{"id":93,"date":"2018-12-31T05:29:42","date_gmt":"2018-12-31T05:29:42","guid":{"rendered":"http:\/\/gantovnik.com\/bio-tips\/?p=93"},"modified":"2018-12-31T05:29:42","modified_gmt":"2018-12-31T05:29:42","slug":"plots-of-nonlinear-functions","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/plots-of-nonlinear-functions\/","title":{"rendered":"Plots of nonlinear functions"},"content":{"rendered":"
import os\nimport matplotlib.pyplot as plt\nimport numpy as np\nos.chdir('\/home\/vg\/Downloads\/projects\/ex15')\nos.getcwd()\n#define model parameters\nx=np.linspace(-2,2,1000)\n#examples of nonlinear functions\nf1=x**2-x-1\nf2=x**3-3*np.sin(x)\nf3=np.exp(x)-2\nf4=1-x**2+np.sin(50\/(1+x**2))\nfig,axes=plt.subplots(1,4,figsize=(12,3),sharey=True) \nfor n,f in enumerate([f1,f2,f3,f4]):\n    axes[n].plot(x,f,lw=1.5)\n    axes[n].axhline(0,ls=':',color='k')\n    axes[n].set_ylim(-5,5)\n    axes[n].set_xticks([-2,-1,0,1,2])\n    axes[n].set_xlabel(r'$x$',fontsize=18)\n\naxes[0].set_ylabel(r'$f(x)$',fontsize=18) \ntitles=[r'$f(x)=x^2-x-1$',r'$f(x)=x^3-3\\sin(x)$',r'$f(x)=\\exp(x)-2$',\nr'$f(x)=\\sin\\left(50\/(1+x^2)\\right)+1-x^2$'] \nfor n,title in enumerate(titles):\n    axes[n].set_title(title)\n\nplt.savefig(\"example15.png\", dpi=100)\nplt.show()\nplt.close()\n\n\"example15\"<\/pre>\n","protected":false},"excerpt":{"rendered":"
import os import matplotlib.pyplot as plt import numpy as np os.chdir(‘\/home\/vg\/Downloads\/projects\/ex15′) os.getcwd() #define model parameters x=np.linspace(-2,2,1000) #examples of nonlinear functions f1=x**2-x-1 f2=x**3-3*np.sin(x) f3=np.exp(x)-2 f4=1-x**2+np.sin(50\/(1+x**2)) fig,axes=plt.subplots(1,4,figsize=(12,3),sharey=True) for n,f in enumerate([f1,f2,f3,f4]): axes[n].plot(x,f,lw=1.5) axes[n].axhline(0,ls=’:’,color=’k’) axes[n].set_ylim(-5,5) axes[n].set_xticks([-2,-1,0,1,2]) axes[n].set_xlabel(r’$x$’,fontsize=18) axes[0].set_ylabel(r’$f(x)$’,fontsize=18) titles=[r’$f(x)=x^2-x-1$’,r’$f(x)=x^3-3\\sin(x)$’,r’$f(x)=\\exp(x)-2$’, r’$f(x)=\\sin\\left(50\/(1+x^2)\\right)+1-x^2$’] for n,title in enumerate(titles): axes[n].set_title(title) plt.savefig(“example15.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_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-93","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\/p8bH0k-1v","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":139,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/multidimensional-spline\/","url_meta":{"origin":93,"position":0},"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 "python"","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":[]},{"id":154,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/inexact-solutions-to-odes\/","url_meta":{"origin":93,"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 "python"","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":2162,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/05\/422-barnsleys-fern-using-imshow\/","url_meta":{"origin":93,"position":2},"title":"#422  Barnsley\u2019s fern using imshow","author":"gantovnik","date":"2024-05-04","format":false,"excerpt":"The Axes method ax.imshow displays an image on the axes. In its basic usage, it takes a two-dimensional array and maps its values to the pixels on an image according to some interpolation scheme and normalization. In this case, im is a three-dimensional array of shape (n, m, 3) in\u2026","rel":"","context":"In "matplotlib"","block_context":{"text":"matplotlib","link":"https:\/\/gantovnik.com\/bio-tips\/category\/matplotlib\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/05\/ex422.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/05\/ex422.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/05\/ex422.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":136,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/multivariate-interpolation\/","url_meta":{"origin":93,"position":3},"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 "python"","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":151,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/direction-fields\/","url_meta":{"origin":93,"position":4},"title":"Direction fields","author":"gantovnik","date":"2019-01-07","format":false,"excerpt":"","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example32","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example32.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example32.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example32.png?resize=525%2C300 1.5x"},"classes":[]},{"id":2059,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/01\/407-multiple-axes-animation-using-python\/","url_meta":{"origin":93,"position":5},"title":"#407 Multiple axes animation using python","author":"gantovnik","date":"2024-01-14","format":false,"excerpt":"y=sin(x)","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\/2024\/01\/ex407.gif?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex407.gif?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/01\/ex407.gif?resize=525%2C300&ssl=1 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/93","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=93"}],"version-history":[{"count":0,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/93\/revisions"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=93"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=93"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=93"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}