Is ListVectorPlot broken in Mathematica 7?

*To*: mathgroup at smc.vnet.net*Subject*: [mg115527] Is ListVectorPlot broken in Mathematica 7?*From*: dwynn <ldlafleur at gmail.com>*Date*: Thu, 13 Jan 2011 03:29:29 -0500 (EST)

(Using Mathematica 7.0.1.0 in Windows Vista) Consider the 3 X 4 (rows X columns) array of 2-dimensional vectors created as follows: In[1]:= vecArray=Table[{(i+4j-4.0),2(i+4j-4.0)},{j,3},{i,4}] Out[1]= {{{1.,2.},{2.,4.},{3.,6.},{4.,8.}},{{5.,10.},{6.,12.},{7.,14.}, {8.,16.}},{{9.,18.},{10.,20.},{11.,22.},{12.,24.}}} The array of norms (magnitudes) of the vectors is: In[2]:= normArray=Map[Norm,vecArray,{2}] Out[2]= {{2.23607,4.47214,6.7082,8.94427}, {11.1803,13.4164,15.6525,17.8885},{20.1246,22.3607,24.5967,26.8328}} A contour plot of the norms of the vectors is created by In[3]:= ListContourPlot[normArray,AspectRatio->Automatic] The output graph has an x-axis extending from 1 to 4 and a y-axis from 1 to 3. The coordinates of the corners of the graph listed in order of INCREASING norm values at the corners are (1,1), (4,1), (1,3), (4,3). This is what I would expect. A plot of the vectors themselves is created by In[4]:= ListVectorPlot[vecArray,VectorPoints->All,AspectRatio- >Automatic] The output graph has an x-axis extending from 1 to 3 and a y-axis from 1 to 4, i.e., the opposite of the contour graph. Above the x-axis are three columns of vectors, each containing four vectors. The coordinates of the corners of the graph listed in terms of increasing apparent vector size are (1,1), (1,4), (3,1), (3,4). This graph seems incorrect. It is apparent that it corresponds to the transpose of the contour plot. Indeed, the following procedure produces a result that DOES correspond to the contour plot: In[5]:= vecArrayTr=Transpose[vecArray] Out[5]= {{{1.,2.},{5.,10.},{9.,18.}},{{2.,4.},{6.,12.},{10.,20.}}, {{3.,6.},{7.,14.},{11.,22.}},{{4.,8.},{8.,16.},{12.,24.}}} In[6]:= ListVectorPlot[vecArrayTr,VectorPoints->All,AspectRatio- >Automatic] The Mathematica documentation seems to predict the opposite. At http://reference.wolfram.com/mathematica/ref/ListContourPlot.html and http://reference.wolfram.com/mathematica/ref/ListVectorPlot.html we read, respectively, "ListContourPlot[array] arranges successive rows of array up the page, and successive columns across."; "ListVectorPlot[array] arranges successive rows of array up the page, and successive columns across." These identical specifications of the two commands suggest to me that the outputs from In[3] and In[4] should match in terms of axes and locations of vectors without needing the transpose operation. What am I failing to understand? L. Dwynn Lafleur Emeritus Professor of Physics University of Louisiana at Lafayette