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‎master/_downloads/dd20cdae2e0fc75c62723bcf0d046ec0/plot_Intro_OT.py‎

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# number of Bakeries to Cafés in a City (in this case Manhattan). We did a
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# quick google map search in Manhattan for bakeries and Cafés:
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#
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# .. image:: images/bak.png
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# .. image:: ../_static/images/bak.png
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# :align: center
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# :alt: bakery-cafe-manhattan
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# :width: 600px
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# The Sinkhorn algorithm is very simple to code. You can implement it directly
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# using the following pseudo-code
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#
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# .. image:: images/sinkhorn.png
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# .. image:: ../_static/images/sinkhorn.png
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# :align: center
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# :alt: Sinkhorn algorithm
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# :width: 440px

‎master/_downloads/f7942777fc8bc11618d8908da9b54edc/plot_Intro_OT.ipynb‎

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## First OT Problem\n\nWe will solve the Bakery/Caf\u00e9s problem of transporting croissants from a\nnumber of Bakeries to Caf\u00e9s in a City (in this case Manhattan). We did a\nquick google map search in Manhattan for bakeries and Caf\u00e9s:\n\n<img src=\"file://images/bak.png\" align=\"center\" alt=\"bakery-cafe-manhattan\" width=\"600px\" height=\"280px\">\n\nWe extracted from this search their positions and generated fictional\nproduction and sale number (that both sum to the same value).\n\nWe have acess to the position of Bakeries ``bakery_pos`` and their\nrespective production ``bakery_prod`` which describe the source\ndistribution. The Caf\u00e9s where the croissants are sold are defined also by\ntheir position ``cafe_pos`` and ``cafe_prod``, and describe the target\ndistribution. For fun we also provide a\nmap ``Imap`` that will illustrate the position of these shops in the city.\n\n\nNow we load the data\n\n\n\n"
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"## First OT Problem\n\nWe will solve the Bakery/Caf\u00e9s problem of transporting croissants from a\nnumber of Bakeries to Caf\u00e9s in a City (in this case Manhattan). We did a\nquick google map search in Manhattan for bakeries and Caf\u00e9s:\n\n<img src=\"file://../_static/images/bak.png\" align=\"center\" alt=\"bakery-cafe-manhattan\" width=\"600px\" height=\"280px\">\n\nWe extracted from this search their positions and generated fictional\nproduction and sale number (that both sum to the same value).\n\nWe have acess to the position of Bakeries ``bakery_pos`` and their\nrespective production ``bakery_prod`` which describe the source\ndistribution. The Caf\u00e9s where the croissants are sold are defined also by\ntheir position ``cafe_pos`` and ``cafe_prod``, and describe the target\ndistribution. For fun we also provide a\nmap ``Imap`` that will illustrate the position of these shops in the city.\n\n\nNow we load the data\n\n\n\n"
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Regularized OT with Sinkhorn\n\nThe Sinkhorn algorithm is very simple to code. You can implement it directly\nusing the following pseudo-code\n\n<img src=\"file://images/sinkhorn.png\" align=\"center\" alt=\"Sinkhorn algorithm\" width=\"440px\" height=\"240px\">\n\nIn this algorithm, $\\oslash$ corresponds to the element-wise division.\n\nAn alternative is to use the POT toolbox with\n`ot.sinkhorn <https://pythonot.github.io/all.html#ot.sinkhorn>`_\n\nBe careful of numerical problems. A good pre-processing for Sinkhorn is to\ndivide the cost matrix ``C`` by its maximum value.\n\n"
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"## Regularized OT with Sinkhorn\n\nThe Sinkhorn algorithm is very simple to code. You can implement it directly\nusing the following pseudo-code\n\n<img src=\"file://../_static/images/sinkhorn.png\" align=\"center\" alt=\"Sinkhorn algorithm\" width=\"440px\" height=\"240px\">\n\nIn this algorithm, $\\oslash$ corresponds to the element-wise division.\n\nAn alternative is to use the POT toolbox with\n`ot.sinkhorn <https://pythonot.github.io/all.html#ot.sinkhorn>`_\n\nBe careful of numerical problems. A good pre-processing for Sinkhorn is to\ndivide the cost matrix ``C`` by its maximum value.\n\n"
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