DV 4주차(1)

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

산점도 응용예제4 (무상관과 독립)

예시자료

- 예시1

x1 = np.random.uniform(low=0, high=1, size=10000)  # 0~1사이의 10000개
y1 = np.random.uniform(low=0, high=1, size=10000) 

plt.plot(x1,y1,',')
plt.plot(x1[0], y1[0],'or')

- 예시2 (원)

_r2 = x1**2 + y1**2 # 반지름
_r2

array([0.32841936, 0.65211343, 0.8620744 , ..., 0.99310561, 0.35628571,
       0.32995271])

len(_r2)

10000

x2=x1[_r2<1]
y2=y1[_r2<1]

plt.plot(x2,y2,',')

- 예시3 (이변량정규분포)

x3 = np.random.randn(10000)
y3 = np.random.randn(10000)

plt.plot(x3,y3,',')

상관계수

예시1, 예시2, 예시3의 산점도를 보고 상관계수가 얼마인지 예상해보라. 실제 계산결과와 확인하라.

np.corrcoef([x1,y1])

array([[1.        , 0.01268214],
       [0.01268214, 1.        ]])

np.corrcoef([x2,y2])

array([[ 1.        , -0.28666195],
       [-0.28666195,  1.        ]])

np.corrcoef([x3,y3])

array([[1.        , 0.00827362],
       [0.00827362, 1.        ]])

독립을 따져보자.

fig, ax = plt.subplots(1,2,figsize=(8,4))
ax[0].plot(x1,y1,',')
ax[1].plot(x2,y2,',')

def g(intval, data, ax, col = 'r'):
    a,b = intval
    x,y = data
    idx = (a<x) & (x<b)
    ax.plot(x[idx], y[idx],',',color=col)

fig

g([-0.1,0.1],[x1,y1],ax[0])
g([-0.1,0.1],[x2,y2],ax[1])
fig

g([0.79,0.99],[x1,y1],ax[0],col='m')
g([0.79,0.99],[x2,y2],ax[1],col='m')
fig

- 예시3

plt.plot(x3,y3,',')

fig, ax = plt.subplots()
ax.plot(x3,y3,',',color='gray')     # g함수 사용하기 위해 이렇게 해보자

g([-2.5,-1.5],[x3,y3],ax,col='r')
fig

g([-2.5,-1.5],[x3,y3],ax,col='r')
g([-0.5,+0.5],[x3,y3],ax,col='b')
g([+1.5,+2.5],[x3,y3],ax,col='g')
fig

idx = (-0.5<x3) & (x3<0.5)
plt.hist(y3[idx])  # 위의 파란색을 뽑아보자

(array([   5.,   32.,  188.,  512.,  938., 1054.,  722.,  303.,   79.,
          16.]),
 array([-3.81904376, -3.09056613, -2.36208849, -1.63361085, -0.90513321,
        -0.17665557,  0.55182207,  1.28029971,  2.00877735,  2.73725499,
         3.46573263]),
 <BarContainer object of 10 artists>)

idx = (-0.5<x3) & (x3<0.5)
plt.hist(y3[idx]);  # 맨 뒤 세미콜론 붙이면 위의 글씨 안나옴

def h(intval, data, ax, col):
    a,b = intval
    x,y = data
    idx = (a<x) &  (x<b)
    ax.hist(y[idx], color=col)

fig,ax = plt.subplots(5,2,figsize=(8,16))
ax[0,0].plot(x3,y3,',',color='gray'); g([-2.5,-1.5],[x3,y3],ax[0,0],col='r')
ax[1,0].plot(x3,y3,',',color='gray'); g([-1.5,-0.5],[x3,y3],ax[1,0],col='g')
ax[2,0].plot(x3,y3,',',color='gray'); g([-0.5,+0.5],[x3,y3],ax[2,0],col='b')
ax[3,0].plot(x3,y3,',',color='gray'); g([+0.5,+1.5],[x3,y3],ax[3,0],col='m')
ax[4,0].plot(x3,y3,',',color='gray'); g([+1.5,+2.5],[x3,y3],ax[4,0],col='lime')

h([-2.5,-1.5],[x3,y3],ax[0,1],col='r')
h([-1.5,-0.5],[x3,y3],ax[1,1],col='g')
h([-0.5,+0.5],[x3,y3],ax[2,1],col='b')
h([+0.5,+1.5],[x3,y3],ax[3,1],col='m')
h([+1.5,+2.5],[x3,y3],ax[4,1],col='lime')

mpl에 대한 미세먼지 팁(1)

!git add .
!git commit -m .
!git push

[main d563e82] .
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 create mode 100644 posts/Data Visualization/.ipynb_checkpoints/DV_4(0926)-checkpoint.ipynb
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 create mode 100644 posts/Data Visualization/DV_2(0914).ipynb
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Total 14 (delta 4), reused 0 (delta 0)
remote: Resolving deltas: 100% (4/4), completed with 2 local objects.
To https://github.com/boram-coco/coco.git
   f1df7bb..d563e82  main -> main

그림만 보고 싶을때

plt.plot([0,1,2,3],[2,3,4,1])

plt.plot([2,3,4,1])    # [0,1,2,3] 이 기본 default 값이므로 생략 가능

plt.plot([2,3,4,1]);   # 그림 위에 올라가는거 없어짐

marker size, line width

plt.plot([2,3,4,1],'o',markersize=13)   # markersize = ms 라고 써도 됨

plt.plot([2,3,4,1],'--',lw=12)

label, legend

plt.plot([2,3,4,1],'--o', label='A')
plt.plot([4,3.2,1,3],'--o', label='B')
plt.legend()  # 범례.. 위의 label

<matplotlib.legend.Legend at 0x7fbc8767d050>

색깔조정 (C0, C1,…)

plt.plot([2,3,4,1],'--o', label='A', color='C1')
plt.plot([4,3.2,1,3],'--o', label='B', color='C0')  # 그래프 위아래의 선 색 변경시 color='C0'
plt.legend() 

<matplotlib.legend.Legend at 0x7fbc86d99750>

title

- 방법1

plt.plot([1,2,3,2])
plt.title('title')

Text(0.5, 1.0, 'title')

- 방법2

fig, ax = plt.subplots()
ax.set_title('asdf')

Text(0.5, 1.0, 'asdf')

suptitle

fig, ax = plt.subplots(2,2)
ax[0,0].plot([1,2,3,2],'--o',label='A',color='C0')
ax[0,0].set_title('(a)')
ax[0,1].plot([3,2.1,1,3],'--o',label='B',color='C1')
ax[0,1].set_title('(b)')
ax[1,0].plot([-3,-2.1,-1,-3],'--o',label='B',color='C2')
ax[1,0].set_title('(c)')
ax[1,1].plot([3,-2.1,1,-3],'--o',label='B',color='C3')
ax[1,1].set_title('(d)')
#plt.suptitle('suptitle') 둘다된다
fig.suptitle('suptitle')

Text(0.5, 0.98, 'suptitle')

tight_layout()

fig, ax = plt.subplots(2,2)
ax[0,0].plot([1,2,3,2],'--o',label='A',color='C0')
ax[0,0].set_title('(a)')
ax[0,1].plot([3,2.1,1,3],'--o',label='B',color='C1')
ax[0,1].set_title('(b)')
ax[1,0].plot([-3,-2.1,-1,-3],'--o',label='B',color='C2')
ax[1,0].set_title('(c)')
ax[1,1].plot([3,-2.1,1,-3],'--o',label='B',color='C3')
ax[1,1].set_title('(d)')
fig.suptitle('suptitle')
fig.tight_layout()   # 컴퓨터에서 알아서 이쁘게 레이아웃 설정

fig, ax, plt 소속

예시

fig, ax = plt.subplots()
ax.plot([1,2,3,1])

- fig에는 있고 ax에는 없는 것

add_axes, tight_layout, suptitle, …

set(dir(fig)) - set(dir(ax))    # fig에만 있는 함수

{'_add_axes_internal',
 '_align_label_groups',
 '_axobservers',
 '_axstack',
 '_button_pick_id',
 '_cachedRenderer',
 '_canvas_callbacks',
 '_constrained',
 '_constrained_layout_pads',
 '_dpi',
 '_get_dpi',
 '_get_draw_artists',
 '_gridspecs',
 '_localaxes',
 '_normalize_grid_string',
 '_original_dpi',
 '_process_projection_requirements',
 '_repr_html_',
 '_scroll_pick_id',
 '_set_dpi',
 '_suplabels',
 '_suptitle',
 '_supxlabel',
 '_supylabel',
 '_tight_parameters',
 'add_axes',
 'add_axobserver',
 'add_gridspec',
 'add_subfigure',
 'add_subplot',
 'align_labels',
 'align_xlabels',
 'align_ylabels',
 'autofmt_xdate',
 'bbox_inches',
 'canvas',
 'clf',
 'colorbar',
 'delaxes',
 'dpi',
 'dpi_scale_trans',
 'draw_without_rendering',
 'execute_constrained_layout',
 'figbbox',
 'figimage',
 'frameon',
 'gca',
 'get_axes',
 'get_constrained_layout',
 'get_constrained_layout_pads',
 'get_dpi',
 'get_edgecolor',
 'get_figheight',
 'get_figwidth',
 'get_frameon',
 'get_linewidth',
 'get_size_inches',
 'get_tight_layout',
 'ginput',
 'legends',
 'number',
 'savefig',
 'sca',
 'set_canvas',
 'set_constrained_layout',
 'set_constrained_layout_pads',
 'set_dpi',
 'set_edgecolor',
 'set_figheight',
 'set_figwidth',
 'set_frameon',
 'set_linewidth',
 'set_size_inches',
 'set_tight_layout',
 'show',
 'subfigs',
 'subfigures',
 'subplot_mosaic',
 'subplotpars',
 'subplots',
 'subplots_adjust',
 'suppressComposite',
 'suptitle',
 'supxlabel',
 'supylabel',
 'tight_layout',
 'transFigure',
 'transSubfigure',
 'waitforbuttonpress'}

- ax에는 있고 fig에는 없는 것

boxplot, hist, plot, set_title, …

set(dir(ax)) - set(dir(fig))   # ax만 있는 함수

{'ArtistList',
 '_add_text',
 '_adjustable',
 '_alias_map',
 '_anchor',
 '_aspect',
 '_autoscaleXon',
 '_autoscaleYon',
 '_autotitlepos',
 '_axes',
 '_axes_class',
 '_axes_locator',
 '_axis_names',
 '_axisbelow',
 '_box_aspect',
 '_check_no_units',
 '_children',
 '_colorbars',
 '_convert_dx',
 '_current_image',
 '_deprecate_noninstance',
 '_facecolor',
 '_fill_between_x_or_y',
 '_frameon',
 '_gen_axes_patch',
 '_gen_axes_spines',
 '_get_axis_list',
 '_get_axis_map',
 '_get_lines',
 '_get_pan_points',
 '_get_patches_for_fill',
 '_get_view',
 '_gridOn',
 '_init_axis',
 '_label_outer_xaxis',
 '_label_outer_yaxis',
 '_left_title',
 '_make_twin_axes',
 '_mouseover_set',
 '_navigate',
 '_navigate_mode',
 '_originalPosition',
 '_parse_scatter_color_args',
 '_pcolor_grid_deprecation_helper',
 '_pcolorargs',
 '_position',
 '_prepare_view_from_bbox',
 '_process_unit_info',
 '_projection_init',
 '_quiver_units',
 '_rasterization_zorder',
 '_remove_legend',
 '_request_autoscale_view',
 '_right_title',
 '_sci',
 '_set_lim_and_transforms',
 '_set_position',
 '_set_title_offset_trans',
 '_set_view',
 '_set_view_from_bbox',
 '_shared_axes',
 '_sharex',
 '_sharey',
 '_stale_viewlims',
 '_subplotspec',
 '_twinned_axes',
 '_unit_change_handler',
 '_unstale_viewLim',
 '_update_image_limits',
 '_update_line_limits',
 '_update_patch_limits',
 '_update_title_position',
 '_update_transScale',
 '_use_sticky_edges',
 '_validate_converted_limits',
 '_viewLim',
 '_xaxis_transform',
 '_xmargin',
 '_yaxis_transform',
 '_ymargin',
 'acorr',
 'add_child_axes',
 'add_collection',
 'add_container',
 'add_image',
 'add_line',
 'add_patch',
 'add_table',
 'angle_spectrum',
 'annotate',
 'apply_aspect',
 'arrow',
 'autoscale',
 'autoscale_view',
 'axhline',
 'axhspan',
 'axis',
 'axison',
 'axline',
 'axvline',
 'axvspan',
 'bar',
 'bar_label',
 'barbs',
 'barh',
 'boxplot',
 'broken_barh',
 'bxp',
 'can_pan',
 'can_zoom',
 'change_geometry',
 'child_axes',
 'cla',
 'clabel',
 'cohere',
 'collections',
 'containers',
 'contains_point',
 'contour',
 'contourf',
 'csd',
 'dataLim',
 'drag_pan',
 'end_pan',
 'errorbar',
 'eventplot',
 'figbox',
 'fill',
 'fill_between',
 'fill_betweenx',
 'fmt_xdata',
 'fmt_ydata',
 'format_coord',
 'format_xdata',
 'format_ydata',
 'get_adjustable',
 'get_anchor',
 'get_aspect',
 'get_autoscale_on',
 'get_autoscalex_on',
 'get_autoscaley_on',
 'get_axes_locator',
 'get_axisbelow',
 'get_box_aspect',
 'get_data_ratio',
 'get_fc',
 'get_frame_on',
 'get_geometry',
 'get_gridspec',
 'get_images',
 'get_legend',
 'get_legend_handles_labels',
 'get_lines',
 'get_navigate',
 'get_navigate_mode',
 'get_position',
 'get_rasterization_zorder',
 'get_renderer_cache',
 'get_shared_x_axes',
 'get_shared_y_axes',
 'get_subplotspec',
 'get_title',
 'get_xaxis',
 'get_xaxis_text1_transform',
 'get_xaxis_text2_transform',
 'get_xaxis_transform',
 'get_xbound',
 'get_xgridlines',
 'get_xlabel',
 'get_xlim',
 'get_xmajorticklabels',
 'get_xminorticklabels',
 'get_xscale',
 'get_xticklabels',
 'get_xticklines',
 'get_xticks',
 'get_yaxis',
 'get_yaxis_text1_transform',
 'get_yaxis_text2_transform',
 'get_yaxis_transform',
 'get_ybound',
 'get_ygridlines',
 'get_ylabel',
 'get_ylim',
 'get_ymajorticklabels',
 'get_yminorticklabels',
 'get_yscale',
 'get_yticklabels',
 'get_yticklines',
 'get_yticks',
 'grid',
 'has_data',
 'hexbin',
 'hist',
 'hist2d',
 'hlines',
 'ignore_existing_data_limits',
 'imshow',
 'in_axes',
 'indicate_inset',
 'indicate_inset_zoom',
 'inset_axes',
 'invert_xaxis',
 'invert_yaxis',
 'is_first_col',
 'is_first_row',
 'is_last_col',
 'is_last_row',
 'label_outer',
 'legend_',
 'locator_params',
 'loglog',
 'magnitude_spectrum',
 'margins',
 'matshow',
 'minorticks_off',
 'minorticks_on',
 'name',
 'numCols',
 'numRows',
 'pcolor',
 'pcolorfast',
 'pcolormesh',
 'phase_spectrum',
 'pie',
 'plot',
 'plot_date',
 'psd',
 'quiver',
 'quiverkey',
 'redraw_in_frame',
 'relim',
 'reset_position',
 'scatter',
 'secondary_xaxis',
 'secondary_yaxis',
 'semilogx',
 'semilogy',
 'set_adjustable',
 'set_anchor',
 'set_aspect',
 'set_autoscale_on',
 'set_autoscalex_on',
 'set_autoscaley_on',
 'set_axes_locator',
 'set_axis_off',
 'set_axis_on',
 'set_axisbelow',
 'set_box_aspect',
 'set_fc',
 'set_frame_on',
 'set_navigate',
 'set_navigate_mode',
 'set_position',
 'set_prop_cycle',
 'set_rasterization_zorder',
 'set_subplotspec',
 'set_title',
 'set_xbound',
 'set_xlabel',
 'set_xlim',
 'set_xmargin',
 'set_xscale',
 'set_xticklabels',
 'set_xticks',
 'set_ybound',
 'set_ylabel',
 'set_ylim',
 'set_ymargin',
 'set_yscale',
 'set_yticklabels',
 'set_yticks',
 'sharex',
 'sharey',
 'specgram',
 'spines',
 'spy',
 'stackplot',
 'stairs',
 'start_pan',
 'stem',
 'step',
 'streamplot',
 'table',
 'tables',
 'tick_params',
 'ticklabel_format',
 'title',
 'titleOffsetTrans',
 'transAxes',
 'transData',
 'transLimits',
 'transScale',
 'tricontour',
 'tricontourf',
 'tripcolor',
 'triplot',
 'twinx',
 'twiny',
 'update_datalim',
 'update_params',
 'use_sticky_edges',
 'viewLim',
 'violin',
 'violinplot',
 'vlines',
 'xaxis',
 'xaxis_date',
 'xaxis_inverted',
 'xcorr',
 'yaxis',
 'yaxis_date',
 'yaxis_inverted'}

set(dir(ax)) & set(dir(fig))   # 교집합

{'_PROPERTIES_EXCLUDED_FROM_SET',
 '__class__',
 '__delattr__',
 '__dict__',
 '__dir__',
 '__doc__',
 '__eq__',
 '__format__',
 '__ge__',
 '__getattribute__',
 '__getstate__',
 '__gt__',
 '__hash__',
 '__init__',
 '__init_subclass__',
 '__le__',
 '__lt__',
 '__module__',
 '__ne__',
 '__new__',
 '__reduce__',
 '__reduce_ex__',
 '__repr__',
 '__setattr__',
 '__setstate__',
 '__sizeof__',
 '__str__',
 '__subclasshook__',
 '__weakref__',
 '_agg_filter',
 '_alpha',
 '_animated',
 '_callbacks',
 '_clipon',
 '_clippath',
 '_cm_set',
 '_default_contains',
 '_gci',
 '_get_clipping_extent_bbox',
 '_gid',
 '_in_layout',
 '_label',
 '_mouseover',
 '_path_effects',
 '_picker',
 '_rasterized',
 '_remove_method',
 '_set_alpha_for_array',
 '_set_artist_props',
 '_set_gc_clip',
 '_sketch',
 '_snap',
 '_stale',
 '_sticky_edges',
 '_tight',
 '_transform',
 '_transformSet',
 '_update_set_signature_and_docstring',
 '_url',
 '_visible',
 'add_artist',
 'add_callback',
 'artists',
 'axes',
 'bbox',
 'callbacks',
 'clear',
 'clipbox',
 'contains',
 'convert_xunits',
 'convert_yunits',
 'draw',
 'draw_artist',
 'figure',
 'findobj',
 'format_cursor_data',
 'get_agg_filter',
 'get_alpha',
 'get_animated',
 'get_children',
 'get_clip_box',
 'get_clip_on',
 'get_clip_path',
 'get_cursor_data',
 'get_default_bbox_extra_artists',
 'get_facecolor',
 'get_figure',
 'get_gid',
 'get_in_layout',
 'get_label',
 'get_path_effects',
 'get_picker',
 'get_rasterized',
 'get_sketch_params',
 'get_snap',
 'get_tightbbox',
 'get_transform',
 'get_transformed_clip_path_and_affine',
 'get_url',
 'get_visible',
 'get_window_extent',
 'get_zorder',
 'have_units',
 'images',
 'is_transform_set',
 'legend',
 'lines',
 'mouseover',
 'patch',
 'patches',
 'pchanged',
 'pick',
 'pickable',
 'properties',
 'remove',
 'remove_callback',
 'set',
 'set_agg_filter',
 'set_alpha',
 'set_animated',
 'set_clip_box',
 'set_clip_on',
 'set_clip_path',
 'set_facecolor',
 'set_figure',
 'set_gid',
 'set_in_layout',
 'set_label',
 'set_path_effects',
 'set_picker',
 'set_rasterized',
 'set_sketch_params',
 'set_snap',
 'set_transform',
 'set_url',
 'set_visible',
 'set_zorder',
 'stale',
 'stale_callback',
 'sticky_edges',
 'text',
 'texts',
 'update',
 'update_from',
 'zorder'}

- plt는 대부분 다 있음. (의미상 명확한건 대충 알아서 fig, ax에 접근해서 처리해준다)

• plt.tight_layout, plt.suptitle, plt.boxplot, plt.hist, plot.plot
• plt.set_title 은 없지만 plt.title 은 있음
• plt.add_axes 는 없음..

set(dir(plt)) & {'add_axes'}

set()

x축, y축 label 설정

fig,ax = plt.subplots()
ax.plot([1,2,3,2])
#ax.set_xlabel('x',size=36, style='italic')
_dct = {'size':36, 'family':'serif', 'style':'italic'}  #family:글꼴
ax.set_xlabel('x',_dct)  #옵션을 딕셔너리 형태로 해서 이렇게 표현도 가능

Text(0.5, 0, 'x')

ax.xaxis.set_label_text('xlabel',size=16,family='serif',weight=1000,style='italic')
#_fontsettings={'size':16,'family':'serif','weight'=1000,'style':'italic'}
#ax.xaxis.set_label_text('xlabel',_fontsettings)
fig

# weight 굵음
# xaxis 도 가능.. (x축)

폰트ref : https://matplotlib.org/stable/api/font_manager_api.html#matplotlib.font_manager.FontProperties

• size:

• fontweight: 0~1000

• family: ‘serif’, ‘sans-serif’, ‘monospace’

• style: ‘normal’, ‘italic’

ax.set_xlabel??

Signature: ax.set_xlabel(xlabel, fontdict=None, labelpad=None, *, loc=None, **kwargs)
Source:   
    def set_xlabel(self, xlabel, fontdict=None, labelpad=None, *,
                   loc=None, **kwargs):
        """
        Set the label for the x-axis.
        Parameters
        ----------
        xlabel : str
            The label text.
        labelpad : float, default: :rc:`axes.labelpad`
            Spacing in points from the Axes bounding box including ticks
            and tick labels.  If None, the previous value is left as is.
        loc : {'left', 'center', 'right'}, default: :rc:`xaxis.labellocation`
            The label position. This is a high-level alternative for passing
            parameters *x* and *horizontalalignment*.
        Other Parameters
        ----------------
        **kwargs : `.Text` properties
            `.Text` properties control the appearance of the label.
        See Also
        --------
        text : Documents the properties supported by `.Text`.
        """
        if labelpad is not None:
            self.xaxis.labelpad = labelpad
        protected_kw = ['x', 'horizontalalignment', 'ha']
        if {*kwargs} & {*protected_kw}:
            if loc is not None:
                raise TypeError(f"Specifying 'loc' is disallowed when any of "
                                f"its corresponding low level keyword "
                                f"arguments ({protected_kw}) are also "
                                f"supplied")
        else:
            loc = (loc if loc is not None
                   else mpl.rcParams['xaxis.labellocation'])
            _api.check_in_list(('left', 'center', 'right'), loc=loc)
            if loc == 'left':
                kwargs.update(x=0, horizontalalignment='left')
            elif loc == 'center':
                kwargs.update(x=0.5, horizontalalignment='center')
            elif loc == 'right':
                kwargs.update(x=1, horizontalalignment='right')
        return self.xaxis.set_label_text(xlabel, fontdict, **kwargs)
File:      ~/anaconda3/envs/py37/lib/python3.7/site-packages/matplotlib/axes/_base.py
Type:      method

숙제

아래와 같이 표준정규분포에서 100개의 난수를 생성하여 \(\boldsymbol{\epsilon}=(\epsilon_1,\epsilon_2,\dots,\epsilon_{100})\) 와 같은 벡터를 만들었다고 하자.

np.random.seed(43052)
ϵ = np.random.randn(100)

아래는 \((t,\epsilon_t)\)를 그린 그림이다. (단 \(t=1,2,\dots,100\))

plt.plot(np.arange(1,101),ϵ,'--o') 

(1) \(\epsilon_t\) 와 \(\epsilon_{t-1}\)은 독립이라고 보여지는가?

(2) 아래의 수식을 만족하는 벡터 \({\boldsymbol y} = (y_1,y_2,\dots, y_{100})\) 을 생성하라. (단 \(y_1=\epsilon_1\))

\[ y_t = y_{t-1} + \epsilon_t\]

(3) \((t,y_t)\)의 dot-connected plot을 그려라.

(4) \(y_t\)와 \(y_{t-1}\)은 독립이라고 볼 수 있는가?