plotyy(spline函数的原理)

plotyy，spline函数的原理？

spline是样条曲线数据插值函数，用法：yy = spline(x,Y,xx)，x和Y是原矢量，xx是要求各点位置矢量，yy是生成的新值。画图可用：plot(xx,yy)

plotyy(spline函数的原理)

该命令用三次样条插值计算出由向量x 与y 确定的一元函数y=f(x)在点xx 处的值。若参量y 是一矩阵，则以y 的每一列和x 配对，再分别计算由它们确定的函数在点xx 处的值。则yy 是一阶数为length(xx)*size(y,2)的矩阵。

plotyy画散点图？

帮你摸索了一下，简单来说就是，先得到句柄，再做相应的修改举个例子你就能看明白了figurex=0:0.1:20;y1=200*exp(-0.05*x).*sin(x);y2=0.8*exp(-0.5*x).*sin(10*x);[AX,H1,H2]=plotyy(x,y1,x,y2,'plot');set(H2,'Marker','^')set(H1,'Marker','o')同理可以修改线型，颜色，等等。我的摸索源自matlab的帮助文件。记住：学习matlab，帮助文件永远是最好的参考书！

matlab怎么设置双Y轴的刻度？

[AX, H1, H2] = plotyy(x,y1,x,y2,'plot','plot');

set(AX(1),'Ylim',[2,6]) %设置左侧y轴的显示范围

set(AX(2),'Ylim',[2,6])

set(AX(1),'yTick',[2:1:6])%设置左侧y轴刻度

set(AX(2),'yTick',[2:1:6])

Python如何实现数据动态化？

Python有些出色的数据可视化库，但很少能渲染GIF或视频动画。本文介绍如何运用MoviePy作为其他库的通用动画插件。

有了 MoviePy ，你可以用一个函数 make_frame(t) 自定义动画，并返回相应的时间t的视频帧（秒）：

Python123456789101112from moviepy.editor import VideoClip def make_frame(t): """ returns an image of the frame at time t """ # ... create the frame with any library return frame_for_time_t # (Height x Width x 3) Numpy array animation = VideoClip(make_frame, duration=3) # 3-second clip # For the export, many options/formats/optimizations are supportedanimation.write_videofile("my_animation.mp4", fps=24) # export as videoanimation.write_gif("my_animation.gif", fps=24) # export as GIF (slow)

在之前的文章中，我用这种方法来做制作矢量图形动画（用Gizeh库），和光线追踪三维场景（由POV-Ray做出）。这篇文章包括 MayaVi、vispy、matplotlib、NumPy 和 Scikit-image 这些科学库。

用Mayavi的动画

Mayavi是一个针对有简单接口的交互3D数据可视化的Python模块。在第一个例子中，我们做一个高度随时间t变化的表面的动画：

Python12345678910111213141516171819202122import numpy as npimport mayavi.mlab as mlabimport moviepy.editor as mpy duration= 2 # duration of the animation in seconds (it will loop) # MAKE A FIGURE WITH MAYAVI fig_myv = mlab.figure(size=(220,220), bgcolor=(1,1,1))X, Y = np.linspace(-2,2,200), np.linspace(-2,2,200)XX, YY = np.meshgrid(X,Y)ZZ = lambda d: np.sinc(XX**2+YY**2)+np.sin(XX+d) # ANIMATE THE FIGURE WITH MOVIEPY, WRITE AN ANIMATED GIF def make_frame(t): mlab.clf() # clear the figure (to reset the colors) mlab.mesh(YY,XX,ZZ(2*np.pi*t/duration), figure=fig_myv) return mlab.screenshot(antialiased=True) animation = mpy.VideoClip(make_frame, duration=duration)animation.write_gif("sinc.gif", fps=20)

另一个例子是一个坐标和观看角度都随时间变化的线框网：

Python12345678910111213141516171819202122232425262728import numpy as npimport mayavi.mlab as mlabimport moviepy.editor as mpy duration = 2 # duration of the animation in seconds (it will loop) # MAKE A FIGURE WITH MAYAVI fig = mlab.figure(size=(500, 500), bgcolor=(1,1,1)) u = np.linspace(0,2*np.pi,100)xx,yy,zz = np.cos(u), np.sin(3*u), np.sin(u) # Pointsl = mlab.plot3d(xx,yy,zz, representation="wireframe", tube_sides=5, line_width=.5, tube_radius=0.2, figure=fig) # ANIMATE THE FIGURE WITH MOVIEPY, WRITE AN ANIMATED GIF def make_frame(t): """ Generates and returns the frame for time t. """ y = np.sin(3*u)*(0.2+0.5*np.cos(2*np.pi*t/duration)) l.mlab_source.set(y = y) # change y-coordinates of the mesh mlab.view(azimuth= 360*t/duration, distance=9) # camera angle return mlab.screenshot(antialiased=True) # return a RGB image animation = mpy.VideoClip(make_frame, duration=duration).resize(0.5)# Video generation takes 10 seconds, GIF generation takes 25sanimation.write_videofile("wireframe.mp4", fps=20)animation.write_gif("wireframe.gif", fps=20)

因为Mayavi有着强大的ITK可视化引擎，它还可以处理复杂数据集。这里有一个源自于Mayavi例子的动画

代码

Animations with Vispy 用Vispy的动画

Vispy是另一个以OpenGL为基础的交互3D可视化库。至于Mayavi，我们用MoviePy先做出一个图和一个网。

Python12345678910111213141516171819202122232425262728from moviepy.editor import VideoClipimport numpy as npfrom vispy import app, scenefrom vispy.gloo.util import _screenshot canvas = scene.SceneCanvas(keys='interactive')view = canvas.central_widget.add_view()view.set_camera('turntable', mode='perspective', up='z', distance=2, azimuth=30., elevation=65.) xx, yy = np.arange(-1,1,.02),np.arange(-1,1,.02)X,Y = np.meshgrid(xx,yy)R = np.sqrt(X**2+Y**2)Z = lambda t : 0.1*np.sin(10*R-2*np.pi*t)surface = scene.visuals.SurfacePlot(x= xx-0.1, y=yy+0.2, z= Z(0), shading='smooth', color=(0.5, 0.5, 1, 1))view.add(surface)canvas.show() # ANIMATE WITH MOVIEPY def make_frame(t): surface.set_data(z = Z(t)) # Update the mathematical surface canvas.on_draw(None) # Update the image on Vispy's canvas return _screenshot((0,0,canvas.size[0],canvas.size[1]))[:,:,:3] animation = VideoClip(make_frame, duration=1).resize(width=350)animation.write_gif('sinc_vispy.gif', fps=20, opt='OptimizePlus')

还有一些更高级的例子（源自于Vispy库），它是用C代码片段中嵌入Python代码，微调了3D渲染的：

代码

用Matplotlib的动画

2D/3D绘图库Matplotlib已经有了动画模块，但我发现moviepy可以做出更轻量级，质量更好的视频，却达到了两倍的速度（不知道为什么？在这里看到更多细节）。这里有个如何使用matplotlib和moviepy的例子：

Python123456789101112131415161718192021222324import matplotlib.pyplot as pltimport numpy as npfrom moviepy.video.io.bindings import mplfig_to_npimageimport moviepy.editor as mpy # DRAW A FIGURE WITH MATPLOTLIB duration = 2 fig_mpl, ax = plt.subplots(1,figsize=(5,3), facecolor='white')xx = np.linspace(-2,2,200) # the x vectorzz = lambda d: np.sinc(xx**2)+np.sin(xx+d) # the (changing) z vectorax.set_title("Elevation in y=0")ax.set_ylim(-1.5,2.5)line, = ax.plot(xx, zz(0), lw=3) # ANIMATE WITH MOVIEPY (UPDATE THE CURVE FOR EACH t). MAKE A GIF. def make_frame_mpl(t): line.set_ydata( zz(2*np.pi*t/duration)) # <= Update the curve return mplfig_to_npimage(fig_mpl) # RGB image of the figure animation =mpy.VideoClip(make_frame_mpl, duration=duration)animation.write_gif("sinc_mpl.gif", fps=20)

Matplotlib有很多漂亮的主题，而且和像Pandas或Scikit-Learn这些数字模块能很好配合。让我们看一个SVM分类器，以更好地明白训练点的数量增加时的地图。

Python1234567891011121314151617181920212223242526272829303132import numpy as npimport matplotlib.pyplot as pltfrom sklearn import svm # sklearn = scikit-learnfrom sklearn.datasets import make_moonsfrom moviepy.editor import VideoClipfrom moviepy.video.io.bindings import mplfig_to_npimage X, Y = make_moons(50, noise=0.1, random_state=2) # semi-random data fig, ax = plt.subplots(1, figsize=(4, 4), facecolor=(1,1,1))fig.subplots_adjust(left=0, right=1, bottom=0)xx, yy = np.meshgrid(np.linspace(-2,3,500), np.linspace(-1,2,500)) def make_frame(t): ax.clear() ax.axis('off') ax.set_title("SVC classification", fontsize=16) classifier = svm.SVC(gamma=2, C=1) # the varying weights make the points appear one after the other weights = np.minimum(1, np.maximum(0, t**2+10-np.arange(50))) classifier.fit(X, Y, sample_weight=weights) Z = classifier.decision_function(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) ax.contourf(xx, yy, Z, cmap=plt.cm.bone, alpha=0.8, vmin=-2.5, vmax=2.5, levels=np.linspace(-2,2,20)) ax.scatter(X[:,0], X[:,1], c=Y, s=50*weights, cmap=plt.cm.bone) return mplfig_to_npimage(fig) animation = VideoClip(make_frame, duration = 7)animation.write_gif("svm.gif", fps=15)

简单明了，背景色代表分类器辨识黑点和白点属于哪里。在一开始没有真正的线索，但随着更多的点出钱，月牙形分布区域渐渐显现了。

用Numpy的动画

如果你正用着Numpy数组（Numpy是一个Python的中央数字库），你不需要任何外部绘图库，你可以直接将这些数组馈入MoviePy。

这通过模拟在法国的僵尸爆发（灵感来自Max Berggren的博客，伯乐在线已有全文翻译：《用Python在地图上模拟疫情扩散》）。法国被仿作一个所有分散和感染的计算都完成的网格（NumPy数组）。每隔一段时间，一些NumPy操作变换网格为有效的RGB图像，并将其发送到Moviepy。

代码

把动画放到一起

什么比一个动画更好呢？两个动画！你可以利用MoviePy视频合成功能，来混合来自不同库的动画：

Python123456import moviepy.editor as mpy# We use the GIFs generated earlier to avoid recomputing the animations.clip_mayavi = mpy.VideoFileClip("sinc.gif")clip_mpl = mpy.VideoFileClip("sinc_mpl.gif").resize(height=clip_mayavi.h)animation = mpy.clips_array([[clip_mpl, clip_mayavi]])animation.write_gif("sinc_plot.gif", fps=20)

Or for something more artistic:

Python12345678# Make the white color transparent in clip_mayaviclip_mayavi2 = (clip_mayavi.fx( mpy.vfx.mask_color, [255,255,255]) .set_opacity(.4) # whole clip is semi-transparent .resize(height=0.85*clip_mpl.h) .set_pos('center')) animation = mpy.CompositeVideoClip([clip_mpl, clip_mayavi2])animation.write_gif("sinc_plot2.gif", fps=20)

也许有点太快了，但有时你必须给你的观众一些可以让他们议论的东西。

你也可以注解动画，当比较不同的过滤器或算法时，注解动画很实用。让我们看看四张由库scikit-image变换的图像：

Python1234567891011121314151617181920212223242526import moviepy.editor as mpyimport skimage.exposure as ske # rescaling, histogram eq.import skimage.filter as skf # gaussian blur clip = mpy.VideoFileClip("sinc.gif")gray = clip.fx(mpy.vfx.blackwhite).to_mask() def apply_effect(effect, title, **kw): """ Returns a clip with the effect applied and a title""" filtr = lambda im: effect(im, **kw) new_clip = gray.fl_image(filtr).to_RGB() txt = (mpy.TextClip(title, font="Purisa-Bold", fontsize=15) .set_position(("center","top")) .set_duration(clip.duration)) return mpy.CompositeVideoClip([new_clip,txt]) # Apply 4 different effects to the original animationequalized = apply_effect(ske.equalize_hist, "Equalized")rescaled = apply_effect(ske.rescale_intensity, "Rescaled")adjusted = apply_effect(ske.adjust_log, "Adjusted")blurred = apply_effect(skf.gaussian_filter, "Blurred", sigma=4) # Put the clips together on a 2x2 grid, and write to a file.finalclip = mpy.clips_array([[ equalized, adjusted ], [ blurred, rescaled ]])final_clip.write_gif("test2x2.gif", fps=20)

如果我们把CompositeVideoClip和clips_array替代成concatenate_videoclips，我们得到标题效果式动画：

Python12345678910111213141516171819202122232425import moviepy.editor as mpyimport skimage.exposure as skeimport skimage.filter as skf clip = mpy.VideoFileClip("sinc.gif")gray = clip.fx(mpy.vfx.blackwhite).to_mask() def apply_effect(effect, label, **kw): """ Returns a clip with the effect applied and a top label""" filtr = lambda im: effect(im, **kw) new_clip = gray.fl_image(filtr).to_RGB() txt = (mpy.TextClip(label, font="Amiri-Bold", fontsize=25, bg_color='white', size=new_clip.size) .set_position(("center")) .set_duration(1)) return mpy.concatenate_videoclips([txt, new_clip]) equalized = apply_effect(ske.equalize_hist, "Equalized")rescaled = apply_effect(ske.rescale_intensity, "Rescaled")adjusted = apply_effect(ske.adjust_log, "Adjusted")blurred = apply_effect(skf.gaussian_filter, "Blurred", sigma=4) clips = [equalized, adjusted, blurred, rescaled]animation = mpy.concatenate_videoclips(clips)animation.write_gif("sinc_cat.gif", fps=15)

最终，处理视频数据时，MoviePy会非常好用，因为这是它的首要任务。最后一个例子，我们通过视频帧阈值和白色像素计数，估计一个细菌种群大小。第三面板显示，人口规模呈指数增长的时间。

代码

一个库就可以做所有动画了？

我希望给了你足够的例子，来提升你的同事对你下次展示中的印象。总之要他的输出能被转换成Numpy数组，其他的库也能用MoviePy来做动画。

一些库有自己的动画模块，但是修复和维护很痛苦！感谢那些在不同背景下测试MoviePy的人们，它变得更稳定了（除非没人再报bug），而且可以适用于各种环境。MoviePy 仍有很多要去做的，但如果作者开始依靠它来做视频和GIF渲染，像Pandas和scikit-Learn依赖matplotlib做绘制，那会很好。

为了本文的完整性，同时也为了更好地满足您的需要，我必须提到的ImageIO，这是另一个可以编写视频的Python库，它专注于提供一个非常简单的接口来读取或写入任何图像，视频或容积数据。比如你用imwrite()写图像，用mimwrite()写视频/ GIF，用volwrite()写体积数据，或只是write()写流数据。