Fit monotonic binned poly-tccd acquisition probability model in 2018-11

This is a DEVELOPMENT model maintained for reference. It illustrates a monotonically increasing model that uses the integral of the probit transform of a quadratic as the model.

However, with the introduction of the floor component, there was not as much problem with monotonicity.

This is an intermediate model which collects the probabilities within narrow magnitude bins and fits a quadratic polynomial model to the data as a function of CCD temperature.

The fit and plot of polynomial coefficients in each mag bin are used as starting values in the fit_acq_prob_model-2018-04-poly-spline-tccd notebook.


In [1]:
import sys
import os
from itertools import count
from pathlib import Path
sys.path.insert(0, str(Path(os.environ['HOME'], 'git', 'skanb', 'pea-test-set')))
import utils as asvt_utils
import numpy as np
import matplotlib.pyplot as plt
from astropy.table import Table, vstack
from astropy.time import Time
import tables
from scipy import stats
from scipy.interpolate import CubicSpline
from Chandra.Time import DateTime
from astropy.table import Table
from chandra_aca.star_probs import get_box_delta

%matplotlib inline

In [2]:
SKA = Path(os.environ['SKA'])

Get acq stats data and clean


In [3]:
# Make a map of AGASC_ID to AGACS 1.7 MAG_ACA.  The acq_stats.h5 file has whatever MAG_ACA
# was in place at the time of planning the loads.
with tables.open_file(str(SKA / 'data' / 'agasc' / 'miniagasc_1p7.h5'), 'r') as h5:
    agasc_mag_aca = h5.root.data.col('MAG_ACA')
    agasc_id = h5.root.data.col('AGASC_ID')
    has_color3 = h5.root.data.col('RSV3') != 0  # 
    red_star = np.isclose(h5.root.data.col('COLOR1'), 1.5)
    mag_aca_err = h5.root.data.col('MAG_ACA_ERR') / 100
    red_mag_err = red_star & ~has_color3  # MAG_ACA, MAG_ACA_ERR is potentially inaccurate

In [4]:
agasc1p7_idx = {id: idx for id, idx in zip(agasc_id, count())}
agasc1p7 = Table([agasc_mag_aca, mag_aca_err, red_mag_err], 
                 names=['mag_aca', 'mag_aca_err', 'red_mag_err'], copy=False)

In [5]:
acq_file = str(SKA / 'data' / 'acq_stats' / 'acq_stats.h5')
with tables.open_file(str(acq_file), 'r') as h5:
    cols = h5.root.data.cols
    names = {'tstart': 'guide_tstart',
             'obsid': 'obsid',
             'obc_id': 'acqid',
             'halfwidth': 'halfw',
             'warm_pix': 'n100_warm_frac',
             'mag_aca': 'mag_aca',
             'mag_obs': 'mean_trak_mag',
             'known_bad': 'known_bad',
             'color': 'color1',
            'img_func': 'img_func', 
            'ion_rad': 'ion_rad',
            'sat_pix': 'sat_pix',
             'agasc_id': 'agasc_id',
             't_ccd': 'ccd_temp',
            'slot': 'slot'}
    acqs = Table([getattr(cols, h5_name)[:] for h5_name in names.values()],
                 names=list(names.keys()))

In [6]:
year_q0 = 1999.0 + 31. / 365.25  # Jan 31 approximately
acqs['year'] = Time(acqs['tstart'], format='cxcsec').decimalyear.astype('f4')
acqs['quarter'] = (np.trunc((acqs['year'] - year_q0) * 4)).astype('f4')

In [7]:
# Create 'fail' column, rewriting history as if the OBC always
# ignore the MS flag in ID'ing acq stars.
#
# UPDATE: is ion_rad being ignored on-board?  (Not as of 2018-11)
#
obc_id = acqs['obc_id']
obc_id_no_ms = (acqs['img_func'] == 'star') & ~acqs['sat_pix'] & ~acqs['ion_rad']
acqs['fail'] = np.where(obc_id | obc_id_no_ms, 0.0, 1.0)
acqs['mag_aca'] = [agasc1p7['mag_aca'][agasc1p7_idx[agasc_id]] for agasc_id in acqs['agasc_id']]
acqs['red_mag_err'] = [agasc1p7['red_mag_err'][agasc1p7_idx[agasc_id]] for agasc_id in acqs['agasc_id']]
acqs['mag_aca_err'] = [agasc1p7['mag_aca_err'][agasc1p7_idx[agasc_id]] for agasc_id in acqs['agasc_id']]
acqs['asvt'] = False

In [8]:
# Filter for year and mag (previously used data through 2007:001)
#
# UPDATE this to be between 4 to 5 years from time of recalibration.
#
# The mag range is restricted to 8.5 < mag < 10.7 because the model
# is only calibrated in that range.  Above 10.7 there is concern that
# stats are actually unreliable (fraction of imposters that happen to
# is high?)  This upper limit is something to play with.
#
year_min = 2014.5
year_max = DateTime('2018-10-30').frac_year
ok = ((acqs['year'] > year_min) & (acqs['year'] < year_max) & 
      (acqs['mag_aca'] > 7.0) & (acqs['mag_aca'] < 11) &
      (~np.isclose(acqs['color'], 0.7)))

In [9]:
# Filter known bad obsids
print('Filtering known bad obsids, start len = {}'.format(np.count_nonzero(ok)))
bad_obsids = [
    # Venus
    2411,2414,6395,7306,7307,7308,7309,7311,7312,7313,7314,7315,7317,7318,7406,583,
    7310,9741,9742,9743,9744,9745,9746,9747,9749,9752,9753,9748,7316,15292,16499,
    16500,16501,16503,16504,16505,16506,16502,
    ]
for badid in bad_obsids:
    ok = ok & (acqs['obsid'] != badid)
print('Filtering known bad obsids, end len = {}'.format(np.count_nonzero(ok)))


Filtering known bad obsids, start len = 54978
Filtering known bad obsids, end len = 54978

Get ASVT data and make it look more like acq stats data


In [10]:
peas = Table.read('pea_analysis_results_2018_299_CCD_temp_performance.csv', format='ascii.csv')
peas = asvt_utils.flatten_pea_test_data(peas)

In [11]:
# Fuzz mag and T_ccd by a bit for plotting and fitting.
fpeas = Table([peas['star_mag'], peas['ccd_temp'], peas['search_box_hw']],
              names=['mag_aca', 't_ccd', 'halfwidth'])
fpeas['year'] = np.random.uniform(2019.0, 2019.5, size=len(peas))
fpeas['color'] = 1.0
fpeas['quarter'] = (np.trunc((fpeas['year'] - year_q0) * 4)).astype('f4')
fpeas['fail'] = 1.0 - peas['search_success']
fpeas['asvt'] = True
fpeas['red_mag_err'] = False
fpeas['mag_obs'] = 0.0

Combine flight acqs and ASVT data


In [12]:
data_all = vstack([acqs[ok]['year', 'fail', 'mag_aca', 't_ccd', 'halfwidth', 'quarter', 
                            'color', 'asvt', 'red_mag_err', 'mag_obs'], 
                   fpeas])
data_all.sort('year')

Compute box probit delta term based on box size


In [13]:
# Adjust probability (in probit space) for box size.  See:
# https://github.com/sot/skanb/blob/master/pea-test-set/fit_box_size_acq_prob.ipynb
data_all['box_delta'] = get_box_delta(data_all['halfwidth'])

In [14]:
data_all = data_all.group_by('quarter')
data_all0 = data_all.copy()  # For later augmentation with simulated red_mag_err stars
data_mean = data_all.groups.aggregate(np.mean)

In [15]:
plt.figure(figsize=(13, 4))
ok = data_all['asvt'] == False
plt.subplot(1, 2, 1)
plt.hist(data_all['mag_aca'][ok], bins=50)
plt.title('Mag_aca distribution')
plt.grid()
plt.subplot(1, 2, 2)
plt.hist(data_all['t_ccd'][ok] + np.random.uniform(-0.3, 0.3, np.count_nonzero(ok)), bins=24)
plt.grid()
plt.title('ACA CCD temperature distribution');


Model definition


In [16]:
def p_fail_binned(pars, 
           t_ccd,
           box_delta=0):
    """
    Acquisition probability model for binned data (no mag dependence)

    :param pars: 7 parameters (3 x offset, 3 x scale, p_fail for bright stars)
    :param tc, tc2: t_ccd, t_ccd ** 2
    :param box_delta: search box half width (arcsec)
    """
    p0, p1, p2 = pars
    
    # Make sure box_delta has right dimensions
    t_ccd, box_delta = np.broadcast_arrays(t_ccd, box_delta)
    tc = (t_ccd + 16) / 10

    tcx = np.linspace(-0.1, 2.0, 40)
    tcy = np.cumsum(stats.norm.cdf(p1 + p2 * tcx))
    probit_p_fail = p0 + np.interp(tc, tcx, tcy) + box_delta
    p_fail = stats.norm.cdf(probit_p_fail)  # transform from probit to linear probability

    return p_fail

def p_acq_fail(data=None):
    """
    Sherpa fit function wrapper to ensure proper use of data in fitting.
    """
    if data is None:
        data = data_all
        
    def sherpa_func(pars, x=None):
        return p_fail_binned(pars, data['t_ccd'], data['box_delta'])

    return sherpa_func

In [17]:
def fit_poly_model(data):
    from sherpa import ui
    
    comp_names = ['p0', 'p1', 'p2']

    data_id = 1
    ui.set_method('simplex')
    ui.set_stat('cash')
    ui.load_user_model(p_acq_fail(data), 'model')
    ui.add_user_pars('model', comp_names)
    ui.set_model(data_id, 'model')
    ui.load_arrays(data_id, np.array(data['year']), np.array(data['fail'], dtype=np.float))

    # Initial fit values from fit of all data
    fmod = ui.get_model_component('model')
    for comp_name in comp_names:
        setattr(fmod, comp_name, 0.0)
        comp = getattr(fmod, comp_name)
        comp.max = 10
    fmod.p0.min = -10
    # fmod.p1.min = 0
    # fmod.p2.min = 0
    # fmod.p2.max = 0.5
    
    ui.fit(data_id)
    return ui.get_fit_results()

Plotting and validation


In [18]:
def plot_fails_mag_aca_vs_t_ccd(mag_bins, year0=None):
    if year0 is None:
        year0 = data_all['year'].min()
    ok = (data_all['year'] >= year0) & ~data_all['fail'].astype(bool)
    da = data_all[ok]
    fuzzx = np.random.uniform(-0.3, 0.3, len(da))
    fuzzy = np.random.uniform(-0.125, 0.125, len(da))
    plt.plot(da['t_ccd'] + fuzzx, da['mag_aca'] + fuzzy, '.C0', markersize=4)

    ok = (data_all['year'] > year0) & data_all['fail'].astype(bool)
    da = data_all[ok]
    fuzzx = np.random.uniform(-0.3, 0.3, len(da))
    fuzzy = np.random.uniform(-0.125, 0.125, len(da))
    plt.plot(da['t_ccd'] + fuzzx, da['mag_aca'] + fuzzy, '.C1', markersize=4, alpha=0.8)
    
    # plt.xlim(-18, -10)
    # plt.ylim(7.0, 11.1)
    x0, x1 = plt.xlim()
    for y in mag_bins:
        plt.plot([x0, x1], [y, y], '-', color='r', linewidth=2, alpha=0.8)
    plt.xlabel('T_ccd (C)')
    plt.ylabel('Mag_aca')
    plt.title(f'Acq successes (blue) and failures (orange) since {year0:.1f}')
    plt.grid()

In [19]:
def plot_fit_grouped(pars, group_col, group_bin, mask=None, log=False, colors='br', label=None, probit=False):
    data = data_all if mask is None else data_all[mask]
    data['model'] = p_acq_fail(data)(pars)

    group = np.trunc(data[group_col] / group_bin)
    data = data.group_by(group)
    data_mean = data.groups.aggregate(np.mean)
    len_groups = np.diff(data.groups.indices)
    data_fail = data_mean['fail']
    model_fail = np.array(data_mean['model'])
    
    fail_sigmas = np.sqrt(data_fail * len_groups) / len_groups
    
    # Possibly plot the data and model probabilities in probit space
    if probit:
        dp = stats.norm.ppf(np.clip(data_fail + fail_sigmas, 1e-6, 1-1e-6))
        dm = stats.norm.ppf(np.clip(data_fail - fail_sigmas, 1e-6, 1-1e-6))
        data_fail = stats.norm.ppf(data_fail)
        model_fail = stats.norm.ppf(model_fail)
        fail_sigmas = np.vstack([data_fail - dm, dp - data_fail])
            
    plt.errorbar(data_mean[group_col], data_fail, yerr=fail_sigmas, 
                 fmt='.' + colors[1:], label=label, markersize=8)
    plt.plot(data_mean[group_col], model_fail, '-' + colors[0])
    
    if log:
        ax = plt.gca()
        ax.set_yscale('log')

In [20]:
def plot_fit_all(parvals, mask=None, probit=False):
    if mask is None:
        mask = np.ones(len(data_all), dtype=bool)
     
    mt = mag_filter(8.5, 10.8) & mask
    plt.figure(figsize=(12, 4))
    for probit in True, False:
        plt.subplot(1, 2, int(probit) + 1)
        for v0, v1, colors in ((-11, -10, 'br'), 
                               (-12, -11, 'gk'), 
                               (-13, -12, 'cm'), 
                               (-14, -13, 'br'), 
                               (-15, -14, 'gk')):
            plot_fit_grouped(parvals, 'mag_aca', 0.25, t_ccd_filter(v0, v1) & mt,
                             colors=colors, label=f'{v0} < t_ccd < {v1}', probit=probit)
        plt.legend(loc='upper left')
        plt.ylim(-3, 3) if probit else plt.ylim(-0.1, 1.1)
        plt.ylabel('p_fail')
        plt.xlabel('year')
        plt.tight_layout()
        plt.grid()
    
    
    mt = t_ccd_filter(-16, -2) & mask
    plt.figure(figsize=(12, 4))
    for probit in True, False:
        plt.subplot(1, 2, int(probit) + 1)
        for v0, v1, colors in ((10.3, 10.7, 'gk'), 
                               (10, 10.3, 'cm'), 
                               (9.5, 10, 'br'), 
                               (9, 9.5, 'gk')):
            plot_fit_grouped(parvals, 'year', 0.25, mag_filter(v0, v1) & mt,
                             colors=colors, label=f'{v0} < mag < {v1}', probit=probit)
        plt.legend(loc='upper left')
        plt.ylim(-3, 3) if probit else plt.ylim(-0.1, 1.1)
        plt.ylabel('p_fail')
        plt.xlabel('mag_aca')
        plt.tight_layout()
        plt.grid()
    
    mt = t_ccd_filter(-16, -2) & mask
    plt.figure(figsize=(12, 4))
    for probit in True, False:
        plt.subplot(1, 2, int(probit) + 1)
        for v0, v1, colors in ((10.3, 10.7, 'gk'), 
                               (10, 10.3, 'cm'), 
                               (9.5, 10, 'br'), 
                               (9, 9.5, 'gk')):
            plot_fit_grouped(parvals, 't_ccd', 0.5, mag_filter(v0, v1) & mt,  
                             colors=colors, label=f'{v0} < mag < {v1}', probit=probit)
        plt.legend(loc='upper left')
        plt.ylim(-3, 3) if probit else plt.ylim(-0.1, 1.1)
        plt.xlabel('t_ccd')
        plt.ylabel('p_fail')
        plt.tight_layout()
        plt.grid()

In [21]:
def mag_filter(mag0, mag1):
    ok = (data_all['mag_aca'] > mag0) & (data_all['mag_aca'] < mag1)
    return ok

In [22]:
def t_ccd_filter(t_ccd0, t_ccd1):
    ok = (data_all['t_ccd'] > t_ccd0) & (data_all['t_ccd'] < t_ccd1)
    return ok

In [23]:
def wp_filter(wp0, wp1):
    ok = (data_all['warm_pix'] > wp0) & (data_all['warm_pix'] < wp1)
    return ok

Define magnitude bins for fitting and show data


In [24]:
mag_centers = np.array([6.3, 8.1, 9.1, 9.55, 9.75, 10.0, 10.25, 10.55, 10.75, 11.0])
mag_bins = (mag_centers[1:] + mag_centers[:-1]) / 2
mag_means = np.array([8.0, 9.0, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75])

In [25]:
for m0, m1, mm in zip(mag_bins[:-1], mag_bins[1:], mag_means):
    ok = (data_all['asvt'] == False) & (data_all['mag_aca'] >= m0) & (data_all['mag_aca'] < m1)
    print(f"m0={m0:.2f} m1={m1:.2f} mean_mag={data_all['mag_aca'][ok].mean():.2f} vs. {mm}")


m0=7.20 m1=8.60 mean_mag=8.04 vs. 8.0
m0=8.60 m1=9.32 mean_mag=8.99 vs. 9.0
m0=9.32 m1=9.65 mean_mag=9.48 vs. 9.5
m0=9.65 m1=9.88 mean_mag=9.76 vs. 9.75
m0=9.88 m1=10.12 mean_mag=9.99 vs. 10.0
m0=10.12 m1=10.40 mean_mag=10.23 vs. 10.25
m0=10.40 m1=10.65 mean_mag=10.50 vs. 10.5
m0=10.65 m1=10.88 mean_mag=10.75 vs. 10.75

In [26]:
plot_fails_mag_aca_vs_t_ccd(mag_bins)


Color != 1.5 fit (this is MOST acq stars)


In [27]:
mask_no_1p5 = ((data_all['red_mag_err'] == False) & 
               (data_all['t_ccd'] > -16))

In [28]:
mag0s, mag1s = mag_bins[:-1], mag_bins[1:]
fits = {}
for m0, m1 in zip(mag0s, mag1s):
    print(m0, m1)
    fits[m0, m1] = fit_poly_model(data_all[mask_no_1p5 & mag_filter(m0, m1)])


7.2 8.6
WARNING: imaging routines will not be available, 
failed to import sherpa.image.ds9_backend due to 
'RuntimeErr: DS9Win unusable: Could not find ds9 on your PATH'
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 27634.1
Final fit statistic   = 875.158 at function evaluation 471
Data points           = 13882
Degrees of freedom    = 13879
Change in statistic   = 26758.9
   model.p0       -2.80137    
   model.p1       -3.1498     
   model.p2       1.37544     
8.6 9.325
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 31916.7
Final fit statistic   = 2412.94 at function evaluation 479
Data points           = 16042
Degrees of freedom    = 16039
Change in statistic   = 29503.8
   model.p0       -2.5554     
   model.p1       -2.10357    
   model.p2       0.572915    
9.325 9.65
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 18072.3
Final fit statistic   = 3911.59 at function evaluation 447
Data points           = 9074
Degrees of freedom    = 9071
Change in statistic   = 14160.7
   model.p0       -1.95592    
   model.p1       -2.45918    
   model.p2       1.18678     
9.65 9.875
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 13320
Final fit statistic   = 4586.36 at function evaluation 458
Data points           = 6681
Degrees of freedom    = 6678
Change in statistic   = 8733.69
   model.p0       -1.91682    
   model.p1       -1.94189    
   model.p2       0.932728    
9.875 10.125
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 12409.2
Final fit statistic   = 5503.32 at function evaluation 459
Data points           = 6224
Degrees of freedom    = 6221
Change in statistic   = 6905.86
   model.p0       -1.9711     
   model.p1       -1.49502    
   model.p2       0.50603     
10.125 10.4
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 9741.21
Final fit statistic   = 6225.58 at function evaluation 472
Data points           = 4886
Degrees of freedom    = 4883
Change in statistic   = 3515.63
   model.p0       -2.08222    
   model.p1       -1.04148    
   model.p2       0.0664174   
10.4 10.65
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 6187.16
Final fit statistic   = 5498.27 at function evaluation 499
Data points           = 3097
Degrees of freedom    = 3094
Change in statistic   = 688.892
   model.p0       -1.91858    
   model.p1       -0.764275   
   model.p2       -0.463674   
10.65 10.875
Dataset               = 1
Method                = neldermead
Statistic             = cash
Initial fit statistic = 5050.81
Final fit statistic   = 4985.27 at function evaluation 448
Data points           = 2526
Degrees of freedom    = 2523
Change in statistic   = 65.5456
   model.p0       -0.568897   
   model.p1       -0.932253   
   model.p2       -0.72214    

In [30]:
colors = [f'kC{i}' for i in range(9)]

plt.figure(figsize=(13, 4))
for subplot in (1, 2):
    plt.subplot(1, 2, subplot)
    probit = (subplot == 2)
    for m0_m1, color, mag_mean in zip(list(fits), colors, mag_means):
        fit = fits[m0_m1]
        m0, m1 = m0_m1
        plot_fit_grouped(fit.parvals, 't_ccd', 1.0, 
                         mask=mask_no_1p5 & mag_filter(m0, m1), 
                         probit=probit, colors=color, label=f'{mag_mean}')
    plt.grid()
    plt.ylabel(('Probit ' if probit else '') + 'p_fail')
    plt.xlabel('T_ccd')
    if probit:
        plt.ylim(-3.5, 3.5)
    plt.legend(fontsize='small', loc='upper left');



In [31]:
# This computes probabilities for 120 arcsec boxes, corresponding to raw data
t_ccds = np.linspace(-16, -0, 20)
plt.figure(figsize=(13, 4))

for subplot in (1, 2):
    plt.subplot(1, 2, subplot)
    for m0_m1, color, mag_mean in zip(list(fits), colors, mag_means):
        fit = fits[m0_m1]
        m0, m1 = m0_m1
        probs = p_fail_binned(fit.parvals, t_ccds)
        if subplot == 2:
            probs = stats.norm.ppf(probs)
        plt.plot(t_ccds, probs, label=f'{mag_mean}')

    plt.legend()
    plt.xlabel('T_ccd')
    plt.ylabel('P_fail' if subplot == 1 else 'Probit(p_fail)')
    plt.grid()



In [32]:
p0s = []
p1s = []
p2s = []
for fit in fits.values():
    ps = fit.parvals
    p0s.append(ps[0])
    p1s.append(ps[1])
    p2s.append(ps[2])
plt.plot(mag_means, p0s, '.-', label='p0')
plt.plot(mag_means, p1s, '.-', label='p1')
plt.plot(mag_means, p2s, '.-', label='p2')
plt.legend(fontsize='small')
plt.grid()



In [33]:
def print_pvals(ps, idx):
    vals_str = ', '.join(f'{p:.3f}' for p in ps)
    print(f'p{idx}s = np.array([{vals_str}])')

In [34]:
print_pvals(p0s, 0)
print_pvals(p1s, 1)
print_pvals(p2s, 2)


p0s = np.array([-2.801, -2.555, -1.956, -1.917, -1.971, -2.082, -1.919, -0.569])
p1s = np.array([-3.150, -2.104, -2.459, -1.942, -1.495, -1.041, -0.764, -0.932])
p2s = np.array([1.375, 0.573, 1.187, 0.933, 0.506, 0.066, -0.464, -0.722])

In [35]:
def calc_p_fail(t_ccds, mags, halfws=120, probit=False):
    """
    Acquisition probability model

    :param t_ccds: CCD temperature(s)
    :param mags: Star mag(s)
    :param box_deltas: 
    """
    mag_means = np.array([8.0, 9.0, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75])
    p0s = np.array([-2.801, -2.555, -1.956, -1.917, -1.971, -2.082, -1.919, -0.569])
    p1s = np.array([-3.150, -2.104, -2.459, -1.942, -1.495, -1.041, -0.764, -0.932])
    p2s = np.array([1.375, 0.573, 1.187, 0.933, 0.506, 0.066, -0.464, -0.722])
    
    # Make sure box_delta has right dimensions
    t_ccds, mags, halfws = np.broadcast_arrays(t_ccds, mags, halfws)
    tcs = (t_ccds + 16) / 10
    box_deltas = get_box_delta(halfws)                                               
    
    tcx = np.linspace(-0.1, 2.0, 40)
    p_fails = []
    for tc, mag, box_delta in zip(tcs.flat, mags.flat, box_deltas.flat):
        p0 = np.interp(mag, mag_means, p0s)
        p1 = np.interp(mag, mag_means, p1s)
        p2 = np.interp(mag, mag_means, p2s)
        tcy = np.cumsum(stats.norm.cdf(p1 + p2 * tcx))
        p_fail = p0 + np.interp(tc, tcx, tcy) + box_delta
        if not probit:
            p_fail = stats.norm.cdf(p_fail)  # transform from probit to linear probability
        p_fails.append(p_fail)

    return np.array(p_fails).reshape(t_ccds.shape)

In [36]:
mags, t_ccds = np.mgrid[8.75:10.75:30j, -16:-4:30j]
p_fails = calc_p_fail(t_ccds, mags, probit=False)

cs = plt.contour(t_ccds, mags, p_fails, levels=[0.05, 0.2, 0.5, 0.75, 0.9], colors=['g', 'b', 'c', 'm', 'r'])
plt.clabel(cs, inline=1, fontsize=10)
plt.grid()
plt.xlim(-17, -4)
plt.ylim(8.5, 11.0)
plt.xlabel('T_ccd (degC)')
plt.ylabel('Mag_ACA')
plt.title('Failure probability');



In [ ]: