{"id":630,"date":"2020-09-17T02:35:12","date_gmt":"2020-09-17T09:35:12","guid":{"rendered":"http:\/\/gantovnik.com\/bio-tips\/?p=630"},"modified":"2020-09-17T02:35:12","modified_gmt":"2020-09-17T09:35:12","slug":"98-making-a-movie-of-a-plot","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2020\/09\/98-making-a-movie-of-a-plot\/","title":{"rendered":"#98 Making a movie of a plot"},"content":{"rendered":"<p>#98 Making a movie of a plot<\/p>\n<p>Consider Gaussian bell function.<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nimport matplotlib.pyplot as plt\r\nimport numpy as np\r\nimport os\r\n\r\nos.chdir(r'D:\\projects\\wordpress\\ex99') \r\nos.getcwd()\r\n\r\ndef f(x, m, s):\r\n    return (1.0\/(np.sqrt(2*np.pi)*s))*np.exp(-0.5*((x-m)\/s)**2)\r\n\r\nm = 0;\r\ns_start = 2;\r\ns_stop = 0.2\r\ns_values = np.linspace(s_start, s_stop, 50) #number of png files\r\nx = np.linspace(m -3*s_start, m + 3*s_start, 1000)\r\n# f is max for x=m (smaller s gives larger max value)\r\nmax_f = f(m, m, s_stop)\r\ny = f(x,m,s_stop)\r\nlines = plt.plot(x,y)\r\nplt.axis(&#x5B;x&#x5B;0], x&#x5B;-1], -0.1, max_f])\r\nplt.xlabel('x')\r\nplt.ylabel('f')\r\nframe_counter = 0\r\nfor s in s_values:\r\n    y = f(x, m, s)\r\n    lines&#x5B;0].set_ydata(y) #update plot data and redraw\r\n    plt.draw()\r\n    plt.savefig(f'tmp_{frame_counter:03d}.png',dpi=300) #unique filename\r\n    frame_counter += 1\r\n<\/pre>\n<p>Install programm ffmpeg for Windows and run the following command:<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nffmpeg -f image2 -i D:\/projects\/wordpress\/ex99\/tmp_%03d.png movie.mpg\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>#98 Making a movie of a plot Consider Gaussian bell function. import matplotlib.pyplot as plt import numpy as np import os os.chdir(r&#8217;D:\\projects\\wordpress\\ex99&#8242;) os.getcwd() def f(x, m, s): return (1.0\/(np.sqrt(2*np.pi)*s))*np.exp(-0.5*((x-m)\/s)**2) m = 0; s_start = 2; s_stop = 0.2 s_values = np.linspace(s_start, s_stop, 50) #number of png files x = np.linspace(m -3*s_start, m + 3*s_start, 1000) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-630","post","type-post","status-publish","format-standard","hentry","category-python"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-aa","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":101,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/solution-of-system-of-nonlinear-equations\/","url_meta":{"origin":630,"position":0},"title":"Solution of system of nonlinear equations","author":"gantovnik","date":"2018-12-31","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np import scipy os.chdir('\/home\/vg\/Downloads\/projects\/ex17') os.getcwd() def f(x): return [x[1]-x[0]**3-2*x[0]**2+1,x[1]+x[0]**2-1] tol=0.1 a,b=-2,2 x=np.linspace(-3,2,5000) y1=x**3+2*x**2-1 y2=-x**2+1 fig,ax=plt.subplots(figsize=(8,4)) ax.plot(x,y1,'k',lw=1.5) ax.plot(x,y2,'k',lw=1.5) sol1=scipy.optimize.fsolve(f,[-2,2]) sol2=scipy.optimize.fsolve(f,[1,-1]) sol3=scipy.optimize.fsolve(f,[-2,-5]) sols=[sol1,sol2,sol3] colors=['r','b','g'] for idx,s in enumerate(sols): ax.plot(s[0],s[1],colors[idx]+'*',markersize=15) for m in np.linspace(-4,3,80): for n in np.linspace(-20,20,40): x_guess=[m,n] sol=scipy.optimize.fsolve(f,x_guess) idx = (abs(sols-sol)**2).sum(axis=1).argmin() ax.plot(x_guess[0],x_guess[1],colors[idx]+'.')\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example17","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example17.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example17.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example17.png?resize=525%2C300 1.5x"},"classes":[]},{"id":154,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/inexact-solutions-to-odes\/","url_meta":{"origin":630,"position":1},"title":"Inexact solutions to ODEs","author":"gantovnik","date":"2019-01-08","format":false,"excerpt":"\u00a0 import os import numpy as np import matplotlib.pyplot as plt import matplotlib as mpl import sympy from IPython.display import display sympy.init_printing() mpl.rcParams['text.usetex'] = True import sympy os.chdir(r'D:\\projects\\wordpress\\ex33') os.getcwd() def plot_direction_field(x, y_x, f_xy, x_lim=(-5, 5), y_lim=(-5, 5), ax=None): f_np = sympy.lambdify((x, y_x), f_xy, 'numpy') x_vec = np.linspace(x_lim[0], x_lim[1], 20) y_vec\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example33","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example33.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example33.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example33.png?resize=525%2C300 1.5x"},"classes":[]},{"id":82,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/plot-with-an-inset\/","url_meta":{"origin":630,"position":2},"title":"#12: Plot with an inset in python","author":"gantovnik","date":"2018-12-29","format":false,"excerpt":"[code language=\"python\"] import os import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np os.chdir('\/home\/vg\/Downloads\/projects\/ex12') os.getcwd() fig = plt.figure(figsize=(10,8)) def f(x): return 1\/(1+x**2) + 0.1\/(1+((3-x)\/0.1)**2) def plot_and_format_axes(ax,x,f,fontsize): ax.plot(x,f(x),linewidth=2) ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(5)) ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4)) ax.set_xlabel(r\"$x$\",fontsize=fontsize) ax.set_ylabel(r\"$f(x)$\",fontsize=fontsize) ax=fig.add_axes([0.1,0.15,0.8,0.8],facecolor=\"#f5f5f5\") x = np.linspace(-4,14,1000) plot_and_format_axes(ax,x,f,18) plt.title('Plot with inset') x0,x1=2.5,3.5 ax.axvline(x0,ymax=0.3,color=\"grey\",linestyle=\":\") ax.axvline(x1,ymax=0.3,color=\"grey\",linestyle=\":\") ax_insert=fig.add_axes([0.5,0.5,0.38,0.42],facecolor='none') x=np.linspace(x0,x1,1000) plot_and_format_axes(ax_insert,x,f,14) plt.savefig(\"example12.png\", dpi=100)\u2026","rel":"","context":"In &quot;matplotlib&quot;","block_context":{"text":"matplotlib","link":"https:\/\/gantovnik.com\/bio-tips\/category\/matplotlib\/"},"img":{"alt_text":"example12","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example12.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example12.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example12.png?resize=525%2C300 1.5x"},"classes":[]},{"id":96,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/bisection-method\/","url_meta":{"origin":630,"position":3},"title":"#16 Bisection method using python","author":"gantovnik","date":"2018-12-31","format":false,"excerpt":"[code language=\"python\"] import os import matplotlib.pyplot as plt import numpy as np os.chdir('\/home\/vg\/Downloads\/projects\/ex16') os.getcwd() f = lambda x: np.exp(x)-2 tol=0.1 a,b=-2,2 x=np.linspace(-2.1,2.1,1000) fig,ax=plt.subplots(1,1,figsize=(12,4)) ax.plot(x,f(x),lw=1.5) ax.axhline(0,ls=':',color='k') ax.set_xticks([-2,-1,0,1,2]) ax.set_xlabel(r'$x$',fontsize=18) ax.set_ylabel(r'$f(x)$',fontsize=18) fa,fb=f(a),f(b) ax.plot(a,fa,'ko') ax.plot(b,fb,'ko') ax.text(a,fa+0.5,r\"$a$\",ha='center',fontsize=18) ax.text(b,fb+0.5,r\"$b$\",ha='center',fontsize=18) n=1 while b-a &gt; tol: m=a+(b-a)\/2 fm=f(m) ax.plot(m,fm,'ko') ax.text(m,fm-0.5,r\"$m_%d$\" % n,ha='center') n=n+1 if (np.sign(fa)==np.sign(fm)): a,fa=m,fm else: b,fb=m,fm\u2026","rel":"","context":"In &quot;optimization&quot;","block_context":{"text":"optimization","link":"https:\/\/gantovnik.com\/bio-tips\/category\/optimization\/"},"img":{"alt_text":"example16","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example16.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example16.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example16.png?resize=525%2C300 1.5x"},"classes":[]},{"id":157,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/numerical-integration-of-odes-using-scipy\/","url_meta":{"origin":630,"position":4},"title":"Numerical integration of ODEs using SciPy","author":"gantovnik","date":"2019-01-09","format":false,"excerpt":"import os import numpy as np import matplotlib.pyplot as plt from scipy import integrate import sympy os.chdir(r'D:\\projects\\wordpress\\ex35') os.getcwd() def plot_direction_field(x, y_x, f_xy, x_lim=(-5, 5), y_lim=(-5, 5), ax=None): f_np = sympy.lambdify((x, y_x), f_xy, 'numpy') x_vec = np.linspace(x_lim[0], x_lim[1], 20) y_vec = np.linspace(y_lim[0], y_lim[1], 20) if ax is None: _, ax =\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example35","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example35.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1746,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/01\/204-mandelbrot-fractal-using-python-2-2-2-2-2-2-2-2-2-2\/","url_meta":{"origin":630,"position":5},"title":"#331 Interpolation with Newton&#8217;s polynomial using python","author":"gantovnik","date":"2023-01-04","format":false,"excerpt":"interpolation.py [code language=\"python\"] def interpolation(c,x,x0): # Evaluate Newton's polynomial at x0. # Degree of polynomial n = len(x) - 1 y0 = c[n] for k in range(1,n+1): y0 = c[n-k] + (x0 - x[n-k]) * y0 return y0 def coef(x,y): # Computes the coefficients of Newton's polynomial. # Number of\u2026","rel":"","context":"In 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