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
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

18015 rows × 5 columns

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
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!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
Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>
_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)
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Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>

  • 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]
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

_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)
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Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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  • 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]
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

_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
Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>

  • 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]
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

_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)
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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>

  • 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]
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

_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)
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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>

  • 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]
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

_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)
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Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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_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
Make this Notebook Trusted to load map: File -> Trust Notebook<iframe src="about:blank" style="position:absolute;width:100%;height:100%;left:0;top:0;border:none !important;" 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onload="this.contentDocument.open();this.contentDocument.write( decodeURIComponent(this.getAttribute('data-html')));this.contentDocument.close();" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe>

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)