{"id":352,"date":"2019-01-28T23:40:57","date_gmt":"2019-01-29T07:40:57","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=352"},"modified":"2019-01-28T23:40:57","modified_gmt":"2019-01-29T07:40:57","slug":"spline","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/spline\/","title":{"rendered":"Spline"},"content":{"rendered":"
\nimport os\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport scipy.interpolate\nos.chdir(r'D:\\projects\\wordpress\\ex57')\nos.getcwd()\nx=np.linspace(0,15,10)\nxn=np.linspace(0,15,50)\ny=np.sin(x) + 0.2*x\ninterp=scipy.interpolate.InterpolatedUnivariateSpline(x,y)\nplt.plot(x,y,'o',xn,interp(xn))\nplt.xlabel('x')\nplt.ylabel('y')\nplt.legend(["$y(x)$", "$s(x)$"],loc='best')\nplt.tight_layout()\nplt.savefig("example57.png", dpi=100)\nplt.show()\nplt.close()\n<\/pre>\n
\"example57\"
\n <\/p>\n","protected":false},"excerpt":{"rendered":"
import os import matplotlib.pyplot as plt import numpy as np import scipy.interpolate os.chdir(r’D:\\projects\\wordpress\\ex57′) os.getcwd() x=np.linspace(0,15,10) xn=np.linspace(0,15,50) y=np.sin(x) + 0.2*x interp=scipy.interpolate.InterpolatedUnivariateSpline(x,y) plt.plot(x,y,’o’,xn,interp(xn)) plt.xlabel(‘x’) plt.ylabel(‘y’) plt.legend(["$y(x)$", "$s(x)$"],loc=’best’) plt.tight_layout() plt.savefig("example57.png", dpi=100) plt.show() plt.close()  <\/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_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":"","jetpack_post_was_ever_published":false},"categories":[2],"tags":[],"class_list":["post-352","post","type-post","status-publish","format-standard","hentry","category-python"],"modified_by":null,"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/s8bH0k-spline","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":121,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/polynomial-interpolation\/","url_meta":{"origin":352,"position":0},"title":"Polynomial interpolation","author":"gantovnik","date":"2019-01-03","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from numpy import polynomial as P from scipy import linalg os.chdir(r'D:\\data\\scripts\\web1\\ex23') os.getcwd() x = np.array([1, 2, 3, 4]) y = np.array([1, 3, 5, 4]) deg = len(x) - 1 A = P.polynomial.polyvander(x, deg) c = linalg.solve(A, y) f1 = P.Polynomial(c)\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example23","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example23.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example23.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example23.png?resize=525%2C300 1.5x"},"classes":[]},{"id":127,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/runge-problem\/","url_meta":{"origin":352,"position":1},"title":"Runge problem","author":"gantovnik","date":"2019-01-03","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from numpy import polynomial as P os.chdir(r'D:\\data\\scripts\\web1\\ex25') os.getcwd() # In the mathematical field of numerical analysis, Runge's phenomenon # is a problem of oscillation at the edges of an interval that occurs # when using polynomial interpolation with polynomials of\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example25","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example25.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example25.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example25.png?resize=525%2C300 1.5x"},"classes":[]},{"id":1877,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/07\/355-animation-of-domain-coloring-using-python\/","url_meta":{"origin":352,"position":2},"title":"#355 Animation of domain coloring using python","author":"gantovnik","date":"2023-07-01","format":false,"excerpt":"[code language=\"python\"] # pip install celluloid #%matplotlib qt import numpy as np from matplotlib import pyplot as plt from matplotlib.colors import hsv_to_rgb from celluloid import Camera fig = plt.figure() camera = Camera(fig) for a in np.linspace(0, 2 * np.pi, 30, endpoint=False): x = np.linspace(-3, 3, 800) X, Y = np.meshgrid(x,\u2026","rel":"","context":"In "animation"","block_context":{"text":"animation","link":"https:\/\/gantovnik.com\/bio-tips\/category\/animation\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex355.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex355.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/07\/ex355.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":82,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/plot-with-an-inset\/","url_meta":{"origin":352,"position":3},"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 "matplotlib"","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":5,"url":"https:\/\/gantovnik.com\/bio-tips\/2016\/12\/example-1-interpolation\/","url_meta":{"origin":352,"position":4},"title":"Example 1: Interpolation","author":"gantovnik","date":"2016-12-08","format":false,"excerpt":"Example 1: Interpolation [code language=\"python\"] #Example 1: Interpolation import numpy as np from scipy import interpolate import matplotlib.pyplot as plt import os os.chdir('C:\\\\Anaconda\\\\mycodes\\\\aerospace') os.getcwd() #create the data points and add noise as follows x = np.linspace(-18,18,36) noise = 0.1 * np.random.random(len(x)) signal = np.sinc(x) + noise #create a linear interpolation\u2026","rel":"","context":"In "matplotlib"","block_context":{"text":"matplotlib","link":"https:\/\/gantovnik.com\/bio-tips\/category\/matplotlib\/"},"img":{"alt_text":"example1","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2016\/12\/example1-300x200.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":370,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/roots-of-equation\/","url_meta":{"origin":352,"position":5},"title":"#52 Roots of equation using python","author":"gantovnik","date":"2019-01-29","format":false,"excerpt":"[code language=\"python\"] import os import numpy as np import matplotlib.pyplot as plt from scipy.optimize import brentq os.chdir(r'D:\\projects\\wordpress\\ex52') os.getcwd() f=lambda x: 0.2+x * np.cos(3\/x) x=np.linspace(-1,1,1000) plt.plot(x,f(x)) plt.axhline(0,color='k') xstar=brentq(f,-0.7,-0.5) print(xstar,f(xstar)) plt.plot(xstar,f(xstar), 'ro') plt.text(-1.0, -0.5, 'x=%6.4f and f(x)=%6.4f' % (xstar, f(xstar))) plt.tight_layout() plt.savefig(\"example52.png\", dpi=300) plt.show() plt.close() [\/code]","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=525%2C300&ssl=1 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