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Which library should I use? Possibly scipy?" />
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data-s-popover-toggle-class="is-selected"
|
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>
|
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|
|
<div class="flex--item fl-grow1 tt-uppercase fc-black-600 fw-bold">Labs</div>
|
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<div class="flex--item px12">
|
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<svg aria-hidden="true" class="svg-icon iconInfoSm" width="14" height="14" viewBox="0 0 14 14"><path d="M7 1a6 6 0 1 1 0 12A6 6 0 0 1 7 1Zm1 10V6H6v5h2Zm0-6V3H6v2h2Z"/></svg>
|
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</div>
|
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</a>
|
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</li>
|
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<li class="ps-relative" aria-current="false">
|
|||
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|
|||
|
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|
|||
|
|
<a id="nav-labs-discussions"
|
|||
|
|
href="/collectives/beta/discussions"
|
|||
|
|
class="pl8 ai-center js-gps-track nav-links--link -link__with-icon"
|
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|
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|
data-gps-track="top_nav.click({is_current: false, location:2, destination:24, has_activity_notification:False})"
|
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aria-controls="" data-controller="" data-s-popover-placement="right"
|
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|
|
aria-current="false"
|
|||
|
|
data-s-popover-auto-show="true" data-s-popover-hide-on-outside-click="never"
|
|||
|
|
>
|
|||
|
|
<svg aria-hidden="true" class="fc-black-400 w16 svg-icon iconSpeechBubble" width="18" height="18" viewBox="0 0 18 18"><path d="m4 15-3 3V4c0-1.1.9-2 2-2h12a2 2 0 0 1 2 2v9a2 2 0 0 1-2 2H4Z"/></svg> <span class="-link--channel-name pl6">Discussions</span>
|
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</a>
|
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</li>
|
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</ol>
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<li class="js-freemium-cta ps-relative">
|
|||
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|
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|
|
<div class="fs-fine tt-uppercase fc-black-600 fw-bold ml8 mt16 mb8">Teams</div>
|
|||
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|
|||
|
|
<div class="bt bl bb bc-black-200 p12 pb6 fc-black-500 blr-sm overflow-hidden">
|
|||
|
|
<strong class="fc-black-600 mb6">Stack Overflow for Teams</strong>
|
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|
|
– Start collaborating and sharing organizational knowledge.
|
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|
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|
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<img class="wmx100 mx-auto my8 h-auto d-block" width="139" height="114" src="https://cdn.sstatic.net/Img/teams/teams-illo-free-sidebar-promo.svg?v=47faa659a05e" alt="">
|
|||
|
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|
|||
|
|
<a href="https://try.stackoverflow.co/why-teams/?utm_source=so-owned&utm_medium=side-bar&utm_campaign=campaign-38&utm_content=cta"
|
|||
|
|
class="w100 s-btn s-btn__filled s-btn__xs bg-orange-400 js-gps-track"
|
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|
data-gps-track="teams.create.left-sidenav.click({ Action: 6 })"
|
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|
|
data-ga="["teams left navigation - anonymous","left nav free cta","stackoverflow.com/teams/create/free",null,null]">Create a free Team</a>
|
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<a href="https://stackoverflow.co/teams/"
|
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|
|
class="w100 s-btn s-btn__muted s-btn__xs js-gps-track"
|
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data-gps-track="teams.create.left-sidenav.click({ Action: 5 })"
|
|||
|
|
data-ga="["teams left navigation - anonymous","left nav free cta","stackoverflow.com/teams",null,null]">Why Teams?</a>
|
|||
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|
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</div>
|
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</li>
|
|||
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<li class="d-flex ai-center jc-space-between ml8 mt32 mb8 js-create-team-cta d-none">
|
|||
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<a href="javascript:void(0)"
|
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class="s-link d-flex fl-grow1 fc-black-400 h:fc-black-600 fs-fine js-gps-track"
|
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|
role="button"
|
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|
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aria-controls="popover-teams-create-cta"
|
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data-controller="s-popover"
|
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data-action="s-popover#toggle"
|
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data-s-popover-placement="bottom-start"
|
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data-s-popover-toggle-class="is-selected"
|
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data-gps-track="teams.create.left-sidenav.click({ Action: ShowInfo })"
|
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|
data-ga="["teams left navigation - anonymous","left nav show teams info",null,null,null]"
|
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>
|
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|
|
<div class="flex--item fl-grow1 fc-black-600 fw-bold tt-uppercase">Teams</div>
|
|||
|
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<div class="flex--item px12">
|
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<svg aria-hidden="true" class="svg-icon iconPlusSm" width="14" height="14" viewBox="0 0 14 14"><path d="M8 2H6v4H2v2h4v4h2V8h4V6H8V2Z"/></svg>
|
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</div>
|
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</a>
|
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</li>
|
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|
<li class="ps-relative js-create-team-cta d-none">
|
|||
|
|
<a href="https://stackoverflowteams.com/teams/create/free/?utm_source=so-owned&utm_medium=side-bar&utm_campaign=campaign-38&utm_content=cta"
|
|||
|
|
class="pl8 js-gps-track nav-links--link"
|
|||
|
|
title="Stack Overflow for Teams is a private, secure spot for your organization's questions and answers."
|
|||
|
|
data-gps-track="teams.create.left-sidenav.click({ Action: FreemiumTeamsCreateClick })"
|
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data-ga="["teams left navigation - anonymous","left nav team click","stackoverflow.com/teams/create/free",null,null]">
|
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<div class="d-flex ai-center">
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<div class="flex--item s-avatar va-middle bg-orange-400">
|
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<div class="s-avatar--letter mtn1">
|
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<svg aria-hidden="true" class="svg-icon iconBriefcaseSm" width="14" height="14" viewBox="0 0 14 14"><path d="M4 3a1 1 0 0 1 1-1h4a1 1 0 0 1 1 1v1h.5c.83 0 1.5.67 1.5 1.5v5c0 .83-.67 1.5-1.5 1.5h-7A1.5 1.5 0 0 1 2 10.5v-5C2 4.67 2.67 4 3.5 4H4V3Zm5 1V3H5v1h4Z"/></svg>
|
|||
|
|
</div>
|
|||
|
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<svg aria-hidden="true" class="native s-avatar--badge svg-icon iconShieldXSm" width="9" height="10" viewBox="0 0 9 10"><path fill="var(--white)" d="M0 1.84 4.5 0 9 1.84v3.17C9 7.53 6.3 10 4.5 10 2.7 10 0 7.53 0 5.01V1.84Z"/><path fill="var(--black-400)" d="M1 2.5 4.5 1 8 2.5v2.51C8 7.34 5.34 9 4.5 9 3.65 9 1 7.34 1 5.01V2.5Zm2.98 3.02L3.2 7h2.6l-.78-1.48a.4.4 0 0 1 .15-.38c.34-.24.73-.7.73-1.14 0-.71-.5-1.23-1.41-1.23-.92 0-1.39.52-1.39 1.23 0 .44.4.9.73 1.14.12.08.18.23.15.38Z"/></svg>
|
|||
|
|
</div>
|
|||
|
|
<div class="flex--item pl6">
|
|||
|
|
Create free Team
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</a>
|
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</li>
|
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|
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</ol>
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</nav>
|
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</div>
|
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<div class="s-popover ws2" id="popover-discover-collectives" role="menu">
|
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<div class="s-popover--arrow"></div>
|
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|
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<div>
|
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|
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<svg aria-hidden="true" class="fc-orange-400 float-right ml24 svg-spot spotCollective" width="48" height="48" viewBox="0 0 48 48"><path d="M25.5 7a2.5 2.5 0 1 0 0-5 2.5 2.5 0 0 0 0 5ZM14 18.25c0-.69.56-1.25 1.25-1.25h22.5c.69 0 1.25.56 1.25 1.25V37.5a1 1 0 0 1-1.6.8l-4.07-3.05a1.25 1.25 0 0 0-.75-.25H15.25c-.69 0-1.25-.56-1.25-1.25v-15.5ZM7 24.5a2.5 2.5 0 1 1-5 0 2.5 2.5 0 0 1 5 0ZM25.5 48a2.5 2.5 0 1 0 0-5 2.5 2.5 0 0 0 0 5ZM48 24.5a2.5 2.5 0 1 1-5 0 2.5 2.5 0 0 1 5 0Z" opacity=".2"/><path d="M21 3.5a3.5 3.5 0 1 1 7 0 3.5 3.5 0 0 1-7 0ZM24.5 2a1.5 1.5 0 1 0 0 3 1.5 1.5 0 0 0 0-3ZM0 23.5a3.5 3.5 0 1 1 7 0 3.5 3.5 0 0 1-7 0ZM3.5 22a1.5 1.5 0 1 0 0 3 1.5 1.5 0 0 0 0-3ZM21 44.5a3.5 3.5 0 1 1 7 0 3.5 3.5 0 0 1-7 0Zm3.5-1.5a1.5 1.5 0 1 0 0 3 1.5 1.5 0 0 0 0-3Zm20-23a3.5 3.5 0 1 0 0 7 3.5 3.5 0 0 0 0-7ZM43 23.5a1.5 1.5 0 1 1 3 0 1.5 1.5 0 0 1-3 0Zm-23.23-3.14a1 1 0 0 1-.13 1.4l-2.08 1.74 2.08 1.73a1 1 0 1 1-1.28 1.54l-2.42-2.02a1.63 1.63 0 0 1 0-2.5l2.42-2.02a1 1 0 0 1 1.4.13Zm7.59 1.41a1 1 0 1 1 1.28-1.54l2.42 2.02c.78.65.78 1.85 0 2.5l-2.42 2.02a1 1 0 1 1-1.28-1.54l2.08-1.73-2.08-1.73ZM24.12 18a1 1 0 0 1 .87 1.12l-1 8a1 1 0 1 1-1.98-.24l1-8a1 1 0 0 1 1.11-.87Zm-11.87-5C11.01 13 10 14 10 15.25v15.5c0 1.24 1 2.25 2.25 2.25h17.33c.06 0 .11.02.15.05l4.07 3.05a2 2 0 0 0 3.2-1.6V15.25c0-1.24-1-2.25-2.25-2.25h-22.5ZM12 15.25c0-.14.11-.25.25-.25h22.5c.14 0 .25.11.25.25V34.5l-4.07-3.05a2.2 2.2 0 0 0-1.35-.45H12.25a.25.25 0 0 1-.25-.25v-15.5Zm7.24-10.68a1 1 0 1 0-.48-1.94A22.04 22.04 0 0 0 2.91 17.7a1 1 0 1 0 1.92.58 20.04 20.04 0 0 1 14.4-13.72Zm11.05-1.66a1 1 0 0 0-.58 1.92c6.45 1.92 11.54 7 13.46 13.46a1 1 0 1 0 1.92-.58 22.05 22.05 0 0 0-14.8-14.8ZM4.57 28.76a1 1 0 0 0-1.94.48 22.03 22.03 0 0 0 16.13 16.13 1 1 0 1 0 .48-1.94A20.03 20.03 0 0 1 4.57 28.76Zm40.8.48a1 1 0 1 0-1.94-.48 20.04 20.04 0 0 1-13.72 14.41 1 1 0 0 0 .58 1.92 22.04 22.04 0 0 0 15.08-15.85Z"/></svg>
|
|||
|
|
<h5 class="pt4 fw-bold">Collectives™ on Stack Overflow</h5>
|
|||
|
|
<p class="my16 fs-caption fc-black-500">Find centralized, trusted content and collaborate around the technologies you use most.</p>
|
|||
|
|
<a href="/collectives"
|
|||
|
|
class="js-gps-track s-btn s-btn__filled s-btn__xs"
|
|||
|
|
data-gps-track="top_nav.click({is_current:false, location:2, destination:18})">
|
|||
|
|
Learn more about Collectives
|
|||
|
|
</a>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
<div class="s-popover ws2"
|
|||
|
|
id="popover-teams-create-cta"
|
|||
|
|
role="menu"
|
|||
|
|
aria-hidden="true">
|
|||
|
|
<div class="s-popover--arrow"></div>
|
|||
|
|
|
|||
|
|
<div class="ps-relative overflow-hidden">
|
|||
|
|
<p class="mb2"><strong>Teams</strong></p>
|
|||
|
|
<p class="mb12 fs-caption fc-black-400">Q&A for work</p>
|
|||
|
|
<p class="mb12 fs-caption fc-black-500">Connect and share knowledge within a single location that is structured and easy to search.</p>
|
|||
|
|
<a href="https://stackoverflow.co/teams/"
|
|||
|
|
class="js-gps-track s-btn s-btn__filled s-btn__xs"
|
|||
|
|
data-gps-track="teams.create.left-sidenav.click({ Action: CtaClick })"
|
|||
|
|
data-ga="["teams left navigation - anonymous","left nav cta","stackoverflow.com/teams",null,null]">
|
|||
|
|
Learn more about Teams
|
|||
|
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</a>
|
|||
|
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</div>
|
|||
|
|
|
|||
|
|
<div class="ps-absolute t8 r8">
|
|||
|
|
<svg aria-hidden="true" class="fc-orange-400 svg-spot spotPeople" width="48" height="48" viewBox="0 0 48 48"><path d="M13.5 28a4.5 4.5 0 1 0 0-9 4.5 4.5 0 0 0 0 9ZM7 30a1 1 0 0 1 1-1h11a1 1 0 0 1 1 1v5h11v-5a1 1 0 0 1 1-1h12a1 1 0 0 1 1 1v10a2 2 0 0 1-2 2H33v5a1 1 0 0 1-1 1H20a1 1 0 0 1-1-1v-5H8a1 1 0 0 1-1-1V30Zm25-6.5a4.5 4.5 0 1 0 9 0 4.5 4.5 0 0 0-9 0ZM24.5 34a4.5 4.5 0 1 0 0-9 4.5 4.5 0 0 0 0 9Z" opacity=".2"/><path d="M16.4 26.08A6 6 0 1 0 7.53 26C5.64 26.06 4 27.52 4 29.45V40a1 1 0 0 0 1 1h9a1 1 0 1 0 0-2h-4v-7a1 1 0 1 0-2 0v7H6v-9.55c0-.73.67-1.45 1.64-1.45H16a1 1 0 0 0 .4-1.92ZM12 18a4 4 0 1 1 0 8 4 4 0 0 1 0-8Zm16.47 14a6 6 0 1 0-8.94 0A3.6 3.6 0 0 0 16 35.5V46a1 1 0 0 0 1 1h14a1 1 0 0 0 1-1V35.5c0-1.94-1.64-3.42-3.53-3.5ZM20 28a4 4 0 1 1 8 0 4 4 0 0 1-8 0Zm-.3 6h8.6c1 0 1.7.75 1.7 1.5V45h-2v-7a1 1 0 1 0-2 0v7h-4v-7a1 1 0 1 0-2 0v7h-2v-9.5c0-.75.7-1.5 1.7-1.5ZM42 22c0 1.54-.58 2.94-1.53 4A3.5 3.5 0 0 1 44 29.45V40a1 1 0 0 1-1 1h-9a1 1 0 1 1 0-2h4v-7a1 1 0 1 1 2 0v7h2v-9.55A1.5 1.5 0 0 0 40.48 28H32a1 1 0 0 1-.4-1.92A6 6 0 1 1 42 22Zm-2 0a4 4 0 1 0-8 0 4 4 0 0 0 8 0Z"/><g opacity=".35"><path d="M17 10a1 1 0 011-1h12a1 1 0 110 2H18a1 1 0 01-1-1Zm1-5a1 1 0 100 2h12a1 1 0 100-2H18ZM14 1a1 1 0 00-1 1v12a1 1 0 001 1h5.09l4.2 4.2a1 1 0 001.46-.04l3.7-4.16H34a1 1 0 001-1V2a1 1 0 00-1-1H14Zm1 12V3h18v10h-5a1 1 0 00-.75.34l-3.3 3.7-3.74-3.75a1 1 0 00-.71-.29H15Z"/></g></svg>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
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|
|||
|
|
<div class="s-popover ws2"
|
|||
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|
id="popover-labs-left-nav"
|
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role="menu"
|
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aria-hidden="true">
|
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<div class="s-popover--arrow"></div>
|
|||
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<svg aria-hidden="true" class="fc-black-600 mb8 svg-icon iconLabs" width="42" height="18"><path d="M11.5 13.624a.374.374 0 0 1-.37.376H5.361a.374.374 0 0 1-.37-.376V4.376c0-.207.165-.376.37-.376H6.62c.204 0 .37.169.37.376v7.611h4.138c.205 0 .371.169.371.377v1.26zm9.432.215c-.07.1-.185.161-.308.161H19.13a.376.376 0 0 1-.356-.254l-.55-1.7h-3.111l-.55 1.7a.377.377 0 0 1-.355.254h-1.494a.376.376 0 0 1-.353-.506l3.39-9.247A.376.376 0 0 1 16.103 4h1.13c.158 0 .299.099.353.247l3.39 9.247a.376.376 0 0 1-.045.345zm-4.157-7.386l-1.219 3.531h2.266l-1.047-3.53zm13.335 5.71a.37.37 0 0 0-.003.524c.956.971 2.047 1.313 3.486 1.313 1.014 0 1.92-.265 2.582-.788.67-.53 1.063-1.306 1.063-2.255 0-.855-.268-1.622-.867-2.145-.456-.41-1.008-.633-1.89-.767l-1.037-.153c-.377-.057-.672-.19-.832-.332-.146-.132-.221-.315-.221-.568 0-.309.11-.56.306-.737.199-.179.518-.312.986-.312.708 0 1.254.151 1.726.601a.37.37 0 0 0 .516-.004l.883-.87a.37.37 0 0 0-.008-.534C35.942 4.334 35.004 4 33.721 4c-1.016 0-1.872.292-2.479.836-.61.548-.935 1.32-.935 2.207 0 .82.243 1.502.781 2.01h.001c.468.437 1.135.716 1.93.826l1.072.153c.508.073.647.147.795.286l.008.007c.14.125.234.34.234.67 0 .332-.124.567-.344.73-.235.174-.617.293-1.165.293-.867 0-1.49-.185-2.066-.76a.37.37 0 0 0-.522-.003l-.92.908zM22.37 14a.374.374 0 0 1-.37-.376V4.376c0-.207.166-.376.37-.376h3.543c.913 0 1.697.264 2.257.78.564.519.863 1.259.863 2.129 0 .845-.377 1.524-.87 1.947.57.433 1.01 1.145 1.01 2.157 0 .941-.317 1.702-.894 2.224-.57.517-1.354.763-2.225.763H22.37zm3.543-1.977c.96 0 .959-1.01.959-1.01s0-1.013-.959-1.013H24v2.023h1.913zm-.115-4.063c1.074 0 1.074-1.015 1.074-1.015s0-1.016-1.074-1.016H24V7.96h1.798z" fill="var(--black-600)"/><path d="M0 4v10a4 4 0 0 0 4 4h34a4 4 0 0 0 4-4V4a4 4 0 0 0-4-4H4a4 4 0 0 0-4 4zm4-2h34a2 2 0 0 1 2 2v10a2 2 0 0 1-2 2H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2z" fill="var(--black-600)"/></svg>
|
|||
|
|
<p class="fs-caption">Get early access and see previews of new features.</p>
|
|||
|
|
<a class="s-btn s-btn__filled s-btn__xs s-btn__icon fs-fine" href="https://stackoverflow.co/labs/"><svg aria-hidden="true" class="svg-icon iconShareSm" width="14" height="14" viewBox="0 0 14 14"><path d="M5 1H3a2 2 0 0 0-2 2v8c0 1.1.9 2 2 2h8a2 2 0 0 0 2-2V9h-2v2H3V3h2V1Zm2 0h6v6h-2V4.5L6.5 9 5 7.5 9.5 3H7V1Z"/></svg> Learn more about Labs</a>
|
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</div>
|
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|
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</div>
|
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|
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|
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|
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<div id="content" class="snippet-hidden">
|
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<div itemprop="mainEntity" itemscope itemtype="https://schema.org/Question">
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<div id="question-header" class="d-flex sm:fd-column">
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<h1 itemprop="name" class="fs-headline1 ow-break-word mb8 flex--item fl1"><a href="/questions/20626994/how-to-calculate-the-inverse-of-the-normal-cumulative-distribution-function-in-p" class="question-hyperlink">How to calculate the inverse of the normal cumulative distribution function in python?</a></h1>
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<p>How do I calculate the inverse of the cumulative distribution function (CDF) of the normal distribution in Python?</p>
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<p>Which library should I use? Possibly scipy? </p>
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data-gps-track="post.click({ item: 4, priv: 0, post_type: 1 })">edited <span title='2015-03-31 14:52:45Z' class='relativetime'>Mar 31, 2015 at 14:52</span></a>
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asked <span title='2013-12-17 05:57:49Z' class='relativetime'>Dec 17, 2013 at 5:57</span>
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<span class="comment-copy">Do you mean the inverse Gaussian distribution (<a href="http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution" rel="nofollow noreferrer">en.wikipedia.org/wiki/Inverse_Gaussian_distribution</a>), or the inverse of the cumulative distribution function of the normal distribution (<a href="http://en.wikipedia.org/wiki/Normal_distribution" rel="nofollow noreferrer">en.wikipedia.org/wiki/Normal_distribution</a>), or something else?</span>
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– <a href="/users/1217358/warren-weckesser"
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title="111,515 reputation"
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class="comment-user">Warren Weckesser</a>
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<span class="comment-date" dir="ltr"><span title='2013-12-17 06:30:48Z, License: CC BY-SA 3.0' class='relativetime-clean'>Dec 17, 2013 at 6:30</span></span>
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<span class="comment-copy">@WarrenWeckesser the second one: inverse of the cumulative distribution function of the normal distribution</span>
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– <a href="/users/1624752/yueyoum"
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<span class="comment-date" dir="ltr"><span title='2013-12-17 06:32:40Z, License: CC BY-SA 3.0' class='relativetime-clean'>Dec 17, 2013 at 6:32</span></span>
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<span class="comment-copy">@WarrenWeckesser i mean the python version of "normsinv" function in excel.</span>
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– <a href="/users/1624752/yueyoum"
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title="2,853 reputation"
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class="comment-user owner">Yueyoum</a>
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<span class="comment-date" dir="ltr"><span title='2013-12-17 06:39:22Z, License: CC BY-SA 3.0' class='relativetime-clean'>Dec 17, 2013 at 6:39</span></span>
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3 Answers
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<p><a href="http://support.microsoft.com/kb/826772" rel="noreferrer">NORMSINV</a> (mentioned in a comment) is the inverse of the CDF of the standard normal distribution. Using <code>scipy</code>, you can compute this with the <code>ppf</code> method of the <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html" rel="noreferrer"><code>scipy.stats.norm</code></a> object. The acronym <code>ppf</code> stands for <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm#PPF" rel="noreferrer"><em>percent point function</em></a>, which is another name for the <a href="https://en.wikipedia.org/wiki/Quantile_function" rel="noreferrer"><em>quantile function</em></a>.</p>
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<pre><code>In [20]: from scipy.stats import norm
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In [21]: norm.ppf(0.95)
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Out[21]: 1.6448536269514722
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</code></pre>
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<p>Check that it is the inverse of the CDF:</p>
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<pre><code>In [34]: norm.cdf(norm.ppf(0.95))
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Out[34]: 0.94999999999999996
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<p>By default, <code>norm.ppf</code> uses mean=0 and stddev=1, which is the "standard" normal distribution. You can use a different mean and standard deviation by specifying the <code>loc</code> and <code>scale</code> arguments, respectively.</p>
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<pre><code>In [35]: norm.ppf(0.95, loc=10, scale=2)
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Out[35]: 13.289707253902945
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</code></pre>
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<p>If you look at the source code for <code>scipy.stats.norm</code>, you'll find that the <code>ppf</code> method ultimately calls <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.ndtri.html" rel="noreferrer"><code>scipy.special.ndtri</code></a>. So to compute the inverse of the CDF of the standard normal distribution, you could use that function directly:</p>
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<pre><code>In [43]: from scipy.special import ndtri
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In [44]: ndtri(0.95)
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Out[44]: 1.6448536269514722
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</code></pre>
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<p><code>ndtri</code> is <em>much</em> faster than <code>norm.ppf</code>:</p>
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<pre><code>In [46]: %timeit norm.ppf(0.95)
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240 µs ± 1.75 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
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In [47]: %timeit ndtri(0.95)
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1.47 µs ± 1.3 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
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data-gps-track="post.click({ item: 4, priv: 0, post_type: 2 })">edited <span title='2022-08-15 14:05:56Z' class='relativetime'>Aug 15, 2022 at 14:05</span></a>
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answered <span title='2013-12-17 06:44:02Z' class='relativetime'>Dec 17, 2013 at 6:44</span>
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<span class="comment-copy">I always think "percent point function" (ppf) is a terrible name. Most people in statistics just use "quantile function".</span>
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– <a href="/users/1670078/william-zhang"
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title="699 reputation"
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class="comment-user">William Zhang</a>
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<span class="comment-date" dir="ltr"><span title='2014-10-04 00:44:33Z, License: CC BY-SA 3.0' class='relativetime-clean'>Oct 4, 2014 at 0:44</span></span>
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<span class="comment-copy">Don't you need to specify the mean and the std on both ppf and cdf?</span>
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– <a href="/users/1391660/bones-felipe"
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<span class="comment-date" dir="ltr"><span title='2021-01-29 19:23:44Z, License: CC BY-SA 4.0' class='relativetime-clean'>Jan 29, 2021 at 19:23</span></span>
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<span class="comment-copy">@bones.felipe, the "standard" normal distribution has mean 0 and standard deviation 1. These are the default values for the location and scale of the <code>scipy.stats.norm</code> methods.</span>
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<span class="comment-date" dir="ltr"><span title='2021-01-29 19:55:51Z, License: CC BY-SA 4.0' class='relativetime-clean'>Jan 29, 2021 at 19:55</span></span>
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<span class="comment-copy">Right, I thought I saw this <code>norm.cdf(norm.ppf(0.95, loc=10, scale=2))</code> and I thought it was weird <code>norm.cdf</code> did not have <code>loc=10</code> and <code>scale=2</code> too, I guess it should.</span>
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<span class="comment-date" dir="ltr"><span title='2021-01-30 05:33:43Z, License: CC BY-SA 4.0' class='relativetime-clean'>Jan 30, 2021 at 5:33</span></span>
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<p>Starting <code>Python 3.8</code>, the standard library provides the <a href="https://docs.python.org/3.8/library/statistics.html?highlight=normaldist#statistics.NormalDist" rel="noreferrer"><code>NormalDist</code></a> object as part of the <a href="https://docs.python.org/3.8/library/statistics.html" rel="noreferrer"><code>statistics</code></a> module.</p>
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<p>It can be used to get the <strong><em>inverse cumulative distribution function</em></strong> (<strong><a href="https://docs.python.org/3.8/library/statistics.html#statistics.NormalDist.inv_cdf" rel="noreferrer"><code>inv_cdf</code></a></strong> - inverse of the <a href="https://docs.python.org/3.8/library/statistics.html#statistics.NormalDist.cdf" rel="noreferrer"><code>cdf</code></a>), also known as the <strong>quantile function</strong> or the <strong>percent-point function</strong> for a given <em>mean</em> (<code>mu</code>) and <em>standard deviation</em> (<code>sigma</code>):</p>
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<pre><code>from statistics import NormalDist
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NormalDist(mu=10, sigma=2).inv_cdf(0.95)
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# 13.289707253902943
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</code></pre>
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<p>Which can be simplified for the <em>standard normal distribution</em> (<code>mu = 0</code> and <code>sigma = 1</code>):</p>
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<pre><code>NormalDist().inv_cdf(0.95)
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# 1.6448536269514715
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answered <span title='2019-03-19 21:58:57Z' class='relativetime'>Mar 19, 2019 at 21:58</span>
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<span class="comment-copy">Great tip! This allows me to drop the dependency on scipy, which I needed just for the single stats.norm.ppf method</span>
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– <a href="/users/5437918/jethro-cao"
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class="comment-user">Jethro Cao</a>
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<span class="comment-date" dir="ltr"><span title='2020-02-21 16:56:27Z, License: CC BY-SA 4.0' class='relativetime-clean'>Feb 21, 2020 at 16:56</span></span>
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<span class="comment-copy">can you use that to transform data with uniform distribution to normal ?</span>
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– <a href="/users/10824677/vanetoj"
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<span class="comment-date" dir="ltr"><span title='2022-03-31 20:51:01Z, License: CC BY-SA 4.0' class='relativetime-clean'>Mar 31, 2022 at 20:51</span></span>
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<pre><code># given random variable X (house price) with population muy = 60, sigma = 40
|
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import scipy as sc
|
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import scipy.stats as sct
|
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sc.version.full_version # 0.15.1
|
|||
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|
|||
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#a. Find P(X<50)
|
|||
|
|
sct.norm.cdf(x=50,loc=60,scale=40) # 0.4012936743170763
|
|||
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|||
|
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#b. Find P(X>=50)
|
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|
sct.norm.sf(x=50,loc=60,scale=40) # 0.5987063256829237
|
|||
|
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|
|||
|
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#c. Find P(60<=X<=80)
|
|||
|
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sct.norm.cdf(x=80,loc=60,scale=40) - sct.norm.cdf(x=60,loc=60,scale=40)
|
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|
|||
|
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#d. how much top most 5% expensive house cost at least? or find x where P(X>=x) = 0.05
|
|||
|
|
sct.norm.isf(q=0.05,loc=60,scale=40)
|
|||
|
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|
|||
|
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#e. how much top most 5% cheapest house cost at least? or find x where P(X<=x) = 0.05
|
|||
|
|
sct.norm.ppf(q=0.05,loc=60,scale=40)
|
|||
|
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</code></pre>
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answered <span title='2015-09-26 15:04:38Z' class='relativetime'>Sep 26, 2015 at 15:04</span>
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<span class="reputation-score" title="reputation score " dir="ltr">3,376</span><span title="4 gold badges" aria-hidden="true"><span class="badge1"></span><span class="badgecount">4</span></span><span class="v-visible-sr">4 gold badges</span><span title="32 silver badges" aria-hidden="true"><span class="badge2"></span><span class="badgecount">32</span></span><span class="v-visible-sr">32 silver badges</span><span title="45 bronze badges" aria-hidden="true"><span class="badge3"></span><span class="badgecount">45</span></span><span class="v-visible-sr">45 bronze badges</span>
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<span class="comment-copy">PS: You can assume 'loc' as 'mean' and 'scale' as 'standard deviation'</span>
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– <a href="/users/4815313/suresh2692"
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title="3,873 reputation"
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class="comment-user">Suresh2692</a>
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<span class="comment-date" dir="ltr"><span title='2017-07-05 11:11:41Z, License: CC BY-SA 3.0' class='relativetime-clean'>Jul 5, 2017 at 11:11</span></span>
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