "MlcdmBSN = minlcdmBSN.x[0]\n",
    "omlcdmBSN = minlcdmBSN.x[1]\n",
    "wolcdmBSN = -1.0\n",
    "walcdmBSN = 0.0\n",
    "hlcdmBSN = minlcdmBSN.x[2]\n",
    "\n",
    "print(\"Minimum chi2:\", minlcdmBSN.fun)\n",
    "print(\"MlcdmBSN =\", MlcdmBSN)\n",
    "print(\"omlcdmBSN =\", omlcdmBSN)\n",
    "print(\"wolcdmBSN =\", wolcdmBSN)\n",
    "print(\"walcdmBSN =\", walcdmBSN)\n",
    "print(\"hlcdmBSN =\", hlcdmBSN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "3a1853ef-9e69-404c-a063-9f5d9dda56a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Δχ^2 για 1σ, 2 παράμετροι: 2.295748928898636\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(6.180074306244173)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#dchi\n",
    "import scipy.stats as stats\n",
    "import scipy.special as special\n",
    "\n",
    "def dchi(nsig, M):\n",
    "    p = special.erf(nsig / np.sqrt(2))\n",
    "    return stats.chi2.ppf(p, M)\n",
    "\n",
    "print(\"Δχ^2 για 1σ, 2 παράμετροι:\", dchi(1, 2)) \n",
    "dchi(2,2,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bc696104-8a0f-4cba-89c1-03ca6d5f5a1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "Fij = cij = errors = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "dccdd9b4-22f2-4120-b6e3-9aa7b1fc1cf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best fit parameters for Ω_0m and h are: Ω_0m = 0.3150 ± 0.0074 and h = 0.6736 ± 0.0049 respectively.\n",
      "\n",
      "Covariance Matrix (cij):\n",
      "[[ 5.48961346e-05 -3.65111525e-05]\n",
      " [-3.65111525e-05  2.44168527e-05]]\n",
      "\n",
      "Errors:\n",
      "[0.00740919 0.00494134]\n"
     ]
    }
   ],
   "source": [
    "# ERRORS\n",
    "#CMB\n",
    "def chi2_local_cmb(om, w0, wa, h):\n",
    "    return chi2R(om, obh2pl, w0, wa, 1, h)\n",
    "\n",
    "d_om = 0.02\n",
    "d_h = 0.002\n",
    "\n",
    "om0 = omlcdmC\n",
    "h0 = hlcdmC\n",
    "\n",
    "f_0_0 = chi2_local_cmb(om0, -1.0, 0.0, h0)\n",
    "\n",
    "f_p_0 = chi2_local_cmb(om0 + d_om, -1.0, 0.0, h0)\n",
    "f_m_0 = chi2_local_cmb(om0 - d_om, -1.0, 0.0, h0)\n",
    "\n",
    "f_0_p = chi2_local_cmb(om0, -1.0, 0.0, h0 + d_h)\n",
    "f_0_m = chi2_local_cmb(om0, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "# f(x+dx, y+dy), f(x+dx, y-dy), f(x-dx, y+dy), f(x-dx, y-dy)\n",
    "f_p_p = chi2_local_cmb(om0 + d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_p_m = chi2_local_cmb(om0 + d_om, -1.0, 0.0, h0 - d_h)\n",
    "f_m_p = chi2_local_cmb(om0 - d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_m_m = chi2_local_cmb(om0 - d_om, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "d2_dom2 = (f_p_0 - 2*f_0_0 + f_m_0) / (d_om**2)\n",
    "d2_dh2 = (f_0_p - 2*f_0_0 + f_0_m) / (d_h**2)\n",
    "d2_dom_dh = (f_p_p - f_p_m - f_m_p + f_m_m) / (4 * d_om * d_h)\n",
    "\n",
    "# Fisher matrix\n",
    "Fij = 0.5 * np.array([\n",
    "    [d2_dom2, d2_dom_dh],\n",
    "    [d2_dom_dh, d2_dh2]\n",
    "])\n",
    "\n",
    "# Covariance Matrix\n",
    "cij = np.linalg.inv(Fij)\n",
    "\n",
    "# 1σ errors\n",
    "errors = np.sqrt(np.diag(cij))\n",
    "\n",
    "\n",
    "print(f\"The best fit parameters for Ω_0m and h are: \"\n",
    "      f\"Ω_0m = {om0:.4f} ± {errors[0]:.4f} and \"\n",
    "      f\"h = {h0:.4f} ± {errors[1]:.4f} respectively.\\n\")\n",
    "\n",
    "print(\"Covariance Matrix (cij):\")\n",
    "print(cij)\n",
    "print(\"\\nErrors:\")\n",
    "print(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "916da077-7b32-4f2f-8696-b2e9a89bf545",
   "metadata": {},
   "outputs": [],
   "source": [
    "Fij = cij = errors = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "8377c45b-9fe5-42bb-92c1-37d6315d477d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best fit parameters for Ω_0m and h are: Ω_0m = 0.2875 ± 0.0274 and h = 0.6469 ± 0.0153 respectively.\n",
      "\n",
      "Covariance Matrix (cij):\n",
      "[[0.00075217 0.00031326]\n",
      " [0.00031326 0.00023511]]\n",
      "\n",
      "Errors:\n",
      "[0.0274257  0.01533319]\n"
     ]
    }
   ],
   "source": [
    "# ERRORS\n",
    "#BAO\n",
    "def chi2_local_bao(om, w0, wa, h):\n",
    "    return chi2bao(om, obh2pl, w0, wa, 1, h)\n",
    "\n",
    "d_om = 0.02\n",
    "d_h = 0.002\n",
    "\n",
    "om0 = omlcdmB\n",
    "h0 = hlcdmB\n",
    "\n",
    "f_0_0 = chi2_local_bao(om0, -1.0, 0.0, h0)\n",
    "\n",
    "f_p_0 = chi2_local_bao(om0 + d_om, -1.0, 0.0, h0)\n",
    "f_m_0 = chi2_local_bao(om0 - d_om, -1.0, 0.0, h0)\n",
    "\n",
    "f_0_p = chi2_local_bao(om0, -1.0, 0.0, h0 + d_h)\n",
    "f_0_m = chi2_local_bao(om0, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "# f(x+dx, y+dy), f(x+dx, y-dy), f(x-dx, y+dy), f(x-dx, y-dy)\n",
    "f_p_p = chi2_local_bao(om0 + d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_p_m = chi2_local_bao(om0 + d_om, -1.0, 0.0, h0 - d_h)\n",
    "f_m_p = chi2_local_bao(om0 - d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_m_m = chi2_local_bao(om0 - d_om, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "d2_dom2 = (f_p_0 - 2*f_0_0 + f_m_0) / (d_om**2)\n",
    "d2_dh2 = (f_0_p - 2*f_0_0 + f_0_m) / (d_h**2)\n",
    "d2_dom_dh = (f_p_p - f_p_m - f_m_p + f_m_m) / (4 * d_om * d_h)\n",
    "\n",
    "# Fisher matrix\n",
    "Fij = 0.5 * np.array([\n",
    "    [d2_dom2, d2_dom_dh],\n",
    "    [d2_dom_dh, d2_dh2]\n",
    "])\n",
    "\n",
    "# Covariance Matrix\n",
    "cij = np.linalg.inv(Fij)\n",
    "\n",
    "# 1σ errors\n",
    "errors = np.sqrt(np.diag(cij))\n",
    "\n",
    "\n",
    "print(f\"The best fit parameters for Ω_0m and h are: \"\n",
    "      f\"Ω_0m = {om0:.4f} ± {errors[0]:.4f} and \"\n",
    "      f\"h = {h0:.4f} ± {errors[1]:.4f} respectively.\\n\")\n",
    "\n",
    "print(\"Covariance Matrix (cij):\")\n",
    "print(cij)\n",
    "print(\"\\nErrors:\")\n",
    "print(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "b4ceba99-729d-4633-8e3d-19817412d4f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Fij = cij = errors = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "392a611a-e1b8-41f6-aa66-9ef3e3b6257b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best fit parameters for Ω_0m and h are: Ω_0m = 0.3175 ± 0.0059 and h = 0.6720 ± 0.0039 respectively.\n",
      "\n",
      "Covariance Matrix (cij):\n",
      "[[ 3.50021996e-05 -2.30061125e-05]\n",
      " [-2.30061125e-05  1.52543217e-05]]\n",
      "\n",
      "Errors:\n",
      "[0.00591627 0.00390568]\n"
     ]
    }
   ],
   "source": [
    "# ERRORS\n",
    "#CMB + ΒΑΟ\n",
    "def chi2_local_cbao(om, w0, wa, h):\n",
    "    return chi2cbao(om, w0, wa, h)\n",
    "\n",
    "d_om = 0.02\n",
    "d_h = 0.002\n",
    "\n",
    "om0 = omlcdmCB\n",
    "h0 = hlcdmCB\n",
    "\n",
    "f_0_0 = chi2_local_cbao(om0, -1.0, 0.0, h0)\n",
    "\n",
    "f_p_0 = chi2_local_cbao(om0 + d_om, -1.0, 0.0, h0)\n",
    "f_m_0 = chi2_local_cbao(om0 - d_om, -1.0, 0.0, h0)\n",
    "\n",
    "f_0_p = chi2_local_cbao(om0, -1.0, 0.0, h0 + d_h)\n",
    "f_0_m = chi2_local_cbao(om0, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "# f(x+dx, y+dy), f(x+dx, y-dy), f(x-dx, y+dy), f(x-dx, y-dy)\n",
    "f_p_p = chi2_local_cbao(om0 + d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_p_m = chi2_local_cbao(om0 + d_om, -1.0, 0.0, h0 - d_h)\n",
    "f_m_p = chi2_local_cbao(om0 - d_om, -1.0, 0.0, h0 + d_h)\n",
    "f_m_m = chi2_local_cbao(om0 - d_om, -1.0, 0.0, h0 - d_h)\n",
    "\n",
    "d2_dom2 = (f_p_0 - 2*f_0_0 + f_m_0) / (d_om**2)\n",
    "d2_dh2 = (f_0_p - 2*f_0_0 + f_0_m) / (d_h**2)\n",
    "d2_dom_dh = (f_p_p - f_p_m - f_m_p + f_m_m) / (4 * d_om * d_h)\n",
    "\n",
    "# Fisher matrix\n",
    "Fij = 0.5 * np.array([\n",
    "    [d2_dom2, d2_dom_dh],\n",
    "    [d2_dom_dh, d2_dh2]\n",
    "])\n",
    "\n",
    "# Covariance Matrix\n",
    "cij = np.linalg.inv(Fij)\n",
    "\n",
    "# 1σ errors\n",
    "errors = np.sqrt(np.diag(cij))\n",
    "\n",
    "\n",
    "print(f\"The best fit parameters for Ω_0m and h are: \"\n",
    "      f\"Ω_0m = {om0:.4f} ± {errors[0]:.4f} and \"\n",
    "      f\"h = {h0:.4f} ± {errors[1]:.4f} respectively.\\n\")\n",
    "\n",
    "print(\"Covariance Matrix (cij):\")\n",
    "print(cij)\n",
    "print(\"\\nErrors:\")\n",
    "print(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "47cbe0e6-c96c-44ca-b89f-96b3b61eab99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams.update({\n",
    "    'font.family': 'serif',\n",
    "    'font.serif': ['Times New Roman'],\n",
    "    'font.size': 18\n",
    "})\n",
    "\n",
    "om_vals = np.linspace(0.25, 0.35, 200) \n",
    "h_vals = np.linspace(0.6, 0.7, 200)\n",
    "OM_grid, H_grid = np.meshgrid(om_vals, h_vals)\n",
    "\n",
    "chi2_vec = np.vectorize(chi2_local_cmb)\n",
    "Z_cmb = chi2_vec(OM_grid, -1.0, 0.0, H_grid)\n",
    "\n",
    "chi2_min = chi2_local_cmb(omlcdmC, -1.0, 0.0, hlcdmC) \n",
    "\n",
    "levels = [\n",
    "    chi2_min + dchi(1,2),  # 1 sigma \n",
    "    chi2_min + dchi(2,2),  # 2 sigma \n",
    "    chi2_min + dchi(3,2)  # 3 sigma \n",
    "]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 6))\n",
    "\n",
    "contour1 = ax.contour(OM_grid, H_grid, Z_cmb, levels=levels, colors='blue', linewidths=0.6)\n",
    "\n",
    "ax.plot(omlcdmC, hlcdmC, 'ko', markersize=8, label='Best fit')\n",
    "\n",
    "ax.set_xlabel(r'$\\Omega_{0m}$') \n",
    "ax.set_ylabel(r'$h$')\n",
    "\n",
    "for spine in ax.spines.values():\n",
    "    spine.set_edgecolor('black')\n",
    "    spine.set_linewidth(1.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "22fe90cb-7134-4901-8e24-1aca3dfe06e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.rcParams.update({\n",
    "    'font.family': 'serif',\n",
    "    'font.serif': ['Times New Roman'],\n",
    "    'font.size': 18\n",
    "})\n",
    "\n",
    "om_vals = np.linspace(0.25, 0.35, 200) \n",
    "h_vals = np.linspace(0.6, 0.7, 200)\n",
    "OM_grid, H_grid = np.meshgrid(om_vals, h_vals)\n",
    "\n",
    "chi2_vec = np.vectorize(chi2_local_cbao)\n",
    "Z_cbao = chi2_vec(OM_grid, -1.0, 0.0, H_grid)\n",
    "\n",
    "chi2_min = chi2_local_cbao(omlcdmCB, wolcdmCB, walcdmCB, hlcdmCB) \n",
    "\n",
    "levels = [\n",
    "    chi2_min + dchi(1,2),  # 1 sigma \n",
    "    chi2_min + dchi(2,2),  # 2 sigma \n",
    "    chi2_min + dchi(3,2)  # 3 sigma \n",
    "]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 6))\n",
    "\n",
    "contour3 = ax.contour(OM_grid, H_grid, Z_cbao, levels=levels, colors='blue', linewidths=0.6)\n",
    "\n",
    "ax.plot(omlcdmCB, hlcdmCB, 'ko', markersize=8, label='Best fit')\n",
    "\n",
    "ax.set_xlabel(r'$\\Omega_{0m}$') \n",
    "ax.set_ylabel(r'$h$')\n",
    "\n",
    "for spine in ax.spines.values():\n",
    "    spine.set_edgecolor('black')\n",
    "    spine.set_linewidth(1.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "d88d02f9-81e5-4868-82a8-c78ee13e4e26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams.update({\n",
    "    'font.family': 'serif',\n",
    "    'font.serif': ['Times New Roman'],\n",
    "    'font.size': 18\n",
    "})\n",
    "\n",
    "om_vals = np.linspace(0.25, 0.35, 200) \n",
    "h_vals = np.linspace(0.6, 0.7, 200)\n",
    "OM_grid, H_grid = np.meshgrid(om_vals, h_vals)\n",
    "\n",
    "chi2_vec = np.vectorize(chi2total)\n",
    "Z_tot = chi2_vec(Mlcdm, OM_grid, -1.0, 0.0, H_grid)\n",
    "\n",
    "chi2_min = chi2total(Mlcdm, omlcdm, wolcdm, walcdm, hlcdm) \n",
    "\n",
    "levels = [\n",
    "    chi2_min + dchi(1,3),  # 1 sigma \n",
    "    chi2_min + dchi(2,3),  # 2 sigma \n",
    "    chi2_min + dchi(3,3)  # 3 sigma \n",
    "]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 6))\n",
    "\n",
    "contour4 = ax.contour(OM_grid, H_grid, Z_tot, levels=levels, colors='blue', linewidths=0.6)\n",
    "\n",
    "ax.plot(omlcdm, hlcdm, 'ko', markersize=8, label='Best fit')\n",
    "\n",
    "ax.set_xlabel(r'$\\Omega_{0m}$') \n",
    "ax.set_ylabel(r'$h$')\n",
    "\n",
    "for spine in ax.spines.values():\n",
    "    spine.set_edgecolor('black')\n",
    "    spine.set_linewidth(1.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d3cd090b-0b8b-49cf-b58a-791dc2bd082c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams.update({\n",
    "    'font.family': 'serif',\n",
    "    'font.serif': ['Times New Roman'],\n",
    "    'font.size': 18\n",
    "})\n",
    "\n",
    "om_vals = np.linspace(0.25, 0.35, 200) \n",
    "h_vals = np.linspace(0.6, 0.7, 200)\n",
    "OM_grid, H_grid = np.meshgrid(om_vals, h_vals)\n",
    "\n",
    "chi2_vec = np.vectorize(chi2_local_bao)\n",
    "Z_bao = chi2_vec(OM_grid, -1.0, 0.0, H_grid)\n",
    "\n",
    "chi2_min = chi2_local_bao(omlcdmB, wolcdmB, walcdmB, hlcdmB) \n",
    "\n",
    "levels = [\n",
    "    chi2_min + dchi(1,2),  # 1 sigma \n",
    "    chi2_min + dchi(2,2),  # 2 sigma \n",
    "    chi2_min + dchi(3,2)  # 3 sigma \n",
    "]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 6))\n",
    "\n",
    "contour5 = ax.contour(OM_grid, H_grid, Z_bao, levels=levels, colors='blue', linewidths=0.6)\n",
    "\n",
    "ax.plot(omlcdmB, hlcdmB, 'ko', markersize=8, label='Best fit')\n",
    "\n",
    "ax.set_xlabel(r'$\\Omega_{0m}$') \n",
    "ax.set_ylabel(r'$h$')\n",
    "\n",
    "for spine in ax.spines.values():\n",
    "    spine.set_edgecolor('black')\n",
    "    spine.set_linewidth(1.5)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "9a04c2d2-8112-4c36-93b1-6807aa9b119c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1150x450 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.rcParams.update({\n",
    "    'font.family': 'serif',\n",
    "    'font.serif': ['Times New Roman'],\n",
    "    'font.size': 18\n",
    "})\n",
    "\n",
    "om_vals = np.linspace(0.25, 0.35, 200) \n",
    "h_vals = np.linspace(0.6, 0.7, 200)\n",
    "OM_grid, H_grid = np.meshgrid(om_vals, h_vals)\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(11.5, 4.5))\n",
    "\n",
    "chi2_vec_bao = np.vectorize(chi2_local_bao)\n",
    "Z_bao = chi2_vec_bao(OM_grid, -1.0, 0.0, H_grid)\n",
    "chi2_min_bao = chi2_local_bao(omlcdmB, wolcdmB, walcdmB, hlcdmB) \n",
    "levels_bao = [chi2_min_bao + dchi(1,2), chi2_min_bao + dchi(2,2), chi2_min_bao + dchi(3,2)]\n",
    "\n",
    "axes[0].contour(OM_grid, H_grid, Z_bao, levels=levels_bao, colors='blue', linewidths=0.6)\n",
    "axes[0].plot(omlcdmB, hlcdmB, 'ko', markersize=8, label='Best fit')\n",
    "axes[0].set_xlabel(r'$\\Omega_{0m}$') \n",
    "axes[0].set_ylabel(r'$h$')\n",
    "\n",
    "chi2_vec_cmb = np.vectorize(chi2_local_cmb)\n",
    "Z_cmb = chi2_vec_cmb(OM_grid, -1.0, 0.0, H_grid)\n",
    "chi2_min_cmb = chi2_local_cmb(omlcdmC, -1.0, 0.0, hlcdmC) \n",
    "levels_cmb = [chi2_min_cmb + dchi(1,2), chi2_min_cmb + dchi(2,2), chi2_min_cmb + dchi(3,2)]\n",
    "\n",
    "axes[1].contour(OM_grid, H_grid, Z_cmb, levels=levels_cmb, colors='blue', linewidths=0.6)\n",
    "axes[1].plot(omlcdmC, hlcdmC, 'ko', markersize=8, label='Best fit')\n",
    "axes[1].set_xlabel(r'$\\Omega_{0m}$') \n",
    "\n",
    "chi2_vec_cbao = np.vectorize(chi2_local_cbao)\n",
    "Z_cbao = chi2_vec_cbao(OM_grid, -1.0, 0.0, H_grid)\n",
    "chi2_min_cbao = chi2_local_cbao(omlcdmCB, wolcdmCB, walcdmCB, hlcdmCB) \n",
    "levels_cbao = [chi2_min_cbao + dchi(1,2), chi2_min_cbao + dchi(2,2), chi2_min_cbao + dchi(3,2)]\n",
    "\n",
    "axes[2].contour(OM_grid, H_grid, Z_cbao, levels=levels_cbao, colors='blue', linewidths=0.6)\n",
    "axes[2].plot(omlcdmCB, hlcdmCB, 'ko', markersize=8, label='Best fit')\n",
    "axes[2].set_xlabel(r'$\\Omega_{0m}$') \n",
    "\n",
    "for ax in axes:\n",
    "    for spine in ax.spines.values():\n",
    "        spine.set_edgecolor('black')\n",
    "        spine.set_linewidth(1.5)\n",
    "\n",
    "axes[1].tick_params(labelleft=False)\n",
    "axes[2].tick_params(labelleft=False)\n",
    "\n",
    "plt.subplots_adjust(wspace=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "d37f12fb-acba-4807-b0bd-7ca2af38b575",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "\n",
    "contour3 = ax.contour(OM_grid, H_grid, Z_cbao, levels=levels_cbao, colors='blue', linewidths=0.6)\n",
    "contour5 = ax.contour(OM_grid, H_grid, Z_bao, levels=levels_bao, colors='blue', linewidths=0.6)\n",
    "\n",
    "ax.plot(omlcdmCB, hlcdmCB, 'ko', markersize=8)\n",
    "ax.plot(omlcdmB, hlcdmB, 'ko', markersize=8)\n",
    "\n",
    "ax.text(0.288, 0.656, \"BAO\", fontsize=12, color='black')\n",
    "ax.text(0.322, 0.685, \"BAO + CMB\", fontsize=12, color='black')\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$\\Omega_{0m}$')\n",
    "ax.set_ylabel(r'$h$')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "750d46f7-5771-4b42-8c47-beda14fe4e6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "chi2_lcdm = 1032.7906234691416\n",
    "Mlcdm = -19.428583683289137\n",
    "omlcdm = 0.3165893182993782\n",
    "wolcdm = -1\n",
    "walcdm = 0\n",
    "hlcdm = 0.6725515834715047\n",
    "\n",
    "chi2_wcdm = 1032.6923784195612\n",
    "Mwcdm = -19.423397513557912\n",
    "omwcdm = 0.31448390671613147\n",
    "wowcdm = -1.0103536947470049\n",
    "wawcdm = 0\n",
    "hwcdm = 0.6751045370485488\n",
    "\n",
    "chi2_cpl = 1031.8200001076264\n",
    "Mcpl = -19.434704769334335\n",
    "omcpl = 0.3145979001968007\n",
    "wocpl = -1.081045814578108\n",
    "wacpl = 0.27987150856828413\n",
    "hcpl = 0.6742663592877898\n",
    "\n",
    "chi2_lcdmC = 0.004707614311938003\n",
    "omlcdmC = 0.3149999481197267\n",
    "wolcdmC = -1.0\n",
    "walcdmC = 0.0\n",
    "hlcdmC = 0.6736130936955896\n",
    "\n",
    "chi2_lcdmB = 4.0444549934327805\n",
    "omlcdmB = 0.2874879190981292\n",
    "wolcdmB = -1.0\n",
    "walcdmB = 0.0\n",
    "hlcdmB = 0.6469409306020726\n",
    "\n",
    "chi2_lcdmCB = 6.5307922863924555\n",
    "omlcdmCB = 0.3174917143112643\n",
    "wolcdmCB = -1.0\n",
    "walcdmCB = 0.0\n",
    "hlcdmCB = 0.6719608654859085\n",
    "\n",
    "chi2_cplCB = 5.832808745700806\n",
    "omcplCB = 0.3352260289605499\n",
    "wocplCB = -0.877049712791573\n",
    "wacplCB = -0.19561928707961693\n",
    "hcplCB = 0.6531740559584444\n",
    "\n",
    "chi2_lcdmBSN = 1029.685644417206\n",
    "MlcdmBSN = -19.51343579819669\n",
    "omlcdmBSN = 0.29427429983291703\n",
    "wolcdmBSN = -1.0\n",
    "walcdmBSN = 0.0\n",
    "hlcdmBSN = 0.6497696615109092\n",
    "\n",
    "np.savez('cosmology_parameters15.npz',\n",
    "         chi2_lcdm=chi2_lcdm, Mlcdm=Mlcdm, omlcdm=omlcdm, wolcdm=wolcdm, walcdm=walcdm, hlcdm=hlcdm,\n",
    "         chi2_wcdm=chi2_wcdm, Mwcdm=Mwcdm, omwcdm=omwcdm, wowcdm=wowcdm, wawcdm=wawcdm, hwcdm=hwcdm,\n",
    "         chi2_cpl=chi2_cpl, Mcpl=Mcpl, omcpl=omcpl, wocpl=wocpl, wacpl=wacpl, hcpl=hcpl,\n",
    "         chi2_lcdmC=chi2_lcdmC, omlcdmC=omlcdmC, wolcdmC=wolcdmC, walcdmC=walcdmC, hlcdmC=hlcdmC,\n",
    "         chi2_lcdmB=chi2_lcdmB, omlcdmB=omlcdmB, wolcdmB=wolcdmB, walcdmB=walcdmB, hlcdmB=hlcdmB,\n",
    "         chi2_lcdmCB=chi2_lcdmCB, omlcdmCB=omlcdmCB, wolcdmCB=wolcdmCB, walcdmCB=walcdmCB, hlcdmCB=hlcdmCB,\n",
    "         chi2_cplCB=chi2_cplCB, omcplCB=omcplCB, wocplCB=wocplCB, wacplCB=wacplCB, hcplCB=hcplCB,\n",
    "         chi2_lcdmBSN=chi2_lcdmBSN, MlcdmBSN=MlcdmBSN, omlcdmBSN=omlcdmBSN, wolcdmBSN=wolcdmBSN, walcdmBSN=walcdmBSN, hlcdmBSN=hlcdmBSN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "077c1d6a-ab5f-4323-b040-25ee2aa4eb38",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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