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(optional)"}],"lineInfo":{"truncatedLoc":"363","truncatedSloc":"265"},"mode":"file"},"image":false,"isCodeownersFile":null,"isPlain":false,"isValidLegacyIssueTemplate":false,"issueTemplate":null,"discussionTemplate":null,"language":"Markdown","languageID":222,"large":false,"planSupportInfo":{"repoIsFork":null,"repoOwnedByCurrentUser":null,"requestFullPath":"/cerncas/hands-on-lattice-exercises/blob/cas_2023/Setup_Instructions.md","showFreeOrgGatedFeatureMessage":null,"showPlanSupportBanner":null,"upgradeDataAttributes":null,"upgradePath":null},"publishBannersInfo":{"dismissActionNoticePath":"/settings/dismiss-notice/publish_action_from_dockerfile","releasePath":"/cerncas/hands-on-lattice-exercises/releases/new?marketplace=true","showPublishActionBanner":false},"rawBlobUrl":"https://github.com/cerncas/hands-on-lattice-exercises/raw/refs/heads/cas_2023/Setup_Instructions.md","renderImageOrRaw":false,"richText":"\u003carticle class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eHands-On Lattice (and Longitudinal) Calculations using Python - Setup Instructions\u003c/h1\u003e\u003ca id=\"user-content-hands-on-lattice-and-longitudinal-calculations-using-python---setup-instructions\" class=\"anchor\" aria-label=\"Permalink: Hands-On Lattice (and Longitudinal) Calculations using Python - Setup Instructions\" href=\"#hands-on-lattice-and-longitudinal-calculations-using-python---setup-instructions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003chr\u003e\n\u003cp dir=\"auto\"\u003eDuring the course we will use \u003cstrong\u003ePython3\u003c/strong\u003e in a \u003cstrong\u003eJupyter notebook\u003c/strong\u003e with \u003ca href=\"https://jupyterlab.readthedocs.io/en/stable/\" rel=\"nofollow\"\u003eJupyterLab\u003c/a\u003e and, mostly, the \u003ca href=\"https://numpy.org/\" rel=\"nofollow\"\u003enumpy\u003c/a\u003e and \u003ca href=\"https://matplotlib.org/\" rel=\"nofollow\"\u003ematplotlib\u003c/a\u003e packages. We will explain in the following sections how to install all necessary software on \u003cstrong\u003eyour laptop\u003c/strong\u003e.\nA basic knowledge of Python is assumed. If you are not familiar with Python, you can find a few resources to fill the gap in the following sections.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo get a better idea of the level of the Python knowledge needed for the course you can browse the \u003ca href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/CAS_Optics_Primer.pdf\"\u003eprimer of the hands-on course\u003c/a\u003e. Do not worry about the theory for the moment (it will be discussed in details during the school) but focus on the Python syntax and data types (tuples, lists,...).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAfter \u003ca href=\"#a-very-short-introduction-to-python\"\u003ea short introduction\u003c/a\u003e, where we provided some useful links to get familiar with Python, we will focus on the \u003ca href=\"#software-setup\"\u003esoftware setup\u003c/a\u003e.\nFinally, in \u003ca href=\"#appendix-python-packages\"\u003eappendix\u003c/a\u003e you will find links and cheatsheets for the most common Python packages that will be used during the course.\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eImportant:\u003c/strong\u003e we kindly ask you to go throw this document \u003cstrong\u003ebefore coming\u003c/strong\u003e to CAS, such as to \u003cstrong\u003eprepare yourself\u003c/strong\u003e (and \u003cstrong\u003eyour laptop\u003c/strong\u003e) for the course.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003chr\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eA very short introduction to Python\u003c/h1\u003e\u003ca id=\"user-content-a-very-short-introduction-to-python\" class=\"anchor\" aria-label=\"Permalink: A very short introduction to Python\" href=\"#a-very-short-introduction-to-python\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can find several nice courses, videos and resources on the internet. Here you have a couple of suggestions you can find on YouTube:\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"http://www.youtube.com/watch?v=kqtD5dpn9C8\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/43002d00aec45990c107202807c77de97c4035ce093b3abc02c1e22c15d3263d/687474703a2f2f696d672e796f75747562652e636f6d2f76692f6b7174443564706e3943382f302e6a7067\" alt=\"Python for Beginners - Learn Python in 1 Hour\" width=\"40%\" data-canonical-src=\"http://img.youtube.com/vi/kqtD5dpn9C8/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e \n \n\u003ca href=\"http://www.youtube.com/watch?v=rfscVS0vtbw\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/9e1999c1532b2f091b8764ca1debbe04294b7efe77012e5f06fb401c7c22a1c0/687474703a2f2f696d672e796f75747562652e636f6d2f76692f72667363565330767462772f302e6a7067\" alt=\"Learn Python - Full Course for Beginners\" width=\"40%\" data-canonical-src=\"http://img.youtube.com/vi/rfscVS0vtbw/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTest Python on a web page\u003c/h3\u003e\u003ca id=\"user-content-test-python-on-a-web-page\" class=\"anchor\" aria-label=\"Permalink: Test Python on a web page\" href=\"#test-python-on-a-web-page\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIf you are not familiar with Python and you have not it installed on your laptop, you can start playing with simple python snippets on the web. Without installing any special software you can connect,\nfor example, to \u003ca href=\"https://gke.mybinder.org/v2/gh/jupyterlab/jupyterlab-demo/try.jupyter.org?urlpath=lab\" rel=\"nofollow\"\u003ejupyterLab\u003c/a\u003e,\nand test the following commands:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"import numpy as np\n\n# Matrix definition\nOmega=np.array([[0, 1],[-1,0]])\nM=np.array([[1, 0],[1,1]])\n\n# Sum and multiplication of matrices\nOmega - M.T @ Omega @ M\n# M.T means the \u0026quot;traspose of M\u0026quot;.\n\n# Function definition\ndef Q(f=1):\n return np.array([[1, 0],[-1/f,1]])\n\n# Eigenvalues and eigenvectors\nnp.linalg.eig(M)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Matrix definition\u003c/span\u003e\n\u003cspan class=\"pl-v\"\u003eOmega\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003earray\u003c/span\u003e([[\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e],[\u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e,\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e]])\n\u003cspan class=\"pl-v\"\u003eM\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003earray\u003c/span\u003e([[\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e],[\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e,\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e]])\n\n\u003cspan class=\"pl-c\"\u003e# Sum and multiplication of matrices\u003c/span\u003e\n\u003cspan class=\"pl-v\"\u003eOmega\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eM\u003c/span\u003e.\u003cspan class=\"pl-v\"\u003eT\u003c/span\u003e @ \u003cspan class=\"pl-v\"\u003eOmega\u003c/span\u003e @ \u003cspan class=\"pl-v\"\u003eM\u003c/span\u003e\n\u003cspan class=\"pl-c\"\u003e# M.T means the \"traspose of M\".\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Function definition\u003c/span\u003e\n\u003cspan class=\"pl-k\"\u003edef\u003c/span\u003e \u003cspan class=\"pl-v\"\u003eQ\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ef\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e):\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003earray\u003c/span\u003e([[\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e],[\u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e/\u003c/span\u003e\u003cspan class=\"pl-s1\"\u003ef\u003c/span\u003e,\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e]])\n\n\u003cspan class=\"pl-c\"\u003e# Eigenvalues and eigenvectors\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003elinalg\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eeig\u003c/span\u003e(\u003cspan class=\"pl-v\"\u003eM\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can compare and check your output with the ones \u003ca href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/tests/SimpleTest.ipynb\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\n\u003chr\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSoftware Setup\u003c/h1\u003e\u003ca id=\"user-content-software-setup\" class=\"anchor\" aria-label=\"Permalink: Software Setup\" href=\"#software-setup\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn this section we will explain how to install Python and JupyterLab on your laptop.\nJupyterLab is a user-friendly environment to work with Python.\nYou can find an overview on JupyterLab \u003ca href=\"https://jupyterlab.readthedocs.io/en/stable/\" rel=\"nofollow\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003eIf you already have your favorite Python distribution installed on your laptop, including JupyterLab, you might want to skip the \u003ca href=\"#installation\"\u003einstallation\u003c/a\u003e and jump to \u003ca href=\"#launch-jupyter-lab\"\u003elaunch Jupyter Lab\u003c/a\u003e and \u003ca href=\"#test-that-everything-works\"\u003etest that everything works\u003c/a\u003e.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInstallation\u003c/h2\u003e\u003ca id=\"user-content-installation\" class=\"anchor\" aria-label=\"Permalink: Installation\" href=\"#installation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWe suggest to install the \u003cstrong\u003eAnaconda\u003c/strong\u003e distribution from \u003ca href=\"https://www.anaconda.com/distribution/\" rel=\"nofollow\"\u003ehttps://www.anaconda.com/distribution/\u003c/a\u003e\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://www.anaconda.com/distribution/\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/anaconda.png\" alt=\"\" width=\"70%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003eWe suggest to install one of the latest distribution (\u003cstrong\u003efor example version 3.9\u003c/strong\u003e).\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eThe installation process clearly depends on your operating system. We suggest you to follow the official documentation for \u003ca href=\"https://docs.anaconda.com/anaconda/install/windows/\" rel=\"nofollow\"\u003eWindows\u003c/a\u003e, \u003ca href=\"https://docs.anaconda.com/anaconda/install/linux/\" rel=\"nofollow\"\u003eLinux\u003c/a\u003e, or \u003ca href=\"https://docs.anaconda.com/anaconda/install/mac-os/\" rel=\"nofollow\"\u003eMac\u003c/a\u003e as appropriate.\nAfter having installed \u003cstrong\u003eAnaconda\u003c/strong\u003e, and \u003ca href=\"https://docs.anaconda.com/anaconda/install/verify-install/\" rel=\"nofollow\"\u003everified your installation\u003c/a\u003e - as suggested in the \u003ca href=\"https://docs.anaconda.com/anaconda/install/\" rel=\"nofollow\"\u003einstallation documentation\u003c/a\u003e - we invite you to start \u003ca href=\"#launch-jupyter-lab\"\u003elaunching Jupyter Lab\u003c/a\u003e and then \u003ca href=\"#test-that-everything-works\"\u003etest that everything works\u003c/a\u003e:\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eLaunch Jupyter Lab\u003c/h2\u003e\u003ca id=\"user-content-launch-jupyter-lab\" class=\"anchor\" aria-label=\"Permalink: Launch Jupyter Lab\" href=\"#launch-jupyter-lab\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eOnce the installation of \u003cstrong\u003eAnaconda\u003c/strong\u003e is finalised or within your existing Python distribution, you should be able to start Jupyter Lab from a terminal:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eOpen a (Anaconda) terminal on your operating system:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cstrong\u003eWindows:\u003c/strong\u003e\nFrom the Start menu, search for and open “Anaconda Prompt”:\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003emacOS:\u003c/strong\u003e\nOpen Launchpad, then click the terminal icon.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eLinux:\u003c/strong\u003e\nOpen a terminal window.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eLaunch Jupyter Lab from your terminal:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-shell notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"jupyter lab\"\u003e\u003cpre\u003ejupyter lab\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eFollow the instructions given in the terminal. You should end-up on your default browser with a page similar to the following:\u003c/p\u003e\n \u003cp align=\"center\" dir=\"auto\"\u003e\n \u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_5b0618b75e4f4df0facf2a609b9354b5.png\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_5b0618b75e4f4df0facf2a609b9354b5.png\" alt=\"\" width=\"70%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n \u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOn the left hand side of the widows you should see all files under the folder in your operating system where you executed the \u003ccode\u003ejupyter lab\u003c/code\u003e command.\nThis will be your \u003cstrong\u003eworking directory\u003c/strong\u003e.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eCreate a new \"Python 3\" \"Notebook\" and start playing with Python! If you are not familiar with Python, you can start playing with simple python snippets. For example, have a look to the following \u003ca href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/tests/PythonExample.ipynb\"\u003enotebook\u003c/a\u003e (courtesy of \u003cem\u003eSimon Albright\u003c/em\u003e).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eTry to import all packages that we will be using in our course:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\" # numpy: our main numerical package\n import numpy as np\n # matplotlib and seaborn: our plotting packages\n import matplotlib.pyplot as plt\n import seaborn as sns\n\n # widget for producing animations:\n from ipywidgets import interactive\n # Note: to produce animations you might need to configure your jupyter lab properly:\n # \u0026gt; pip install ipywidgets\n # \u0026gt; jupyter nbextension enable --py widgetsnbextension\n # \u0026gt; jupyter labextension install @jupyter-widgets/jupyterlab-manager\n\n # linear algebra and optimisation algorithms\n from numpy.linalg import norm\n from scipy.optimize import minimize\n # some other useful package\n from copy import deepcopy\"\u003e\u003cpre\u003e \u003cspan class=\"pl-c\"\u003e# numpy: our main numerical package\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# matplotlib and seaborn: our plotting packages\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ematplotlib\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003epyplot\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eplt\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eseaborn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003esns\u003c/span\u003e\n\n \u003cspan class=\"pl-c\"\u003e# widget for producing animations:\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eipywidgets\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003einteractive\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# Note: to produce animations you might need to configure your jupyter lab properly:\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# \u0026gt; pip install ipywidgets\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# \u0026gt; jupyter nbextension enable --py widgetsnbextension\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# \u0026gt; jupyter labextension install @jupyter-widgets/jupyterlab-manager\u003c/span\u003e\n\n \u003cspan class=\"pl-c\"\u003e# linear algebra and optimisation algorithms\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003elinalg\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enorm\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003escipy\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eoptimize\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eminimize\u003c/span\u003e\n \u003cspan class=\"pl-c\"\u003e# some other useful package\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003efrom\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ecopy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003edeepcopy\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eif you happen to experience any problem, please check to have installed the whole anaconda distribution distribution. Alternatively, you can try to go back to your terminal, and install each single package independently, e.g.:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"pip install numpy matplotlib seaborn scipy ipywidgets jupyter jupyterlab\"\u003e\u003cpre\u003e\u003cspan class=\"pl-s1\"\u003epip\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003einstall\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ematplotlib\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eseaborn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003escipy\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eipywidgets\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ejupyter\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ejupyterlab\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eJust before the start of the lattice calculation course\u003c/strong\u003e, we will ask you to clone the \u003cstrong\u003ecas_2023\u003c/strong\u003e branch of this repository in your \u003cstrong\u003eworking directory\u003c/strong\u003e, and start \u003ccode\u003ejupyter lab\u003c/code\u003e within it:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-shell notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"git clone -b cas_2023 https://github.com/cerncas/hands-on-lattice-exercises/\ncd hands-on-lattice-exercises\njupyter lab\"\u003e\u003cpre\u003egit clone -b cas_2023 https://github.com/cerncas/hands-on-lattice-exercises/\n\u003cspan class=\"pl-c1\"\u003ecd\u003c/span\u003e hands-on-lattice-exercises\njupyter lab\u003c/pre\u003e\u003c/div\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eOptional:\u003c/strong\u003e instead of running Jupyter lab within a browser, you can use your favourite editor and/or IDE ((Integrated Development Environment), e.g.\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eyou can use \u003ccode\u003ejupyter notebook\u003c/code\u003e instead of \u003ccode\u003ejupyter lab\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eyou can try out \u003ca href=\"https://github.com/jupyterlab/jupyterlab-desktop\"\u003ejupyterlab-desktop\u003c/a\u003e application.\u003c/li\u003e\n\u003cli\u003eyou can try out \u003ca href=\"https://code.visualstudio.com\" rel=\"nofollow\"\u003eVisual Studio Code\u003c/a\u003e application.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTest that everything works!\u003c/h2\u003e\u003ca id=\"user-content-test-that-everything-works\" class=\"anchor\" aria-label=\"Permalink: Test that everything works!\" href=\"#test-that-everything-works\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003ePlease, make sure to go throw all the examples below to familiarize with the typical Python concepts that will be used during the course, but also to verify your installation.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eIndexing\u003c/h3\u003e\u003ca id=\"user-content-indexing\" class=\"anchor\" aria-label=\"Permalink: Indexing\" href=\"#indexing\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eGenerate a random array and select specific elements:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"import numpy as np\n\n# Create an array\narray1d = np.random.uniform(size=10)\n# Print selected elements\nprint(\u0026quot;Entire array: \u0026quot; + str(array1d) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Specific element: \u0026quot; + str(array1d[5]) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Last element: \u0026quot; + str(array1d[-1]) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Specific elements: \u0026quot; + str(array1d[3:7]) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;First 5 elements array: \u0026quot; + str(array1d[:5]) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Last 5 elements array: \u0026quot; + str(array1d[5:]) + \u0026quot;\\n\u0026quot;)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Create an array\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003erandom\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003euniform\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003esize\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e10\u003c/span\u003e)\n\u003cspan class=\"pl-c\"\u003e# Print selected elements\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Entire array: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Specific element: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e[\u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e]) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Last element: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e[\u003cspan class=\"pl-c1\"\u003e-\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e]) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Specific elements: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e[\u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e:\u003cspan class=\"pl-c1\"\u003e7\u003c/span\u003e]) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"First 5 elements array: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e[:\u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e]) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Last 5 elements array: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e[\u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e:]) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ewill result in, e.g.:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-shell notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Entire array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777 0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]\n\nSpecific element: 0.9786363385079204\n\nLast element: 0.5928534616865488\n\nSpecific elements: [0.60573004 0.81588777 0.97863634 0.51376609]\n\nFirst 5 elements array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777]\n\nLast 5 elements array: [0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]\"\u003e\u003cpre\u003eEntire array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777 0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]\n\nSpecific element: 0.9786363385079204\n\nLast element: 0.5928534616865488\n\nSpecific elements: [0.60573004 0.81588777 0.97863634 0.51376609]\n\nFirst 5 elements array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777]\n\nLast 5 elements array: [0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eImplicit loops\u003c/h3\u003e\u003ca id=\"user-content-implicit-loops\" class=\"anchor\" aria-label=\"Permalink: Implicit loops\" href=\"#implicit-loops\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn contrast to programming languages like C++, Python can handle vectors. No loop is required, e.g. to multiply each element with a constant or squaring it:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-python notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"import numpy as np\n\n# Create an array\narray1d = np.random.uniform(size=10)\n\nprint(\u0026quot;Entire array: \u0026quot; + str(array1d) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Each element muliplied by 5: \u0026quot; + str(5 * array1d) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Each element squared: \u0026quot; + str(array1d**2) + \u0026quot;\\n\u0026quot;)\nprint(\u0026quot;Square root of each element: \u0026quot; + str(np.sqrt(array1d)) + \u0026quot;\\n\u0026quot;)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003eimport\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enumpy\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eas\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e\n\n\u003cspan class=\"pl-c\"\u003e# Create an array\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003erandom\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003euniform\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003esize\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e10\u003c/span\u003e)\n\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Entire array: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Each element muliplied by 5: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e*\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Each element squared: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e**\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\n\u003cspan class=\"pl-en\"\u003eprint\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Square root of each element: \"\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-en\"\u003estr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enp\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003esqrt\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003earray1d\u003c/span\u003e)) \u003cspan class=\"pl-c1\"\u003e+\u003c/span\u003e \u003cspan class=\"pl-s\"\u003e\"\u003cspan class=\"pl-cce\"\u003e\\n\u003c/span\u003e\"\u003c/span\u003e)\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ewill result in, e.g.:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-shell notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Entire array: [0.2240143 0.35153156 0.68864907 0.14062298 0.77280195 0.26872206 0.9135403 0.8776261 0.26158576 0.93883652]\n\nEach element muliplied by 5: [1.12007151 1.75765782 3.44324537 0.70311488 3.86400975 1.34361029 4.56770149 4.3881305 1.30792879 4.69418259]\n\nEach element squared: [0.05018241 0.12357444 0.47423755 0.01977482 0.59722285 0.07221154 0.83455588 0.77022757 0.06842711 0.88141401]\n\nSquare root of each element: [0.47330149 0.59290097 0.82984883 0.3749973 0.87909155 0.51838408 0.95579302 0.936817 0.51145455 0.96893577]\"\u003e\u003cpre\u003eEntire array: [0.2240143 0.35153156 0.68864907 0.14062298 0.77280195 0.26872206 0.9135403 0.8776261 0.26158576 0.93883652]\n\nEach element muliplied by 5: [1.12007151 1.75765782 3.44324537 0.70311488 3.86400975 1.34361029 4.56770149 4.3881305 1.30792879 4.69418259]\n\nEach element squared: [0.05018241 0.12357444 0.47423755 0.01977482 0.59722285 0.07221154 0.83455588 0.77022757 0.06842711 0.88141401]\n\nSquare root of each element: [0.47330149 0.59290097 0.82984883 0.3749973 0.87909155 0.51838408 0.95579302 0.936817 0.51145455 0.96893577]\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can perform also some linear algebra tests:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"import numpy as np\nimport pandas as pd\nfrom matplotlib import pyplot as plt\nimport seaborn as sns\nimport sympy as sy\n\n# Matrix definition\nOmega=np.array([[0, 1],[-1,0]])\nM=np.array([[1, 0],[1,1]])\n\n# Sum and multiplication of matrices\nOmega - M.T @ Omega @ M\n# M.T means the \u0026quot;traspose of M\u0026quot;.\n\n# Function definition\ndef Q(f=1):\n return np.array([[1, 0],[-1/f,1]])\n\n#Eigenvalues and eigenvectors\nnp.linalg.eig(M)\"\u003e\u003cpre lang=\"python=\" class=\"notranslate\"\u003e\u003ccode\u003eimport numpy as np\nimport pandas as pd\nfrom matplotlib import pyplot as plt\nimport seaborn as sns\nimport sympy as sy\n\n# Matrix definition\nOmega=np.array([[0, 1],[-1,0]])\nM=np.array([[1, 0],[1,1]])\n\n# Sum and multiplication of matrices\nOmega - M.T @ Omega @ M\n# M.T means the \"traspose of M\".\n\n# Function definition\ndef Q(f=1):\n return np.array([[1, 0],[-1/f,1]])\n\n#Eigenvalues and eigenvectors\nnp.linalg.eig(M)\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePlotting\u003c/h3\u003e\u003ca id=\"user-content-plotting\" class=\"anchor\" aria-label=\"Permalink: Plotting\" href=\"#plotting\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can create a simple plot as follow:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"# check a simple plot\n%matplotlib inline\n\nplt.plot([0,10],[0,10],'ob-')\nplt.xlabel('My x-label [arb. units]')\nplt.ylabel('My y-label [arb. units]')\nplt.title('My title')\"\u003e\u003cpre lang=\"python=\" class=\"notranslate\"\u003e\u003ccode\u003e# check a simple plot\n%matplotlib inline\n\nplt.plot([0,10],[0,10],'ob-')\nplt.xlabel('My x-label [arb. units]')\nplt.ylabel('My y-label [arb. units]')\nplt.title('My title')\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ewhich should result in the following plot:\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_b7610a37c41729a79bc4b0a5d863594b.png\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_b7610a37c41729a79bc4b0a5d863594b.png\" alt=\"\" width=\"40%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOr something fancier:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"# an sns plot\nsns.set(style=\u0026quot;ticks\u0026quot;)\nrs = np.random.RandomState(11)\nx = rs.normal(size=1000)\ny = rs.normal(size=1000)\nsns.jointplot(x=x, y=y, kind=\u0026quot;hex\u0026quot;)\"\u003e\u003cpre lang=\"python=\" class=\"notranslate\"\u003e\u003ccode\u003e# an sns plot\nsns.set(style=\"ticks\")\nrs = np.random.RandomState(11)\nx = rs.normal(size=1000)\ny = rs.normal(size=1000)\nsns.jointplot(x=x, y=y, kind=\"hex\")\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_1c7eaa74ee5422c62408cc9a57f7f0de.png\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_1c7eaa74ee5422c62408cc9a57f7f0de.png\" alt=\"\" width=\"40%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePandas dataframes\u003c/h3\u003e\u003ca id=\"user-content-pandas-dataframes\" class=\"anchor\" aria-label=\"Permalink: Pandas dataframes\" href=\"#pandas-dataframes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can import some information in a pandas dataframe from the internet :\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"# a simple pandas dataframe (GDP world statistics)\nmyDF=pd.read_csv('https://stats.oecd.org/sdmx-json/data/DP_LIVE/.GDP.../OECD?contentType=csv\u0026amp;detail=code\u0026amp;separator=comma\u0026amp;csv-lang=en')\nmyDF[(myDF['TIME']==2018) \u0026amp; (myDF['MEASURE']=='MLN_USD')]\nmyDF.head()\"\u003e\u003cpre lang=\"python=\" class=\"notranslate\"\u003e\u003ccode\u003e# a simple pandas dataframe (GDP world statistics)\nmyDF=pd.read_csv('https://stats.oecd.org/sdmx-json/data/DP_LIVE/.GDP.../OECD?contentType=csv\u0026amp;detail=code\u0026amp;separator=comma\u0026amp;csv-lang=en')\nmyDF[(myDF['TIME']==2018) \u0026amp; (myDF['MEASURE']=='MLN_USD')]\nmyDF.head()\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ethat gives\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_90f1a933f3f7092f2a4d4b50725e61ae.png\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_90f1a933f3f7092f2a4d4b50725e61ae.png\" alt=\"\" width=\"70%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAnimations\u003c/h3\u003e\u003ca id=\"user-content-animations\" class=\"anchor\" aria-label=\"Permalink: Animations\" href=\"#animations\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eIMPORTANT\u003c/strong\u003e: we will use animation in Python. Please check that the following code is running or your machine.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"# to have the animation you need to configure properly your jupyter lab\n# From https://towardsdatascience.com/interactive-controls-for-jupyter-notebooks-f5c94829aee6\n\n# \u0026gt; pip install ipywidgets\n# \u0026gt; jupyter nbextension enable --py widgetsnbextension\n# \u0026gt; jupyter labextension install @jupyter-widgets/jupyterlab-manager\n\n# Possibly you need also nodejs \n# https://anaconda.org/conda-forge/nodejs\n# \u0026gt; conda install -c conda-forge nodejs \n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom ipywidgets import interactive\n\nt = np.linspace(0,10,1000)\ndef plotIt(f):\n plt.plot(t, np.sin(2*np.pi*f*t))\n plt.grid(True)\n \ninteractive_plot = interactive(plotIt,f=(0,1,.1),continuous_update=True)\noutput = interactive_plot.children[-1]\noutput.layout.height = '300px'\ninteractive_plot\"\u003e\u003cpre lang=\"python=\" class=\"notranslate\"\u003e\u003ccode\u003e# to have the animation you need to configure properly your jupyter lab\n# From https://towardsdatascience.com/interactive-controls-for-jupyter-notebooks-f5c94829aee6\n\n# \u0026gt; pip install ipywidgets\n# \u0026gt; jupyter nbextension enable --py widgetsnbextension\n# \u0026gt; jupyter labextension install @jupyter-widgets/jupyterlab-manager\n\n# Possibly you need also nodejs \n# https://anaconda.org/conda-forge/nodejs\n# \u0026gt; conda install -c conda-forge nodejs \n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom ipywidgets import interactive\n\nt = np.linspace(0,10,1000)\ndef plotIt(f):\n plt.plot(t, np.sin(2*np.pi*f*t))\n plt.grid(True)\n \ninteractive_plot = interactive(plotIt,f=(0,1,.1),continuous_update=True)\noutput = interactive_plot.children[-1]\noutput.layout.height = '300px'\ninteractive_plot\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_0dff4499bd5e7b21942e1990cd76d0e9.png\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_0dff4499bd5e7b21942e1990cd76d0e9.png\" alt=\"\" width=\"40%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003chr\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAppendix: Python Packages\u003c/h2\u003e\u003ca id=\"user-content-appendix-python-packages\" class=\"anchor\" aria-label=\"Permalink: Appendix: Python Packages\" href=\"#appendix-python-packages\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eYou can leverage python's capability by exploring a galaxy of packages. Below you can find the most useful for our course (focus mostly on \u003ccode\u003enumpy\u003c/code\u003e and \u003ccode\u003ematplotlib\u003c/code\u003e) and some very popular ones.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003enumpy\u003c/em\u003e package\u003c/h3\u003e\u003ca id=\"user-content-the-numpy-package\" class=\"anchor\" aria-label=\"Permalink: The numpy package\" href=\"#the-numpy-package\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the \u003cem\u003enumpy\u003c/em\u003e package have a look at the following \u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\nYou can google many other resources, but the one presented of the poster covers the set of instructions you should familiar with.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_6ffb4d07b1ebb895528f2a34aae41ec6.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003ematplotlib\u003c/em\u003e package\u003c/h3\u003e\u003ca id=\"user-content-the-matplotlib-package\" class=\"anchor\" aria-label=\"Permalink: The matplotlib package\" href=\"#the-matplotlib-package\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the \u003cem\u003ematplotlib\u003c/em\u003e package have a look at the following \u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_4b54812812e21978b600b860ba1ddf5b.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003elinalg\u003c/em\u003e module\u003c/h3\u003e\u003ca id=\"user-content-the-linalg-module\" class=\"anchor\" aria-label=\"Permalink: The linalg module\" href=\"#the-linalg-module\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the Linear Algebra (linalg) module have a look at the following \u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_SciPy_Cheat_Sheet_Linear_Algebra.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_SciPy_Cheat_Sheet_Linear_Algebra.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_15561fc12184bb0ae3f9cf7b1850317a.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003epandas\u003c/em\u003e package (optional)\u003c/h3\u003e\u003ca id=\"user-content-the-pandas-package-optional\" class=\"anchor\" aria-label=\"Permalink: The pandas package (optional)\" href=\"#the-pandas-package-optional\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the \u003cem\u003epandas\u003c/em\u003e package have a look at the following \u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PandasPythonForDataScience.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PandasPythonForDataScience.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_90383c01e29d29fb6a5516c613e22c4d.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003eseaborn\u003c/em\u003e package (optional)\u003c/h3\u003e\u003ca id=\"user-content-the-seaborn-package-optional\" class=\"anchor\" aria-label=\"Permalink: The seaborn package (optional)\" href=\"#the-seaborn-package-optional\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the \u003cem\u003eseaborn\u003c/em\u003e package have a look at the following \u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Seaborn_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Seaborn_Cheat_Sheet.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_9a3c3f5ca48bbd567a0662df20dbd16f.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe \u003cem\u003esympy\u003c/em\u003e package (optional)\u003c/h3\u003e\u003ca id=\"user-content-the-sympy-package-optional\" class=\"anchor\" aria-label=\"Permalink: The sympy package (optional)\" href=\"#the-sympy-package-optional\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get familiar with the \u003cem\u003esympy\u003c/em\u003e package have a look at the following \u003ca href=\"http://daabzlatex.s3.amazonaws.com/9065616cce623384fe5394eddfea4c52.pdf\" rel=\"nofollow\"\u003esummary poster\u003c/a\u003e.\u003c/p\u003e\n\u003cp align=\"center\" dir=\"auto\"\u003e\n\u003ca href=\"http://daabzlatex.s3.amazonaws.com/9065616cce623384fe5394eddfea4c52.pdf\" rel=\"nofollow\"\u003e\u003cimg src=\"/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_fc7a06ea6135d2bf17311bd7a91f1a9f.png\" alt=\"\" width=\"90%\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003c/p\u003e\n\u003c/article\u003e","renderedFileInfo":null,"shortPath":null,"symbolsEnabled":true,"tabSize":8,"topBannersInfo":{"overridingGlobalFundingFile":false,"globalPreferredFundingPath":null,"showInvalidCitationWarning":false,"citationHelpUrl":"https://docs.github.com/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files","actionsOnboardingTip":null},"truncated":false,"viewable":true,"workflowRedirectUrl":null,"symbols":{"timed_out":true,"not_analyzed":false,"symbols":[{"name":"Hands-On Lattice (and Longitudinal) Calculations using Python - Setup Instructions","kind":"section_1","ident_start":2,"ident_end":84,"extent_start":0,"extent_end":1404,"fully_qualified_name":"Hands-On Lattice (and Longitudinal) Calculations using Python - Setup 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height="16" fill="currentColor" style="display:inline-block;user-select:none;vertical-align:text-bottom;overflow:visible"><path d="M8 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3ZM1.5 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Zm13 0a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Z"></path></svg></button></div></div></div></div><div></div></div><div class="Box-sc-g0xbh4-0 hGyMdv"><section aria-labelledby="file-name-id-wide file-name-id-mobile" class="Box-sc-g0xbh4-0 fGqKFv"><div class="Box-sc-g0xbh4-0 eoaCFS js-snippet-clipboard-copy-unpositioned" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Hands-On Lattice (and Longitudinal) Calculations using Python - Setup Instructions</h1><a id="user-content-hands-on-lattice-and-longitudinal-calculations-using-python---setup-instructions" class="anchor" aria-label="Permalink: Hands-On Lattice (and Longitudinal) Calculations using Python - Setup Instructions" href="#hands-on-lattice-and-longitudinal-calculations-using-python---setup-instructions"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <hr> <p dir="auto">During the course we will use <strong>Python3</strong> in a <strong>Jupyter notebook</strong> with <a href="https://jupyterlab.readthedocs.io/en/stable/" rel="nofollow">JupyterLab</a> and, mostly, the <a href="https://numpy.org/" rel="nofollow">numpy</a> and <a href="https://matplotlib.org/" rel="nofollow">matplotlib</a> packages. We will explain in the following sections how to install all necessary software on <strong>your laptop</strong>. A basic knowledge of Python is assumed. If you are not familiar with Python, you can find a few resources to fill the gap in the following sections.</p> <p dir="auto">To get a better idea of the level of the Python knowledge needed for the course you can browse the <a href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/CAS_Optics_Primer.pdf">primer of the hands-on course</a>. Do not worry about the theory for the moment (it will be discussed in details during the school) but focus on the Python syntax and data types (tuples, lists,...).</p> <p dir="auto">After <a href="#a-very-short-introduction-to-python">a short introduction</a>, where we provided some useful links to get familiar with Python, we will focus on the <a href="#software-setup">software setup</a>. Finally, in <a href="#appendix-python-packages">appendix</a> you will find links and cheatsheets for the most common Python packages that will be used during the course.</p> <blockquote> <p dir="auto"><strong>Important:</strong> we kindly ask you to go throw this document <strong>before coming</strong> to CAS, such as to <strong>prepare yourself</strong> (and <strong>your laptop</strong>) for the course.</p> </blockquote> <hr> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">A very short introduction to Python</h1><a id="user-content-a-very-short-introduction-to-python" class="anchor" aria-label="Permalink: A very short introduction to Python" href="#a-very-short-introduction-to-python"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">You can find several nice courses, videos and resources on the internet. Here you have a couple of suggestions you can find on YouTube:</p> <p align="center" dir="auto"> <a href="http://www.youtube.com/watch?v=kqtD5dpn9C8" rel="nofollow"><img src="https://camo.githubusercontent.com/43002d00aec45990c107202807c77de97c4035ce093b3abc02c1e22c15d3263d/687474703a2f2f696d672e796f75747562652e636f6d2f76692f6b7174443564706e3943382f302e6a7067" alt="Python for Beginners - Learn Python in 1 Hour" width="40%" data-canonical-src="http://img.youtube.com/vi/kqtD5dpn9C8/0.jpg" style="max-width: 100%;"></a> <a href="http://www.youtube.com/watch?v=rfscVS0vtbw" rel="nofollow"><img src="https://camo.githubusercontent.com/9e1999c1532b2f091b8764ca1debbe04294b7efe77012e5f06fb401c7c22a1c0/687474703a2f2f696d672e796f75747562652e636f6d2f76692f72667363565330767462772f302e6a7067" alt="Learn Python - Full Course for Beginners" width="40%" data-canonical-src="http://img.youtube.com/vi/rfscVS0vtbw/0.jpg" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Test Python on a web page</h3><a id="user-content-test-python-on-a-web-page" class="anchor" aria-label="Permalink: Test Python on a web page" href="#test-python-on-a-web-page"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">If you are not familiar with Python and you have not it installed on your laptop, you can start playing with simple python snippets on the web. Without installing any special software you can connect, for example, to <a href="https://gke.mybinder.org/v2/gh/jupyterlab/jupyterlab-demo/try.jupyter.org?urlpath=lab" rel="nofollow">jupyterLab</a>, and test the following commands:</p> <div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="import numpy as np # Matrix definition Omega=np.array([[0, 1],[-1,0]]) M=np.array([[1, 0],[1,1]]) # Sum and multiplication of matrices Omega - M.T @ Omega @ M # M.T means the "traspose of M". # Function definition def Q(f=1): return np.array([[1, 0],[-1/f,1]]) # Eigenvalues and eigenvectors np.linalg.eig(M)"><pre><span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span> <span class="pl-c"># Matrix definition</span> <span class="pl-v">Omega</span><span class="pl-c1">=</span><span class="pl-s1">np</span>.<span class="pl-en">array</span>([[<span class="pl-c1">0</span>, <span class="pl-c1">1</span>],[<span class="pl-c1">-</span><span class="pl-c1">1</span>,<span class="pl-c1">0</span>]]) <span class="pl-v">M</span><span class="pl-c1">=</span><span class="pl-s1">np</span>.<span class="pl-en">array</span>([[<span class="pl-c1">1</span>, <span class="pl-c1">0</span>],[<span class="pl-c1">1</span>,<span class="pl-c1">1</span>]]) <span class="pl-c"># Sum and multiplication of matrices</span> <span class="pl-v">Omega</span> <span class="pl-c1">-</span> <span class="pl-v">M</span>.<span class="pl-v">T</span> @ <span class="pl-v">Omega</span> @ <span class="pl-v">M</span> <span class="pl-c"># M.T means the "traspose of M".</span> <span class="pl-c"># Function definition</span> <span class="pl-k">def</span> <span class="pl-v">Q</span>(<span class="pl-s1">f</span><span class="pl-c1">=</span><span class="pl-c1">1</span>): <span class="pl-k">return</span> <span class="pl-s1">np</span>.<span class="pl-en">array</span>([[<span class="pl-c1">1</span>, <span class="pl-c1">0</span>],[<span class="pl-c1">-</span><span class="pl-c1">1</span><span class="pl-c1">/</span><span class="pl-s1">f</span>,<span class="pl-c1">1</span>]]) <span class="pl-c"># Eigenvalues and eigenvectors</span> <span class="pl-s1">np</span>.<span class="pl-s1">linalg</span>.<span class="pl-en">eig</span>(<span class="pl-v">M</span>)</pre></div> <p dir="auto">You can compare and check your output with the ones <a href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/tests/SimpleTest.ipynb">here</a>.</p> <hr> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Software Setup</h1><a id="user-content-software-setup" class="anchor" aria-label="Permalink: Software Setup" href="#software-setup"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In this section we will explain how to install Python and JupyterLab on your laptop. JupyterLab is a user-friendly environment to work with Python. You can find an overview on JupyterLab <a href="https://jupyterlab.readthedocs.io/en/stable/" rel="nofollow">here</a>.</p> <blockquote> <p dir="auto">If you already have your favorite Python distribution installed on your laptop, including JupyterLab, you might want to skip the <a href="#installation">installation</a> and jump to <a href="#launch-jupyter-lab">launch Jupyter Lab</a> and <a href="#test-that-everything-works">test that everything works</a>.</p> </blockquote> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Installation</h2><a id="user-content-installation" class="anchor" aria-label="Permalink: Installation" href="#installation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">We suggest to install the <strong>Anaconda</strong> distribution from <a href="https://www.anaconda.com/distribution/" rel="nofollow">https://www.anaconda.com/distribution/</a></p> <p align="center" dir="auto"> <a href="https://www.anaconda.com/distribution/" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/anaconda.png" alt="" width="70%" style="max-width: 100%;"></a> </p> <blockquote> <p dir="auto">We suggest to install one of the latest distribution (<strong>for example version 3.9</strong>).</p> </blockquote> <p dir="auto">The installation process clearly depends on your operating system. We suggest you to follow the official documentation for <a href="https://docs.anaconda.com/anaconda/install/windows/" rel="nofollow">Windows</a>, <a href="https://docs.anaconda.com/anaconda/install/linux/" rel="nofollow">Linux</a>, or <a href="https://docs.anaconda.com/anaconda/install/mac-os/" rel="nofollow">Mac</a> as appropriate. After having installed <strong>Anaconda</strong>, and <a href="https://docs.anaconda.com/anaconda/install/verify-install/" rel="nofollow">verified your installation</a> - as suggested in the <a href="https://docs.anaconda.com/anaconda/install/" rel="nofollow">installation documentation</a> - we invite you to start <a href="#launch-jupyter-lab">launching Jupyter Lab</a> and then <a href="#test-that-everything-works">test that everything works</a>:</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Launch Jupyter Lab</h2><a id="user-content-launch-jupyter-lab" class="anchor" aria-label="Permalink: Launch Jupyter Lab" href="#launch-jupyter-lab"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Once the installation of <strong>Anaconda</strong> is finalised or within your existing Python distribution, you should be able to start Jupyter Lab from a terminal:</p> <ol dir="auto"> <li> <p dir="auto">Open a (Anaconda) terminal on your operating system:</p> <ul dir="auto"> <li><strong>Windows:</strong> From the Start menu, search for and open “Anaconda Prompt”:</li> <li><strong>macOS:</strong> Open Launchpad, then click the terminal icon.</li> <li><strong>Linux:</strong> Open a terminal window.</li> </ul> </li> <li> <p dir="auto">Launch Jupyter Lab from your terminal:</p> <div class="highlight highlight-source-shell notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="jupyter lab"><pre>jupyter lab</pre></div> </li> <li> <p dir="auto">Follow the instructions given in the terminal. You should end-up on your default browser with a page similar to the following:</p> <p align="center" dir="auto"> <a target="_blank" rel="noopener noreferrer" href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_5b0618b75e4f4df0facf2a609b9354b5.png"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_5b0618b75e4f4df0facf2a609b9354b5.png" alt="" width="70%" style="max-width: 100%;"></a> </p> <p dir="auto">On the left hand side of the widows you should see all files under the folder in your operating system where you executed the <code>jupyter lab</code> command. This will be your <strong>working directory</strong>.</p> </li> <li> <p dir="auto">Create a new "Python 3" "Notebook" and start playing with Python! If you are not familiar with Python, you can start playing with simple python snippets. For example, have a look to the following <a href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/tests/PythonExample.ipynb">notebook</a> (courtesy of <em>Simon Albright</em>).</p> </li> <li> <p dir="auto">Try to import all packages that we will be using in our course:</p> <div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content=" # numpy: our main numerical package import numpy as np # matplotlib and seaborn: our plotting packages import matplotlib.pyplot as plt import seaborn as sns # widget for producing animations: from ipywidgets import interactive # Note: to produce animations you might need to configure your jupyter lab properly: # > pip install ipywidgets # > jupyter nbextension enable --py widgetsnbextension # > jupyter labextension install @jupyter-widgets/jupyterlab-manager # linear algebra and optimisation algorithms from numpy.linalg import norm from scipy.optimize import minimize # some other useful package from copy import deepcopy"><pre> <span class="pl-c"># numpy: our main numerical package</span> <span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span> <span class="pl-c"># matplotlib and seaborn: our plotting packages</span> <span class="pl-k">import</span> <span class="pl-s1">matplotlib</span>.<span class="pl-s1">pyplot</span> <span class="pl-k">as</span> <span class="pl-s1">plt</span> <span class="pl-k">import</span> <span class="pl-s1">seaborn</span> <span class="pl-k">as</span> <span class="pl-s1">sns</span> <span class="pl-c"># widget for producing animations:</span> <span class="pl-k">from</span> <span class="pl-s1">ipywidgets</span> <span class="pl-k">import</span> <span class="pl-s1">interactive</span> <span class="pl-c"># Note: to produce animations you might need to configure your jupyter lab properly:</span> <span class="pl-c"># > pip install ipywidgets</span> <span class="pl-c"># > jupyter nbextension enable --py widgetsnbextension</span> <span class="pl-c"># > jupyter labextension install @jupyter-widgets/jupyterlab-manager</span> <span class="pl-c"># linear algebra and optimisation algorithms</span> <span class="pl-k">from</span> <span class="pl-s1">numpy</span>.<span class="pl-s1">linalg</span> <span class="pl-k">import</span> <span class="pl-s1">norm</span> <span class="pl-k">from</span> <span class="pl-s1">scipy</span>.<span class="pl-s1">optimize</span> <span class="pl-k">import</span> <span class="pl-s1">minimize</span> <span class="pl-c"># some other useful package</span> <span class="pl-k">from</span> <span class="pl-s1">copy</span> <span class="pl-k">import</span> <span class="pl-s1">deepcopy</span></pre></div> <p dir="auto">if you happen to experience any problem, please check to have installed the whole anaconda distribution distribution. Alternatively, you can try to go back to your terminal, and install each single package independently, e.g.:</p> <div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="pip install numpy matplotlib seaborn scipy ipywidgets jupyter jupyterlab"><pre><span class="pl-s1">pip</span> <span class="pl-s1">install</span> <span class="pl-s1">numpy</span> <span class="pl-s1">matplotlib</span> <span class="pl-s1">seaborn</span> <span class="pl-s1">scipy</span> <span class="pl-s1">ipywidgets</span> <span class="pl-s1">jupyter</span> <span class="pl-s1">jupyterlab</span></pre></div> </li> <li> <p dir="auto"><strong>Just before the start of the lattice calculation course</strong>, we will ask you to clone the <strong>cas_2023</strong> branch of this repository in your <strong>working directory</strong>, and start <code>jupyter lab</code> within it:</p> <div class="highlight highlight-source-shell notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="git clone -b cas_2023 https://github.com/cerncas/hands-on-lattice-exercises/ cd hands-on-lattice-exercises jupyter lab"><pre>git clone -b cas_2023 https://github.com/cerncas/hands-on-lattice-exercises/ <span class="pl-c1">cd</span> hands-on-lattice-exercises jupyter lab</pre></div> </li> <li> <p dir="auto"><strong>Optional:</strong> instead of running Jupyter lab within a browser, you can use your favourite editor and/or IDE ((Integrated Development Environment), e.g.</p> <ul dir="auto"> <li>you can use <code>jupyter notebook</code> instead of <code>jupyter lab</code></li> <li>you can try out <a href="https://github.com/jupyterlab/jupyterlab-desktop">jupyterlab-desktop</a> application.</li> <li>you can try out <a href="https://code.visualstudio.com" rel="nofollow">Visual Studio Code</a> application.</li> </ul> </li> </ol> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Test that everything works!</h2><a id="user-content-test-that-everything-works" class="anchor" aria-label="Permalink: Test that everything works!" href="#test-that-everything-works"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <blockquote> <p dir="auto">Please, make sure to go throw all the examples below to familiarize with the typical Python concepts that will be used during the course, but also to verify your installation.</p> </blockquote> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Indexing</h3><a id="user-content-indexing" class="anchor" aria-label="Permalink: Indexing" href="#indexing"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Generate a random array and select specific elements:</p> <div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="import numpy as np # Create an array array1d = np.random.uniform(size=10) # Print selected elements print("Entire array: " + str(array1d) + "\n") print("Specific element: " + str(array1d[5]) + "\n") print("Last element: " + str(array1d[-1]) + "\n") print("Specific elements: " + str(array1d[3:7]) + "\n") print("First 5 elements array: " + str(array1d[:5]) + "\n") print("Last 5 elements array: " + str(array1d[5:]) + "\n")"><pre><span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span> <span class="pl-c"># Create an array</span> <span class="pl-s1">array1d</span> <span class="pl-c1">=</span> <span class="pl-s1">np</span>.<span class="pl-s1">random</span>.<span class="pl-en">uniform</span>(<span class="pl-s1">size</span><span class="pl-c1">=</span><span class="pl-c1">10</span>) <span class="pl-c"># Print selected elements</span> <span class="pl-en">print</span>(<span class="pl-s">"Entire array: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Specific element: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>[<span class="pl-c1">5</span>]) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Last element: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>[<span class="pl-c1">-</span><span class="pl-c1">1</span>]) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Specific elements: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>[<span class="pl-c1">3</span>:<span class="pl-c1">7</span>]) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"First 5 elements array: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>[:<span class="pl-c1">5</span>]) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Last 5 elements array: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>[<span class="pl-c1">5</span>:]) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>)</pre></div> <p dir="auto">will result in, e.g.:</p> <div class="highlight highlight-source-shell notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Entire array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777 0.97863634 0.51376609 0.19763518 0.7649532 0.59285346] Specific element: 0.9786363385079204 Last element: 0.5928534616865488 Specific elements: [0.60573004 0.81588777 0.97863634 0.51376609] First 5 elements array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777] Last 5 elements array: [0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]"><pre>Entire array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777 0.97863634 0.51376609 0.19763518 0.7649532 0.59285346] Specific element: 0.9786363385079204 Last element: 0.5928534616865488 Specific elements: [0.60573004 0.81588777 0.97863634 0.51376609] First 5 elements array: [0.09402447 0.05647033 0.79670378 0.60573004 0.81588777] Last 5 elements array: [0.97863634 0.51376609 0.19763518 0.7649532 0.59285346]</pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Implicit loops</h3><a id="user-content-implicit-loops" class="anchor" aria-label="Permalink: Implicit loops" href="#implicit-loops"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In contrast to programming languages like C++, Python can handle vectors. No loop is required, e.g. to multiply each element with a constant or squaring it:</p> <div class="highlight highlight-source-python notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="import numpy as np # Create an array array1d = np.random.uniform(size=10) print("Entire array: " + str(array1d) + "\n") print("Each element muliplied by 5: " + str(5 * array1d) + "\n") print("Each element squared: " + str(array1d**2) + "\n") print("Square root of each element: " + str(np.sqrt(array1d)) + "\n")"><pre><span class="pl-k">import</span> <span class="pl-s1">numpy</span> <span class="pl-k">as</span> <span class="pl-s1">np</span> <span class="pl-c"># Create an array</span> <span class="pl-s1">array1d</span> <span class="pl-c1">=</span> <span class="pl-s1">np</span>.<span class="pl-s1">random</span>.<span class="pl-en">uniform</span>(<span class="pl-s1">size</span><span class="pl-c1">=</span><span class="pl-c1">10</span>) <span class="pl-en">print</span>(<span class="pl-s">"Entire array: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span>) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Each element muliplied by 5: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-c1">5</span> <span class="pl-c1">*</span> <span class="pl-s1">array1d</span>) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Each element squared: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">array1d</span><span class="pl-c1">**</span><span class="pl-c1">2</span>) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>) <span class="pl-en">print</span>(<span class="pl-s">"Square root of each element: "</span> <span class="pl-c1">+</span> <span class="pl-en">str</span>(<span class="pl-s1">np</span>.<span class="pl-en">sqrt</span>(<span class="pl-s1">array1d</span>)) <span class="pl-c1">+</span> <span class="pl-s">"<span class="pl-cce">\n</span>"</span>)</pre></div> <p dir="auto">will result in, e.g.:</p> <div class="highlight highlight-source-shell notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Entire array: [0.2240143 0.35153156 0.68864907 0.14062298 0.77280195 0.26872206 0.9135403 0.8776261 0.26158576 0.93883652] Each element muliplied by 5: [1.12007151 1.75765782 3.44324537 0.70311488 3.86400975 1.34361029 4.56770149 4.3881305 1.30792879 4.69418259] Each element squared: [0.05018241 0.12357444 0.47423755 0.01977482 0.59722285 0.07221154 0.83455588 0.77022757 0.06842711 0.88141401] Square root of each element: [0.47330149 0.59290097 0.82984883 0.3749973 0.87909155 0.51838408 0.95579302 0.936817 0.51145455 0.96893577]"><pre>Entire array: [0.2240143 0.35153156 0.68864907 0.14062298 0.77280195 0.26872206 0.9135403 0.8776261 0.26158576 0.93883652] Each element muliplied by 5: [1.12007151 1.75765782 3.44324537 0.70311488 3.86400975 1.34361029 4.56770149 4.3881305 1.30792879 4.69418259] Each element squared: [0.05018241 0.12357444 0.47423755 0.01977482 0.59722285 0.07221154 0.83455588 0.77022757 0.06842711 0.88141401] Square root of each element: [0.47330149 0.59290097 0.82984883 0.3749973 0.87909155 0.51838408 0.95579302 0.936817 0.51145455 0.96893577]</pre></div> <p dir="auto">You can perform also some linear algebra tests:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="import numpy as np import pandas as pd from matplotlib import pyplot as plt import seaborn as sns import sympy as sy # Matrix definition Omega=np.array([[0, 1],[-1,0]]) M=np.array([[1, 0],[1,1]]) # Sum and multiplication of matrices Omega - M.T @ Omega @ M # M.T means the "traspose of M". # Function definition def Q(f=1): return np.array([[1, 0],[-1/f,1]]) #Eigenvalues and eigenvectors np.linalg.eig(M)"><pre lang="python=" class="notranslate"><code>import numpy as np import pandas as pd from matplotlib import pyplot as plt import seaborn as sns import sympy as sy # Matrix definition Omega=np.array([[0, 1],[-1,0]]) M=np.array([[1, 0],[1,1]]) # Sum and multiplication of matrices Omega - M.T @ Omega @ M # M.T means the "traspose of M". # Function definition def Q(f=1): return np.array([[1, 0],[-1/f,1]]) #Eigenvalues and eigenvectors np.linalg.eig(M) </code></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Plotting</h3><a id="user-content-plotting" class="anchor" aria-label="Permalink: Plotting" href="#plotting"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">You can create a simple plot as follow:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="# check a simple plot %matplotlib inline plt.plot([0,10],[0,10],'ob-') plt.xlabel('My x-label [arb. units]') plt.ylabel('My y-label [arb. units]') plt.title('My title')"><pre lang="python=" class="notranslate"><code># check a simple plot %matplotlib inline plt.plot([0,10],[0,10],'ob-') plt.xlabel('My x-label [arb. units]') plt.ylabel('My y-label [arb. units]') plt.title('My title') </code></pre></div> <p dir="auto">which should result in the following plot:</p> <p align="center" dir="auto"> <a target="_blank" rel="noopener noreferrer" href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_b7610a37c41729a79bc4b0a5d863594b.png"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_b7610a37c41729a79bc4b0a5d863594b.png" alt="" width="40%" style="max-width: 100%;"></a> </p> <p dir="auto">Or something fancier:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="# an sns plot sns.set(style="ticks") rs = np.random.RandomState(11) x = rs.normal(size=1000) y = rs.normal(size=1000) sns.jointplot(x=x, y=y, kind="hex")"><pre lang="python=" class="notranslate"><code># an sns plot sns.set(style="ticks") rs = np.random.RandomState(11) x = rs.normal(size=1000) y = rs.normal(size=1000) sns.jointplot(x=x, y=y, kind="hex") </code></pre></div> <p align="center" dir="auto"> <a target="_blank" rel="noopener noreferrer" href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_1c7eaa74ee5422c62408cc9a57f7f0de.png"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_1c7eaa74ee5422c62408cc9a57f7f0de.png" alt="" width="40%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Pandas dataframes</h3><a id="user-content-pandas-dataframes" class="anchor" aria-label="Permalink: Pandas dataframes" href="#pandas-dataframes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">You can import some information in a pandas dataframe from the internet :</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="# a simple pandas dataframe (GDP world statistics) myDF=pd.read_csv('https://stats.oecd.org/sdmx-json/data/DP_LIVE/.GDP.../OECD?contentType=csv&detail=code&separator=comma&csv-lang=en') myDF[(myDF['TIME']==2018) & (myDF['MEASURE']=='MLN_USD')] myDF.head()"><pre lang="python=" class="notranslate"><code># a simple pandas dataframe (GDP world statistics) myDF=pd.read_csv('https://stats.oecd.org/sdmx-json/data/DP_LIVE/.GDP.../OECD?contentType=csv&detail=code&separator=comma&csv-lang=en') myDF[(myDF['TIME']==2018) & (myDF['MEASURE']=='MLN_USD')] myDF.head() </code></pre></div> <p dir="auto">that gives</p> <p align="center" dir="auto"> <a target="_blank" rel="noopener noreferrer" href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_90f1a933f3f7092f2a4d4b50725e61ae.png"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_90f1a933f3f7092f2a4d4b50725e61ae.png" alt="" width="70%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Animations</h3><a id="user-content-animations" class="anchor" aria-label="Permalink: Animations" href="#animations"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <blockquote> <p dir="auto"><strong>IMPORTANT</strong>: we will use animation in Python. Please check that the following code is running or your machine.</p> </blockquote> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="# to have the animation you need to configure properly your jupyter lab # From https://towardsdatascience.com/interactive-controls-for-jupyter-notebooks-f5c94829aee6 # > pip install ipywidgets # > jupyter nbextension enable --py widgetsnbextension # > jupyter labextension install @jupyter-widgets/jupyterlab-manager # Possibly you need also nodejs # https://anaconda.org/conda-forge/nodejs # > conda install -c conda-forge nodejs import numpy as np import matplotlib.pyplot as plt from ipywidgets import interactive t = np.linspace(0,10,1000) def plotIt(f): plt.plot(t, np.sin(2*np.pi*f*t)) plt.grid(True) interactive_plot = interactive(plotIt,f=(0,1,.1),continuous_update=True) output = interactive_plot.children[-1] output.layout.height = '300px' interactive_plot"><pre lang="python=" class="notranslate"><code># to have the animation you need to configure properly your jupyter lab # From https://towardsdatascience.com/interactive-controls-for-jupyter-notebooks-f5c94829aee6 # > pip install ipywidgets # > jupyter nbextension enable --py widgetsnbextension # > jupyter labextension install @jupyter-widgets/jupyterlab-manager # Possibly you need also nodejs # https://anaconda.org/conda-forge/nodejs # > conda install -c conda-forge nodejs import numpy as np import matplotlib.pyplot as plt from ipywidgets import interactive t = np.linspace(0,10,1000) def plotIt(f): plt.plot(t, np.sin(2*np.pi*f*t)) plt.grid(True) interactive_plot = interactive(plotIt,f=(0,1,.1),continuous_update=True) output = interactive_plot.children[-1] output.layout.height = '300px' interactive_plot </code></pre></div> <p align="center" dir="auto"> <a target="_blank" rel="noopener noreferrer" href="/cerncas/hands-on-lattice-exercises/blob/cas_2023/_img_instructions/upload_0dff4499bd5e7b21942e1990cd76d0e9.png"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_0dff4499bd5e7b21942e1990cd76d0e9.png" alt="" width="40%" style="max-width: 100%;"></a> </p> <hr> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Appendix: Python Packages</h2><a id="user-content-appendix-python-packages" class="anchor" aria-label="Permalink: Appendix: Python Packages" href="#appendix-python-packages"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">You can leverage python's capability by exploring a galaxy of packages. Below you can find the most useful for our course (focus mostly on <code>numpy</code> and <code>matplotlib</code>) and some very popular ones.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>numpy</em> package</h3><a id="user-content-the-numpy-package" class="anchor" aria-label="Permalink: The numpy package" href="#the-numpy-package"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the <em>numpy</em> package have a look at the following <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf" rel="nofollow">summary poster</a>. You can google many other resources, but the one presented of the poster covers the set of instructions you should familiar with.</p> <p align="center" dir="auto"> <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_6ffb4d07b1ebb895528f2a34aae41ec6.png" alt="" width="90%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>matplotlib</em> package</h3><a id="user-content-the-matplotlib-package" class="anchor" aria-label="Permalink: The matplotlib package" href="#the-matplotlib-package"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the <em>matplotlib</em> package have a look at the following <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf" rel="nofollow">summary poster</a>.</p> <p align="center" dir="auto"> <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_4b54812812e21978b600b860ba1ddf5b.png" alt="" width="90%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>linalg</em> module</h3><a id="user-content-the-linalg-module" class="anchor" aria-label="Permalink: The linalg module" href="#the-linalg-module"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the Linear Algebra (linalg) module have a look at the following <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_SciPy_Cheat_Sheet_Linear_Algebra.pdf" rel="nofollow">summary poster</a>.</p> <p align="center" dir="auto"> <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_SciPy_Cheat_Sheet_Linear_Algebra.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_15561fc12184bb0ae3f9cf7b1850317a.png" alt="" width="90%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>pandas</em> package (optional)</h3><a id="user-content-the-pandas-package-optional" class="anchor" aria-label="Permalink: The pandas package (optional)" href="#the-pandas-package-optional"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the <em>pandas</em> package have a look at the following <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PandasPythonForDataScience.pdf" rel="nofollow">summary poster</a>.</p> <p align="center" dir="auto"> <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PandasPythonForDataScience.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_90383c01e29d29fb6a5516c613e22c4d.png" alt="" width="90%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>seaborn</em> package (optional)</h3><a id="user-content-the-seaborn-package-optional" class="anchor" aria-label="Permalink: The seaborn package (optional)" href="#the-seaborn-package-optional"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the <em>seaborn</em> package have a look at the following <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Seaborn_Cheat_Sheet.pdf" rel="nofollow">summary poster</a>.</p> <p align="center" dir="auto"> <a href="https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Seaborn_Cheat_Sheet.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_9a3c3f5ca48bbd567a0662df20dbd16f.png" alt="" width="90%" style="max-width: 100%;"></a> </p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The <em>sympy</em> package (optional)</h3><a id="user-content-the-sympy-package-optional" class="anchor" aria-label="Permalink: The sympy package (optional)" href="#the-sympy-package-optional"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get familiar with the <em>sympy</em> package have a look at the following <a href="http://daabzlatex.s3.amazonaws.com/9065616cce623384fe5394eddfea4c52.pdf" rel="nofollow">summary poster</a>.</p> <p align="center" dir="auto"> <a href="http://daabzlatex.s3.amazonaws.com/9065616cce623384fe5394eddfea4c52.pdf" rel="nofollow"><img src="/cerncas/hands-on-lattice-exercises/raw/cas_2023/_img_instructions/upload_fc7a06ea6135d2bf17311bd7a91f1a9f.png" alt="" width="90%" style="max-width: 100%;"></a> </p> 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