A Jupyter Notebook for marine chronologies using Bchron!

Introduction

What is Bchron?

Bcrhon is an R package that enables quick calibration of radiocarbon dates under various calibration curves (including user generated ones); Age-depth modelling as per the algorithm of Haslett and Panell (2008); Relative sea level rate estimation incoporating time uncertainty in polynomial regression models; and non-parametric phase modelling via Gaussian mixtures as a means to determine the activity of a site.

Who created BChron?

Bchron was developped by John Haslett and Andrew Parnell. To learn more about Bchron and its development, visit this page.

Why use this notebook?

We provide a user-friendly interface where no R knowledge is required. The notebook will use a set of prompts to set up a run in Bchron, plot the results, and save the pertinent information to several text files.

How to use this notebook?

Jupyter Notebook allows to intertwine explanation text and cells of code. To run the code within a cell, press the "play" button above or enter SHIFT+ENTER on your keyboard. We made this notebook as intuitive as possible using prompts and GUIs whenever possible (The GUI may hide behind your browser window). All you have to do is run the cells in order.

Let's start with something simple. Let's say 'Hello World!' using Python. Run the cell below and make sure the 'Hello World' prints underneath the code cell.


In [1]:
print("Hello, World!")
print('Congratulations, you have run your first Python code!')


Hello, World!
Congratulations, you have run your first Python code!

What do you need to run this Notebook?

Software

  1. Jupyter Notebook
  2. Python 3.4+ with the following modules:
    1. lipd (pip install lipd)
    2. numpy (standard with Anaconda Install)
    3. pandas (standard with Anaconda Install)
    4. matplotlib (standard with Anaconda Install)
  3. An up-to-date version of R installed on your computer
  4. The Bchron package. In a R console, type install.packages('Bchron')

Record

A record in LiPD format. This notebook assumes that the column are organized using this format. To learn more about LiPD and utilities to format your dataset, vist this page.

Import a LiPD file

Now that you have a sense of how this workbook works, let's import a LiPD file and create a folder on your local computer where to save the chrocological information.


In [2]:
# Import the LiPD package and locate your files
from lipd.start import *


Where are your files stored?
1. Online URL
2. Browse Computer
3. Downloads folder
4. Notebooks folder

Option: 4

In [3]:
# Load the LiPD files

loadLipds()


Found: 2 LiPD file(s)
processing: ODP1098B.lpd
Fetching update for lipdnames.csv
processing: SAm-LagunaChepicdeJong2013.lpd
Process Complete

Enter the name of the record you wish to analyze at the prompt


In [5]:
# Enter the name of the record you wish to analyze

record = input ("Which record would you like to analyze? ")


Which record would you like to analyze? ODP1098B.lpd

Enter the name of the folder in which you want to save the Bchron output and press enter. Note that if you wish to run alternative age models (for instance by changing the reservoir age correction), you need to enter a different folder name.


In [6]:
## Create a new folder in the current LiPD directory.

from ipywidgets import widgets
from IPython.display import display
newpath = widgets.Text(description = "Enter the name of your folder.\n")
display(newpath)

def createpath(sender): 
    import os
    
    if not os.path.exists(newpath.value):
        os.makedirs(newpath.value)
    else:
        print("Warning: All previous outputs will be overidden.\n \
        To save in a new directory, please choose another name before continuing.")
        
newpath.on_submit(createpath)


Warning: All previous outputs will be overidden.
         To save in a new directory, please choose another name before continuing.

Set-Up

The following cells will guide you through preparing the necessary text files for the Bchron run.

Get the data and metadata

The next few cells will import the relevant data and metadata to set up the Bchron run.


In [7]:
# Get the metadata (To display lat/lon)

lipd_m = getMetadata("ODP1098B.lpd")

# Get the chronology data in a Panda DataFrame for ease of use

df_meta_l, df_data_l, df_chron_l = lipd_to_df("ODP1098B.lpd")


Process Complete
Process Complete

Reservoir Age Correction

The Bchron run is set to use the most recent Marine calibration curve (Marine13 as of May 2016). Any correction to the standard marine reservoir age needs to be added to the 14C data prior import into Bchron. We recommend using data from the 14CHRONO website and using the mean and standard error of the mean as the reservoir age correction and associated error. Alternatively you can enter your own value for the reservoir age correction.

Option1: Use the website and this Notebook to calculate the reservoir age correction.

The first cell displays the latitude and longitude of the record of interest for use on the website.


In [8]:
print("Latitude: " + str(lipd_m.get('geo').get('geometry').get('coordinates')[0]))
print("Longitude: " + str(lipd_m.get('geo').get('geometry').get('coordinates')[1]))


Latitude: -64.86
Longitude: -64.2

In [9]:
import pandas as pd
import numpy as np  
import math

data = pd.read_clipboard()

# Calculate the average DR and standard error of the mean

corr = data.mean()['DeltaR']
corr_err = data.std()['DeltaR'] 
datapoints = data.shape[0]
max_dist = data.max()['distance (km)']

# Save the data to a textfile and generate a log
dir = os.getcwd()+"/"+newpath.value
data.to_csv(os.path.join(dir,"Reservoir_Age.txt"),sep=' ', index=False, 
           header = True)
text_file = open(os.path.join(dir,"ReservoirAgeCorr_Info.txt"),"w")
text_file.write("The reservoir age correction was estimated from the \
chrono database.\n")
text_file.write("The reservoir age corrections was estimated on " +
                str(datapoints) + " datapoints.\n")
text_file.write("DR = " + str(math.floor(corr)) + " years.\n")
text_file.write("DR sigma = " + str(math.floor(corr_err)) + " years, expressed as the standard \
error of the mean.\n")
text_file.write("The maximum distance between the core location and \
measured reservoir ages is " + str(max_dist) + "km.\n")
text_file.close()  

# check your work

print("Don't forget to check your work!")

data


Don't forget to check your work!
Out[9]:
MapNo Lon Lat DeltaR DeltaRErr Reference Locality ReservoirAge ReservoirErr distance (km)
NaN 522 -67.28 -67.87 956 40 Berkman, P A:1996 25-30 m depth 1267 41 362
NaN 521 -67.00 -68.65 1016 39 Berkman, P A:1996 25-30 m depth 1327 40 439
NaN 523 -56.98 -63.40 829 50 Bjorck, S, H:1991 Hope Bay 1160 51 386
NaN 368 -72.65 -51.70 221 40 Ingram, B L :1996 Puerto Natales, Chile 530 41 1541
NaN 516 -45.63 -61.72 831 50 Peck, L S, a:1996 Signy Island, Antarctica 1123 52 987
NaN 517 -45.63 -61.72 701 45 Peck, L S, a:1996 Signy Island, Antarctica 1009 47 987
NaN 518 -45.63 -61.72 872 45 Peck, L S, a:1996 Signy Island, Antarctica 1181 47 987
NaN 1081 -62.07 -38.92 143 40 Gomez, et al:2008 Parejas Creek 442 41 2888
NaN 1079 -62.10 -38.90 -229 40 Gomez, et al:2008 Belgrano Port 91 41 2890
NaN 1080 -62.10 -38.90 41 40 Gomez, et al:2008 Belgrano Port 356 41 2890 NaN

Option 2: Enter your own reservoir age correction


In [9]:
corr = input("Enter the DeltaR value (in years): ")
corr_err = input("Enter the DeltaR uncertainty (in years): ")

# Open a text file to store the relevant information
text_file = open(os.path.join(dir,"ReservoirAgeCorr_Info.txt"),"w")
text_file.write("The reservoir age correction was given by the user.\n")
text_file.write("DR = " + str(corr) + ".\n")
text_file.write("DR sigma = " + str(corr_err)+ ".\n")
text_file.close()


Enter the DeltaR value: 74
Enter the DeltaR uncertainty: 70

Perform the correction


In [12]:
corr_14C = np.floor((df_chron_l.age14C - corr).values)
err_14C = np.floor(np.sqrt(df_chron_l.age14Cuncertainty**2 + corr_err**2).values)

Prepare Bchron data and metadata

The next cell prepares the text file necessary for the Bchron run.

First let's generate the radiocarbon table


In [13]:
# Get the Id column
Id = []
for i in np.arange(0,49,1):
    Id.append(os.path.splitext(record)[0] + '_' + str(i+1))
    
# create the dataframe

radio = pd.DataFrame({'Id': Id,
                     'ages' : corr_14C,
                     'ageSds' : err_14C,
                     'position' : df_chron_l.depth,
                     'CalCurves' : 'marine13'})

# Save it to a text file

radio.to_csv(os.path.join((path+'/'+newpath.value),
            (os.path.splitext(record)[0] + '_radiocarbon.txt')), sep = '\t', 
            index = False, header = True)

Then let's generate positions for the age model (i.e. where climate proxy observations are made.)


In [18]:
df_data_l.to_csv(os.path.join((path+'/'+newpath.value),(os.path.splitext(record)[0] 
                + '_depth.txt')),
                columns = ['depth'], index = False, header = False)

# Return some strings for use in Bchron
wd  = path +'/'+newpath.value
radio_text = os.path.splitext(record)[0] + '_radiocarbon.txt'
depth_text = os.path.splitext(record)[0] + '_depth.txt'
record_name = os.path.splitext(record)[0]

Bchron Run

Since BChron was coded in R, we need to let Python and R communicate with each other.


In [16]:
%load_ext rpy2.ipython

Now let's setup some of Bchron optional arguments. Leave blank if you wish to use the default parameters.


In [17]:
iter = float(input("How many iterations do you wish to perform?: "))
max_t = float(input("When was the specimen collected (Years B.P.)?: "))
%R -i iter
%R -i wd
%R -i radio_text
%R -i depth_text
%R -i max_t
%R -i record_name


How many iterations do you wish to perform?: 10000
When was the specimen collected (Years B.P.)?: -58

Perform the Bchron run and return a plot


In [19]:
%%R

library(Bchron)
setwd(wd)
library("Bchron", lib.loc="/Library/Frameworks/R.framework/Versions/3.2/Resources/library")
radiocarbon_data <- read.delim(radio_text)
depth_data <- read.table(depth_text, quote="\"")
run=Bchronology(ages=radiocarbon_data$ages,ageSds=radiocarbon_data$ageSds, 
                calCurves=radiocarbon_data$CalCurves,positions=radiocarbon_data$position,
                predictPositions=depth_data$V1,iterations=iter,extractDate=max_t)
plot(run,main=record_name,xlab='Age (cal years BP)',ylab='Depth (cm)',las=1)


//anaconda/lib/python3.5/site-packages/rpy2/robjects/functions.py:106: UserWarning: Loading required package: inline

  res = super(Function, self).__call__(*new_args, **new_kwargs)
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Save the output of the chronology into text files


In [23]:
import pandas.rpy.common as com

run = com.load_data('run')


//anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:4: FutureWarning: The pandas.rpy module is deprecated and will be removed in a future version. We refer to external packages like rpy2. 
See here for a guide on how to port your code to rpy2: http://pandas.pydata.org/pandas-docs/stable/r_interface.html

Progammers' corner

Look at the variables. Refresh the cell as you open/close/rerun the Notebook


In [22]:
whos


Variable                Type                  Data/Info
-------------------------------------------------------
ACTIVE                  str                   active
ALL                     str                   all
ANCHOR                  str                   anchor
APPLICATION_NAME        str                   lipd
ARC                     str                   arc
BASELINE                str                   baseline
BEVEL                   str                   bevel
BOTH                    str                   both
BOTTOM                  str                   bottom
BROWSE                  str                   browse
BUTT                    str                   butt
BaseWidget              type                  <class 'tkinter.BaseWidget'>
BitmapImage             type                  <class 'tkinter.BitmapImage'>
BooleanVar              type                  <class 'tkinter.BooleanVar'>
Button                  type                  <class 'tkinter.Button'>
CASCADE                 str                   cascade
CENTER                  str                   center
CHAR                    str                   char
CHECKBUTTON             str                   checkbutton
CHORD                   str                   chord
CLIENT_SECRET_FILE      str                   client_secret.json
COMMAND                 str                   command
CURRENT                 str                   current
CallWrapper             type                  <class 'tkinter.CallWrapper'>
Canvas                  type                  <class 'tkinter.Canvas'>
Checkbutton             type                  <class 'tkinter.Checkbutton'>
Convert                 type                  <class 'lipd.pkg_resource<...>eseries.Convert.Convert'>
DISABLED                str                   disabled
DOI                     SRE_Pattern           re.compile('\\b(10[.][0-9<...>?!["&\\\'<>,])\\S)+)\\b')
DOTBOX                  str                   dotbox
DoubleVar               type                  <class 'tkinter.DoubleVar'>
E                       str                   e
EMPTY                   list                  n=9
END                     str                   end
EW                      str                   ew
EXCEPTION               int                   8
EXTENDED                str                   extended
Entry                   type                  <class 'tkinter.Entry'>
Event                   type                  <class 'tkinter.Event'>
FALSE                   int                   0
FIRST                   str                   first
FLAT                    str                   flat
Frame                   type                  <class 'tkinter.Frame'>
GROOVE                  str                   groove
Grid                    type                  <class 'tkinter.Grid'>
HIDDEN                  str                   hidden
HORIZONTAL              str                   horizontal
INSERT                  str                   insert
INSIDE                  str                   inside
Id                      list                  n=49
Image                   module                <module 'PIL.Image' from <...>e-packages/PIL/Image.py'>
ImageTk                 module                <module 'PIL.ImageTk' fro<...>packages/PIL/ImageTk.py'>
IntVar                  type                  <class 'tkinter.IntVar'>
LAST                    str                   last
LEFT                    str                   left
Label                   type                  <class 'tkinter.Label'>
LabelFrame              type                  <class 'tkinter.LabelFrame'>
LiPD                    type                  <class 'lipd.pkg_resources.lipd.LiPD.LiPD'>
LiPD_Library            type                  <class 'lipd.pkg_resource<...>PD_Library.LiPD_Library'>
LiPD_to_df              function              <function LiPD_to_df at 0x10540fb70>
Listbox                 type                  <class 'tkinter.Listbox'>
MITER                   str                   miter
MOVETO                  str                   moveto
MULTIPLE                str                   multiple
MapFrame                type                  <class 'lipd.pkg_resource<...>lpers.MapFrame.MapFrame'>
Menu                    type                  <class 'tkinter.Menu'>
Menubutton              type                  <class 'tkinter.Menubutton'>
Message                 type                  <class 'tkinter.Message'>
Misc                    type                  <class 'tkinter.Misc'>
N                       str                   n
NE                      str                   ne
NO                      int                   0
NOAA_DATA_LINES         list                  n=3
NOAA_EMPTY              list                  n=5
NOAA_KEYS               list                  n=3
NOAA_VAR_LINES          list                  n=8
NONE                    str                   none
NORMAL                  str                   normal
NS                      str                   ns
NSEW                    str                   nsew
NUMERIC                 str                   numeric
NW                      str                   nw
NoDefaultRoot           function              <function NoDefaultRoot at 0x1044d22f0>
OFF                     int                   0
ON                      int                   1
OUTSIDE                 str                   outside
OptionMenu              type                  <class 'tkinter.OptionMenu'>
PAGES                   str                   pages
PIESLICE                str                   pieslice
PROJECTING              str                   projecting
Pack                    type                  <class 'tkinter.Pack'>
PanedWindow             type                  <class 'tkinter.PanedWindow'>
PhotoImage              type                  <class 'tkinter.PhotoImage'>
Place                   type                  <class 'tkinter.Place'>
RADIOBUTTON             str                   radiobutton
RAISED                  str                   raised
READABLE                int                   2
RE_VAR                  SRE_Pattern           re.compile('#{2}(\\w)+')
RE_VAR_SPLIT            SRE_Pattern           re.compile('(\\w+)(\\s+)([\\w\\W\\s]+)')
RIDGE                   str                   ridge
RIGHT                   str                   right
ROUND                   str                   round
Radiobutton             type                  <class 'tkinter.Radiobutton'>
S                       str                   s
SCOPES                  str                   https://www.googleapis.com/auth/drive
SCROLL                  str                   scroll
SE                      str                   se
SEL                     str                   sel
SEL_FIRST               str                   sel.first
SEL_LAST                str                   sel.last
SEPARATOR               str                   separator
SINGLE                  str                   single
SOLID                   str                   solid
SUNKEN                  str                   sunken
SW                      str                   sw
Scale                   type                  <class 'tkinter.Scale'>
Scrollbar               type                  <class 'tkinter.Scrollbar'>
Spinbox                 type                  <class 'tkinter.Spinbox'>
StringVar               type                  <class 'tkinter.StringVar'>
TOP                     str                   top
TRUE                    int                   1
TS                      function              <function TS at 0x1128ba400>
TS_to_df                function              <function TS_to_df at 0x112728bf8>
Tcl                     function              <function Tcl at 0x1044d2f28>
TclError                type                  <class '_tkinter.TclError'>
TclVersion              float                 8.5
Text                    type                  <class 'tkinter.Text'>
TimeSeries              type                  <class 'lipd.pkg_resource<...>s.TimeSeries.TimeSeries'>
TimeSeries_Library      type                  <class 'lipd.pkg_resource<...>rary.TimeSeries_Library'>
Tk                      type                  <class 'tkinter.Tk'>
TkVersion               float                 8.5
Toplevel                type                  <class 'tkinter.Toplevel'>
UNDERLINE               str                   underline
UNITS                   str                   units
VERTICAL                str                   vertical
Variable                type                  <class 'tkinter.Variable'>
W                       str                   w
WORD                    str                   word
WRITABLE                int                   4
Widget                  type                  <class 'tkinter.Widget'>
Wm                      type                  <class 'tkinter.Wm'>
X                       str                   x
XView                   type                  <class 'tkinter.XView'>
Y                       str                   y
YES                     int                   1
YView                   type                  <class 'tkinter.YView'>
age                     ndarray               1000x126: 126000 elems, type `float64`, 1008000 bytes (984.375 kb)
all_cap_re              SRE_Pattern           re.compile('([a-z0-9])([A-Z])')
browse_dialog           function              <function browse_dialog at 0x1044f9730>
check_file_age          function              <function check_file_age at 0x1044f96a8>
check_ts                function              <function check_ts at 0x1128ba378>
collections             module                <module 'collections' fro<...>collections/__init__.py'>
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In [24]:
run


Out[24]:
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 'phi':          0    1    2    3    4    5    6    7    8    9  ...    39   40   41  \
 1.0     0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 ...   0.0  0.0  0.0   
 2.0     0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 ...   0.0  0.0  0.0   
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 1.0      416.0   805.0   859.0  1355.0  1719.0  2434.0  2857.0  3292.0   
 2.0      777.0   945.0  1172.0  1625.0  1700.0  1974.0  2230.0  2705.0   
 3.0      566.0   946.0   993.0  1313.0  1471.0  2329.0  2688.0  3045.0   
 4.0      541.0   824.0   962.0  1421.0  1506.0  1870.0  2084.0  2833.0   
 5.0      838.0  1016.0  1052.0  1442.0  1685.0  2072.0  2419.0  3004.0   
 6.0      816.0   925.0  1050.0  1399.0  1665.0  2309.0  2685.0  3140.0   
 7.0      487.0   940.0  1036.0  1517.0  1758.0  2167.0  2439.0  2828.0   
 8.0      806.0   970.0  1105.0  1500.0  1635.0  2330.0  2843.0  3025.0   
 9.0      973.0  1197.0  1234.0  1686.0  1844.0  2541.0  2736.0  3069.0   
 10.0     881.0  1197.0  1236.0  1769.0  1941.0  2436.0  2678.0  3042.0   
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 13.0     753.0  1110.0  1178.0  1927.0  2046.0  2196.0  2476.0  2970.0   
 14.0     681.0   978.0  1069.0  1895.0  1985.0  2222.0  2406.0  2736.0   
 15.0     489.0   714.0  1219.0  1738.0  1960.0  2018.0  2282.0  3001.0   
 16.0     884.0  1160.0  1184.0  1353.0  1557.0  1788.0  2034.0  2886.0   
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 29.0     714.0  1252.0  1367.0  1822.0  1860.0  2150.0  2447.0  2843.0   
 30.0     799.0  1190.0  1257.0  1788.0  1935.0  2152.0  2214.0  2695.0   
 ...        ...     ...     ...     ...     ...     ...     ...     ...   
 971.0    853.0  1064.0  1343.0  1523.0  1627.0  1789.0  2113.0  2389.0   
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 977.0    456.0   756.0   838.0  1979.0  2053.0  2222.0  2418.0  2747.0   
 978.0    634.0   818.0  1123.0  1471.0  1625.0  2392.0  2574.0  2884.0   
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 980.0    381.0   727.0   845.0  1470.0  1660.0  2392.0  2489.0  3028.0   
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 988.0    717.0   904.0  1375.0  1790.0  1982.0  2350.0  2791.0  3223.0   
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 990.0    824.0  1184.0  1353.0  1728.0  1765.0  2348.0  2480.0  2722.0   
 991.0    989.0  1339.0  1441.0  1619.0  1712.0  1853.0  1959.0  2472.0   
 992.0    375.0   870.0  1094.0  1393.0  1771.0  1941.0  2155.0  2631.0   
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 994.0    604.0  1129.0  1336.0  1602.0  1703.0  2255.0  2427.0  2831.0   
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 996.0    888.0  1001.0  1228.0  1690.0  1855.0  2206.0  2626.0  2763.0   
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 1000.0   725.0   863.0   984.0  1487.0  1718.0  2285.0  2497.0  2986.0   
 
             8       9    ...          39       40       41       42       43  \
 1.0     3400.0  3577.0   ...     11006.0  11567.0  11967.0  12107.0  12207.0   
 2.0     3178.0  3578.0   ...     10994.0  11471.0  11998.0  12104.0  12168.0   
 3.0     3257.0  3426.0   ...     10796.0  11511.0  11830.0  12030.0  12080.0   
 4.0     3326.0  3637.0   ...     10718.0  11020.0  11618.0  11791.0  12111.0   
 5.0     3234.0  3680.0   ...     10870.0  11337.0  12037.0  12091.0  12138.0   
 6.0     3458.0  3519.0   ...     10668.0  11389.0  11968.0  12126.0  12199.0   
 7.0     3136.0  3506.0   ...     10650.0  11198.0  11931.0  12109.0  12203.0   
 8.0     3133.0  3413.0   ...     10592.0  11370.0  11952.0  12111.0  12140.0   
 9.0     3358.0  3484.0   ...     10423.0  11032.0  11757.0  11894.0  12036.0   
 10.0    3235.0  3458.0   ...     10319.0  11170.0  11822.0  12121.0  12220.0   
 11.0    3209.0  3358.0   ...     10568.0  11226.0  11859.0  11921.0  12148.0   
 12.0    3317.0  3462.0   ...     10853.0  11412.0  11784.0  12183.0  12205.0   
 13.0    3193.0  3431.0   ...     10857.0  11221.0  11783.0  12100.0  12141.0   
 14.0    3218.0  3474.0   ...     11027.0  11559.0  11952.0  12033.0  12156.0   
 15.0    3301.0  3491.0   ...     10864.0  11437.0  11715.0  11940.0  12280.0   
 16.0    3372.0  3434.0   ...     10853.0  11417.0  11978.0  12148.0  12245.0   
 17.0    3468.0  3594.0   ...     10828.0  11755.0  12030.0  12198.0  12409.0   
 18.0    3541.0  3751.0   ...     10808.0  11589.0  12037.0  12164.0  12423.0   
 19.0    3613.0  3800.0   ...     11090.0  11775.0  12152.0  12183.0  12485.0   
 20.0    3689.0  3878.0   ...     11090.0  11717.0  12310.0  12414.0  12489.0   
 21.0    3574.0  3655.0   ...     11107.0  11506.0  12202.0  12326.0  12469.0   
 22.0    3278.0  3521.0   ...     11334.0  11575.0  12063.0  12217.0  12345.0   
 23.0    3384.0  3655.0   ...     11072.0  11617.0  12037.0  12131.0  12216.0   
 24.0    3519.0  3624.0   ...     11123.0  11689.0  11937.0  12192.0  12403.0   
 25.0    3576.0  3757.0   ...     10940.0  11815.0  12104.0  12193.0  12278.0   
 26.0    3536.0  3710.0   ...     10920.0  11407.0  11951.0  12000.0  12285.0   
 27.0    3327.0  3543.0   ...     10959.0  11367.0  11882.0  12149.0  12186.0   
 28.0    3271.0  3473.0   ...     10850.0  11602.0  12006.0  12152.0  12375.0   
 29.0    3322.0  3739.0   ...     11023.0  11487.0  11863.0  12110.0  12233.0   
 30.0    3300.0  3650.0   ...     11043.0  11855.0  11985.0  12148.0  12308.0   
 ...        ...     ...   ...         ...      ...      ...      ...      ...   
 971.0   3157.0  3313.0   ...     11003.0  11485.0  11730.0  11839.0  11952.0   
 972.0   3135.0  3234.0   ...     11236.0  11343.0  11560.0  11817.0  11932.0   
 973.0   3188.0  3284.0   ...     11252.0  11607.0  11846.0  12036.0  12086.0   
 974.0   3012.0  3131.0   ...     11201.0  11562.0  11711.0  11878.0  12005.0   
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 978.0   2948.0  3010.0   ...     11169.0  11315.0  11432.0  11508.0  11671.0   
 979.0   2972.0  3289.0   ...     11173.0  11335.0  11692.0  11750.0  11860.0   
 980.0   3151.0  3275.0   ...     11378.0  11541.0  11664.0  11769.0  11918.0   
 981.0   3258.0  3314.0   ...     11219.0  11413.0  11618.0  11781.0  11930.0   
 982.0   3345.0  3437.0   ...     11386.0  11443.0  11686.0  11776.0  11913.0   
 983.0   3417.0  3782.0   ...     11203.0  11657.0  11710.0  11808.0  11950.0   
 984.0   3578.0  3947.0   ...     11196.0  11304.0  11543.0  11658.0  11877.0   
 985.0   3779.0  3912.0   ...     11137.0  11310.0  11448.0  11623.0  11670.0   
 986.0   3531.0  3689.0   ...     11115.0  11304.0  11612.0  11664.0  11817.0   
 987.0   3558.0  3781.0   ...     11129.0  11318.0  11448.0  11740.0  11796.0   
 988.0   3640.0  3942.0   ...     11191.0  11265.0  11576.0  11668.0  11757.0   
 989.0   3274.0  3565.0   ...     11200.0  11276.0  11433.0  11609.0  11832.0   
 990.0   3230.0  3395.0   ...     11447.0  11529.0  11605.0  11718.0  11825.0   
 991.0   3102.0  3208.0   ...     11531.0  11663.0  11751.0  11852.0  11911.0   
 992.0   3295.0  3345.0   ...     11457.0  11506.0  11568.0  11676.0  11869.0   
 993.0   3269.0  3413.0   ...     11404.0  11522.0  11718.0  11740.0  11806.0   
 994.0   3267.0  3426.0   ...     11273.0  11401.0  11747.0  11831.0  11981.0   
 995.0   3376.0  3620.0   ...     11216.0  11482.0  11816.0  11940.0  12038.0   
 996.0   3122.0  3196.0   ...     11227.0  11605.0  11697.0  11908.0  11966.0   
 997.0   2831.0  3041.0   ...     11056.0  11294.0  11588.0  11831.0  11954.0   
 998.0   3223.0  3316.0   ...     11106.0  11380.0  11563.0  11746.0  11895.0   
 999.0   3173.0  3315.0   ...     11252.0  11417.0  11675.0  11824.0  12003.0   
 1000.0  3088.0  3358.0   ...     11173.0  11580.0  11758.0  11889.0  11999.0   
 
              44       45       46       47       48  
 1.0     12264.0  12458.0  12577.0  12641.0  13079.0  
 2.0     12213.0  12253.0  12413.0  12500.0  12658.0  
 3.0     12170.0  12264.0  12384.0  12406.0  12526.0  
 4.0     12180.0  12333.0  12410.0  12488.0  12625.0  
 5.0     12211.0  12333.0  12441.0  12507.0  12658.0  
 6.0     12248.0  12375.0  12455.0  12482.0  12550.0  
 7.0     12247.0  12353.0  12395.0  12489.0  12621.0  
 8.0     12192.0  12446.0  12575.0  12627.0  12828.0  
 9.0     12125.0  12329.0  12556.0  12613.0  12885.0  
 10.0    12308.0  12449.0  12655.0  12720.0  13070.0  
 11.0    12274.0  12468.0  12657.0  12718.0  13086.0  
 12.0    12259.0  12470.0  12638.0  12735.0  13103.0  
 13.0    12218.0  12648.0  12695.0  12828.0  13303.0  
 14.0    12302.0  12655.0  12691.0  12745.0  12930.0  
 15.0    12419.0  12566.0  12604.0  12710.0  12905.0  
 16.0    12381.0  12551.0  12838.0  12882.0  12933.0  
 17.0    12472.0  12650.0  12832.0  12893.0  12949.0  
 18.0    12456.0  12659.0  12861.0  12927.0  13035.0  
 19.0    12505.0  12639.0  12882.0  12947.0  13211.0  
 20.0    12540.0  12684.0  12819.0  12856.0  13206.0  
 21.0    12483.0  12793.0  12860.0  12916.0  13213.0  
 22.0    12426.0  12474.0  12833.0  12885.0  13167.0  
 23.0    12504.0  12649.0  12773.0  12882.0  13232.0  
 24.0    12449.0  12624.0  12853.0  12887.0  13317.0  
 25.0    12387.0  12491.0  12877.0  12927.0  13105.0  
 26.0    12348.0  12500.0  12861.0  12956.0  13146.0  
 27.0    12296.0  12501.0  12870.0  12951.0  13155.0  
 28.0    12396.0  12637.0  12951.0  13008.0  13199.0  
 29.0    12301.0  12936.0  12984.0  13045.0  13276.0  
 30.0    12532.0  12760.0  12998.0  13078.0  13265.0  
 ...         ...      ...      ...      ...      ...  
 971.0   11973.0  12068.0  12228.0  12335.0  12590.0  
 972.0   12036.0  12071.0  12341.0  12363.0  12590.0  
 973.0   12117.0  12241.0  12317.0  12414.0  12566.0  
 974.0   12106.0  12146.0  12328.0  12369.0  12653.0  
 975.0   12083.0  12274.0  12430.0  12472.0  12556.0  
 976.0   12085.0  12263.0  12310.0  12446.0  12503.0  
 977.0   12117.0  12238.0  12316.0  12353.0  12603.0  
 978.0   11944.0  12284.0  12423.0  12455.0  12603.0  
 979.0   11893.0  12086.0  12220.0  12448.0  12589.0  
 980.0   12097.0  12253.0  12341.0  12504.0  12619.0  
 981.0   12030.0  12145.0  12240.0  12407.0  12489.0  
 982.0   11954.0  12209.0  12315.0  12377.0  12429.0  
 983.0   12058.0  12183.0  12239.0  12346.0  12441.0  
 984.0   11966.0  12065.0  12109.0  12254.0  12467.0  
 985.0   11726.0  11979.0  12322.0  12418.0  12526.0  
 986.0   11954.0  12073.0  12374.0  12424.0  12526.0  
 987.0   11875.0  11950.0  12162.0  12202.0  12516.0  
 988.0   11930.0  12117.0  12228.0  12340.0  12404.0  
 989.0   11979.0  12082.0  12148.0  12330.0  12614.0  
 990.0   11964.0  12104.0  12247.0  12421.0  12516.0  
 991.0   12001.0  12091.0  12120.0  12351.0  12529.0  
 992.0   12075.0  12191.0  12238.0  12375.0  12461.0  
 993.0   11946.0  12242.0  12338.0  12446.0  12509.0  
 994.0   12149.0  12207.0  12354.0  12432.0  12578.0  
 995.0   12114.0  12263.0  12305.0  12429.0  12504.0  
 996.0   12105.0  12225.0  12306.0  12544.0  12724.0  
 997.0   12128.0  12273.0  12390.0  12459.0  12563.0  
 998.0   12151.0  12331.0  12485.0  12565.0  12788.0  
 999.0   12061.0  12172.0  12288.0  12429.0  12570.0  
 1000.0  12089.0  12233.0  12361.0  12516.0  12627.0  
 
 [1000 rows x 49 columns],
 'thetaPredict':            0       1       2       3       4       5       6       7    \
 1.0      350.0   411.0   444.0   505.0   536.0   571.0   621.0   721.0   
 2.0      772.0   777.0   831.0   861.0   869.0   876.0   883.0   898.0   
 3.0      557.0   565.0   628.0   706.0   738.0   770.0   788.0   817.0   
 4.0      472.0   535.0   580.0   666.0   709.0   737.0   756.0   793.0   
 5.0      813.0   836.0   883.0   891.0   895.0   899.0   966.0   993.0   
 6.0      806.0   815.0   825.0   872.0   885.0   887.0   889.0   917.0   
 7.0      334.0   450.0   546.0   671.0   699.0   727.0   755.0   842.0   
 8.0      780.0   804.0   847.0   864.0   874.0   885.0   897.0   963.0   
 9.0      960.0   972.0  1038.0  1088.0  1104.0  1121.0  1137.0  1170.0   
 10.0     874.0   880.0   926.0  1093.0  1113.0  1133.0  1153.0  1178.0   
 11.0     908.0   912.0   920.0   937.0   945.0   985.0  1036.0  1079.0   
 12.0     656.0   752.0   855.0   965.0   991.0  1017.0  1043.0  1096.0   
 13.0     744.0   752.0   830.0   998.0  1029.0  1044.0  1058.0  1086.0   
 14.0     616.0   676.0   739.0   765.0   777.0   790.0   802.0   900.0   
 15.0     477.0   488.0   500.0   523.0   534.0   546.0   561.0   625.0   
 16.0     842.0   881.0   915.0   987.0  1049.0  1054.0  1067.0  1106.0   
 17.0     815.0   839.0   915.0   965.0   987.0  1006.0  1025.0  1092.0   
 18.0     616.0   617.0   644.0   703.0   732.0   762.0   792.0   851.0   
 19.0     622.0   645.0   729.0   838.0   866.0   878.0   890.0   913.0   
 20.0     749.0   804.0   835.0   891.0   920.0  1069.0  1159.0  1269.0   
 21.0     826.0   867.0   886.0   920.0   937.0   960.0   984.0  1031.0   
 22.0     728.0   733.0   739.0   753.0   759.0   766.0   773.0   864.0   
 23.0     414.0   427.0   481.0   597.0   646.0   696.0   746.0   846.0   
 24.0     739.0   751.0   773.0   783.0   817.0   849.0   866.0   890.0   
 25.0     602.0   609.0   638.0   688.0   713.0   738.0   763.0   881.0   
 26.0    1002.0  1021.0  1029.0  1042.0  1049.0  1055.0  1062.0  1085.0   
 27.0     638.0   692.0   743.0   903.0  1027.0  1049.0  1071.0  1115.0   
 28.0     922.0   924.0   943.0   984.0  1008.0  1034.0  1060.0  1112.0   
 29.0     662.0   710.0   927.0  1002.0  1040.0  1077.0  1115.0  1190.0   
 30.0     725.0   793.0   923.0   968.0   987.0  1017.0  1048.0  1126.0   
 ...        ...     ...     ...     ...     ...     ...     ...     ...   
 971.0    843.0   852.0   873.0   917.0   939.0   961.0   983.0  1027.0   
 972.0   1124.0  1171.0  1178.0  1200.0  1211.0  1220.0  1228.0  1244.0   
 973.0    937.0   950.0  1029.0  1068.0  1075.0  1079.0  1084.0  1093.0   
 974.0    595.0   628.0   654.0   705.0   731.0   753.0   775.0   827.0   
 975.0    660.0   671.0   691.0   734.0   755.0   786.0   845.0   963.0   
 976.0    793.0   795.0   817.0   864.0   888.0   912.0   936.0   983.0   
 977.0    430.0   454.0   498.0   589.0   634.0   657.0   678.0   720.0   
 978.0    626.0   633.0   651.0   690.0   709.0   728.0   748.0   786.0   
 979.0    374.0   426.0   452.0   497.0   520.0   559.0   597.0   673.0   
 980.0    340.0   378.0   403.0   451.0   474.0   498.0   522.0   551.0   
 981.0    396.0   479.0   527.0   617.0   662.0   706.0   751.0   841.0   
 982.0    497.0   533.0   644.0   720.0   738.0   755.0   773.0   809.0   
 983.0    469.0   515.0   551.0   622.0   657.0   693.0   728.0   799.0   
 984.0    715.0   726.0   778.0   783.0   786.0   789.0   791.0   800.0   
 985.0    357.0   366.0   419.0   533.0   583.0   610.0   638.0   692.0   
 986.0     -2.0    27.0   346.0   423.0   462.0   501.0   540.0   617.0   
 987.0    403.0   431.0   462.0   527.0   559.0   591.0   624.0   688.0   
 988.0    688.0   714.0   735.0   774.0   793.0   813.0   832.0   871.0   
 989.0    603.0   617.0   657.0   743.0   785.0   828.0   871.0   957.0   
 990.0    806.0   823.0   858.0   933.0   971.0  1009.0  1046.0  1121.0   
 991.0    985.0   989.0  1027.0  1140.0  1258.0  1272.0  1287.0  1315.0   
 992.0    371.0   375.0   422.0   525.0   577.0   629.0   680.0   784.0   
 993.0    462.0   469.0   488.0   527.0   547.0   571.0   594.0   642.0   
 994.0    331.0   582.0   638.0   712.0   750.0   787.0   916.0  1034.0   
 995.0    645.0   647.0   676.0   740.0   772.0   803.0   835.0   899.0   
 996.0    852.0   885.0   899.0   922.0   934.0   946.0   958.0   981.0   
 997.0    909.0   914.0   918.0   925.0   929.0   932.0   936.0   943.0   
 998.0    711.0   725.0   795.0   814.0   824.0   834.0   843.0   863.0   
 999.0    726.0   742.0   774.0   842.0   876.0   910.0   944.0  1012.0   
 1000.0   681.0   721.0   738.0   767.0   781.0   796.0   810.0   839.0   
 
            8       9     ...         116      117      118      119      120  \
 1.0      771.0   827.0   ...     11008.0  11036.0  11111.0  11226.0  11280.0   
 2.0      905.0  1036.0   ...     10995.0  11003.0  11037.0  11110.0  11155.0   
 3.0      838.0   965.0   ...     10806.0  10888.0  11065.0  11359.0  11391.0   
 4.0      812.0   879.0   ...     10721.0  10754.0  10799.0  10876.0  10906.0   
 5.0     1007.0  1030.0   ...     10873.0  10924.0  10949.0  11158.0  11170.0   
 6.0      922.0   975.0   ...     10673.0  10740.0  11066.0  11265.0  11289.0   
 7.0      901.0   978.0   ...     10651.0  10664.0  10723.0  10878.0  10948.0   
 8.0      967.0  1024.0   ...     10599.0  10699.0  10958.0  11150.0  11169.0   
 9.0     1186.0  1208.0   ...     10423.0  10430.0  10459.0  10503.0  10570.0   
 10.0    1189.0  1213.0   ...     10323.0  10383.0  10729.0  10865.0  10993.0   
 11.0    1090.0  1179.0   ...     10580.0  10698.0  10739.0  10758.0  10766.0   
 12.0    1122.0  1169.0   ...     10854.0  10862.0  10898.0  10980.0  11066.0   
 13.0    1100.0  1137.0   ...     10859.0  10882.0  10985.0  11128.0  11154.0   
 14.0     946.0  1014.0   ...     11033.0  11148.0  11202.0  11216.0  11257.0   
 15.0     697.0   916.0   ...     10865.0  10887.0  11075.0  11187.0  11222.0   
 16.0    1125.0  1170.0   ...     10854.0  10861.0  10915.0  11112.0  11160.0   
 17.0    1128.0  1167.0   ...     10831.0  10867.0  10950.0  10992.0  11052.0   
 18.0     880.0  1158.0   ...     10811.0  10856.0  11203.0  11305.0  11353.0   
 19.0     925.0  1073.0   ...     11092.0  11124.0  11296.0  11460.0  11487.0   
 20.0    1307.0  1364.0   ...     11104.0  11195.0  11247.0  11402.0  11446.0   
 21.0    1055.0  1119.0   ...     11109.0  11135.0  11255.0  11334.0  11355.0   
 22.0     981.0  1053.0   ...     11335.0  11353.0  11415.0  11436.0  11444.0   
 23.0     896.0   963.0   ...     11076.0  11140.0  11405.0  11556.0  11566.0   
 24.0     898.0   960.0   ...     11126.0  11171.0  11532.0  11568.0  11584.0   
 25.0     940.0   992.0   ...     10945.0  11014.0  11245.0  11584.0  11615.0   
 26.0    1130.0  1186.0   ...     10923.0  10964.0  11041.0  11082.0  11127.0   
 27.0    1137.0  1189.0   ...     10961.0  10984.0  11079.0  11085.0  11088.0   
 28.0    1139.0  1236.0   ...     10851.0  10859.0  10939.0  11044.0  11142.0   
 29.0    1227.0  1298.0   ...     11024.0  11034.0  11079.0  11112.0  11123.0   
 30.0    1164.0  1217.0   ...     11046.0  11083.0  11285.0  11664.0  11686.0   
 ...        ...     ...   ...         ...      ...      ...      ...      ...   
 971.0   1049.0  1175.0   ...     11005.0  11035.0  11133.0  11194.0  11218.0   
 972.0   1252.0  1315.0   ...     11236.0  11238.0  11246.0  11255.0  11260.0   
 973.0   1097.0  1179.0   ...     11255.0  11296.0  11352.0  11456.0  11472.0   
 974.0    913.0  1025.0   ...     11202.0  11215.0  11275.0  11348.0  11381.0   
 975.0   1022.0  1100.0   ...     11269.0  11283.0  11305.0  11316.0  11321.0   
 976.0   1007.0  1075.0   ...     11400.0  11408.0  11445.0  11490.0  11511.0   
 977.0    742.0   789.0   ...     11260.0  11359.0  11384.0  11407.0  11417.0   
 978.0    805.0   940.0   ...     11169.0  11175.0  11199.0  11228.0  11242.0   
 979.0    711.0   802.0   ...     11174.0  11184.0  11232.0  11268.0  11279.0   
 980.0    651.0   774.0   ...     11378.0  11380.0  11387.0  11395.0  11399.0   
 981.0    886.0   952.0   ...     11219.0  11222.0  11236.0  11252.0  11268.0   
 982.0    826.0   996.0   ...     11386.0  11387.0  11390.0  11394.0  11396.0   
 983.0    834.0   883.0   ...     11204.0  11221.0  11296.0  11387.0  11429.0   
 984.0    806.0   892.0   ...     11196.0  11198.0  11208.0  11219.0  11225.0   
 985.0    720.0   828.0   ...     11137.0  11139.0  11146.0  11154.0  11158.0   
 986.0    656.0   716.0   ...     11116.0  11126.0  11179.0  11272.0  11277.0   
 987.0    720.0   815.0   ...     11129.0  11136.0  11168.0  11206.0  11223.0   
 988.0    891.0  1092.0   ...     11192.0  11198.0  11217.0  11226.0  11228.0   
 989.0    999.0  1147.0   ...     11200.0  11204.0  11218.0  11233.0  11243.0   
 990.0   1159.0  1252.0   ...     11447.0  11449.0  11460.0  11484.0  11500.0   
 991.0   1329.0  1380.0   ...     11531.0  11536.0  11558.0  11585.0  11597.0   
 992.0    835.0   959.0   ...     11457.0  11459.0  11468.0  11482.0  11484.0   
 993.0    666.0   920.0   ...     11405.0  11419.0  11473.0  11499.0  11503.0   
 994.0   1091.0  1212.0   ...     11273.0  11278.0  11299.0  11325.0  11337.0   
 995.0    931.0  1038.0   ...     11216.0  11217.0  11224.0  11232.0  11235.0   
 996.0    993.0  1092.0   ...     11227.0  11231.0  11246.0  11265.0  11274.0   
 997.0    947.0   980.0   ...     11056.0  11060.0  11078.0  11099.0  11108.0   
 998.0    883.0  1027.0   ...     11106.0  11110.0  11125.0  11144.0  11153.0   
 999.0   1046.0  1109.0   ...     11252.0  11260.0  11292.0  11320.0  11352.0   
 1000.0   853.0   911.0   ...     11182.0  11346.0  11396.0  11406.0  11411.0   
 
             121      122      123      124      125  
 1.0     11308.0  11320.0  11330.0  11365.0  11430.0  
 2.0     11188.0  11332.0  11451.0  11454.0  11456.0  
 3.0     11408.0  11430.0  11448.0  11457.0  11465.0  
 4.0     10919.0  10935.0  10948.0  10954.0  10960.0  
 5.0     11179.0  11221.0  11305.0  11309.0  11314.0  
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 30.0    11704.0  11726.0  11744.0  11753.0  11762.0  
 ...         ...      ...      ...      ...      ...  
 971.0   11238.0  11334.0  11421.0  11430.0  11439.0  
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 990.0   11507.0  11516.0  11520.0  11521.0  11522.0  
 991.0   11606.0  11619.0  11628.0  11633.0  11638.0  
 992.0   11486.0  11487.0  11489.0  11490.0  11492.0  
 993.0   11506.0  11509.0  11512.0  11513.0  11515.0  
 994.0   11346.0  11358.0  11367.0  11372.0  11377.0  
 995.0   11243.0  11275.0  11296.0  11307.0  11317.0  
 996.0   11281.0  11289.0  11296.0  11300.0  11325.0  
 997.0   11116.0  11126.0  11143.0  11164.0  11185.0  
 998.0   11160.0  11198.0  11238.0  11258.0  11277.0  
 999.0   11386.0  11392.0  11398.0  11400.0  11403.0  
 1000.0  11415.0  11419.0  11423.0  11425.0  11427.0  
 
 [1000 rows x 126 columns]}

In [ ]: