Ejemplo n.º 1
0
def results_to_table(stripes, params):
    """ Build latex tables from a file of results """
    # Background params
    bg_data = []
    for i, stripe in enumerate(stripes):
        #print i, stripe, params[i]
        bg_data.append([stripe, params[i][1], params[i][2] ])
    bg_table = tex.DataTable(sc.array(bg_data), 'lcc', "Spheroid Parameters", "spheroidtable",
                          ["Stripe","$q$","$r_0$"])
    tex.deluxe_table(bg_table, roundoff=3)
    # Sgr params
    sgr_data = []
    for i, stripe in enumerate(stripes):
        if stripe==9 or stripe==22 or stripe==82:
            theta, phi = (ma.pi-eval(params[i][6]) ), (eval(params[i][7]) + ma.pi) #not sure if needed anymore
        else:
            theta, phi = eval(params[i][6]), eval(params[i][7])
        theta, phi = coor.angle_bounds3(theta*deg, phi*deg, phi_max=180.0)
        theta, phi = theta*rad, phi*rad
        sgr_data.append([stripe, params[i][3], params[i][4], params[i][5], str(theta),
                         str(phi), params[i][8] ])
    sgr_table = tex.DataTable(sc.array(sgr_data), 'lcccccc', "Sagittarius Stream Parameters",
                              "sgrtable", ["Stripe","$\epsilon$","$\mu$ ({}^{\circ})", "R (kpc)",
                                           "\theta (rad)", "\phi (rad)", "\sigma"])
    tex.deluxe_table(sgr_table, roundoff=3)
Ejemplo n.º 2
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def integrate_stripes(stripes, fit):
    mu_min = [170.0, 165.0, 150.0, 135.0, 135.0, 135.0, 135.0, 135.0, 135.0, 135.0,
              135.0, 133.0, 133.0, 131.0, 133.0, 311.0, 310.0, 310.0]
    mu_max = [235.0, 227.0, 229.0, 235.0, 235.0, 235.0, 240.0, 240.0, 235.0, 240.0,
              230.0, 249.0, 210.0, 225.0, 230.0, 416.0, 419.0, 420.0]
    N_stars = [19386, 18734, 11096, 17044, 18736, 15409, 12519, 12248, 8853, 7328,
               5479, 4450, 3486, 2425, 971, 9511, 16119, 16603]
    deg = 180.0/ma.pi
    for i in range(len(stripes)):
        if stripes[i] != 82:  continue
        params = twg.ParamSet()
        params.wedge = stripes[i]
        params.background = [0.0, 1.0, float(fit[i][1]), float(fit[i][2]), 1.0]
        # flip the weird angles, and convert to degrees
        if stripes[i]==9 or stripes[i]==22 or stripes[i]==82:
            theta, phi = (ma.pi-eval(fit[i][6]) ), (eval(fit[i][7]) + ma.pi)
        else:
            theta, phi = eval(fit[i][6]), eval(fit[i][7])
        theta, phi = coor.angle_bounds3(theta*deg, phi*deg, phi_max=180.0)
        params.streams = [ [float(fit[i][3]), float(fit[i][4]), float(fit[i][5]),
                            94.682, 116.0, float(fit[i][8])] ]  #normal to 82
        #params.streams = [ [float(fit[i][3]), float(fit[i][4]), float(fit[i][5]),
        #                    theta, phi, float(fit[i][8])] ]
        # Set g limits
        if (stripes[i]==9) or (stripes[i]==10):  g_max = 23.5
        elif (stripes[i]==11) or (stripes[i]==12):  g_max = 23.0
        else:  g_max = 22.5
        params.stripe = [(mu_min[i], mu_max[i], 10),(-1.25, 1.25, 10),(16.0,g_max,10)]
        params.update_refs()
        params.print_params()
        name = "sim_stripe_"+str(stripes[i])+"_NormNoCon.txt"
        print "STARTING: "+name
        stream_gen(params, 0, N_stars[i], fileout=name, convolve=0)
Ejemplo n.º 3
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def make_table_werrors(stripes, params):
    file2 = "../sgrnorth_paper/results_errors_final.txt"
    errors = fi.read_data(file2)
    for i, stripe in enumerate(stripes):
        if stripe == 9 or stripe == 22 or stripe == 82:
            theta, phi = (ma.pi - eval(params[i][6])), (
                eval(params[i][7]) + ma.pi)  #not sure if needed anymore
        else:
            theta, phi = float(params[i][6]), float(params[i][7])
        theta, phi = coor.angle_bounds3(theta * deg, phi * deg, phi_max=180.0)
        theta, phi = theta * rad, phi * rad
        fit = [
            stripe,
            float(params[i][3]),
            float(params[i][4]),
            float(params[i][5]), theta, phi,
            float(params[i][8])
        ]
        # put it together
        out = str(stripe) + " & "
        for j in range(2, 8):
            out = out + str(round(fit[j - 1], 2)) + r" \pm " + str(
                round(errors[i, j], 2)) + r" & "
        out = out + r" \\"
        print out, "\n"
        back = [
            stripe,
        ]
Ejemplo n.º 4
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def results_to_table(stripes, params):
    """ Build latex tables from a file of results """
    # Background params
    bg_data = []
    for i, stripe in enumerate(stripes):
        #print i, stripe, params[i]
        bg_data.append([stripe, params[i][1], params[i][2]])
    bg_table = tex.DataTable(sc.array(bg_data), 'lcc', "Spheroid Parameters",
                             "spheroidtable", ["Stripe", "$q$", "$r_0$"])
    tex.deluxe_table(bg_table, roundoff=3)
    # Sgr params
    sgr_data = []
    for i, stripe in enumerate(stripes):
        if stripe == 9 or stripe == 22 or stripe == 82:
            theta, phi = (ma.pi - eval(params[i][6])), (
                eval(params[i][7]) + ma.pi)  #not sure if needed anymore
        else:
            theta, phi = eval(params[i][6]), eval(params[i][7])
        theta, phi = coor.angle_bounds3(theta * deg, phi * deg, phi_max=180.0)
        theta, phi = theta * rad, phi * rad
        sgr_data.append([
            stripe, params[i][3], params[i][4], params[i][5],
            str(theta),
            str(phi), params[i][8]
        ])
    sgr_table = tex.DataTable(
        sc.array(sgr_data), 'lcccccc', "Sagittarius Stream Parameters",
        "sgrtable", [
            "Stripe", "$\epsilon$", "$\mu$ ({}^{\circ})", "R (kpc)",
            "\theta (rad)", "\phi (rad)", "\sigma"
        ])
    tex.deluxe_table(sgr_table, roundoff=3)
Ejemplo n.º 5
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def integrate_stripes(stripes, fit):
    mu_min = [
        170.0, 165.0, 150.0, 135.0, 135.0, 135.0, 135.0, 135.0, 135.0, 135.0,
        135.0, 133.0, 133.0, 131.0, 133.0, 311.0, 310.0, 310.0
    ]
    mu_max = [
        235.0, 227.0, 229.0, 235.0, 235.0, 235.0, 240.0, 240.0, 235.0, 240.0,
        230.0, 249.0, 210.0, 225.0, 230.0, 416.0, 419.0, 420.0
    ]
    N_stars = [
        19386, 18734, 11096, 17044, 18736, 15409, 12519, 12248, 8853, 7328,
        5479, 4450, 3486, 2425, 971, 9511, 16119, 16603
    ]
    deg = 180.0 / ma.pi
    for i in range(len(stripes)):
        if stripes[i] != 82: continue
        params = twg.ParamSet()
        params.wedge = stripes[i]
        params.background = [0.0, 1.0, float(fit[i][1]), float(fit[i][2]), 1.0]
        # flip the weird angles, and convert to degrees
        if stripes[i] == 9 or stripes[i] == 22 or stripes[i] == 82:
            theta, phi = (ma.pi - eval(fit[i][6])), (eval(fit[i][7]) + ma.pi)
        else:
            theta, phi = eval(fit[i][6]), eval(fit[i][7])
        theta, phi = coor.angle_bounds3(theta * deg, phi * deg, phi_max=180.0)
        params.streams = [[
            float(fit[i][3]),
            float(fit[i][4]),
            float(fit[i][5]), 94.682, 116.0,
            float(fit[i][8])
        ]]  #normal to 82
        #params.streams = [ [float(fit[i][3]), float(fit[i][4]), float(fit[i][5]),
        #                    theta, phi, float(fit[i][8])] ]
        # Set g limits
        if (stripes[i] == 9) or (stripes[i] == 10): g_max = 23.5
        elif (stripes[i] == 11) or (stripes[i] == 12): g_max = 23.0
        else: g_max = 22.5
        params.stripe = [(mu_min[i], mu_max[i], 10), (-1.25, 1.25, 10),
                         (16.0, g_max, 10)]
        params.update_refs()
        params.print_params()
        name = "sim_stripe_" + str(stripes[i]) + "_NormNoCon.txt"
        print "STARTING: " + name
        stream_gen(params, 0, N_stars[i], fileout=name, convolve=0)
Ejemplo n.º 6
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def make_table_werrors(stripes, params):
    file2="../sgrnorth_paper/results_errors_final.txt"
    errors=fi.read_data(file2)
    for i, stripe in enumerate(stripes):
        if stripe==9 or stripe==22 or stripe==82:
            theta, phi = (ma.pi-eval(params[i][6]) ), (eval(params[i][7]) + ma.pi) #not sure if needed anymore
        else:
            theta, phi = float(params[i][6]), float(params[i][7])
        theta, phi = coor.angle_bounds3(theta*deg, phi*deg, phi_max=180.0)
        theta, phi = theta*rad, phi*rad
        fit = [stripe, float(params[i][3]), float(params[i][4]), float(params[i][5]),
               theta, phi, float(params[i][8]) ]
        # put it together
        out = str(stripe)+" & "
        for j in range(2,8):
            out = out + str(round(fit[j-1],2))+r" \pm "+str(round(errors[i,j],2))+r" & "
        out = out + r" \\"
        print out, "\n"
        back = [stripe, ]
Ejemplo n.º 7
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import astro_coordinates as co
import math as ma

deg = 180.0/ma.pi

# milkyway thetas and phis
mw_t = [-1.50, -1.53, -1.31, -1.70, -1.91, -1.91, -2.33, -1.92, -1.97, -2.40, -2.36, -2.62, 0.60, -2.20]
mw_p = [-0.06, -0.05, -0.01, 0.15, -0.22, -0.14, -0.27, -0.22, -0.32, -0.10, -0.19, -0.30, -1.20, -2.10]

# BlueGene thetas and phis
bg_t = [1.1, 1.2, 1.3, 1.5, 1.8, 1.9, 2.3, 2.0, 2.1, 2.4, 2.3, 2.6, 2.4, 2.7]
bg_ts = [0.5, 1.3, 0.5, 0.2, 0.8, 0.7, 0.7, 0.8, 0.7, 1.6, 0.3, 0.9, 1.0, 1.6]
bg_p = [3.0, -2.9, 3.1, -3.0, 2.9, 3.0, 2.9, 2.9, 3.0, 3.0, 3.0, 3.0, 1.9, 1.4]
bg_ps = [2.0, 0.5, 0.3, 1.0, 0.3, 0.6, 0.5, 0.3, 1.0, 2.0, 0.7, 2.0, 2.5, 1.6]

for i in range(len(mw_t)):
    print bg_t[i], bg_ts[i], bg_p[i], bg_ps[i], mw_t[i], mw_p[i]
    x, y = co.angle_bounds3(mw_t[i]*deg, mw_p[i]*deg, phi_max=180.0)
    theta, phi = x/deg, y/deg
    dt, dp = abs(theta-bg_t[i])/bg_ts[i], abs(phi-bg_p[i])/bg_ps[i]
    print theta, dt, phi, dp, "\n"
Ejemplo n.º 8
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def sgr_xyz_plots(stripes, params):
    """ Plots stream positions & directions in galactic XYZ"""
    positions = sc.zeros((len(stripes),3))
    vectors = sc.zeros((len(stripes),3))
    for i, stripe in enumerate(stripes):
        positions[i,0], positions[i,1], positions[i,2] = coor.GC2xyz(
            eval(params[i][4]), 0.0, eval(params[i][5]), stripe)
        if stripe==9 or stripe==22 or stripe==82:
            theta, phi = (ma.pi-eval(params[i][6]) ), (eval(params[i][7]) + ma.pi)
        else:
            theta, phi = eval(params[i][6]), eval(params[i][7])
        theta, phi = coor.angle_bounds3(theta*deg, phi*deg, phi_max=180.0)
        theta, phi = theta*rad, phi*rad
        print stripe, theta, phi
        vectors[i,0] = ma.sin(theta)*ma.cos(phi)
        vectors[i,1] = ma.sin(theta)*ma.sin(phi)
        vectors[i,2] = ma.cos(theta)
    off = 1.0
    """ Plot xy """
    plt.figure(1)
    #ax = plt.subplot(111)
    plt.scatter(GC[0], GC[1], s=40, edgecolor="k", marker="o", facecolor="black")
    plt.text(GC[0]+off, GC[1]+off, "GC", fontsize=10)
    plt.scatter(sun[0], sun[1], s=20, edgecolor="k", marker=(8,2,0), facecolor="white")
    plt.text(sun[0]+off, sun[1]+off, "Sun", fontsize=10)
    plt.scatter(Sgr[0], Sgr[1], s=20, edgecolor="k", marker="o", facecolor="black")
    plt.text(Sgr[0]+off, Sgr[1]+off, "Sgr Core", fontsize=10)
    t = sc.arange(0.0, 2.0*ma.pi, 0.01)
    plt.plot(30.0*sc.cos(t), 30.0*sc.sin(t), "k:")
    offset_x = [0.0, 0.0, 0.0, -1.0, -2.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0,
                -2.0, -3.2, -3.0, 0.5, 0.0, 0.0, -1.0]
    offset_y = [0.0, 0.0, -1.0, -1.9, 0.2, 0.5, 0.5, -1.0, -2.0, -3.0, -3.0,
              -2.9, -2.5, 0.5, 0.5, -2.0, -2.0, -2.25]
    for i in range(len(stripes)):
        #plt.annotate(str(stripes[i]), xy=(positions[i,0], positions[i,1]),
        #            xytext=( (positions[i,0]+(vectors[i,0]*100.0)), (positions[i,1]+(vectors[i,1]*100.0)) ),
        #            arrowprops=dict(facecolor='black', arrowstyle="->") )
        if stripes[i] < 75:  color='white'
        else:  color='black'
        plt.arrow(positions[i,0], positions[i,1], vectors[i,0]*10.0, vectors[i,1]*10.0,
                  width=0.20, head_width=1.5, facecolor=color)
        if stripes[i] < 20 or stripes[i] > 19:
            plt.text(positions[i,0]+offset_x[i], positions[i,1]+offset_y[i],
                     r"$"+str(stripes[i])+r"$", fontsize=10)
    plt.xlabel(r"$X_{GC}$ (kpc)")
    plt.ylabel(r"$Y_{GC}$ (kpc)")
    plt.axis('equal')
    plt.ylim(-30, 30)
    plt.xlim(-30, 30)
    locs, labels = plt.xticks()
    for i in range(len(labels)):  labels[i] = r"$"+str(locs[i])+r"$"
    plt.xticks(locs, labels, fontsize=12)
    locs, labels = plt.yticks()
    for i in range(len(labels)):  labels[i] = r"$"+str(locs[i])+r"$"
    plt.yticks(locs, labels, fontsize=12)
    """ Plot xz """
    plt.figure(2)
    #ax = plt.subplot(111)
    plt.scatter(GC[0], GC[2], s=40, edgecolor="k", marker="o", facecolor="black")
    plt.text(GC[0]+off, GC[2]+off, r"GC", fontsize=10)
    plt.scatter(sun[0], sun[2], s=20, edgecolor="k", marker=(8,2,0), facecolor="white")
    plt.text(sun[0]+off, sun[2]+off, "Sun", fontsize=10)
    plt.scatter(Sgr[0], Sgr[2], s=20, edgecolor="k", marker="o", facecolor="black")
    plt.text(Sgr[0]+off, Sgr[2]+off, "Sgr Core", fontsize=10)
    plt.plot([-30.0, 30.0], [0.0, 0.0], "k:")
    offset_x = [0.2, 0.0, 0.0, -0.2, 0.0, 0.0, 0.0, -0.5, 1.0, 1.0, 0.5,
                0.75, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0]
    offset_z = [0.0, 0.0, 0.0, -2.5, 0.0, 0.0, -2.0, 0.5, -1.0, -1.0, 0.25,
                -1.0, -0.5, 0.0, -0.5, 0.0, 0.5, 0.5]
    for i in range(len(stripes)):
        #plt.annotate(str(stripes[i]), xytext=(positions[i,0], positions[i,2]),
        #            xy=( (positions[i,0]+(vectors[i,0]*10.0)), (positions[i,2]+(vectors[i,2]*10.0)) ),
        #            arrowprops=dict(facecolor='black', arrowstyle="->") )
        if stripes[i] < 75:  color='white'
        else:  color='black'
        plt.arrow(positions[i,0], positions[i,2], vectors[i,0]*10.0, vectors[i,2]*10.0,
                  width=0.25, head_width=2.0, facecolor=color)
        if stripes[i] < 20 or stripes[i] > 19:
            plt.text(positions[i,0]+offset_x[i], positions[i,2]+offset_z[i],
                     r"$"+str(stripes[i])+r"$", fontsize=10)
    plt.xlabel(r"$X_{GC}$ (kpc)")
    plt.ylabel(r"$Z_{GC}$ (kpc)")
    plt.axis('equal')
    plt.xlim(-45, 45)
    plt.ylim(-40, 50)
    locs, labels = plt.xticks()
    for i in range(len(labels)):  labels[i] = r"$"+str(locs[i])+r"$"
    plt.xticks(locs, labels, fontsize=12)
    locs, labels = sc.arange(-40.0, 50.0, 20.0), []
    for i in range(len(locs)):  labels.append(r"$"+str(locs[i])+r"$")
    plt.yticks(locs, labels, fontsize=12)
    # done
    plt.show()
Ejemplo n.º 9
0
def sgr_xyz_plots(stripes, params):
    """ Plots stream positions & directions in galactic XYZ"""
    positions = sc.zeros((len(stripes), 3))
    vectors = sc.zeros((len(stripes), 3))
    for i, stripe in enumerate(stripes):
        positions[i, 0], positions[i, 1], positions[i, 2] = coor.GC2xyz(
            eval(params[i][4]), 0.0, eval(params[i][5]), stripe)
        if stripe == 9 or stripe == 22 or stripe == 82:
            theta, phi = (ma.pi - eval(params[i][6])), (eval(params[i][7]) +
                                                        ma.pi)
        else:
            theta, phi = eval(params[i][6]), eval(params[i][7])
        theta, phi = coor.angle_bounds3(theta * deg, phi * deg, phi_max=180.0)
        theta, phi = theta * rad, phi * rad
        print stripe, theta, phi
        vectors[i, 0] = ma.sin(theta) * ma.cos(phi)
        vectors[i, 1] = ma.sin(theta) * ma.sin(phi)
        vectors[i, 2] = ma.cos(theta)
    off = 1.0
    """ Plot xy """
    plt.figure(1)
    #ax = plt.subplot(111)
    plt.scatter(GC[0],
                GC[1],
                s=40,
                edgecolor="k",
                marker="o",
                facecolor="black")
    plt.text(GC[0] + off, GC[1] + off, "GC", fontsize=10)
    plt.scatter(sun[0],
                sun[1],
                s=20,
                edgecolor="k",
                marker=(8, 2, 0),
                facecolor="white")
    plt.text(sun[0] + off, sun[1] + off, "Sun", fontsize=10)
    plt.scatter(Sgr[0],
                Sgr[1],
                s=20,
                edgecolor="k",
                marker="o",
                facecolor="black")
    plt.text(Sgr[0] + off, Sgr[1] + off, "Sgr Core", fontsize=10)
    t = sc.arange(0.0, 2.0 * ma.pi, 0.01)
    plt.plot(30.0 * sc.cos(t), 30.0 * sc.sin(t), "k:")
    offset_x = [
        0.0, 0.0, 0.0, -1.0, -2.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0, -2.0, -3.2,
        -3.0, 0.5, 0.0, 0.0, -1.0
    ]
    offset_y = [
        0.0, 0.0, -1.0, -1.9, 0.2, 0.5, 0.5, -1.0, -2.0, -3.0, -3.0, -2.9,
        -2.5, 0.5, 0.5, -2.0, -2.0, -2.25
    ]
    for i in range(len(stripes)):
        #plt.annotate(str(stripes[i]), xy=(positions[i,0], positions[i,1]),
        #            xytext=( (positions[i,0]+(vectors[i,0]*100.0)), (positions[i,1]+(vectors[i,1]*100.0)) ),
        #            arrowprops=dict(facecolor='black', arrowstyle="->") )
        if stripes[i] < 75: color = 'white'
        else: color = 'black'
        plt.arrow(positions[i, 0],
                  positions[i, 1],
                  vectors[i, 0] * 10.0,
                  vectors[i, 1] * 10.0,
                  width=0.20,
                  head_width=1.5,
                  facecolor=color)
        if stripes[i] < 20 or stripes[i] > 19:
            plt.text(positions[i, 0] + offset_x[i],
                     positions[i, 1] + offset_y[i],
                     r"$" + str(stripes[i]) + r"$",
                     fontsize=10)
    plt.xlabel(r"$X_{GC}$ (kpc)")
    plt.ylabel(r"$Y_{GC}$ (kpc)")
    plt.axis('equal')
    plt.ylim(-30, 30)
    plt.xlim(-30, 30)
    locs, labels = plt.xticks()
    for i in range(len(labels)):
        labels[i] = r"$" + str(locs[i]) + r"$"
    plt.xticks(locs, labels, fontsize=12)
    locs, labels = plt.yticks()
    for i in range(len(labels)):
        labels[i] = r"$" + str(locs[i]) + r"$"
    plt.yticks(locs, labels, fontsize=12)
    """ Plot xz """
    plt.figure(2)
    #ax = plt.subplot(111)
    plt.scatter(GC[0],
                GC[2],
                s=40,
                edgecolor="k",
                marker="o",
                facecolor="black")
    plt.text(GC[0] + off, GC[2] + off, r"GC", fontsize=10)
    plt.scatter(sun[0],
                sun[2],
                s=20,
                edgecolor="k",
                marker=(8, 2, 0),
                facecolor="white")
    plt.text(sun[0] + off, sun[2] + off, "Sun", fontsize=10)
    plt.scatter(Sgr[0],
                Sgr[2],
                s=20,
                edgecolor="k",
                marker="o",
                facecolor="black")
    plt.text(Sgr[0] + off, Sgr[2] + off, "Sgr Core", fontsize=10)
    plt.plot([-30.0, 30.0], [0.0, 0.0], "k:")
    offset_x = [
        0.2, 0.0, 0.0, -0.2, 0.0, 0.0, 0.0, -0.5, 1.0, 1.0, 0.5, 0.75, 0.0,
        0.0, 0.5, 0.0, 0.0, 0.0
    ]
    offset_z = [
        0.0, 0.0, 0.0, -2.5, 0.0, 0.0, -2.0, 0.5, -1.0, -1.0, 0.25, -1.0, -0.5,
        0.0, -0.5, 0.0, 0.5, 0.5
    ]
    for i in range(len(stripes)):
        #plt.annotate(str(stripes[i]), xytext=(positions[i,0], positions[i,2]),
        #            xy=( (positions[i,0]+(vectors[i,0]*10.0)), (positions[i,2]+(vectors[i,2]*10.0)) ),
        #            arrowprops=dict(facecolor='black', arrowstyle="->") )
        if stripes[i] < 75: color = 'white'
        else: color = 'black'
        plt.arrow(positions[i, 0],
                  positions[i, 2],
                  vectors[i, 0] * 10.0,
                  vectors[i, 2] * 10.0,
                  width=0.25,
                  head_width=2.0,
                  facecolor=color)
        if stripes[i] < 20 or stripes[i] > 19:
            plt.text(positions[i, 0] + offset_x[i],
                     positions[i, 2] + offset_z[i],
                     r"$" + str(stripes[i]) + r"$",
                     fontsize=10)
    plt.xlabel(r"$X_{GC}$ (kpc)")
    plt.ylabel(r"$Z_{GC}$ (kpc)")
    plt.axis('equal')
    plt.xlim(-45, 45)
    plt.ylim(-40, 50)
    locs, labels = plt.xticks()
    for i in range(len(labels)):
        labels[i] = r"$" + str(locs[i]) + r"$"
    plt.xticks(locs, labels, fontsize=12)
    locs, labels = sc.arange(-40.0, 50.0, 20.0), []
    for i in range(len(locs)):
        labels.append(r"$" + str(locs[i]) + r"$")
    plt.yticks(locs, labels, fontsize=12)
    # done
    plt.show()