import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx
import folium
from IPython.display import HTML

df=pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')

t = Year
x = Latitude
y = Longitude
f = Magnitude

1. 데이터 정의

1980 이상 7시간 반 걸림

_df = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year>="1980"').reset_index().iloc[:,1:]
_df

2. $f(x) = y + \epsilon$ 정의

$y$ = Magnitude, 지진 규모로 정의

f = _df.loc[:,"Magnitude"]

plt.plot(f,'-')

[<matplotlib.lines.Line2D at 0x7f3cac455100>]

plt.plot( _df.Latitude,_df.Longitude,'.')

[<matplotlib.lines.Line2D at 0x7f3ca67d4880>]

fig = plt.figure(figsize=(9, 6))
ax = fig.add_subplot(111, projection='3d')
img = ax.scatter(_df.Latitude, _df.Longitude, _df.Magnitude, c= _df.Magnitude,  cmap=plt.hot())
fig.colorbar(img)
plt.show()

_dfgraph = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year>="1980"').reset_index().iloc[:,1:].reset_index()

fig = plt.figure(figsize=(9,6))
ax = fig.add_subplot(111, projection='3d')
ax.set_zticklabels(_dfgraph.Year)
img = ax.scatter(_dfgraph.Latitude, _dfgraph.Longitude, _dfgraph.index,c= _dfgraph.Magnitude, cmap=plt.hot())
fig.colorbar(img)
plt.show()

/tmp/ipykernel_180670/2573661339.py:3: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_zticklabels(_dfgraph.Year)

lst=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,3]].\
to_numpy().tolist() for i in range(2016-1980)]

from folium import plugins 
data=(np.random.normal(size=(100,3)) + np.array([[28,77,5]])).tolist() # (좌표,weight)를 의미함, 그리고 numpy는 list가 될 수 없기 때문에 tolist 옵션 사용
m=folium.Map([28,77],zoom_start=6,scrollWheelZoom=False)
plugins.HeatMap(data).add_to(m)

<folium.plugins.heat_map.HeatMap at 0x7f3ca67ec220>

m=folium.Map(scrollWheelZoom=False)
plugins.HeatMapWithTime(lst,radius=5,index=list(range(1980,2016))).add_to(m)
m

!pip install basemap

Requirement already satisfied: basemap in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (1.3.2)
Requirement already satisfied: pyshp<2.2,>=1.2 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (2.1.3)
Requirement already satisfied: matplotlib<3.6,>=1.5 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (3.5.1)
Requirement already satisfied: numpy<1.23,>=1.21 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (1.21.2)
Requirement already satisfied: six<1.16,>=1.10 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (1.15.0)
Requirement already satisfied: pyproj<3.4.0,>=1.9.3 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (3.3.0)
Requirement already satisfied: basemap-data<1.4,>=1.3.2 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from basemap) (1.3.2)
Requirement already satisfied: packaging>=20.0 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (21.3)
Requirement already satisfied: pillow>=6.2.0 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (8.4.0)
Requirement already satisfied: pyparsing>=2.2.1 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (3.0.4)
Requirement already satisfied: kiwisolver>=1.0.1 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (1.3.2)
Requirement already satisfied: python-dateutil>=2.7 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (2.8.2)
Requirement already satisfied: cycler>=0.10 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (0.11.0)
Requirement already satisfied: fonttools>=4.22.0 in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from matplotlib<3.6,>=1.5->basemap) (4.28.5)
Requirement already satisfied: certifi in /home/csy/anaconda3/envs/csy/lib/python3.8/site-packages (from pyproj<3.4.0,>=1.9.3->basemap) (2020.6.20)

from mpl_toolkits.basemap import Basemap

---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
/tmp/ipykernel_374698/3341290477.py in <module>
----> 1 from mpl_toolkits.basemap import Basemap

~/anaconda3/envs/csy/lib/python3.8/site-packages/mpl_toolkits/basemap/__init__.py in <module>
     24 
     25 from matplotlib import __version__ as _matplotlib_version
---> 26 from matplotlib.cbook import dedent
     27 # check to make sure matplotlib is not too old.
     28 _matplotlib_version = LooseVersion(_matplotlib_version)

ImportError: cannot import name 'dedent' from 'matplotlib.cbook' (/home/csy/anaconda3/envs/csy/lib/python3.8/site-packages/matplotlib/cbook/__init__.py)

from itertools import chain

def draw_map(m, scale=0.2):
    # draw a shaded-relief image
    m.shadedrelief(scale=scale)
    
    # lats and longs are returned as a dictionary
    lats = m.drawparallels(np.linspace(-90, 90, 13))
    lons = m.drawmeridians(np.linspace(-180, 180, 13))

    # keys contain the plt.Line2D instances
    lat_lines = chain(*(tup[1][0] for tup in lats.items()))
    lon_lines = chain(*(tup[1][0] for tup in lons.items()))
    all_lines = chain(lat_lines, lon_lines)
    
    # cycle through these lines and set the desired style
    for line in all_lines:
        line.set(linestyle='-', alpha=0.3, color='w')

fig = plt.figure(figsize=(8, 6), edgecolor='w')
m = Basemap(projection='moll', resolution=None,
            lat_0=0, lon_0=0)
lon = _df.Longitude
lat = _df.Latitude
x,y = m(lon, lat)
m.plot(x, y, 'r.', markersize=1)
draw_map(m)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
/tmp/ipykernel_374698/1034213983.py in <module>
      1 fig = plt.figure(figsize=(8, 6), edgecolor='w')
----> 2 m = Basemap(projection='moll', resolution=None,
      3             lat_0=0, lon_0=0)
      4 lon = _df.Longitude
      5 lat = _df.Latitude

NameError: name 'Basemap' is not defined

<Figure size 576x432 with 0 Axes>

fig = plt.figure(figsize=(8, 6), edgecolor='w')
m = Basemap(projection='cyl', resolution=None,
            llcrnrlat=-90, urcrnrlat=90,
            llcrnrlon=-180, urcrnrlon=180, )
lon = _df.Longitude
lat = _df.Latitude
x,y = m(lon, lat)
m.plot(x, y, 'r.', markersize=1)
draw_map(m)

3. $(x_i,y_i)$와 $(x_j,y_j)$ 사이의 유클리드 거리 정의

$x$ = Latitude, 위도로 정의
$y$ = Longitude, 경도로 정의
지진의 영향이 주변에만 끼치는 것을 고려하여 경도, 위도의 차이가 90도 이내인 경우만 거리 계산

$$dist((x_i,y_i),(x_j,y_j)) = \sqrt{((x_j-x_i)^2-(y_j-y_i)^2}$$

def dist(i,j):
    if abs( _df.Latitude[j] - _df.Latitude[i] ) > 90: 
        return 10000  
    elif abs( _df.Longitude[j] - _df.Longitude[i] ) > 90: 
        return 10000
    else:
        return np.sqrt( ( ( _df.Latitude[j] - _df.Latitude[i] )**2) + ( ( _df.Longitude[j] - _df.Longitude[i])**2) )

4. 거리를 이용한 $W_{i,j}$ 행렬 정의

a weighted adjacency matrix $W$
동일한 지점 상의 거리는 0이 되어 $W_{i,j}$가 1이 될 것이다(대각행렬은 모두 1)
연결강도로 생각

$$W_{i,j}=\begin{cases}{exp(-\frac{[dist(i,j)]^2}{2\theta^2})} & \quad \text{if } dist(i,j) \leq κ \\ 0 & \quad \text{otherwise} \end{cases}$$

def weight(i,j,theta=150,kappa=1000):
    return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) ) if dist(i,j) <= kappa else 0

6시간 정도 걸림

W = np.array([[weight(i,j) for i in range(len(_df))] for j in range(len(_df))])

W.round(3)

array([[1.   , 0.   , 0.   , ..., 0.   , 0.   , 0.   ],
       [0.   , 1.   , 1.   , ..., 0.975, 0.994, 0.973],
       [0.   , 1.   , 1.   , ..., 0.974, 0.994, 0.973],
       ...,
       [0.   , 0.975, 0.974, ..., 1.   , 0.944, 1.   ],
       [0.   , 0.994, 0.994, ..., 0.944, 1.   , 0.942],
       [0.   , 0.973, 0.973, ..., 1.   , 0.942, 1.   ]])

plt.hist(W.reshape(-1))

(array([1.82473166e+08, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
        0.00000000e+00, 0.00000000e+00, 1.24600000e+03, 2.44446200e+06,
        3.04767400e+07, 1.09144611e+08]),
 array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ]),
 <BarContainer object of 10 artists>)

그래프

nx.draw(nx.Graph(W))

5. $W_{i,j}$ 행렬을 이용한 차수 행렬 정의

$D$ = Degree Matrix

D = np.diag(W.sum(axis=1))

D

array([[ 3578.13338639,     0.        ,     0.        , ...,
            0.        ,     0.        ,     0.        ],
       [    0.        , 10290.14834876,     0.        , ...,
            0.        ,     0.        ,     0.        ],
       [    0.        ,     0.        , 10289.94278233, ...,
            0.        ,     0.        ,     0.        ],
       ...,
       [    0.        ,     0.        ,     0.        , ...,
         9774.22328895,     0.        ,     0.        ],
       [    0.        ,     0.        ,     0.        , ...,
            0.        , 10272.51002303,     0.        ],
       [    0.        ,     0.        ,     0.        , ...,
            0.        ,     0.        ,  9751.63187566]])

6. Graph Laplacian matrix 정의

$L = D - W$

L = D - W

L

array([[ 3.57713339e+03,  0.00000000e+00,  0.00000000e+00, ...,
         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 0.00000000e+00,  1.02891483e+04, -9.99999877e-01, ...,
        -9.74559591e-01, -9.93753342e-01, -9.73285239e-01],
       [ 0.00000000e+00, -9.99999877e-01,  1.02889428e+04, ...,
        -9.74459287e-01, -9.93804320e-01, -9.73181667e-01],
       ...,
       [ 0.00000000e+00, -9.74559591e-01, -9.74459287e-01, ...,
         9.77322329e+03, -9.44181666e-01, -9.99973372e-01],
       [ 0.00000000e+00, -9.93753342e-01, -9.93804320e-01, ...,
        -9.44181666e-01,  1.02715100e+04, -9.42335310e-01],
       [ 0.00000000e+00, -9.73285239e-01, -9.73181667e-01, ...,
        -9.99973372e-01, -9.42335310e-01,  9.75063188e+03]])

7. 고유값 분해

${\bf L} = {\boldsymbol\Psi} {\boldsymbol\Lambda} {\boldsymbol\Psi}^\top$

λ, Ψ = np.linalg.eig(L)

Λ = np.diag(λ)

푸리에

fbar = np.abs(np.fft.fft(f**2))/len(f)
plt.plot(fbar,'.')

[<matplotlib.lines.Line2D at 0x7f3ca64adac0>]

fbar[0]

34.68253024701637

len(f)/2

9007.5

fbar2=np.zeros(10978)
#fbar2[0] = fbar[0] 
fbar2[0] = 0
fbar2[1:10978] = 2*fbar[1:10978]
plt.plot(fbar2,'.')

[<matplotlib.lines.Line2D at 0x7f3ca6358d00>]

fbar2[:10]

array([0.        , 0.0365602 , 0.1231017 , 0.03533143, 0.03085851,
       0.19118625, 0.08708694, 0.02447058, 0.02343862, 0.09155752])

8. p

$compk = f @ np.outer(Ψ[:,k], Ψ[:,k]) $
- $k = 1, 2, 3, 8000$
$p = (sum(comp1^2),sum(comp2^2),…,sum(comp8000^2))$
$p = p/sum(p)$
- 0.2 0.1 ...
—> 5개의 최상의 컴포넌트만 골랐더니 70%

def comp(i):
    return (f @ np.outer( Ψ[:,i], Ψ[:,i]))

def p(i):
    return sum(comp(i)**2)

p(0)

621620.5734246754

array_1 = np.array([p(i) for i in range(1,len(_df))])

varprop = array_1/array_1.sum()

_index = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop}).sort_values('varprop',ascending=False)
_indexlst = _index.iloc[:25,0].tolist()

_indexlst

[15503,
 12429,
 10593,
 1794,
 10157,
 1967,
 1,
 9795,
 13728,
 16675,
 4990,
 11769,
 10636,
 3519,
 6972,
 4694,
 526,
 10592,
 3235,
 6611,
 8934,
 12451,
 7782,
 14016,
 1706]

plt.plot( (f @ np.outer( Ψ[:,0], Ψ[:,0]))**2)
plt.ylim(0,40)

(0.0, 40.0)

fig,ax =plt.subplots(5,5)
k=0
for i in range(5):
    for j in range(5):
        ax[i][j].plot((f @ np.outer(Ψ[:,_indexlst[k]], Ψ[:,_indexlst[k]]))**2)
        # ax[i][j].set_ylim([-2,7])
        ax[i][j].set_title(k)
        k=k+1
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

9. PCA

comp1 = f @ np.outer( Ψ[:,0], Ψ[:,0])

comp2 = f @ np.outer( Ψ[:,_indexlst[0]], Ψ[:,_indexlst[0]])

comp3 = f @ np.outer( Ψ[:,_indexlst[1]], Ψ[:,_indexlst[1]])

comp4 = f @ np.outer( Ψ[:,_indexlst[2]], Ψ[:,_indexlst[2]])

comp5 = f @ np.outer( Ψ[:,_indexlst[3]], Ψ[:,_indexlst[3]])

comp6 = f @ np.outer( Ψ[:,_indexlst[4]], Ψ[:,_indexlst[4]])

_df["comp1"] = comp1

_df["comp2"] = comp2

_df["comp3"] = comp3

_df["comp4"] = comp4

_df["comp5"] = comp5

_df["comp6"] = comp6

_df["compall"] = comp1 + comp2 +comp3 + comp4 + comp5 + comp6

_df["compall2"] = comp2 +comp3 + comp4 + comp5 + comp6

_lst=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,3]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst1=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,5]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst2=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,6]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst3=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,7]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst4=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,8]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst5=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,9]].\
to_numpy().tolist() for i in range(2016-1980)]

__lst6=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,10]].\
to_numpy().tolist() for i in range(2016-1980)]

__lstall=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,11]].\
to_numpy().tolist() for i in range(2016-1980)]

__lstall2=[_df.assign(Year=list(map(lambda x: x.split('/')[-1], _df.Date))).\
groupby('Year').\
pipe(list)[i][1].iloc[:,[1,2,12]].\
to_numpy().tolist() for i in range(2016-1980)]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(1980,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst2,radius=50,index=list(range(1980,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

인도네시아 (2.491 96.280, 2.707 96.045, 0.599 122.350)
필리핀 (6.270 124.029, 6.948 124.025, 15.439 121.711, 6.834 124.006)
셀레베스 해 (5.898 124.424)

_df.sort_values("comp2")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst3,radius=50,index=list(range(1980,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

인도네시아 (1.281 121.799, -2.825 119.727, -0.123 121.654)
인도양 (-9.245 114.185, -9.364 112.874, 0.029 97.604)
셀레베스 해 (1.127 121.775, 5.255 122.168)
필리핀 (16.058 119.838)

_df.sort_values("comp3")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst4,radius=50,index=list(range(1980,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst5,radius=5,index=list(range(2000,2016))).add_to(_m)
_m

남태평양 (53.635 -163.148, 54.511 -161.708, -36.267 -72.956, -36.272 -72.964, -36.405 -73.074, -36.409 -73.030)
칠레 (-36.227 -72.878, -36.422 -72.960)
미국Kenai Peninsula Borough School District, AK, USA (60.113 -152.953)

_df.sort_values("comp4")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst5,radius=50,index=list(range(1980,2016))).add_to(_m)
_m

태즈먼 해(-47.906 165.653, -47.624 165.261) 뉴질랜드 아래
카르키스탄 (40.081 71.410, 40.068 71.542, 39.770 72.007, 42.946 72.764)
랍티브 해 (75.530 122.760) 시베리아
타지키스탄 (39.189 71.857, 39.119 71.836)

_df.sort_values("comp5")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lst6,radius=50,index=list(range(1980,2016))).add_to(_m)
_m

필리핀 (15.096 118.504)
인도네시아 (0.986 120.115, 1.028 120.098, 1.016 120.254, -8.194 112.413, 1.158 120.495)
인도양 (-6.998 104.016, -10.161 110.890)

_df.sort_values("comp6")[-10:-1]

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lstall,radius=5,index=list(range(1980,2016))).add_to(_m)
_m

_m=folium.Map(scrollWheelZoom=False)
#plugins.HeatMapWithTime(_lst,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst1,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst2,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst3,radius=5,index=list(range(2000,2016))).add_to(_m)
#plugins.HeatMapWithTime(__lst4,radius=5,index=list(range(2000,2016))).add_to(_m)
plugins.HeatMapWithTime(__lstall2,radius=50,index=list(range(1980,2016))).add_to(_m)
_m

ref: https://jakevdp.github.io/PythonDataScienceHandbook/04.13-geographic-data-with-basemap.html

fig = plt.figure(figsize=(8, 6), edgecolor='w')
m = Basemap(projection='cyl', resolution=None,
            llcrnrlat=-90, urcrnrlat=90,
            llcrnrlon=-180, urcrnrlon=180, )
lon = _df.Longitude
lat = _df.Latitude
x,y = m(lon, lat)
scale = 100
m.plot(x, y, 'g.', markersize=5, alpha=0.1)
#m.plot(x[np.argsort(λ)[1:10]], y[np.argsort(λ)[1:10]], 'r-', markersize=10)
m.scatter(x[np.argsort(λ)[0]], y[np.argsort(λ)[0]], color='orange', s=abs(f[np.argsort(λ)[0]])*scale)
m.scatter(x[np.argsort(λ)[1:10]], y[np.argsort(λ)[1:10]], color='violet', s=abs(f[np.argsort(λ)[1:10]])*scale)
m.scatter(x[np.argsort(λ)[11:20]], y[np.argsort(λ)[11:20]], color='purple', s=abs(f[np.argsort(λ)[11:20]])*scale)
draw_map(m)

fig = plt.figure(figsize=(8, 6), edgecolor='w')
m = Basemap(projection='cyl', resolution=None,
            llcrnrlat=-90, urcrnrlat=90,
            llcrnrlon=-180, urcrnrlon=180, )
lon = _df.Longitude
lat = _df.Latitude
x,y = m(lon, lat)
scale = 100
m.plot(x, y, 'g.', markersize=5, alpha=0.1)
#m.plot(x[np.argsort(λ)[1:10]], y[np.argsort(λ)[1:10]], 'r-', markersize=10)
m.scatter(x[np.argsort(λ)[0:100]], y[np.argsort(λ)[0:100]], color='orange', s=abs(f_hat[np.argsort(λ)[0:100]])*scale)
m.scatter(x[np.argsort(λ)[101:200]], y[np.argsort(λ)[101:200]], color='violet', s=abs(f_hat[np.argsort(λ)[101:200]])*scale)
m.scatter(x[np.argsort(λ)[201:300]], y[np.argsort(λ)[201:300]], color='purple', s=abs(f_hat[np.argsort(λ)[201:300]])*scale)
draw_map(m)

fig = plt.figure(figsize=(8, 6), edgecolor='w')
m = Basemap(projection='moll', resolution=None,
            lat_0=0, lon_0=0)
lon = _df.Longitude
lat = _df.Latitude
x,y = m(lon, lat)
scale = 100
m.plot(x, y, 'g.', markersize=5, alpha=0.1)
#m.plot(x[np.argsort(λ)[1:10]], y[np.argsort(λ)[1:10]], 'r-', markersize=10)
m.scatter(x[np.argsort(λ)[0]], y[np.argsort(λ)[0]], color='orange', s=abs(f[np.argsort(λ)[0]])*scale)
m.scatter(x[np.argsort(λ)[1:10]], y[np.argsort(λ)[1:10]], color='violet', s=abs(f[np.argsort(λ)[1:10]])*scale)
m.scatter(x[np.argsort(λ)[11:20]], y[np.argsort(λ)[11:20]], color='purple', s=abs(f[np.argsort(λ)[11:20]])*scale)
draw_map(m)

	Date	Latitude	Longitude	Magnitude	Year
0	01/01/1980	38.8150	-27.7800	6.7	1980
1	01/02/1980	5.9840	126.1880	6.0	1980
2	01/02/1980	5.9350	126.1320	5.7	1980
3	01/03/1980	0.0360	67.1750	5.7	1980
4	01/03/1980	5.6880	126.0230	5.8	1980
...	...	...	...	...	...
18010	12/28/2016	38.3917	-118.8941	5.6	2016
18011	12/28/2016	38.3777	-118.8957	5.5	2016
18012	12/28/2016	36.9179	140.4262	5.9	2016
18013	12/29/2016	-9.0283	118.6639	6.3	2016
18014	12/30/2016	37.3973	141.4103	5.5	2016

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5
11190	12/28/2003	0.599	122.350	5.9	2003	5.874157	0.017704	-0.002335	-8.120344e-08	0.000025
5782	10/29/1992	6.834	124.006	6.2	1992	5.874157	0.026856	-0.001837	-9.122568e-08	0.000015
5477	04/28/1992	5.602	124.054	5.9	1992	5.874157	0.027816	-0.001910	-9.144086e-08	0.000017
4182	08/10/1989	5.898	124.424	6.1	1989	5.874157	0.028131	-0.001844	-9.472459e-08	0.000016
1174	05/06/1983	15.439	121.711	5.6	1983	5.874157	0.034066	-0.001331	-7.289800e-08	0.000003
14707	05/31/2010	6.948	124.025	6.0	2010	5.874157	0.036716	-0.001839	-9.122534e-08	0.000015
12267	11/30/2005	6.270	124.029	6.4	2005	5.874157	0.042883	-0.001887	-9.132453e-08	0.000016
15969	07/25/2012	2.707	96.045	6.4	2012	5.874157	0.047767	-0.001210	3.951160e-07	0.000037
15024	01/15/2011	2.491	96.280	5.7	2011	5.874157	0.081307	-0.001191	3.940426e-07	0.000037

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5
1264	07/17/1983	-0.123	121.654	5.5	1983	5.874157	-0.000610	0.036657	-7.440705e-08	0.000026
8901	03/05/1999	5.255	122.168	5.9	1999	5.874157	-0.000593	0.041061	-7.742313e-08	0.000018
13365	11/27/2007	16.058	119.838	5.9	2007	5.874157	-0.000390	0.042386	-6.141290e-08	0.000003
13860	11/16/2008	1.127	121.775	5.5	2008	5.874157	-0.000622	0.049155	-7.510590e-08	0.000024
2608	05/27/1986	-2.825	119.727	5.5	1986	5.874157	-0.000624	0.049492	-6.410852e-08	0.000031
12154	09/06/2005	0.029	97.604	5.6	2005	5.874157	-0.000592	0.062296	3.861851e-07	0.000039
3558	04/04/1988	-9.364	112.874	5.9	1988	5.874157	-0.000463	0.082414	2.273487e-08	0.000040
2094	04/13/1985	-9.245	114.185	5.9	1985	5.874157	-0.000479	0.122212	3.519875e-09	0.000040
12517	06/16/2006	1.281	121.799	5.6	2006	5.874157	-0.000642	0.141106	-7.523098e-08	0.000024

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5
15053	02/11/2011	-36.422	-72.960	6.9	2011	5.874157	-3.545413e-08	5.613215e-07	0.002668	1.436927e-06
15738	01/23/2012	-36.409	-73.030	6.1	2012	5.874157	-3.543298e-08	5.611292e-07	0.002733	1.436569e-06
14617	03/16/2010	-36.405	-73.074	5.9	2010	5.874157	-3.541846e-08	5.609985e-07	0.002761	1.436318e-06
6968	03/23/1995	-36.272	-72.964	5.5	1995	5.874157	-3.549687e-08	5.616619e-07	0.003235	1.437796e-06
6966	03/22/1995	-36.267	-72.956	5.5	1995	5.874157	-3.550120e-08	5.616991e-07	0.003254	1.437875e-06
7864	10/17/1996	60.113	-152.953	5.5	1996	5.874157	-1.331768e-08	-1.849718e-08	0.003773	-3.327150e-08
14636	04/02/2010	-36.227	-72.878	6.0	2010	5.874157	-3.534464e-08	5.613700e-07	0.004794	1.435320e-06
13276	10/02/2007	54.511	-161.708	6.3	2007	5.874157	-3.054198e-08	1.003346e-07	0.013946	2.561608e-07
8755	10/17/1998	53.635	-163.148	5.5	1998	5.874157	-3.295018e-08	1.206336e-07	0.013970	3.381446e-07

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5
10874	05/22/2003	42.946	72.764	5.5	2003	5.874157	-4.867238e-07	0.000020	-1.188247e-09	0.023525
12542	07/06/2006	39.119	71.836	5.8	2006	5.874157	-4.994410e-07	0.000021	-2.414147e-08	0.024013
11635	11/17/2004	39.189	71.857	5.8	2004	5.874157	-5.077115e-07	0.000021	-1.712401e-08	0.024357
10554	09/05/2002	39.770	72.007	5.5	2002	5.874157	-5.064030e-07	0.000021	-1.294895e-08	0.024883
4497	03/24/1990	-47.624	165.261	5.5	1990	5.874157	-4.617791e-06	0.000032	-2.734283e-07	0.026724
1214	06/10/1983	75.530	122.760	5.6	1983	5.874157	-3.576784e-06	0.000028	-3.603062e-08	0.041963
786	05/06/1982	40.068	71.542	5.6	1982	5.874157	-5.223084e-07	0.000021	-2.435318e-08	0.048411
15494	07/19/2011	40.081	71.410	6.1	2011	5.874157	-5.353855e-07	0.000021	-1.756360e-08	0.076119
4485	03/13/1990	-47.906	165.653	5.5	1990	5.874157	-4.652431e-06	0.000032	-2.748547e-07	0.168473

	Date	Latitude	Longitude	Magnitude	Year	comp1	comp2	comp3	comp4	comp5	comp6
10880	05/26/2003	1.158	120.495	5.5	2003	5.874157	-0.000265	0.001792	-6.669462e-08	0.000024	0.099456
13102	06/26/2007	-10.492	108.149	6.0	2007	5.874157	-0.000195	0.000994	2.006147e-07	0.000042	0.100627
1147	04/16/1983	-10.161	110.890	5.7	1983	5.874157	-0.000190	0.001127	9.562641e-08	0.000041	0.110521
8728	09/28/1998	-8.194	112.413	6.6	1998	5.874157	-0.000209	0.001363	3.146269e-08	0.000040	0.111002
7709	07/16/1996	1.016	120.254	6.6	1996	5.874157	-0.000268	0.001827	-6.583256e-08	0.000025	0.146105
10524	08/13/2002	-6.998	104.016	5.8	2002	5.874157	-0.000228	0.001026	3.090438e-07	0.000042	0.193822
7803	09/10/1996	1.028	120.098	5.8	1996	5.874157	-0.000269	0.001840	-6.513500e-08	0.000025	0.227989
7481	02/06/1996	0.986	120.115	5.7	1996	5.874157	-0.000269	0.001841	-6.515779e-08	0.000025	0.240644
10614	10/12/2002	15.096	118.504	6.1	2002	5.874157	-0.000171	0.000949	-5.372691e-08	0.000005	0.265117