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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"Suspected incorrect axis transformation of symlog","articleBody":"Hi, @mdboom.\nCan you roughly explain the meaning of _linscale_adj in SymmetricalLogTransform which was introduced via [d8bf0fed4d62324489ffe1d21d114c87ae9ca6a4](https://github.com/matplotlib/matplotlib/commit/d8bf0fed4d62324489ffe1d21d114c87ae9ca6a4)?\n\n\u003cpre\u003e\u003ccode\u003e\nclass SymmetricalLogTransform(Transform):\n    input_dims = 1\n    output_dims = 1\n    is_separable = True\n    has_inverse = True\n\n    def __init__(self, base, linthresh, linscale):\n        Transform.__init__(self)\n        self.base = base\n        self.linthresh = linthresh\n        self.linscale = linscale\n        self._linscale_adj = (linscale / (1.0 - self.base ** -1))\n        self._log_base = np.log(base)\n\u003c/code\u003e\u003c/pre\u003e\n\nI am quite puzzled by it.\n\nAccording to the [documentation](http://matplotlib.org/api/pyplot_api.html?highlight=xscale#matplotlib.pyplot.xscale) about linscalex / linscaley, its value is the number of decades to use for each half of the linear range. For example, when linscale == 1.0 (the default), the space used for the positive and negative halves of the linear range will be equal to one decade in the logarithmic range.\n\nAs I understand it, it means that when the base is 10 and the linthresh equals to 1, the length of the interval between 0 and 1 should equal to the interval between 1(10^0) and 10(10^1). And this feature seems to be very useful that user can adjust the relative ratio between linear range and logarithmic range.\n\nHowever, since the _linscale_adj amplifies the original linscale by 1/(1-1/base), the actual place for the linear range will be 1.11x compared to logarithmic range per decade.\n\nFor example,\n\n\u003cpre\u003e\u003ccode\u003e\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nx = np.array([0, 1, 5, 10, 100, 1000])\ny = np.array([0] * 6)\n\nplt.scatter(x, y)\nplt.xscale('symlog', linthreshx=10, basex=10, linscalex=1)\nplt.grid(True)\nplt.show()\n\u003c/code\u003e\u003c/pre\u003e\n\n![base10](https://cloud.githubusercontent.com/assets/13389038/18077096/a834e702-6eb5-11e6-9cb5-e0d1cc049763.png)\n\nIf the base is set to 2, the linear range will be 2x than logarithmic range per decade and this issue may be more considerable:\n\n\u003cpre\u003e\u003ccode\u003e\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nx = np.array([0, 0.5, 1, 2, 4, 8, 16])\ny = np.array([0] * 7)\n\nplt.scatter(x, y)\nplt.xscale('symlog', linthreshx=2, basex=2, linscalex=1)\nplt.grid(True)\nplt.show()\n\u003c/code\u003e\u003c/pre\u003e\n\n![base2](https://cloud.githubusercontent.com/assets/13389038/18077163/33f0ba3c-6eb6-11e6-9d00-3cb1f6defc51.png)\n\nSince _linscale_adj is relatively independent and is only used to be a coefficient of transformation for symlog, it seems not to be a bug. So, what is the meaning of the scaling of _linscale_adj which related to its base?\n\nWell, as a user, the figures showed above is very weird and I used to set the linscale manually to 0.9 (base=10) to make each tick interval to be equal.\n\nThanks.\n","author":{"url":"https://github.com/desert0616","@type":"Person","name":"desert0616"},"datePublished":"2016-08-30T05:46:40.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":19},"url":"https://github.com/7008/matplotlib/issues/7008"}