Using tikzlibrary spy without magnifying line width and/or mark size

Question

I am having two set of data and am trying to create an inset to show, where they differ. Therefore, it does not help me to simply magnify the area in a "canvas style" thus magnifying also mark sizes and linewidths but I would rather keep the latter two the same as in the original picture. Does anybody know a workaround? Thanks

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{spy}

\pagestyle{empty}   
\begin{document}

\begin{tikzpicture}[spy using outlines=
    {circle, magnification=10, connect spies}]

\begin{semilogyaxis}[
scale only axis,
width=6cm,
height=4.5cm,
xmin=-3, xmax=3,
ymin=1e-11, ymax=1e-01,
yminorticks=true,
axis on top]

\addplot [
color=green,
only marks,
mark=x, clip marker paths=true,
mark options={solid}]
coordinates{
(1.60852,6.13283e-05)(1.62527,6.78766e-05)(1.64203,7.16948e-05)(1.65879,7.09775e-05)(1.67554,6.64539e-05)(1.6923,6.0881e-05)(1.70905,5.65543e-05)(1.72581,5.32983e-05)(1.74256,4.89298e-05)(1.75932,4.17484e-05)(1.77607,3.27146e-05)(1.79283,2.49779e-05)(1.80958,2.06858e-05)(1.82634,1.84003e-05)(1.84309,1.49936e-05)(1.85985,1.04606e-05)(1.87661,8.34593e-06)(1.89336,9.58471e-06)(1.91012,9.76351e-06)(1.92687,6.34117e-06)(1.94363,2.77806e-06)(1.96038,1.74742e-06)(1.97714,2.82344e-06)(1.99389,3.65428e-06)(2.01065,4.17071e-06)(2.0274,2.0308e-06)(2.04416,4.41266e-07)(2.06092,3.22697e-06)(2.07767,8.75464e-06)(2.09443,9.65132e-06)(2.11118,2.4596e-06)(2.12794,1.68688e-05)(2.14469,0.0369094)(2.16145,8.18512e-05)(2.1782,7.60426e-06)(2.19496,4.54191e-07)(2.21171,1.32399e-06)(2.22847,1.89883e-06)(2.24522,1.44121e-06)(2.26198,6.10898e-07)(2.27874,8.34218e-08)(2.29549,2.48243e-07)(2.31225,4.85005e-07)(2.329,3.81316e-07)(2.34576,6.46304e-08)(2.36251,9.62666e-08)(2.37927,3.36753e-07)(2.39602,2.88187e-07)(2.41278,7.51928e-08)(2.42953,1.27397e-08)(2.44629,8.43959e-08)(2.46304,1.24876e-07)(2.4798,8.67822e-08)(2.49656,3.41846e-08)(2.51331,2.77954e-08)(2.53007,6.15079e-08)(2.54682,8.5494e-08)(2.56358,6.64095e-08)(2.58033,2.22405e-08)
};

\addplot [
color=blue,
solid]
coordinates{
(1.84938,1.30191e-05)(1.85147,1.24146e-05)(1.85357,1.18242e-05)(1.85566,1.12571e-05)(1.85776,1.07224e-05)(1.85985,1.02289e-05)(1.86194,9.78453e-06)(1.86404,9.39637e-06)(1.86613,9.07009e-06)(1.86823,8.80985e-06)(1.87032,8.61807e-06)(1.87242,8.4953e-06)(1.87451,8.44012e-06)(1.87661,8.4491e-06)(1.8787,8.51687e-06)(1.88079,8.63625e-06)(1.88289,8.79835e-06)(1.88498,8.99292e-06)(1.88708,9.20857e-06)(1.88917,9.43317e-06)(1.89127,9.65423e-06)(1.89336,9.85928e-06)(1.89546,1.00364e-05)(1.89755,1.01744e-05)(1.89964,1.02635e-05)(1.90174,1.02956e-05)(1.90383,1.02643e-05)(1.90593,1.01655e-05)(1.90802,9.99744e-06)(1.91012,9.76053e-06)(1.91221,9.45755e-06)(1.91431,9.09343e-06)(1.9164,8.675e-06)(1.91849,8.21075e-06)(1.92059,7.7104e-06)(1.92268,7.18453e-06)(1.92478,6.6441e-06)(1.92687,6.10007e-06)(1.92897,5.56291e-06)(1.93106,5.04223e-06)(1.93316,4.54651e-06)(1.93525,4.08287e-06)(1.93734,3.65687e-06)(1.93944,3.27255e-06)(1.94153,2.93248e-06)(1.94363,2.63793e-06)(1.94572,2.38896e-06)(1.94782,2.18482e-06)(1.94991,2.02432e-06)(1.952,1.90591e-06)(1.9541,1.82782e-06)(1.95619,1.78861e-06)(1.95829,1.78716e-06)(1.96038,1.82173e-06)(1.96248,1.89056e-06)(1.96457,1.99278e-06)(1.96667,2.12518e-06)(1.96876,2.28247e-06)(1.97085,2.46321e-06)(1.97295,2.65945e-06)(1.97504,2.8575e-06)(1.97714,3.06279e-06)(1.97923,3.2508e-06)(1.98133,3.41339e-06)(1.98342,3.57804e-06)(1.98552,3.65166e-06)(1.98761,3.79048e-06)(1.9897,3.74879e-06)(1.9918,3.91375e-06)(1.99389,3.76293e-06)(1.99599,3.71475e-06)(1.99808,3.87484e-06)(2.00018,3.92901e-06)(2.00227,4.178e-06)(2.00437,4.24233e-06)(2.00646,4.22731e-06)(2.00855,4.14918e-06)(2.01065,4.01573e-06)(2.01274,3.83296e-06)(2.01484,3.60685e-06)(2.01693,3.34385e-06)(2.01903,3.05116e-06)(2.02112,2.73675e-06)(2.02322,2.40927e-06)(2.02531,2.07799e-06)(2.0274,1.75262e-06)(2.0295,1.44312e-06)(2.03159,1.15948e-06)(2.03369,9.11526e-07)(2.03578,7.0866e-07)(2.03788,5.59614e-07)(2.03997,4.72219e-07)(2.04207,4.53168e-07)(2.04416,5.07796e-07)(2.04625,6.39886e-07)(2.04835,8.51495e-07)(2.05044,1.14281e-06)(2.05254,1.51206e-06)(2.05463,1.95543e-06)(2.05673,2.46705e-06)(2.05882,3.03904e-06)(2.06092,3.66158e-06)(2.06301,4.323e-06)(2.0651,5.01004e-06)(2.0672,5.70797e-06)(2.06929,6.40096e-06)(2.07139,7.07229e-06)(2.07348,7.70479e-06)(2.07558,8.28118e-06)(2.07767,8.78445e-06)(2.07976,9.19836e-06)(2.08186,9.50782e-06)(2.08395,9.69939e-06)(2.08605,9.76175e-06)(2.08814,9.68615e-06)(2.09024,9.4669e-06)(2.09233,9.10192e-06)(2.09443,8.59317e-06)(2.09652,7.94732e-06)(2.09861,7.17635e-06)(2.10071,6.29829e-06)(2.1028,5.33825e-06)(2.1049,4.32966e-06)(2.10699,3.31601e-06)(2.10909,2.35333e-06)(2.11118,1.51382e-06)(2.11328,8.91237e-07)(2.11537,6.09225e-07)(2.11746,8.34295e-07)(2.11956,1.79686e-06)(2.12165,3.82617e-06)(2.12375,7.41074e-06)(2.12584,1.33072e-05)(2.12794,2.27472e-05)(2.13003,3.7857e-05)(2.13213,6.2577e-05)(2.13422,0.000104901)(2.13631,0.000183099)(2.13841,0.000346694)(2.1405,0.000770869)(2.1426,0.00247743)(2.14469,0.0346725)(2.14679,0.0135714)(2.14888,0.00204092)(2.15098,0.000789018)(2.15307,0.000411883)(2.15516,0.000248454)(2.15726,0.000162664)(2.15935,0.000111989)(2.16145,7.95987e-05)(2.16354,5.77251e-05)(2.16564,4.23617e-05)(2.16773,3.12647e-05)(2.16983,2.30911e-05)(2.17192,1.69936e-05)(2.17401,1.24127e-05)(2.17611,8.96461e-06)(2.1782,6.37723e-06)(2.1803,4.45205e-06)(2.18239,3.04056e-06)(2.18449,2.02931e-06)(2.18658,1.33006e-06)(2.18868,8.73189e-07)(2.19077,6.03157e-07)(2.19286,4.75303e-07)(2.19496,4.53544e-07)(2.19705,5.08686e-07)(2.19915,6.1714e-07)(2.20124,7.59934e-07)(2.20334,9.21937e-07)(2.20543,1.09122e-06)(2.20752,1.25855e-06)(2.20962,1.41693e-06)(2.21171,1.56123e-06)(2.21381,1.68787e-06)(2.2159,1.79456e-06)(2.218,1.88003e-06)(2.22009,1.94383e-06)(2.22219,1.98616e-06)(2.22428,2.00771e-06)(2.22637,2.00954e-06)(2.22847,1.99297e-06)(2.23056,1.95951e-06)(2.23266,1.91076e-06)(2.23475,1.84839e-06)(2.23685,1.77408e-06)(2.23894,1.68953e-06)(2.24104,1.59639e-06)(2.24313,1.49628e-06)(2.24522,1.39079e-06)(2.24732,1.28146e-06)(2.24941,1.1698e-06)(2.25151,1.05724e-06)(2.2536,9.45213e-07)(2.2557,8.35071e-07)(2.25779,7.28129e-07)(2.25989,6.25636e-07)(2.26198,5.28777e-07)(2.26407,4.38655e-07)(2.26617,3.56282e-07)(2.26826,2.82563e-07)(2.27036,2.18282e-07)(2.27245,1.6409e-07)(2.27455,1.20492e-07)(2.27664,8.78404e-08)(2.27874,6.63308e-08)(2.28083,5.60087e-08)(2.28292,5.67917e-08)(2.28502,6.85251e-08)(2.28711,9.11319e-08)(2.28921,1.25176e-07)(2.2913,1.83365e-07)(2.2934,2.35926e-07)(2.29549,3.00471e-07)(2.29759,3.52233e-07)(2.29968,3.75768e-07)(2.30177,4.23818e-07)(2.30387,4.44905e-07)(2.30596,4.73498e-07)(2.30806,4.86677e-07)(2.31015,5.00881e-07)(2.31225,5.05618e-07)(2.31434,5.06775e-07)(2.31644,5.02347e-07)(2.31853,4.91622e-07)(2.32062,4.75873e-07)(2.32272,4.5387e-07)(2.32481,4.26127e-07)(2.32691,3.93243e-07)(2.329,3.55609e-07)(2.3311,3.14355e-07)(2.33319,2.70807e-07)(2.33528,2.26376e-07)(2.33738,1.82719e-07)(2.33947,1.41526e-07)(2.34157,1.04383e-07)(2.34366,7.27429e-08)(2.34576,4.7825e-08)(2.34785,3.05318e-08)(2.34995,2.14156e-08)(2.35204,2.06542e-08)(2.35413,2.80435e-08)(2.35623,4.30203e-08)(2.35832,6.47028e-08)(2.36042,9.19422e-08)(2.36251,1.23388e-07)(2.36461,1.57559e-07)(2.3667,1.92918e-07)(2.3688,2.2794e-07)(2.37089,2.61182e-07)(2.37298,2.91342e-07)(2.37508,3.17301e-07)(2.37717,3.38164e-07)(2.37927,3.53282e-07)(2.38136,3.62261e-07)(2.38346,3.6496e-07)(2.38555,3.61483e-07)(2.38765,3.52156e-07)(2.38974,3.37494e-07)(2.39183,3.18177e-07)(2.39393,2.95001e-07)(2.39602,2.68848e-07)(2.39812,2.40642e-07)(2.40021,2.11312e-07)(2.40231,1.81763e-07)(2.4044,1.52838e-07)(2.4065,1.25302e-07)(2.40859,9.98169e-08)(2.41068,7.69271e-08)(2.41278,5.70548e-08)(2.41487,4.04942e-08)(2.41697,2.74137e-08)(2.41906,1.78614e-08)(2.42116,1.17752e-08)(2.42325,8.99388e-09)(2.42535,9.27207e-09)(2.42744,1.22952e-08)(2.42953,1.76959e-08)(2.43163,2.50697e-08)(2.43372,3.39908e-08)(2.43582,4.40264e-08)(2.43791,5.47486e-08)(2.44001,6.57463e-08)(2.4421,7.66395e-08)(2.4442,8.7088e-08)(2.44629,9.67897e-08)(2.44838,1.05492e-07)(2.45048,1.12998e-07)(2.45257,1.1915e-07)(2.45467,1.23846e-07)(2.45676,1.27032e-07)(2.45886,1.2869e-07)(2.46095,1.2885e-07)(2.46304,1.27572e-07)(2.46514,1.24951e-07)(2.46723,1.21107e-07)(2.46933,1.1618e-07)(2.47142,1.10331e-07)(2.47352,1.03731e-07)(2.47561,9.65601e-08)(2.47771,8.90023e-08)(2.4798,8.12406e-08)(2.48189,7.34538e-08)(2.48399,6.58129e-08)(2.48608,5.84775e-08)(2.48818,5.1593e-08)(2.49027,4.52885e-08)(2.49237,3.96746e-08)(2.49446,3.48419e-08)(2.49656,3.08605e-08)(2.49865,2.77788e-08)(2.50074,2.56242e-08)(2.50284,2.44032e-08)(2.50493,2.41019e-08)(2.50703,2.46878e-08)(2.50912,2.61106e-08)(2.51122,2.83041e-08)(2.51331,3.11882e-08)(2.51541,3.46707e-08)(2.5175,3.86495e-08)(2.51959,4.30152e-08)(2.52169,4.76529e-08)(2.52378,5.24448e-08)(2.52588,5.72723e-08)(2.52797,6.20186e-08)(2.53007,6.65706e-08)(2.53216,7.08209e-08)(2.53426,7.46701e-08)(2.53635,7.80281e-08)(2.53844,8.0816e-08)(2.54054,8.29674e-08)(2.54263,8.44292e-08)(2.54473,8.51629e-08)(2.54682,8.51451e-08)(2.54892,8.43673e-08)(2.55101,8.28367e-08)(2.55311,8.05755e-08)(2.5552,7.76205e-08)(2.55729,7.40223e-08)(2.55939,6.98448e-08)
};

\coordinate (spypointthree) at (axis cs:2.14469,0.0346725);
\coordinate (spyviewerthree) at (axis cs:-1,1e-05);
\spy[size=2cm] on (spypointthree) in node [fill=white] at (spyviewerthree);
\end{semilogyaxis}
\end{tikzpicture}

\end{document}

Answer 1

I apologize for this solution beforehand; this is not a clean solution.

---

Why is the magnified part even enhanced in that way? (Well, it's the spy library after all!)

The PGF/TikZ manual^{[section 49.1 “Magnifying a Part of a Picture”]} describes:

Note that this magnication uses what is called a canvas transformation in this manual: Everything is magnied, including line width and text.

Great! What does the manual^{[section 68.4 “Coordinate Versus Canvas Transformations”]} have to say about “canvas transformation”?

[…] Whereas a scaling by a factor of, say, 2 of the canvas causes everything to be scaled by this factor (including the thickness of lines and text), a scaling of two in the coordinate system causes only the coordinates to be scaled, but not the line width nor text.

By default, all transformations only apply to the coordinate transformation system. However, using the command \pgflowlevel it is possible to apply a transformation to the canvas.

Coordinate transformations are often preferable over canvas transformations.

You don't say?
Section 22.4 “Canvas Transformations” describes a TikZ key to explicitly use the canvas transformations, but no way to explicitly not use it and to use the crucial coordinate transformation instead.

---

I have only found a very manual way to archieve this.
First I have defined four macros:

• The first one, \myplots, is just a placeholder for the plots. We need them twice, first for the actual plot, and a second time for the part that is spied on. The coordinate-ish spying is done via a scale around key.
• The second one is just the factor that the peak gets magnified (called \spyfactor). We want that factor not to be hard-coded because we need it to calculate the coordinate that is to be scaled around. (TikZ calc library is needed for this.)

• There was a problem when I tried to use the already declared coordinate/node spypoint and spyviewer inside the scope's optional argument:

  No shape named spyviewer is known.
  No shape named spypoint is known.
  

  Therefore, I defined yet another two very simple macros that just hold the coordinates for the spied-on and the spied to coordinates.

The circles around those two coordinates are now nodes with a minimum size. The line between those circles is now a drawn edge.

The actual magnified part is a re-drawn and clipped part of the actual part.

The point that we scale around is f  ²/(f  ²-1) times on the line from the spied-to to the spied-on point. Or in TikZ:

scale around={\spyfactor:($(\spyviewer)!\spyfactor^2/(\spyfactor^2-1)!(\spypoint)$)}

   f       f²/(f²-1)
 ———————————————————————
    2    4/ 3 = 1.3333…
    3    9/ 8 = 1.125
  √10   10/ 9 = 1.1111…
    4   16/15 = 1.0666…
    ⁞      ⁞       ⁞

Some thoughts:

• The clip circle's radius is reduced by the half of the line width so that no part of the magnified picture is on the “magnifying glass”.

• The magnification factor (which is just a scale but as a canvas transformation) is not the same as the coordination transformation. In fact it is

   <magnifying scale> = <coordinate scale>²
  

  This is not very surprising, because when we scale two times in x direction and two times in y direction the result is four times as big.

MWE

\documentclass[border=5pt,tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{spy,calc}
\newcommand*\myplots[1][]{
    \addplot[#1,
        color=green,
        only marks,
        mark=x, clip marker paths=true,
        mark options=solid]
        coordinates {(1.60852,6.13283e-05)(1.62527,6.78766e-05)(1.64203,7.16948e-05)(1.65879,7.09775e-05)(1.67554,6.64539e-05)(1.6923,6.0881e-05)(1.70905,5.65543e-05)(1.72581,5.32983e-05)(1.74256,4.89298e-05)(1.75932,4.17484e-05)(1.77607,3.27146e-05)(1.79283,2.49779e-05)(1.80958,2.06858e-05)(1.82634,1.84003e-05)(1.84309,1.49936e-05)(1.85985,1.04606e-05)(1.87661,8.34593e-06)(1.89336,9.58471e-06)(1.91012,9.76351e-06)(1.92687,6.34117e-06)(1.94363,2.77806e-06)(1.96038,1.74742e-06)(1.97714,2.82344e-06)(1.99389,3.65428e-06)(2.01065,4.17071e-06)(2.0274,2.0308e-06)(2.04416,4.41266e-07)(2.06092,3.22697e-06)(2.07767,8.75464e-06)(2.09443,9.65132e-06)(2.11118,2.4596e-06)(2.12794,1.68688e-05)(2.14469,0.0369094)(2.16145,8.18512e-05)(2.1782,7.60426e-06)(2.19496,4.54191e-07)(2.21171,1.32399e-06)(2.22847,1.89883e-06)(2.24522,1.44121e-06)(2.26198,6.10898e-07)(2.27874,8.34218e-08)(2.29549,2.48243e-07)(2.31225,4.85005e-07)(2.329,3.81316e-07)(2.34576,6.46304e-08)(2.36251,9.62666e-08)(2.37927,3.36753e-07)(2.39602,2.88187e-07)(2.41278,7.51928e-08)(2.42953,1.27397e-08)(2.44629,8.43959e-08)(2.46304,1.24876e-07)(2.4798,8.67822e-08)(2.49656,3.41846e-08)(2.51331,2.77954e-08)(2.53007,6.15079e-08)(2.54682,8.5494e-08)(2.56358,6.64095e-08)(2.58033,2.22405e-08)};
    \addplot[#1,
        color=blue,
        solid]
        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\newcommand*\spyviewer{axis cs:-1,1e-05}
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    xmin=-3, xmax=3,
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    axis on top]
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Output