{"id":133,"date":"2019-01-03T17:05:05","date_gmt":"2019-01-04T01:05:05","guid":{"rendered":"http:\/\/gantovnik.com\/bio-tips\/?p=133"},"modified":"2022-12-13T19:18:58","modified_gmt":"2022-12-14T03:18:58","slug":"spline-interpolation-3","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/spline-interpolation-3\/","title":{"rendered":"#27 Spline interpolation"},"content":{"rendered":"<pre>import os\r\nimport matplotlib.pyplot as plt\r\nimport numpy as np\r\nfrom scipy import interpolate\r\nos.chdir(r'D:\\data\\scripts\\web1\\ex27')\r\nos.getcwd()\r\nx = np.array([0, 1, 2, 3, 4, 5, 6, 7])\r\ny = np.array([3, 4, 3.5, 2, 1, 1.5, 1.25, 0.9])\r\nxx = np.linspace(x.min(), x.max(), 100)\r\nfig, ax = plt.subplots(figsize=(8, 4))\r\nax.scatter(x, y)\r\nfor n in [1, 3, 5, 7]:\r\n    f = interpolate.interp1d(x, y, kind=n)\r\n    ax.plot(xx, f(xx), label='order %d' % n)\r\n\r\nax.legend()\r\nax.set_ylabel(r\"$y$\", fontsize=18)\r\nax.set_xlabel(r\"$x$\", fontsize=18)\r\nfig.tight_layout()\r\nax.set_title(\"Spline Interpolation\")\r\nfig.tight_layout()\r\nplt.savefig(\"example27.png\", dpi=100)\r\nplt.show()\r\nplt.close()\r\n\r\n<img data-recalc-dims=\"1\" decoding=\"async\" class=\"  wp-image-134 aligncenter\" src=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example27.png?resize=632%2C316\" alt=\"example27\" width=\"632\" height=\"316\" srcset=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example27.png?w=800&amp;ssl=1 800w, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example27.png?resize=300%2C150&amp;ssl=1 300w, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example27.png?resize=768%2C384&amp;ssl=1 768w\" sizes=\"(max-width: 632px) 100vw, 632px\" \/><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>import os import matplotlib.pyplot as plt import numpy as np from scipy import interpolate os.chdir(r&#8217;D:\\data\\scripts\\web1\\ex27&#8242;) os.getcwd() x = np.array([0, 1, 2, 3, 4, 5, 6, 7]) y = np.array([3, 4, 3.5, 2, 1, 1.5, 1.25, 0.9]) xx = np.linspace(x.min(), x.max(), 100) fig, ax = plt.subplots(figsize=(8, 4)) ax.scatter(x, y) for n in [1, 3, 5, 7]: [&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_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-133","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-29","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":130,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/spline-interpolation-2\/","url_meta":{"origin":133,"position":0},"title":"Spline interpolation","author":"gantovnik","date":"2019-01-03","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from scipy import interpolate os.chdir(r'D:\\data\\scripts\\web1\\ex26') os.getcwd() def runge(x): return 1\/(1 + 25 * x**2) x = np.linspace(-1, 1, 11) y = runge(x) f = interpolate.interp1d(x, y, kind=3) xx = np.linspace(-1, 1, 100) fig, ax = plt.subplots(figsize=(8, 4)) ax.plot(xx, runge(xx), 'k',\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example26","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example26.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example26.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example26.png?resize=525%2C300 1.5x"},"classes":[]},{"id":121,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/polynomial-interpolation\/","url_meta":{"origin":133,"position":1},"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 &quot;python&quot;","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":136,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/multivariate-interpolation\/","url_meta":{"origin":133,"position":2},"title":"Multivariate interpolation","author":"gantovnik","date":"2019-01-04","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from scipy import interpolate os.chdir(r'D:\\data\\scripts\\web1\\ex28') os.getcwd() x = y = np.linspace(-2, 2, 20) def f(x, y): return np.exp(-(x + .5)**2 - 2*(y + .5)**2) - np.exp(-(x - .5)**2 - 2*(y - .5)**2) X, Y = np.meshgrid(x, y) # simulate noisy\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example28","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example28.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example28.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example28.png?resize=525%2C300 1.5x"},"classes":[]},{"id":124,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/polynomial-fit\/","url_meta":{"origin":133,"position":3},"title":"Polynomial fit","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\\ex24') os.getcwd() x = np.array([1, 2, 3, 4]) y = np.array([1, 3, 5, 4]) f1 = P.Polynomial.fit(x, y, 1) f2 = P.Polynomial.fit(x, y, 2) f3 = P.Polynomial.fit(x, y, 3) xx = np.linspace(x.min(), x.max(), 100)\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example24","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=525%2C300 1.5x"},"classes":[]},{"id":127,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/runge-problem\/","url_meta":{"origin":133,"position":4},"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 &quot;python&quot;","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":139,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/multidimensional-spline\/","url_meta":{"origin":133,"position":5},"title":"Multidimensional Spline","author":"gantovnik","date":"2019-01-04","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from scipy import interpolate os.chdir(r'D:\\data\\scripts\\web1\\ex29') os.getcwd() np.random.seed(115925231) x = y = np.linspace(-1, 1, 100) X, Y = np.meshgrid(x, y) def f(x, y): return np.exp(-x**2 - y**2) * np.cos(4*x) * np.sin(6*y) Z = f(X, Y) N = 500 xdata = np.random.uniform(-1,\u2026","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example29","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example29.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example29.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example29.png?resize=525%2C300 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/comments?post=133"}],"version-history":[{"count":0,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/133\/revisions"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}