menu 52182 Words | access_time : ~ 173 min.

This section gives:¶

1. Some basic intro to python, and OOP.
2. Data types - what is nan?
3. Lists, dictionaries, dataframes.
4. Numpy.
5. Plotting - line, image.
6. Different kinds of data.
7. Visualize data and show what it means.

</font>

How variables work¶

In [1]:

x = 5
print(x)
print(type(x))

x = "IUCAA"
print(x)
print(type(x))

5
<class 'int'>
IUCAA
<class 'str'>

In [2]:

print(x)
print(type(x))

IUCAA
<class 'str'>

In [3]:

x = ["Stars", "Galaxies", "Quasars"]
print(x)
print(type(x))

['Stars', 'Galaxies', 'Quasars']
<class 'list'>

In [ ]:

# Add new element
x.append(42)

In [4]:

x = {"Mass": 2e30, "Radius": 6.9e9, "Type": "G2V", "Surface Temperature": 5778}
print(x)
print(type(x))

{'Mass': 2e+30, 'Radius': 6900000000.0, 'Type': 'G2V', 'Surface Temperature': 5778}
<class 'dict'>

In [ ]:

# Add new element
x["Luminosity"] = "1 solar luminos"

Using functions¶

In [5]:

x = 7
y = 9
z = x+y*(x-1)**3
print(z)

1951

In [6]:

def fun(v1,v2):
    return v1+v2*(v1-1)**3

In [7]:

print(fun(x,y))

1951

Objects¶

In [8]:

x = 2
help(x)

Help on int object:

class int(object)
 |  int(x=0) -> integer
 |  int(x, base=10) -> integer
 |  
 |  Convert a number or string to an integer, or return 0 if no arguments
 |  are given.  If x is a number, return x.__int__().  For floating point
 |  numbers, this truncates towards zero.
 |  
 |  If x is not a number or if base is given, then x must be a string,
 |  bytes, or bytearray instance representing an integer literal in the
 |  given base.  The literal can be preceded by '+' or '-' and be surrounded
 |  by whitespace.  The base defaults to 10.  Valid bases are 0 and 2-36.
 |  Base 0 means to interpret the base from the string as an integer literal.
 |  >>> int('0b100', base=0)
 |  4
 |  
 |  Methods defined here:
 |  
 |  __abs__(self, /)
 |      abs(self)
 |  
 |  __add__(self, value, /)
 |      Return self+value.
 |  
 |  __and__(self, value, /)
 |      Return self&value.
 |  
 |  __bool__(self, /)
 |      self != 0
 |  
 |  __ceil__(...)
 |      Ceiling of an Integral returns itself.
 |  
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |  
 |  __eq__(self, value, /)
 |      Return self==value.
 |  
 |  __float__(self, /)
 |      float(self)
 |  
 |  __floor__(...)
 |      Flooring an Integral returns itself.
 |  
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |  
 |  __format__(...)
 |      default object formatter
 |  
 |  __ge__(self, value, /)
 |      Return self>=value.
 |  
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |  
 |  __getnewargs__(...)
 |  
 |  __gt__(self, value, /)
 |      Return self>value.
 |  
 |  __hash__(self, /)
 |      Return hash(self).
 |  
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |  
 |  __int__(self, /)
 |      int(self)
 |  
 |  __invert__(self, /)
 |      ~self
 |  
 |  __le__(self, value, /)
 |      Return self<=value.
 |  
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |  
 |  __lt__(self, value, /)
 |      Return self<value.
 |  
 |  __mod__(self, value, /)
 |      Return self%value.
 |  
 |  __mul__(self, value, /)
 |      Return self*value.
 |  
 |  __ne__(self, value, /)
 |      Return self!=value.
 |  
 |  __neg__(self, /)
 |      -self
 |  
 |  __new__(*args, **kwargs) from builtins.type
 |      Create and return a new object.  See help(type) for accurate signature.
 |  
 |  __or__(self, value, /)
 |      Return self|value.
 |  
 |  __pos__(self, /)
 |      +self
 |  
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |  
 |  __radd__(self, value, /)
 |      Return value+self.
 |  
 |  __rand__(self, value, /)
 |      Return value&self.
 |  
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |  
 |  __repr__(self, /)
 |      Return repr(self).
 |  
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |  
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |  
 |  __rmod__(self, value, /)
 |      Return value%self.
 |  
 |  __rmul__(self, value, /)
 |      Return value*self.
 |  
 |  __ror__(self, value, /)
 |      Return value|self.
 |  
 |  __round__(...)
 |      Rounding an Integral returns itself.
 |      Rounding with an ndigits argument also returns an integer.
 |  
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |  
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |  
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |  
 |  __rsub__(self, value, /)
 |      Return value-self.
 |  
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |  
 |  __rxor__(self, value, /)
 |      Return value^self.
 |  
 |  __sizeof__(...)
 |      Returns size in memory, in bytes
 |  
 |  __str__(self, /)
 |      Return str(self).
 |  
 |  __sub__(self, value, /)
 |      Return self-value.
 |  
 |  __truediv__(self, value, /)
 |      Return self/value.
 |  
 |  __trunc__(...)
 |      Truncating an Integral returns itself.
 |  
 |  __xor__(self, value, /)
 |      Return self^value.
 |  
 |  bit_length(...)
 |      int.bit_length() -> int
 |      
 |      Number of bits necessary to represent self in binary.
 |      >>> bin(37)
 |      '0b100101'
 |      >>> (37).bit_length()
 |      6
 |  
 |  conjugate(...)
 |      Returns self, the complex conjugate of any int.
 |  
 |  from_bytes(...) from builtins.type
 |      int.from_bytes(bytes, byteorder, *, signed=False) -> int
 |      
 |      Return the integer represented by the given array of bytes.
 |      
 |      The bytes argument must be a bytes-like object (e.g. bytes or bytearray).
 |      
 |      The byteorder argument determines the byte order used to represent the
 |      integer.  If byteorder is 'big', the most significant byte is at the
 |      beginning of the byte array.  If byteorder is 'little', the most
 |      significant byte is at the end of the byte array.  To request the native
 |      byte order of the host system, use `sys.byteorder' as the byte order value.
 |      
 |      The signed keyword-only argument indicates whether two's complement is
 |      used to represent the integer.
 |  
 |  to_bytes(...)
 |      int.to_bytes(length, byteorder, *, signed=False) -> bytes
 |      
 |      Return an array of bytes representing an integer.
 |      
 |      The integer is represented using length bytes.  An OverflowError is
 |      raised if the integer is not representable with the given number of
 |      bytes.
 |      
 |      The byteorder argument determines the byte order used to represent the
 |      integer.  If byteorder is 'big', the most significant byte is at the
 |      beginning of the byte array.  If byteorder is 'little', the most
 |      significant byte is at the end of the byte array.  To request the native
 |      byte order of the host system, use `sys.byteorder' as the byte order value.
 |      
 |      The signed keyword-only argument determines whether two's complement is
 |      used to represent the integer.  If signed is False and a negative integer
 |      is given, an OverflowError is raised.
 |  
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |  
 |  denominator
 |      the denominator of a rational number in lowest terms
 |  
 |  imag
 |      the imaginary part of a complex number
 |  
 |  numerator
 |      the numerator of a rational number in lowest terms
 |  
 |  real
 |      the real part of a complex number

All variables in python are objects.¶

Every "variable" in python has some associated functions.

Possible to have custom data structure?

</font>

In [9]:

class number:
    def __init__(self,value):
        self.value = value
    def __add__(self,value):
        return number(self.value+value.value)
    def __str__(self):
        return str(self.value)

In [10]:

a = number(2)
b = number(3)

In [11]:

c = a+b
print(c)

5

Inheritance¶

In [29]:

class Celestial:
    def __init__(self,ra,dec,distance):
        self.ra = ra
        self.dec = dec
        self.distance = distance
        
class Star(Celestial):
    def __init__(self,ra,dec,startype,distance):
        super(Star,self).__init__(ra,dec,distance)
        self.startype=startype
    def info(self):
        print(f"A Star of type {self.startype}")
        print(f"Plane of sky position:{self.ra} deg,{self.dec} deg")
        print(f"Distance from Earth: {self.distance} pc")

In [30]:

sirius = Star(101.2833,-16.7161,"a1v",2.64)

In [31]:

sirius.info()

A Star of type a1v
Plane of sky position:101.2833 deg,-16.7161 deg
Distance from Earth: 2.64 pc

Numerical compute operations¶

Scientific workflow needs array manipulation, and work with matrices. How is this done?

Use packages

Packages can be thought to be python files which have a bunch of functions. These functions can be called in our script and used on our variables, or "objects".

</font>

Package list we will be using:

• $\color{#219ebc}{Numpy}$: Array manipulation, operations and our bread & butter.
  

• $\color{#ffb703}{Matplotlib}$: Visualization - plotting graphs and making images.
  

• $\color{#ef476f}{Astropy}$: FITS loading and manipulation.
  

• $\color{#76c893}{Pandas}$: Data loader, and basic data manipulation.
  

---

• $\color{#d08c60}{Scikit-learn}$: Machine learning package.
  

• $\color{#dc2f02}{Pytorch}$: Deep learning package.
  

</font>

In [1]:

import numpy as np
from matplotlib import pyplot as plt 

In [13]:

x = np.linspace(-50,50,1000)
print(x)
print(type(x))

[-50.         -49.8998999  -49.7997998  -49.6996997  -49.5995996
 -49.4994995  -49.3993994  -49.2992993  -49.1991992  -49.0990991
 -48.998999   -48.8988989  -48.7987988  -48.6986987  -48.5985986
 -48.4984985  -48.3983984  -48.2982983  -48.1981982  -48.0980981
 -47.997998   -47.8978979  -47.7977978  -47.6976977  -47.5975976
 -47.4974975  -47.3973974  -47.2972973  -47.1971972  -47.0970971
 -46.996997   -46.8968969  -46.7967968  -46.6966967  -46.5965966
 -46.4964965  -46.3963964  -46.2962963  -46.1961962  -46.0960961
 -45.995996   -45.8958959  -45.7957958  -45.6956957  -45.5955956
 -45.4954955  -45.3953954  -45.2952953  -45.1951952  -45.0950951
 -44.99499499 -44.89489489 -44.79479479 -44.69469469 -44.59459459
 -44.49449449 -44.39439439 -44.29429429 -44.19419419 -44.09409409
 -43.99399399 -43.89389389 -43.79379379 -43.69369369 -43.59359359
 -43.49349349 -43.39339339 -43.29329329 -43.19319319 -43.09309309
 -42.99299299 -42.89289289 -42.79279279 -42.69269269 -42.59259259
 -42.49249249 -42.39239239 -42.29229229 -42.19219219 -42.09209209
 -41.99199199 -41.89189189 -41.79179179 -41.69169169 -41.59159159
 -41.49149149 -41.39139139 -41.29129129 -41.19119119 -41.09109109
 -40.99099099 -40.89089089 -40.79079079 -40.69069069 -40.59059059
 -40.49049049 -40.39039039 -40.29029029 -40.19019019 -40.09009009
 -39.98998999 -39.88988989 -39.78978979 -39.68968969 -39.58958959
 -39.48948949 -39.38938939 -39.28928929 -39.18918919 -39.08908909
 -38.98898899 -38.88888889 -38.78878879 -38.68868869 -38.58858859
 -38.48848849 -38.38838839 -38.28828829 -38.18818819 -38.08808809
 -37.98798799 -37.88788789 -37.78778779 -37.68768769 -37.58758759
 -37.48748749 -37.38738739 -37.28728729 -37.18718719 -37.08708709
 -36.98698699 -36.88688689 -36.78678679 -36.68668669 -36.58658659
 -36.48648649 -36.38638639 -36.28628629 -36.18618619 -36.08608609
 -35.98598599 -35.88588589 -35.78578579 -35.68568569 -35.58558559
 -35.48548549 -35.38538539 -35.28528529 -35.18518519 -35.08508509
 -34.98498498 -34.88488488 -34.78478478 -34.68468468 -34.58458458
 -34.48448448 -34.38438438 -34.28428428 -34.18418418 -34.08408408
 -33.98398398 -33.88388388 -33.78378378 -33.68368368 -33.58358358
 -33.48348348 -33.38338338 -33.28328328 -33.18318318 -33.08308308
 -32.98298298 -32.88288288 -32.78278278 -32.68268268 -32.58258258
 -32.48248248 -32.38238238 -32.28228228 -32.18218218 -32.08208208
 -31.98198198 -31.88188188 -31.78178178 -31.68168168 -31.58158158
 -31.48148148 -31.38138138 -31.28128128 -31.18118118 -31.08108108
 -30.98098098 -30.88088088 -30.78078078 -30.68068068 -30.58058058
 -30.48048048 -30.38038038 -30.28028028 -30.18018018 -30.08008008
 -29.97997998 -29.87987988 -29.77977978 -29.67967968 -29.57957958
 -29.47947948 -29.37937938 -29.27927928 -29.17917918 -29.07907908
 -28.97897898 -28.87887888 -28.77877878 -28.67867868 -28.57857858
 -28.47847848 -28.37837838 -28.27827828 -28.17817818 -28.07807808
 -27.97797798 -27.87787788 -27.77777778 -27.67767768 -27.57757758
 -27.47747748 -27.37737738 -27.27727728 -27.17717718 -27.07707708
 -26.97697698 -26.87687688 -26.77677678 -26.67667668 -26.57657658
 -26.47647648 -26.37637638 -26.27627628 -26.17617618 -26.07607608
 -25.97597598 -25.87587588 -25.77577578 -25.67567568 -25.57557558
 -25.47547548 -25.37537538 -25.27527528 -25.17517518 -25.07507508
 -24.97497497 -24.87487487 -24.77477477 -24.67467467 -24.57457457
 -24.47447447 -24.37437437 -24.27427427 -24.17417417 -24.07407407
 -23.97397397 -23.87387387 -23.77377377 -23.67367367 -23.57357357
 -23.47347347 -23.37337337 -23.27327327 -23.17317317 -23.07307307
 -22.97297297 -22.87287287 -22.77277277 -22.67267267 -22.57257257
 -22.47247247 -22.37237237 -22.27227227 -22.17217217 -22.07207207
 -21.97197197 -21.87187187 -21.77177177 -21.67167167 -21.57157157
 -21.47147147 -21.37137137 -21.27127127 -21.17117117 -21.07107107
 -20.97097097 -20.87087087 -20.77077077 -20.67067067 -20.57057057
 -20.47047047 -20.37037037 -20.27027027 -20.17017017 -20.07007007
 -19.96996997 -19.86986987 -19.76976977 -19.66966967 -19.56956957
 -19.46946947 -19.36936937 -19.26926927 -19.16916917 -19.06906907
 -18.96896897 -18.86886887 -18.76876877 -18.66866867 -18.56856857
 -18.46846847 -18.36836837 -18.26826827 -18.16816817 -18.06806807
 -17.96796797 -17.86786787 -17.76776777 -17.66766767 -17.56756757
 -17.46746747 -17.36736737 -17.26726727 -17.16716717 -17.06706707
 -16.96696697 -16.86686687 -16.76676677 -16.66666667 -16.56656657
 -16.46646647 -16.36636637 -16.26626627 -16.16616617 -16.06606607
 -15.96596597 -15.86586587 -15.76576577 -15.66566567 -15.56556557
 -15.46546547 -15.36536537 -15.26526527 -15.16516517 -15.06506507
 -14.96496496 -14.86486486 -14.76476476 -14.66466466 -14.56456456
 -14.46446446 -14.36436436 -14.26426426 -14.16416416 -14.06406406
 -13.96396396 -13.86386386 -13.76376376 -13.66366366 -13.56356356
 -13.46346346 -13.36336336 -13.26326326 -13.16316316 -13.06306306
 -12.96296296 -12.86286286 -12.76276276 -12.66266266 -12.56256256
 -12.46246246 -12.36236236 -12.26226226 -12.16216216 -12.06206206
 -11.96196196 -11.86186186 -11.76176176 -11.66166166 -11.56156156
 -11.46146146 -11.36136136 -11.26126126 -11.16116116 -11.06106106
 -10.96096096 -10.86086086 -10.76076076 -10.66066066 -10.56056056
 -10.46046046 -10.36036036 -10.26026026 -10.16016016 -10.06006006
  -9.95995996  -9.85985986  -9.75975976  -9.65965966  -9.55955956
  -9.45945946  -9.35935936  -9.25925926  -9.15915916  -9.05905906
  -8.95895896  -8.85885886  -8.75875876  -8.65865866  -8.55855856
  -8.45845846  -8.35835836  -8.25825826  -8.15815816  -8.05805806
  -7.95795796  -7.85785786  -7.75775776  -7.65765766  -7.55755756
  -7.45745746  -7.35735736  -7.25725726  -7.15715716  -7.05705706
  -6.95695696  -6.85685686  -6.75675676  -6.65665666  -6.55655656
  -6.45645646  -6.35635636  -6.25625626  -6.15615616  -6.05605606
  -5.95595596  -5.85585586  -5.75575576  -5.65565566  -5.55555556
  -5.45545546  -5.35535536  -5.25525526  -5.15515516  -5.05505506
  -4.95495495  -4.85485485  -4.75475475  -4.65465465  -4.55455455
  -4.45445445  -4.35435435  -4.25425425  -4.15415415  -4.05405405
  -3.95395395  -3.85385385  -3.75375375  -3.65365365  -3.55355355
  -3.45345345  -3.35335335  -3.25325325  -3.15315315  -3.05305305
  -2.95295295  -2.85285285  -2.75275275  -2.65265265  -2.55255255
  -2.45245245  -2.35235235  -2.25225225  -2.15215215  -2.05205205
  -1.95195195  -1.85185185  -1.75175175  -1.65165165  -1.55155155
  -1.45145145  -1.35135135  -1.25125125  -1.15115115  -1.05105105
  -0.95095095  -0.85085085  -0.75075075  -0.65065065  -0.55055055
  -0.45045045  -0.35035035  -0.25025025  -0.15015015  -0.05005005
   0.05005005   0.15015015   0.25025025   0.35035035   0.45045045
   0.55055055   0.65065065   0.75075075   0.85085085   0.95095095
   1.05105105   1.15115115   1.25125125   1.35135135   1.45145145
   1.55155155   1.65165165   1.75175175   1.85185185   1.95195195
   2.05205205   2.15215215   2.25225225   2.35235235   2.45245245
   2.55255255   2.65265265   2.75275275   2.85285285   2.95295295
   3.05305305   3.15315315   3.25325325   3.35335335   3.45345345
   3.55355355   3.65365365   3.75375375   3.85385385   3.95395395
   4.05405405   4.15415415   4.25425425   4.35435435   4.45445445
   4.55455455   4.65465465   4.75475475   4.85485485   4.95495495
   5.05505506   5.15515516   5.25525526   5.35535536   5.45545546
   5.55555556   5.65565566   5.75575576   5.85585586   5.95595596
   6.05605606   6.15615616   6.25625626   6.35635636   6.45645646
   6.55655656   6.65665666   6.75675676   6.85685686   6.95695696
   7.05705706   7.15715716   7.25725726   7.35735736   7.45745746
   7.55755756   7.65765766   7.75775776   7.85785786   7.95795796
   8.05805806   8.15815816   8.25825826   8.35835836   8.45845846
   8.55855856   8.65865866   8.75875876   8.85885886   8.95895896
   9.05905906   9.15915916   9.25925926   9.35935936   9.45945946
   9.55955956   9.65965966   9.75975976   9.85985986   9.95995996
  10.06006006  10.16016016  10.26026026  10.36036036  10.46046046
  10.56056056  10.66066066  10.76076076  10.86086086  10.96096096
  11.06106106  11.16116116  11.26126126  11.36136136  11.46146146
  11.56156156  11.66166166  11.76176176  11.86186186  11.96196196
  12.06206206  12.16216216  12.26226226  12.36236236  12.46246246
  12.56256256  12.66266266  12.76276276  12.86286286  12.96296296
  13.06306306  13.16316316  13.26326326  13.36336336  13.46346346
  13.56356356  13.66366366  13.76376376  13.86386386  13.96396396
  14.06406406  14.16416416  14.26426426  14.36436436  14.46446446
  14.56456456  14.66466466  14.76476476  14.86486486  14.96496496
  15.06506507  15.16516517  15.26526527  15.36536537  15.46546547
  15.56556557  15.66566567  15.76576577  15.86586587  15.96596597
  16.06606607  16.16616617  16.26626627  16.36636637  16.46646647
  16.56656657  16.66666667  16.76676677  16.86686687  16.96696697
  17.06706707  17.16716717  17.26726727  17.36736737  17.46746747
  17.56756757  17.66766767  17.76776777  17.86786787  17.96796797
  18.06806807  18.16816817  18.26826827  18.36836837  18.46846847
  18.56856857  18.66866867  18.76876877  18.86886887  18.96896897
  19.06906907  19.16916917  19.26926927  19.36936937  19.46946947
  19.56956957  19.66966967  19.76976977  19.86986987  19.96996997
  20.07007007  20.17017017  20.27027027  20.37037037  20.47047047
  20.57057057  20.67067067  20.77077077  20.87087087  20.97097097
  21.07107107  21.17117117  21.27127127  21.37137137  21.47147147
  21.57157157  21.67167167  21.77177177  21.87187187  21.97197197
  22.07207207  22.17217217  22.27227227  22.37237237  22.47247247
  22.57257257  22.67267267  22.77277277  22.87287287  22.97297297
  23.07307307  23.17317317  23.27327327  23.37337337  23.47347347
  23.57357357  23.67367367  23.77377377  23.87387387  23.97397397
  24.07407407  24.17417417  24.27427427  24.37437437  24.47447447
  24.57457457  24.67467467  24.77477477  24.87487487  24.97497497
  25.07507508  25.17517518  25.27527528  25.37537538  25.47547548
  25.57557558  25.67567568  25.77577578  25.87587588  25.97597598
  26.07607608  26.17617618  26.27627628  26.37637638  26.47647648
  26.57657658  26.67667668  26.77677678  26.87687688  26.97697698
  27.07707708  27.17717718  27.27727728  27.37737738  27.47747748
  27.57757758  27.67767768  27.77777778  27.87787788  27.97797798
  28.07807808  28.17817818  28.27827828  28.37837838  28.47847848
  28.57857858  28.67867868  28.77877878  28.87887888  28.97897898
  29.07907908  29.17917918  29.27927928  29.37937938  29.47947948
  29.57957958  29.67967968  29.77977978  29.87987988  29.97997998
  30.08008008  30.18018018  30.28028028  30.38038038  30.48048048
  30.58058058  30.68068068  30.78078078  30.88088088  30.98098098
  31.08108108  31.18118118  31.28128128  31.38138138  31.48148148
  31.58158158  31.68168168  31.78178178  31.88188188  31.98198198
  32.08208208  32.18218218  32.28228228  32.38238238  32.48248248
  32.58258258  32.68268268  32.78278278  32.88288288  32.98298298
  33.08308308  33.18318318  33.28328328  33.38338338  33.48348348
  33.58358358  33.68368368  33.78378378  33.88388388  33.98398398
  34.08408408  34.18418418  34.28428428  34.38438438  34.48448448
  34.58458458  34.68468468  34.78478478  34.88488488  34.98498498
  35.08508509  35.18518519  35.28528529  35.38538539  35.48548549
  35.58558559  35.68568569  35.78578579  35.88588589  35.98598599
  36.08608609  36.18618619  36.28628629  36.38638639  36.48648649
  36.58658659  36.68668669  36.78678679  36.88688689  36.98698699
  37.08708709  37.18718719  37.28728729  37.38738739  37.48748749
  37.58758759  37.68768769  37.78778779  37.88788789  37.98798799
  38.08808809  38.18818819  38.28828829  38.38838839  38.48848849
  38.58858859  38.68868869  38.78878879  38.88888889  38.98898899
  39.08908909  39.18918919  39.28928929  39.38938939  39.48948949
  39.58958959  39.68968969  39.78978979  39.88988989  39.98998999
  40.09009009  40.19019019  40.29029029  40.39039039  40.49049049
  40.59059059  40.69069069  40.79079079  40.89089089  40.99099099
  41.09109109  41.19119119  41.29129129  41.39139139  41.49149149
  41.59159159  41.69169169  41.79179179  41.89189189  41.99199199
  42.09209209  42.19219219  42.29229229  42.39239239  42.49249249
  42.59259259  42.69269269  42.79279279  42.89289289  42.99299299
  43.09309309  43.19319319  43.29329329  43.39339339  43.49349349
  43.59359359  43.69369369  43.79379379  43.89389389  43.99399399
  44.09409409  44.19419419  44.29429429  44.39439439  44.49449449
  44.59459459  44.69469469  44.79479479  44.89489489  44.99499499
  45.0950951   45.1951952   45.2952953   45.3953954   45.4954955
  45.5955956   45.6956957   45.7957958   45.8958959   45.995996
  46.0960961   46.1961962   46.2962963   46.3963964   46.4964965
  46.5965966   46.6966967   46.7967968   46.8968969   46.996997
  47.0970971   47.1971972   47.2972973   47.3973974   47.4974975
  47.5975976   47.6976977   47.7977978   47.8978979   47.997998
  48.0980981   48.1981982   48.2982983   48.3983984   48.4984985
  48.5985986   48.6986987   48.7987988   48.8988989   48.998999
  49.0990991   49.1991992   49.2992993   49.3993994   49.4994995
  49.5995996   49.6996997   49.7997998   49.8998999   50.        ]
<class 'numpy.ndarray'>

In [14]:

gauss = np.exp(-x**2/100.0)
print(gauss)

[1.38879439e-11 1.53485501e-11 1.69593705e-11 1.87354905e-11
 2.06934725e-11 2.28514965e-11 2.52295142e-11 2.78494161e-11
 3.07352160e-11 3.39132500e-11 3.74123958e-11 4.12643108e-11
 4.55036924e-11 5.01685615e-11 5.53005724e-11 6.09453493e-11
 6.71528551e-11 7.39777913e-11 8.14800350e-11 8.97251142e-11
 9.87847260e-11 1.08737300e-10 1.19668614e-10 1.31672458e-10
 1.44851365e-10 1.59317399e-10 1.75193016e-10 1.92611999e-10
 2.11720473e-10 2.32678010e-10 2.55658827e-10 2.80853093e-10
 3.08468340e-10 3.38731003e-10 3.71888089e-10 4.08208981e-10
 4.47987410e-10 4.91543583e-10 5.39226490e-10 5.91416415e-10
 6.48527650e-10 7.11011437e-10 7.79359158e-10 8.54105792e-10
 9.35833652e-10 1.02517644e-09 1.12282362e-09 1.22952520e-09
 1.34609681e-09 1.47342529e-09 1.61247472e-09 1.76429285e-09
 1.93001819e-09 2.11088755e-09 2.30824424e-09 2.52354696e-09
 2.75837931e-09 3.01446017e-09 3.29365481e-09 3.59798691e-09
 3.92965156e-09 4.29102926e-09 4.68470098e-09 5.11346446e-09
 5.58035175e-09 6.08864812e-09 6.64191241e-09 7.24399895e-09
 7.89908125e-09 8.61167735e-09 9.38667727e-09 1.02293724e-08
 1.11454873e-08 1.21412135e-08 1.32232468e-08 1.43988257e-08
 1.56757747e-08 1.70625493e-08 1.85682850e-08 2.02028497e-08
 2.19769005e-08 2.39019435e-08 2.59903996e-08 2.82556737e-08
 3.07122294e-08 3.33756695e-08 3.62628218e-08 3.93918315e-08
 4.27822595e-08 4.64551888e-08 5.04333374e-08 5.47411799e-08
 5.94050776e-08 6.44534171e-08 6.99167600e-08 7.58280013e-08
 8.22225404e-08 8.91384626e-08 9.66167345e-08 1.04701412e-07
 1.13439862e-07 1.22883000e-07 1.33085546e-07 1.44106291e-07
 1.56008392e-07 1.68859673e-07 1.82732964e-07 1.97706441e-07
 2.13864010e-07 2.31295700e-07 2.50098093e-07 2.70374774e-07
 2.92236814e-07 3.15803288e-07 3.41201818e-07 3.68569161e-07
 3.98051823e-07 4.29806727e-07 4.64001909e-07 5.00817265e-07
 5.40445351e-07 5.83092217e-07 6.28978313e-07 6.78339435e-07
 7.31427739e-07 7.88512813e-07 8.49882819e-07 9.15845703e-07
 9.86730476e-07 1.06288857e-06 1.14469531e-06 1.23255138e-06
 1.32688453e-06 1.42815122e-06 1.53683849e-06 1.65346584e-06
 1.77858733e-06 1.91279368e-06 2.05671459e-06 2.21102115e-06
 2.37642839e-06 2.55369799e-06 2.74364112e-06 2.94712149e-06
 3.16505851e-06 3.39843067e-06 3.64827907e-06 3.91571123e-06
 4.20190500e-06 4.50811274e-06 4.83566575e-06 5.18597893e-06
 5.56055561e-06 5.96099278e-06 6.38898650e-06 6.84633763e-06
 7.33495783e-06 7.85687598e-06 8.41424476e-06 9.00934777e-06
 9.64460685e-06 1.03225899e-05 1.10460190e-05 1.18177790e-05
 1.26409266e-05 1.35186998e-05 1.44545276e-05 1.54520410e-05
 1.65150832e-05 1.76477217e-05 1.88542602e-05 2.01392509e-05
 2.15075081e-05 2.29641220e-05 2.45144731e-05 2.61642474e-05
 2.79194526e-05 2.97864343e-05 3.17718939e-05 3.38829064e-05
 3.61269398e-05 3.85118750e-05 4.10460261e-05 4.37381630e-05
 4.65975333e-05 4.96338865e-05 5.28574984e-05 5.62791974e-05
 5.99103908e-05 6.37630932e-05 6.78499556e-05 7.21842962e-05
 7.67801316e-05 8.16522102e-05 8.68160464e-05 9.22879569e-05
 9.80850969e-05 1.04225500e-04 1.10728117e-04 1.17612860e-04
 1.24900643e-04 1.32613428e-04 1.40774275e-04 1.49407384e-04
 1.58538153e-04 1.68193223e-04 1.78400537e-04 1.89189396e-04
 2.00590513e-04 2.12636079e-04 2.25359821e-04 2.38797068e-04
 2.52984818e-04 2.67961805e-04 2.83768573e-04 3.00447549e-04
 3.18043118e-04 3.36601701e-04 3.56171837e-04 3.76804269e-04
 3.98552025e-04 4.21470509e-04 4.45617596e-04 4.71053720e-04
 4.97841975e-04 5.26048215e-04 5.55741155e-04 5.86992476e-04
 6.19876934e-04 6.54472474e-04 6.90860340e-04 7.29125194e-04
 7.69355239e-04 8.11642338e-04 8.56082143e-04 9.02774223e-04
 9.51822198e-04 1.00333387e-03 1.05742138e-03 1.11420132e-03
 1.17379489e-03 1.23632807e-03 1.30193173e-03 1.37074182e-03
 1.44289948e-03 1.51855128e-03 1.59784928e-03 1.68095129e-03
 1.76802098e-03 1.85922806e-03 1.95474848e-03 2.05476457e-03
 2.15946526e-03 2.26904622e-03 2.38371006e-03 2.50366653e-03
 2.62913269e-03 2.76033311e-03 2.89750004e-03 3.04087363e-03
 3.19070214e-03 3.34724206e-03 3.51075841e-03 3.68152485e-03
 3.85982393e-03 4.04594729e-03 4.24019581e-03 4.44287989e-03
 4.65431958e-03 4.87484480e-03 5.10479558e-03 5.34452218e-03
 5.59438536e-03 5.85475656e-03 6.12601804e-03 6.40856315e-03
 6.70279647e-03 7.00913401e-03 7.32800339e-03 7.65984404e-03
 8.00510734e-03 8.36425683e-03 8.73776834e-03 9.12613019e-03
 9.52984333e-03 9.94942149e-03 1.03853913e-02 1.08382925e-02
 1.13086780e-02 1.17971139e-02 1.23041800e-02 1.28304695e-02
 1.33765891e-02 1.39431594e-02 1.45308147e-02 1.51402032e-02
 1.57719870e-02 1.64268421e-02 1.71054587e-02 1.78085406e-02
 1.85368061e-02 1.92909870e-02 2.00718294e-02 2.08800933e-02
 2.17165523e-02 2.25819940e-02 2.34772198e-02 2.44030445e-02
 2.53602963e-02 2.63498169e-02 2.73724612e-02 2.84290968e-02
 2.95206042e-02 3.06478766e-02 3.18118192e-02 3.30133493e-02
 3.42533960e-02 3.55328999e-02 3.68528123e-02 3.82140956e-02
 3.96177223e-02 4.10646748e-02 4.25559451e-02 4.40925340e-02
 4.56754510e-02 4.73057135e-02 4.89843464e-02 5.07123814e-02
 5.24908566e-02 5.43208155e-02 5.62033070e-02 5.81393840e-02
 6.01301032e-02 6.21765240e-02 6.42797082e-02 6.64407186e-02
 6.86606187e-02 7.09404716e-02 7.32813391e-02 7.56842810e-02
 7.81503540e-02 8.06806107e-02 8.32760987e-02 8.59378595e-02
 8.86669278e-02 9.14643298e-02 9.43310827e-02 9.72681933e-02
 1.00276657e-01 1.03357456e-01 1.06511559e-01 1.09739920e-01
 1.13043477e-01 1.16423148e-01 1.19879835e-01 1.23414420e-01
 1.27027760e-01 1.30720693e-01 1.34494030e-01 1.38348560e-01
 1.42285042e-01 1.46304207e-01 1.50406759e-01 1.54593367e-01
 1.58864671e-01 1.63221275e-01 1.67663748e-01 1.72192624e-01
 1.76808395e-01 1.81511518e-01 1.86302406e-01 1.91181429e-01
 1.96148916e-01 2.01205148e-01 2.06350359e-01 2.11584738e-01
 2.16908422e-01 2.22321497e-01 2.27823998e-01 2.33415906e-01
 2.39097146e-01 2.44867589e-01 2.50727046e-01 2.56675272e-01
 2.62711960e-01 2.68836743e-01 2.75049191e-01 2.81348813e-01
 2.87735051e-01 2.94207282e-01 3.00764819e-01 3.07406905e-01
 3.14132716e-01 3.20941358e-01 3.27831870e-01 3.34803217e-01
 3.41854296e-01 3.48983929e-01 3.56190868e-01 3.63473792e-01
 3.70831305e-01 3.78261938e-01 3.85764150e-01 3.93336324e-01
 4.00976768e-01 4.08683716e-01 4.16455329e-01 4.24289692e-01
 4.32184817e-01 4.40138640e-01 4.48149025e-01 4.56213762e-01
 4.64330568e-01 4.72497087e-01 4.80710892e-01 4.88969485e-01
 4.97270297e-01 5.05610689e-01 5.13987956e-01 5.22399323e-01
 5.30841950e-01 5.39312930e-01 5.47809295e-01 5.56328013e-01
 5.64865990e-01 5.73420074e-01 5.81987056e-01 5.90563668e-01
 5.99146590e-01 6.07732450e-01 6.16317824e-01 6.24899239e-01
 6.33473179e-01 6.42036079e-01 6.50584338e-01 6.59114310e-01
 6.67622316e-01 6.76104639e-01 6.84557533e-01 6.92977222e-01
 7.01359901e-01 7.09701743e-01 7.17998899e-01 7.26247503e-01
 7.34443672e-01 7.42583511e-01 7.50663115e-01 7.58678574e-01
 7.66625972e-01 7.74501396e-01 7.82300934e-01 7.90020680e-01
 7.97656737e-01 8.05205222e-01 8.12662267e-01 8.20024021e-01
 8.27286659e-01 8.34446379e-01 8.41499409e-01 8.48442008e-01
 8.55270472e-01 8.61981134e-01 8.68570369e-01 8.75034600e-01
 8.81370296e-01 8.87573976e-01 8.93642218e-01 8.99571655e-01
 9.05358983e-01 9.11000959e-01 9.16494410e-01 9.21836232e-01
 9.27023394e-01 9.32052942e-01 9.36921999e-01 9.41627771e-01
 9.46167546e-01 9.50538700e-01 9.54738700e-01 9.58765100e-01
 9.62615554e-01 9.66287806e-01 9.69779705e-01 9.73089194e-01
 9.76214324e-01 9.79153248e-01 9.81904226e-01 9.84465626e-01
 9.86835925e-01 9.89013712e-01 9.90997689e-01 9.92786670e-01
 9.94379587e-01 9.95775486e-01 9.96973530e-01 9.97973001e-01
 9.98773299e-01 9.99373944e-01 9.99774575e-01 9.99974950e-01
 9.99974950e-01 9.99774575e-01 9.99373944e-01 9.98773299e-01
 9.97973001e-01 9.96973530e-01 9.95775486e-01 9.94379587e-01
 9.92786670e-01 9.90997689e-01 9.89013712e-01 9.86835925e-01
 9.84465626e-01 9.81904226e-01 9.79153248e-01 9.76214324e-01
 9.73089194e-01 9.69779705e-01 9.66287806e-01 9.62615554e-01
 9.58765100e-01 9.54738700e-01 9.50538700e-01 9.46167546e-01
 9.41627771e-01 9.36921999e-01 9.32052942e-01 9.27023394e-01
 9.21836232e-01 9.16494410e-01 9.11000959e-01 9.05358983e-01
 8.99571655e-01 8.93642218e-01 8.87573976e-01 8.81370296e-01
 8.75034600e-01 8.68570369e-01 8.61981134e-01 8.55270472e-01
 8.48442008e-01 8.41499409e-01 8.34446379e-01 8.27286659e-01
 8.20024021e-01 8.12662267e-01 8.05205222e-01 7.97656737e-01
 7.90020680e-01 7.82300934e-01 7.74501396e-01 7.66625972e-01
 7.58678574e-01 7.50663115e-01 7.42583511e-01 7.34443672e-01
 7.26247503e-01 7.17998899e-01 7.09701743e-01 7.01359901e-01
 6.92977222e-01 6.84557533e-01 6.76104639e-01 6.67622316e-01
 6.59114310e-01 6.50584338e-01 6.42036079e-01 6.33473179e-01
 6.24899239e-01 6.16317824e-01 6.07732450e-01 5.99146590e-01
 5.90563668e-01 5.81987056e-01 5.73420074e-01 5.64865990e-01
 5.56328013e-01 5.47809295e-01 5.39312930e-01 5.30841950e-01
 5.22399323e-01 5.13987956e-01 5.05610689e-01 4.97270297e-01
 4.88969485e-01 4.80710892e-01 4.72497087e-01 4.64330568e-01
 4.56213762e-01 4.48149025e-01 4.40138640e-01 4.32184817e-01
 4.24289692e-01 4.16455329e-01 4.08683716e-01 4.00976768e-01
 3.93336324e-01 3.85764150e-01 3.78261938e-01 3.70831305e-01
 3.63473792e-01 3.56190868e-01 3.48983929e-01 3.41854296e-01
 3.34803217e-01 3.27831870e-01 3.20941358e-01 3.14132716e-01
 3.07406905e-01 3.00764819e-01 2.94207282e-01 2.87735051e-01
 2.81348813e-01 2.75049191e-01 2.68836743e-01 2.62711960e-01
 2.56675272e-01 2.50727046e-01 2.44867589e-01 2.39097146e-01
 2.33415906e-01 2.27823998e-01 2.22321497e-01 2.16908422e-01
 2.11584738e-01 2.06350359e-01 2.01205148e-01 1.96148916e-01
 1.91181429e-01 1.86302406e-01 1.81511518e-01 1.76808395e-01
 1.72192624e-01 1.67663748e-01 1.63221275e-01 1.58864671e-01
 1.54593367e-01 1.50406759e-01 1.46304207e-01 1.42285042e-01
 1.38348560e-01 1.34494030e-01 1.30720693e-01 1.27027760e-01
 1.23414420e-01 1.19879835e-01 1.16423148e-01 1.13043477e-01
 1.09739920e-01 1.06511559e-01 1.03357456e-01 1.00276657e-01
 9.72681933e-02 9.43310827e-02 9.14643298e-02 8.86669278e-02
 8.59378595e-02 8.32760987e-02 8.06806107e-02 7.81503540e-02
 7.56842810e-02 7.32813391e-02 7.09404716e-02 6.86606187e-02
 6.64407186e-02 6.42797082e-02 6.21765240e-02 6.01301032e-02
 5.81393840e-02 5.62033070e-02 5.43208155e-02 5.24908566e-02
 5.07123814e-02 4.89843464e-02 4.73057135e-02 4.56754510e-02
 4.40925340e-02 4.25559451e-02 4.10646748e-02 3.96177223e-02
 3.82140956e-02 3.68528123e-02 3.55328999e-02 3.42533960e-02
 3.30133493e-02 3.18118192e-02 3.06478766e-02 2.95206042e-02
 2.84290968e-02 2.73724612e-02 2.63498169e-02 2.53602963e-02
 2.44030445e-02 2.34772198e-02 2.25819940e-02 2.17165523e-02
 2.08800933e-02 2.00718294e-02 1.92909870e-02 1.85368061e-02
 1.78085406e-02 1.71054587e-02 1.64268421e-02 1.57719870e-02
 1.51402032e-02 1.45308147e-02 1.39431594e-02 1.33765891e-02
 1.28304695e-02 1.23041800e-02 1.17971139e-02 1.13086780e-02
 1.08382925e-02 1.03853913e-02 9.94942149e-03 9.52984333e-03
 9.12613019e-03 8.73776834e-03 8.36425683e-03 8.00510734e-03
 7.65984404e-03 7.32800339e-03 7.00913401e-03 6.70279647e-03
 6.40856315e-03 6.12601804e-03 5.85475656e-03 5.59438536e-03
 5.34452218e-03 5.10479558e-03 4.87484480e-03 4.65431958e-03
 4.44287989e-03 4.24019581e-03 4.04594729e-03 3.85982393e-03
 3.68152485e-03 3.51075841e-03 3.34724206e-03 3.19070214e-03
 3.04087363e-03 2.89750004e-03 2.76033311e-03 2.62913269e-03
 2.50366653e-03 2.38371006e-03 2.26904622e-03 2.15946526e-03
 2.05476457e-03 1.95474848e-03 1.85922806e-03 1.76802098e-03
 1.68095129e-03 1.59784928e-03 1.51855128e-03 1.44289948e-03
 1.37074182e-03 1.30193173e-03 1.23632807e-03 1.17379489e-03
 1.11420132e-03 1.05742138e-03 1.00333387e-03 9.51822198e-04
 9.02774223e-04 8.56082143e-04 8.11642338e-04 7.69355239e-04
 7.29125194e-04 6.90860340e-04 6.54472474e-04 6.19876934e-04
 5.86992476e-04 5.55741155e-04 5.26048215e-04 4.97841975e-04
 4.71053720e-04 4.45617596e-04 4.21470509e-04 3.98552025e-04
 3.76804269e-04 3.56171837e-04 3.36601701e-04 3.18043118e-04
 3.00447549e-04 2.83768573e-04 2.67961805e-04 2.52984818e-04
 2.38797068e-04 2.25359821e-04 2.12636079e-04 2.00590513e-04
 1.89189396e-04 1.78400537e-04 1.68193223e-04 1.58538153e-04
 1.49407384e-04 1.40774275e-04 1.32613428e-04 1.24900643e-04
 1.17612860e-04 1.10728117e-04 1.04225500e-04 9.80850969e-05
 9.22879569e-05 8.68160464e-05 8.16522102e-05 7.67801316e-05
 7.21842962e-05 6.78499556e-05 6.37630932e-05 5.99103908e-05
 5.62791974e-05 5.28574984e-05 4.96338865e-05 4.65975333e-05
 4.37381630e-05 4.10460261e-05 3.85118750e-05 3.61269398e-05
 3.38829064e-05 3.17718939e-05 2.97864343e-05 2.79194526e-05
 2.61642474e-05 2.45144731e-05 2.29641220e-05 2.15075081e-05
 2.01392509e-05 1.88542602e-05 1.76477217e-05 1.65150832e-05
 1.54520410e-05 1.44545276e-05 1.35186998e-05 1.26409266e-05
 1.18177790e-05 1.10460190e-05 1.03225899e-05 9.64460685e-06
 9.00934777e-06 8.41424476e-06 7.85687598e-06 7.33495783e-06
 6.84633763e-06 6.38898650e-06 5.96099278e-06 5.56055561e-06
 5.18597893e-06 4.83566575e-06 4.50811274e-06 4.20190500e-06
 3.91571123e-06 3.64827907e-06 3.39843067e-06 3.16505851e-06
 2.94712149e-06 2.74364112e-06 2.55369799e-06 2.37642839e-06
 2.21102115e-06 2.05671459e-06 1.91279368e-06 1.77858733e-06
 1.65346584e-06 1.53683849e-06 1.42815122e-06 1.32688453e-06
 1.23255138e-06 1.14469531e-06 1.06288857e-06 9.86730476e-07
 9.15845703e-07 8.49882819e-07 7.88512813e-07 7.31427739e-07
 6.78339435e-07 6.28978313e-07 5.83092217e-07 5.40445351e-07
 5.00817265e-07 4.64001909e-07 4.29806727e-07 3.98051823e-07
 3.68569161e-07 3.41201818e-07 3.15803288e-07 2.92236814e-07
 2.70374774e-07 2.50098093e-07 2.31295700e-07 2.13864010e-07
 1.97706441e-07 1.82732964e-07 1.68859673e-07 1.56008392e-07
 1.44106291e-07 1.33085546e-07 1.22883000e-07 1.13439862e-07
 1.04701412e-07 9.66167345e-08 8.91384626e-08 8.22225404e-08
 7.58280013e-08 6.99167600e-08 6.44534171e-08 5.94050776e-08
 5.47411799e-08 5.04333374e-08 4.64551888e-08 4.27822595e-08
 3.93918315e-08 3.62628218e-08 3.33756695e-08 3.07122294e-08
 2.82556737e-08 2.59903996e-08 2.39019435e-08 2.19769005e-08
 2.02028497e-08 1.85682850e-08 1.70625493e-08 1.56757747e-08
 1.43988257e-08 1.32232468e-08 1.21412135e-08 1.11454873e-08
 1.02293724e-08 9.38667727e-09 8.61167735e-09 7.89908125e-09
 7.24399895e-09 6.64191241e-09 6.08864812e-09 5.58035175e-09
 5.11346446e-09 4.68470098e-09 4.29102926e-09 3.92965156e-09
 3.59798691e-09 3.29365481e-09 3.01446017e-09 2.75837931e-09
 2.52354696e-09 2.30824424e-09 2.11088755e-09 1.93001819e-09
 1.76429285e-09 1.61247472e-09 1.47342529e-09 1.34609681e-09
 1.22952520e-09 1.12282362e-09 1.02517644e-09 9.35833652e-10
 8.54105792e-10 7.79359158e-10 7.11011437e-10 6.48527650e-10
 5.91416415e-10 5.39226490e-10 4.91543583e-10 4.47987410e-10
 4.08208981e-10 3.71888089e-10 3.38731003e-10 3.08468340e-10
 2.80853093e-10 2.55658827e-10 2.32678010e-10 2.11720473e-10
 1.92611999e-10 1.75193016e-10 1.59317399e-10 1.44851365e-10
 1.31672458e-10 1.19668614e-10 1.08737300e-10 9.87847260e-11
 8.97251142e-11 8.14800350e-11 7.39777913e-11 6.71528551e-11
 6.09453493e-11 5.53005724e-11 5.01685615e-11 4.55036924e-11
 4.12643108e-11 3.74123958e-11 3.39132500e-11 3.07352160e-11
 2.78494161e-11 2.52295142e-11 2.28514965e-11 2.06934725e-11
 1.87354905e-11 1.69593705e-11 1.53485501e-11 1.38879439e-11]

In [15]:

# plt.plot(x,gauss)
# plt.plot(x,gauss,color='red')
plt.plot(x,gauss,color='red',linestyle='--')
plt.xlabel("X-value")
plt.ylabel("f(x)")
plt.title("Gaussian function")

Out[15]:

Text(0.5, 1.0, 'Gaussian function')

Image visualization¶

Let us define a 2-D Gaussian of the form: $$e^{-(x-5)^2/25-(y-5)^2/25}+e^{-(x+5)^2/25-(y+5)^2/25}$$

</font>

In [16]:

x = np.linspace(-10,10,1000)
y = np.linspace(-10,10,1000)
xx,yy = np.meshgrid(x,y)
doublegauss = np.exp(-(xx-5)**2/25.0-(yy-5)**2/25.0)+np.exp(-(xx+5)**2/25.0-(yy+5)**2/25.0)

In [17]:

plt.imshow(doublegauss,cmap='RdYlBu_r',origin='lower')

Out[17]:

<matplotlib.image.AxesImage at 0x7f2a42e73be0>

In [18]:

plt.figure(figsize=(10,8))
plt.contourf(x,y,doublegauss,100,cmap='RdYlBu_r')
plt.colorbar()

Out[18]:

<matplotlib.colorbar.Colorbar at 0x7f2a41b53f28>

Not a number¶

NaN is a special floating point value meant to reperesent anything that is "not a number" or "not data".

</font>

In [99]:

n1 = float("nan")
n2 = float("Nan")
n3 = float("NaN")
n4 = float("NAN")
n5 = np.nan
print(n1, n2, n3, n4,n5)

nan nan nan nan nan

In [100]:

print(n1 == 0)
print(n1 == 100)
print(n2 < 0)

False
False
False

Question:¶

What is the expected output of n5==n5?

https://forms.gle/nJcCS5S88jwVbpkh9

</font>

In [102]:

print(n5 == n5)

False

Can we visualize astro data?¶

Astrophysics data is generally available in FITS format. Think of them as a file with multiple "shelves".

• Each data set - for example, one wavelength of observation - can be put in one shelf.
• Each shelf has a "data" and a "header".
  • Header contains information on the satellite, location of object, Field of view, resolution, etc.
  • Data contains the actual counts.

We are going to use $\color{#ef476f}{Astropy}$ for this!

</font>

In [2]:

from astropy.io import fits

Data available at: https://www.lmsal.com/hek/hcr?cmd=view-event&event-id=ivo%3A%2F%2Fsot.lmsal.com%2FVOEvent%23VOEvent_IRIS_20141022_081850_3860261381_2014-10-22T08%3A18%3A502014-10-22T08%3A18%3A50.xml

In [20]:

!mkdir Data/

In [21]:

!wget https://www.lmsal.com/solarsoft/irisa/data/level2_compressed/2014/10/22/20141022_081850_3860261381/iris_l2_20141022_081850_3860261381_SDO.tar.gz

--2021-05-30 18:40:50--  https://www.lmsal.com/solarsoft/irisa/data/level2_compressed/2014/10/22/20141022_081850_3860261381/iris_l2_20141022_081850_3860261381_SDO.tar.gz
Resolving www.lmsal.com (www.lmsal.com)... 166.21.250.149
Connecting to www.lmsal.com (www.lmsal.com)|166.21.250.149|:443... connected.
HTTP request sent, awaiting response... 302 Found
Location: https://iris.aws.lmsal.com/data/level2_compressed/2014/10/22/20141022_081850_3860261381/iris_l2_20141022_081850_3860261381_SDO.tar.gz [following]
--2021-05-30 18:40:52--  https://iris.aws.lmsal.com/data/level2_compressed/2014/10/22/20141022_081850_3860261381/iris_l2_20141022_081850_3860261381_SDO.tar.gz
Resolving iris.aws.lmsal.com (iris.aws.lmsal.com)... 54.192.66.40, 54.192.66.129, 54.192.66.111, ...
Connecting to iris.aws.lmsal.com (iris.aws.lmsal.com)|54.192.66.40|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 6317064603 (5.9G) [application/x-tar]
Saving to: ‘iris_l2_20141022_081850_3860261381_SDO.tar.gz’

iris_l2_20141022_08 100%[===================>]   5.88G  1.99MB/s    in 51m 17s 

2021-05-30 19:32:10 (1.96 MB/s) - ‘iris_l2_20141022_081850_3860261381_SDO.tar.gz’ saved [6317064603/6317064603]

tar: Data: Not found in archive
tar: Exiting with failure status due to previous errors

In [24]:

!tar -xvf iris_l2_20141022_081850_3860261381_SDO.tar.gz 

aia_l2_20141022_081850_3860261381_131.fits
aia_l2_20141022_081850_3860261381_211.fits
aia_l2_20141022_081850_3860261381_335.fits
aia_l2_20141022_081850_3860261381_304.fits
aia_l2_20141022_081850_3860261381_94.fits
aia_l2_20141022_081850_3860261381_193.fits
aia_l2_20141022_081850_3860261381_1700.fits
aia_l2_20141022_081850_3860261381_171.fits
aia_l2_20141022_081850_3860261381_1600.fits

In [3]:

aia = fits.open("aia_l2_20141022_081850_3860261381_171.fits")
print(aia.info())

Filename: aia_l2_20141022_081850_3860261381_171.fits
No.    Name      Ver    Type      Cards   Dimensions   Format
  0  PRIMARY       1 PrimaryHDU     147   (472, 470, 2987)   int16   
  1                1 ImageHDU        27   (20, 2987)   float64   
  2                1 TableHDU        28   2987R x 4C   [A0, A0, A0, A100]   
None

In [4]:

aia[0].header

Out[4]:

SIMPLE  =                    T / Written by IDL:  Sat May 16 21:17:17 2020      
BITPIX  =                   16 / Number of bits per data pixel                  
NAXIS   =                    3 / Number of data axes                            
NAXIS1  =                  472 /                                                
NAXIS2  =                  470 /                                                
NAXIS3  =                 2987 /                                                
EXTEND  =                    T / FITS data may contain extensions               
DATE    = '2020-05-17'         / Creation UTC (CCCC-MM-DD) date of FITS header  
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy  
COMMENT and Astrophysics', volume 376, page 359; bibcode 2001A&A...376..359H    
TELESCOP= '        '           /                                                
INSTRUME= 'AIA_3   '           /                                                
DATA_LEV=              2.00000 /                                                
LVL_NUM =              2.00000 /                                                
VER_RF2 = 'A2I-2018-05-18'     /                                                
DATE_RF2= '2020-05-16T22:32:19.556' /                                           
DATA_SRC=              1.00000 /                                                
ORIGIN  = 'SDO AIA_3 171'      /                                                
BLD_VERS= 'V8R6X   '           /                                                
LUTID   =                    0 /                                                
OBSID   = '20141022_081850_3860261381' /                                        
OBS_DESC= '        '           /                                                
OBSLABEL= '        '           /                                                
OBSTITLE= '        '           /                                                
DATE_OBS= '2014-10-22T08:08:59.340' /                                           
DATE_END= '2014-10-22T18:18:47.340' /                                           
STARTOBS= '2014-10-22T08:18:50.590' /                                           
ENDOBS  = '2014-10-22T18:08:31.246' /                                           
OBSREP  =                    1 /                                                
CAMERA  =                    3 /                                                
STATUS  = '        '           /                                                
BTYPE   = '        '           /                                                
BUNIT   = '        '           /                                                
BSCALE  =                 1.00 /                                                
BZERO   =                    0 /                                                
HLZ     = '        '           /                                                
SAA     = '        '           /                                                
SAT_ROT =              45.0001 /                                                
DSUN_OBS=        148876070843. /                                                
TR_MODE = '        '           /                                                
FOVY    =        382.000011206 /                                                
FOVX    =        383.200011253 /                                                
XCEN    =             -249.189 /                                                
YCEN    =             -302.089 /                                                
SUMSPTRL=                    1 /                                                
SUMSPAT =                    1 /                                                
EXPTIME =        1.85838086065 /                                                
EXPMIN  =       0.234813004732 /                                                
EXPMAX  =        2.00020790100 /                                                
DATAMEAN=              933.197 /                                                
DATARMS =              1056.33 /                                                
DATAMEDN=              593.284 /                                                
DATAMIN =             -1182.16 /                                                
DATAMAX =              18980.8 /                                                
DATAVALS=            662636080 /                                                
MISSVALS=                    0 /                                                
NSATPIX =                    0 /                                                
NSPIKES =                    0 /                                                
TOTVALS =            662636080 /                                                
PERCENTD=              100.000 /                                                
DATASKEW=              3.87836 /                                                
DATAKURT=              30.4687 /                                                
DATAP01 =              54.0981 /                                                
DATAP10 =              149.153 /                                                
DATAP25 =              283.913 /                                                
DATAP75 =              1170.06 /                                                
DATAP90 =              2189.26 /                                                
DATAP95 =              2967.73 /                                                
DATAP98 =              3927.73 /                                                
DATAP99 =              4686.64 /                                                
NEXP    =                 2987 /                                                
MISSRAS =                    0 /                                                
PC1_1   =             0.699094 /                                                
PC1_2   =             0.715059 /                                                
PC2_1   =            -0.715059 /                                                
PC2_2   =             0.699094 /                                                
PC3_1   =              0.00000 /                                                
PC3_2   =              0.00000 /                                                
NWIN    =                    1 /                                                
TDET1   = 'SJI     '           /                                                
TDESC1  = '171_THIN'           /                                                
TWAVE1  =                  171 /                                                
TDMEAN1 =              933.197 /                                                
TDRMS1  =              1056.33 /                                                
TDMEDN1 =              593.284 /                                                
TDMIN1  =             -1182.16 /                                                
TDMAX1  =              18980.8 /                                                
TDVALS1 =            662636080 /                                                
TMISSV1 =                    0 /                                                
TSATPX1 =                    0 /                                                
TSPIKE1 =                    0 /                                                
TTOTV1  =            662636080 /                                                
TPCTD1  =              100.000 /                                                
TDSKEW1 =              3.87836 /                                                
TDKURT1 =              30.4687 /                                                
TDP01_1 =              54.0981 /                                                
TDP10_1 =              149.153 /                                                
TDP25_1 =              283.913 /                                                
TDP75_1 =              1170.06 /                                                
TDP90_1 =              2189.26 /                                                
TDP95_1 =              2967.73 /                                                
TDP98_1 =              3927.73 /                                                
TDP99_1 =              4686.64 /                                                
TSR1    =                    1 /                                                
TER1    =                  470 /                                                
TSC1    =                    1 /                                                
TEC1    =                  472 /                                                
CDELT1  =       0.600000023842 /                                                
CDELT2  =       0.600000023842 /                                                
CDELT3  =        12.2531815137 /                                                
CRPIX1  =              237.000 /                                                
CRPIX2  =              236.000 /                                                
CRPIX3  =              1494.00 /                                                
CRVAL1  =             -249.189 /                                                
CRVAL2  =             -302.089 /                                                
CRVAL3  =        17576.7500000 /                                                
CTYPE1  = 'HPLN-TAN'           /                                                
CTYPE2  = 'HPLT-TAN'           /                                                
CTYPE3  = 'Time    '           /                                                
CUNIT1  = 'arcsecs '           /                                                
CUNIT2  = 'arcsecs '           /                                                
CUNIT3  = 'seconds '           /                                                
KEYWDDOC= 'http:   '           /                                                
HISTORY FITSHEAD2STRUCT run at: Sat Nov  4 05:33:30 2017                        
HISTORY mreadfits_shm VERSION:  1.20                                            
HISTORY read_sdo VERSION:  2.10                                                 
HISTORY read_sdo  xll,xyy,nx,ny: 1192,1192,1192,1192,1192,1192,1192,1192,1192,11
HISTORY read_sdo  Orig FILE: /SUM4/D624152183/S00000/image_lev1.fits            
HISTORY read_sdo  Orig DATE: 2014-10-26T05:09:46                                
HISTORY read_sdo  fovx,fovy: 535.34368,450.21624                                
HISTORY read_sdo  Orig CRPIX1,CRPIX2: 2054.5901,2047.5400                       
HISTORY read_sdo  Orig CDELT1,CDELT2: 0.59948900,0.59948900                     
HISTORY read_sdo  Orig CROTA2: 0.019268000                                      
HISTORY ssw_service_track_fov VERSION:  2.10                                    
HISTORY ssw_service_track_fov  jobid: ssw_service_171103_114718_21895           
HISTORY ssw_service_track_fov  ref_info: @2014/10/22 13:13:40.500               
HISTORY ssw_service_track_fov  xll,xyy,nx,ny: 1192,1159,893,751                 
HISTORY ssw_service_track_fov  fovx,fovy: 535.000,450.000                       
HISTORY ssw_service_track_fov  Orig CRPIX1&2: 2054.5901,2047.5400               
HISTORY ssw_service_track_fov  CFITSIO adjusted                                 
HISTORY FITSHEAD2STRUCT run at: Tue Nov  7 02:09:19 2017                        
HISTORY mreadfits_shm VERSION:  1.20                                            
HISTORY read_sdo VERSION:  2.10                                                 
HISTORY FITSHEAD2STRUCT run at: Sat May 16 20:36:50 2020                        
HISTORY mreadfits_shm VERSION:  1.20                                            
HISTORY read_sdo VERSION:  2.10                                                 
HISTORY IRIS-AIA RF2                                                            

In [5]:

aiadata = aia[0].data
aiahead = aia[0].header

In [6]:

print(aiadata.shape)

(2987, 470, 472)

In [7]:

from astropy.wcs import WCS

In [8]:

wcs  = WCS(aiahead)
print(wcs)

WCS Keywords

Number of WCS axes: 3
CTYPE : 'HPLN-TAN'  'HPLT-TAN'  'Time'  
CRVAL : -0.06921916666666666  -0.0839136111111111  17576.75  
CRPIX : 237.0  236.0  1494.0  
PC1_1 PC1_2 PC1_3  : 0.699094  0.715059  0.0  
PC2_1 PC2_2 PC2_3  : -0.715059  0.699094  0.0  
PC3_1 PC3_2 PC3_3  : 0.0  0.0  1.0  
CDELT : 0.00016666667328944445  0.00016666667328944445  12.2531815137  
NAXIS : 472  470  2987

WARNING: FITSFixedWarning: 'unitfix' made the change 'Changed units:
  'arcsecs' -> 'arcsec',
  'arcsecs' -> 'arcsec',
  'seconds' -> 's'. [astropy.wcs.wcs]

In [9]:

#Plot at first time step.
ind = 50
plt.figure(figsize=(8,8))
plt.subplot(projection = wcs.dropaxis(-1))
plt.imshow(np.log10(aiadata[ind]),cmap='Blues_r')

Out[9]:

<matplotlib.image.AxesImage at 0x7f207e3e09b0>

In [125]:

aia1 = fits.open("aia_l2_20141022_081850_3860261381_171.fits")
aiadata1 = aia1[0].data
wcs1  = WCS(aia1[0].header)

aia2 = fits.open("aia_l2_20141022_081850_3860261381_1700.fits")
aiadata2 = aia2[0].data
wcs2  = WCS(aia2[0].header)

index = -50

tmp_aiadata1 = np.log10(aiadata1[index])
tmp_aiadata2 = np.log10(aiadata2[index])

plt.figure(figsize=(10,10))
plt.imshow(tmp_aiadata2,origin='lower',cmap='Reds_r',alpha=1.0)
plt.imshow(tmp_aiadata1,origin='lower',cmap='Blues_r',alpha=0.7)

Out[125]:

<matplotlib.image.AxesImage at 0x7f20776f8cc0>

In [140]:

def nanptp(x):
    return np.nanmax(x)-np.nanmin(x)

In [157]:

index = -10

aia1 = fits.open("aia_l2_20141022_081850_3860261381_171.fits") # Red
aiadata1 = np.log10(aia1[0].data[index])
aiadata1 = 255*(aiadata1-np.nanmin(aiadata1))/nanptp(aiadata1)

aia2 = fits.open("aia_l2_20141022_081850_3860261381_193.fits") # Green
aiadata2 = np.log10(aia2[0].data[index])
aiadata2 = 255*(aiadata2-np.nanmin(aiadata2))/nanptp(aiadata2)

aia3 = fits.open("aia_l2_20141022_081850_3860261381_131.fits") # Blue
aiadata3 = np.log10(aia3[0].data[index])
aiadata3 = 255*(aiadata3-np.nanmin(aiadata3))/nanptp(aiadata3)

tmp_aiadata = np.asarray([aiadata1,aiadata2,aiadata3]).transpose(1,2,0).astype(int)

plt.figure(figsize=(10,10))
plt.imshow(tmp_aiadata,origin='lower', interpolation='nearest')

Out[157]:

<matplotlib.image.AxesImage at 0x7f2076dd7978>

Fourier transform¶

Fourier transform breaks down a signal into sinusoids of various frequencies. This may be done in 1D or 2D or 3D. We now see a cute example of the effect of FFT on an image

</font>

In [68]:

aia1 = fits.open("aia_l2_20141022_081850_3860261381_171.fits")
aiadata1 = aia1[0].data
wcs1  = WCS(aia1[0].header)

WARNING: FITSFixedWarning: 'unitfix' made the change 'Changed units:
  'arcsecs' -> 'arcsec',
  'arcsecs' -> 'arcsec',
  'seconds' -> 's'. [astropy.wcs.wcs]

In [111]:

index = -50

tmp_aiadata1 = np.log10(aiadata1[index])

plt.figure(figsize=(6,6))
plt.imshow(tmp_aiadata1,origin='lower',cmap='hot')

Out[111]:

<matplotlib.image.AxesImage at 0x7f2077b4b9e8>

In [70]:

tmp_aiadata1_fft = np.fft.fft2(tmp_aiadata1)
tmp_aiadata1_fft_amp,tmp_aiadata1_fft_phase = np.abs(tmp_aiadata1_fft),np.angle(tmp_aiadata1_fft)

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(np.log10(tmp_aiadata1_fft_amp),origin='lower',cmap='hot')
plt.title("Amplitude")
plt.subplot(1,2,2)
plt.imshow(tmp_aiadata1_fft_phase,origin='lower',cmap='hot')
plt.title("Phase")

Out[70]:

Text(0.5, 1.0, 'Phase')

In [106]:

tmp_aiadata1_fft = np.fft.fft2(tmp_aiadata1)
tmp_aiadata1_fft_amp,tmp_aiadata1_fft_phase = np.abs(tmp_aiadata1_fft),np.angle(tmp_aiadata1_fft)

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(np.fft.fftshift(np.log10(tmp_aiadata1_fft_amp)),origin='lower',cmap='hot')
plt.title("Amplitude")
plt.subplot(1,2,2)
plt.imshow(np.fft.fftshift(tmp_aiadata1_fft_phase),origin='lower',cmap='hot')
plt.title("Phase")

Out[106]:

Text(0.5, 1.0, 'Phase')

In [107]:

tmp_aiadata1_ifft = np.abs(np.fft.ifft2(tmp_aiadata1_fft_amp*np.exp(1j*tmp_aiadata1_fft_phase)))

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(tmp_aiadata1_ifft,origin='lower',cmap='hot')
plt.title("Inverse FT")
plt.subplot(1,2,2)
plt.imshow(tmp_aiadata1,origin='lower',cmap='hot')
plt.title("Original")

Out[107]:

Text(0.5, 1.0, 'Original')

Filtering: High and Low pass filters¶

In [95]:

xx,yy = np.meshgrid(np.linspace(-5,5,tmp_aiadata2.shape[0]),np.linspace(-5,5,tmp_aiadata2.shape[1]))
highpassfilter = 1-np.exp(-15*(xx)**2-16*(yy)**2).T

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(highpassfilter,origin='lower',cmap='gray')
plt.title("High pass filter, Fourier space")
plt.subplot(1,2,2)
plt.imshow(np.log10(np.fft.fftshift(tmp_aiadata1_fft_amp)),origin='lower',cmap='hot')
plt.title("AIA data: Fourier amplitude")

Out[95]:

Text(0.5, 1.0, 'Filter in Fourier space')

Question: What does high pass filter give us?¶

https://forms.gle/mrLBofNaSTewQUuM6

In [96]:

highpassfilter = np.fft.fftshift(highpassfilter)
tmp_aiadata1_ifft = np.abs(np.fft.ifft2(highpassfilter*tmp_aiadata1_fft_amp*np.exp(1j*tmp_aiadata1_fft_phase)))

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(tmp_aiadata1_ifft,origin='lower',cmap='hot')
plt.title("Inverse FT high pass filter")
plt.subplot(1,2,2)
plt.imshow(tmp_aiadata1,origin='lower',cmap='hot')
plt.title("Original")

Out[96]:

Text(0.5, 1.0, 'Original')

In [105]:

xx,yy = np.meshgrid(np.linspace(-5,5,tmp_aiadata1.shape[0]),np.linspace(-5,5,tmp_aiadata1.shape[1]))
lowpassfilter = np.exp(-16*(xx)**2-16*(yy)**2).T

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(lowpassfilter,origin='lower',cmap='gray')
plt.title("Low pass filter: Fourier space")
plt.subplot(1,2,2)
plt.imshow(np.log10(np.fft.fftshift(tmp_aiadata1_fft_amp)),origin='lower',cmap='hot')
plt.title("AIA amplitude: Fourier space")

Out[105]:

Text(0.5, 1.0, 'AIA amplitude: Fourier space')

In [104]:

lowpassfilter = np.fft.fftshift(lowpassfilter)
tmp_aiadata1_ifft = np.abs(np.fft.ifft2(lowpassfilter*tmp_aiadata1_fft_amp*np.exp(1j*tmp_aiadata1_fft_phase)))

plt.figure(figsize=(12,6))
plt.subplot(1,2,1)
plt.imshow(tmp_aiadata1_ifft,origin='lower',cmap='hot')
plt.title("Inverse FT low pass filter")
plt.subplot(1,2,2)
plt.imshow(tmp_aiadata1,origin='lower',cmap='hot')
plt.title("Original")

Out[104]:

Text(0.5, 1.0, 'Original')

Visualizing data frames¶

Not all astro data comes in fits format. Sometimes, tabulated data is saved as `csv' or Comma Separated Values. Think of these as Excel sheets with the column names as some variable, and rows representing different observations of these variables.

$\color{#76c893}{Pandas}$ is the go-to library for working with such data. Let's see how this works out.

</font>

First, I have some data downloaded already. Let's get it from Google drive.

In [1]:

!gdown --id 1D7OZ_ibIjl-2clagDXHBgiX_-BxAycmK Data/

Downloading...
From: https://drive.google.com/uc?id=1D7OZ_ibIjl-2clagDXHBgiX_-BxAycmK
To: /content/Skyserver_12_15_2020 3 45 07 AM.csv
82.5MB [00:01, 80.8MB/s]

In [2]:

import pandas as pd

In [4]:

Data = pd.read_csv("Skyserver_12_15_2020 3 45 07 AM.csv",comment="#")

In [5]:

Data.head()

Out[5]:

	objid	ra	dec	u	g	r	i	z	run	rerun	camcol	field	specobjid	class	redshift	plate	mjd	fiberid
0	1237678877245244171	318.951692	9.315146	19.51665	18.50036	17.95667	17.53139	17.32035	7777	301	5	53	819657923239110656	GALAXY	0.114299	728	52520	10
1	1237668332026986542	217.940001	14.608378	19.13548	18.55482	17.95603	17.68272	17.63717	5322	301	3	56	6154252554903769088	QSO	1.802680	5466	56033	304
2	1237664092899115053	129.948221	25.213328	19.54955	18.19434	17.83220	17.51329	17.47054	4335	301	3	130	2173034979993348096	GALAXY	0.070813	1930	53347	175
3	1237654604252119048	160.357788	3.567886	17.72343	16.65830	16.23667	16.07098	16.02797	2126	301	1	275	649647859372681216	STAR	0.000570	577	52367	13
4	1237661360769400880	226.001700	38.619699	16.60500	15.66234	15.39406	15.29443	15.29302	3699	301	2	227	5817649714997514240	STAR	-0.000184	5167	56066	454

In [6]:

Data['ra'].values.shape

Out[6]:

(500000,)

In [10]:

Data.columns

Out[10]:

Index(['objid', 'ra', 'dec', 'u', 'g', 'r', 'i', 'z', 'run', 'rerun', 'camcol',
       'field', 'specobjid', 'class', 'redshift', 'plate', 'mjd', 'fiberid'],
      dtype='object')

In [19]:

Data.hist(column = ["u","g","r","i","z"],figsize=(12,12),bins=30)

Out[19]:

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7ffab0a47c10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffab0a0de90>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x7ffab09c52d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffab097a850>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x7ffab0930dd0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffab08f0390>]],
      dtype=object)

Why is magnitude negative? Let's check

In [20]:

Data['i'].min()

Out[20]:

-9999.0

-9999.0 or any such number represents missing data. Hence, we have two options:

1. Drop rows where the value is this filler value.
2. Interpolate across these values.

</font>

Question: When do we interpolate?¶

https://forms.gle/AfTrZVzmJCu7oh9GA

</font>

I don't like interpolation, so I will drop the rows.

In [29]:

#First, replace with nan
Data = Data.replace(-9999.0,np.nan)
Data.dropna(inplace=True)

In [30]:

Data['i'].min()

Out[30]:

7.652014

In [31]:

Data.hist(column = ["u","g","r","i","z"],figsize=(12,12),bins=30)

Out[31]:

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7ffab05b6290>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffaafb48dd0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x7ffaafaf9f90>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffaafaba650>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x7ffaafa6ec50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ffaafa31210>]],
      dtype=object)

Exercise¶

Make a video with as many frames of this data as you like (there are 2500 or so frames), and as many passbands as you like, and submit. You may use any wavelength and any colormap you like. You will need to add the frame number on the title and keep updating it in the video. As a hint, use the `celluloid' library for making the vide.

!pip install celluloid

In [11]:

from celluloid import Camera

In [13]:

# Write code to load data, take frame and then make video.
# Check the example code here and adapt it: https://github.com/jwkvam/celluloid.
fig = plt.figure(figsize=(8,8))
camera = Camera(fig)
for ind in np.arange(10):
    val = np.log10(aiadata[ind])
    plt.imshow(val,cmap='Blues_r',clim=(np.nanpercentile(np.log10(aiadata),5),np.nanpercentile(np.log10(aiadata),99)),origin='lower')
    camera.snap()    

/home/uvishal/.local/lib/python3.6/site-packages/ipykernel_launcher.py:7: RuntimeWarning: divide by zero encountered in log10
  import sys
/home/uvishal/.local/lib/python3.6/site-packages/ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in log10
  import sys

In [14]:

from IPython.display import HTML
animation = camera.animate()
HTML(animation.to_html5_video())

Out[14]: