quiver plot in Python using 2D arrays

Question

Hi I am trying to use the quiver plot to create a vector field plot. Here is my logic and approach, I first create the x,y coordinates for position by np.arange and use a step size of 0.1. Then I mesh the grid for x,y. Then I import the x component of the function Fx, and the y component Fy into python as .dat files. The .dat files are each 2D arrays (just a square matrix). I then use the quiver command for the meshed x,y coordinates and the Fx,Fy 2d arrays. However the quiver plot output does not make much sense at all in terms of what I was expecting.

Is there a problem with my code that I am overlooking? Does np.arange work if the step size is not an integer amount? I printed out all the arrays to manually check the data and everything seems fine.

Could it be that my four 2D arrays do not all have the same shape? The two .dat files I import are each 40x40 square matrices. Not sure if this is matching up well with the grid I meshed.

Other than that, I am unsure as to what the issue is. Any help or suggestions would be greatly appreciated. I can add the data in my .dat file if that will help. Thanks! ( I have checked all other examples on stack overflow for this problem and it seems my code is logically correct so I am very stuck)

import numpy as np
import matplotlib.pyplot as plt

data = np.genfromtxt('file1.dat')
data2 = np.genfromtxt('file2.dat')

nx = 2
ny = 2
x=np.arange(-nx,nx,0.1)
y=np.arange(-ny,ny,0.1)
xi,yi=np.meshgrid(x,y)
Fx = data[::5] #picks out every 5 rows in the matrix
Fy = data2[::5] 
#print(Fx)
#print(Fy)
#print(xi)
#print(yi)

plt.axes([0.065, 0.065, 0.9, 0.9])
plt.quiver(xi,yi,Fx,Fy, alpha=.5)
plt.quiver(xi,yi,Fx,Fy, edgecolor='k',facecolor='none', linewidth=.5)

plt.show()

EDIT: .dat files below as asked. If there is a way to import the .dat file let me know, I realize this is a lot of numbers and formatted horribly. Fx is listed first, then the Fy array. I am expecting a very nice quiver plot in which I have some kind of circular pattern/ circular flow. The arrows should all form a clockwise and or counter clockwise flow.

  -30.9032192      0.512708426      0.511251688      0.508112907      0.503038108      0.495766401      0.486015081      0.473499298      0.457935333      0.439051390      0.416606665      0.390406251      0.360321403      0.326310992      0.288441181      0.246901810      0.202013552      0.154238343      0.104165822       5.24933599E-02   0.00000000      -5.24933599E-02 -0.104165822     -0.154238343     -0.202013552     -0.246901810     -0.288441181     -0.326310992     -0.360321403     -0.390406251     -0.416606665     -0.439051390     -0.457935333     -0.473499298     -0.486015081     -0.495766401     -0.503038108     -0.508112907     -0.511251688     -0.512708426       30.9032192    

  0.640149713      0.648661256      0.646115780      0.638335168      -13.4731970      -13.0613079      0.587181866      0.561966598      0.533295572      0.501472771      0.466741979      0.429292738      0.389282435      0.346857786      0.302170664      0.255400449      0.206771404      0.156560570      0.105099753       5.27719632E-02   2.10129052E-08  -5.27718328E-02 -0.105099864     -0.156560570     -0.206771582     -0.255400449     -0.302170008     -0.346857607     -0.389282405     -0.429292321     -0.466741502     -0.501472294     -0.533295095     -0.561966538     -0.587181747       13.0613060       13.4731960     -0.638335109     -0.646115661     -0.648661256     -0.640149713    

  0.799892545      0.824215114      0.801061392      0.776797950      0.753669202      0.730814993      0.707295001      0.682291210      0.655105412      -8.68122292      -8.12608242      0.554765701      0.513439834      0.467435867      0.416336209      0.359773695      0.297508597      0.229575798      0.156477526       7.93530941E-02   6.53175791E-10  -7.93530941E-02 -0.156477645     -0.229576021     -0.297508597     -0.359773695     -0.416336179     -0.467435598     -0.513440192     -0.554765582       8.12608242       8.68122387     -0.655105233     -0.682291508     -0.707294881     -0.730815291     -0.753669143     -0.776797950     -0.801061392     -0.824215114     -0.799892545    

  0.940612555      0.983826339      0.933131218      0.884394646      0.842061043      0.804476202      0.769944012      0.737089813      0.704840183      0.672395170      0.639202237      0.604933023      0.569452882      0.532750905      0.494812310      -2.68859553      -2.16188312      0.365726620      0.304749787      0.205249593       6.78142031E-09 -0.205249622     -0.304749817     -0.365726680       2.16188359       2.68859553     -0.494812399     -0.532750905     -0.569453001     -0.604932964     -0.639202118     -0.672395170     -0.704840362     -0.737089515     -0.769943893     -0.804476202     -0.842061162     -0.884394407     -0.933131695     -0.983826339     -0.940612555    

  0.999167860       1.05166125      0.986028075      0.923735499      0.870001256      0.822448075      0.778727889      0.736939847      0.695574820      0.653458953      0.609715879      0.563743949      0.515199065      0.463976830      0.410177410      0.354019582      0.295616359      0.234412342      0.167968050       9.07804966E-02  -8.54922577E-10  -9.07804891E-02 -0.167968005     -0.234412268     -0.295616418     -0.354019672     -0.410177410     -0.463976830     -0.515199006     -0.563743949     -0.609715819     -0.653458893     -0.695574880     -0.736939907     -0.778727889     -0.822448075     -0.870001316     -0.923735559     -0.986028075      -1.05166125     -0.999167860    


  0.940612555      0.983826339      0.932870448      0.884094179      0.841758013      0.804004610      0.768958390      0.735091329      0.701199591      0.666386902      0.630052805      0.591893077      0.551910400      0.510422051      0.468044579      0.425626040      0.384017974      0.343483299      0.302600116     -0.377980769       8.43500270E-10  0.377980769     -0.302600116     -0.343483359     -0.384017944     -0.425625950     -0.468044549     -0.510422230     -0.551910520     -0.591892898     -0.630052805     -0.666386902     -0.701199770     -0.735090971     -0.768958986     -0.804005086     -0.841758251     -0.884094059     -0.932870448     -0.983826339     -0.940612555    


 0.799892545      0.824215114      0.807587028      0.790868759      0.775763810      0.761242151      0.746228993      0.729784787      0.711097538      0.689466000      0.664264023      -6.33222771      -5.70436525      0.561126649      0.514991641      0.460934460      0.396892428      0.320130050      0.227872163      0.119494393      -1.02303694E-08 -0.119494416     -0.227872089     -0.320129842     -0.396892160     -0.460934043     -0.514991641     -0.561126769       5.70436525       6.33222771     -0.664264023     -0.689466000     -0.711097836     -0.729784369     -0.746228993     -0.761242330     -0.775764227     -0.790868759     -0.807587445     -0.824215114     -0.799892545 

  0.640149713      0.648661256      0.658376634      0.663496077      0.663335323      -12.7135134      -12.2490902      0.630356669      0.608760655      0.581994295      0.550120413      0.513214111      0.471384048      0.424800932      0.373717010      0.318486720      0.259573966      0.197552294      0.133099481       6.69753179E-02  -1.07370708E-08  -6.69753179E-02 -0.133099481     -0.197552368     -0.259573698     -0.318486512     -0.373717397     -0.424800485     -0.471384078     -0.513214111     -0.550120771     -0.581994355     -0.608760655     -0.630356669       12.2490902       12.7135134     -0.663335383     -0.663496077     -0.658376753     -0.648661256     -0.640149713    

 -30.9032192      0.512708426      0.511251688      0.508112907      0.503038108      0.495766401      0.486015081      0.473499298      0.457935333      0.439051390      0.416606665      0.390406251      0.360321403      0.326310992      0.288441181      0.246901810      0.202013552      0.154238343      0.104165822       5.24933599E-02   0.00000000      -5.24933599E-02 -0.104165822     -0.154238343     -0.202013552     -0.246901810     -0.288441181     -0.326310992     -0.360321403     -0.390406251     -0.416606665     -0.439051390     -0.457935333     -0.473499298     -0.486015081     -0.495766401     -0.503038108     -0.508112907     -0.511251688     -0.512708426       30.9032192   

Now Fy array:

 -0.205083355     -0.525830388     -0.552687049     -0.580741763     -0.609929502     -0.640149713     -0.671258569     -0.703064799     -0.735320449     -0.767719150     -0.799892545     -0.831412077     -0.861791074     -0.890495777     -0.916961849     -0.940612555     -0.960886896     -0.977269113     -0.989315629     -0.996686459     -0.999167860     -0.996686459     -0.989315629     -0.977269113     -0.960886896     -0.940612555     -0.916961849     -0.890495777     -0.861791074     -0.831412077     -0.799892545     -0.767719150     -0.735320449     -0.703064799     -0.671258569     -0.640149713     -0.609929502     -0.580741763     -0.552687049     -0.525830388     -0.205083355    
 -0.495766401     -0.496165156     -0.509083092     -0.549605310       13.5129404       13.0519953     -0.646288395     -0.672055602     -0.695797563     -0.717920899     -0.738660455     -0.758110344     -0.776252687     -0.792979062     -0.808119476     -0.821464479     -0.832787395     -0.841867268     -0.848508835     -0.852558434     -0.853919387     -0.852558374     -0.848508716     -0.841867328     -0.832787514     -0.821464896     -0.808119833     -0.792978704     -0.776252151     -0.758110642     -0.738660395     -0.717920780     -0.695797503     -0.672055602     -0.646288335       13.0519953       13.5129395     -0.549605191     -0.509083092     -0.496165156     -0.495766401    

 -0.416606665     -0.387658477     -0.370003909     -0.412325561     -0.451486528     -0.484789789     -0.512974977     -0.536900580     -0.557342112       8.73137856       8.12754345     -0.604040861     -0.616312325     -0.627466083     -0.637651145     -0.646887839     -0.655064702     -0.661947429     -0.667217672     -0.670547307     -0.671688557     -0.670547426     -0.667217493     -0.661947429     -0.655064702     -0.646887779     -0.637651086     -0.627466381     -0.616312623     -0.604041040       8.12754345       8.73137951     -0.557341993     -0.536900103     -0.512975276     -0.484789670     -0.451485991     -0.412325561     -0.370003909     -0.387658477     -0.416606665   

 -0.246901810     -0.228335708     -0.217398927     -0.246074528     -0.271431714     -0.291785061     -0.307664692     -0.319617361     -0.328106791     -0.333535194     -0.336277753     -0.336733580     -0.335400879     -0.333002120     -0.330682963       2.81363893       2.24033999     -0.348281264     -0.372185618     -0.395866930     -0.403591305     -0.395866960     -0.372185677     -0.348281264       2.24033999       2.81363893     -0.330682874     -0.333002120     -0.335400909     -0.336733490     -0.336277664     -0.333535045     -0.328106642     -0.319617361     -0.307664692     -0.291785270     -0.271431714     -0.246074289     -0.217398927     -0.228335708     -0.246901810    
   0.00000000      -3.97699699E-02  -8.22334886E-02  -9.01840925E-02  -9.43243951E-02  -9.68469381E-02  -9.79287177E-02  -9.75681171E-02  -9.57226083E-02  -9.23085213E-02  -8.71856511E-02  -8.01347122E-02  -7.08276853E-02  -5.87978214E-02  -4.34263758E-02  -2.40071025E-02  -4.12676527E-05   2.79203784E-02   5.66387177E-02   7.90976062E-02   8.76100808E-02   7.90975988E-02   5.66387326E-02   2.79204026E-02  -4.12871887E-05  -2.40071043E-02  -4.34263758E-02  -5.87978400E-02  -7.08276406E-02  -8.01346377E-02  -8.71856511E-02  -9.23085883E-02  -9.57226381E-02  -9.75680798E-02  -9.79286432E-02  -9.68469679E-02  -9.43244398E-02  -9.01841149E-02  -8.22335258E-02  -3.97699960E-02   0.00000000    

 0.246901810      0.149554759       5.41899577E-02   6.69130459E-02   8.30149651E-02   9.62892994E-02  0.106718197      0.114569001      0.119987577      0.122970015      0.123354375      0.120809816      0.114815064      0.104622498       8.91864598E-02   6.69886991E-02   3.55363674E-02  -1.02187870E-02  -8.21609423E-02 -0.177876130     -0.191068053     -0.177876085      -8.21608678E-02  -1.02187609E-02   3.55363339E-02   6.69886544E-02   8.91865119E-02  0.104622573      0.114814982      0.120810024      0.123354279      0.122969493      0.119987287      0.114568666      0.106718197       9.62890834E-02   8.30147490E-02   6.69130459E-02   5.41902333E-02  0.149555355      0.246901810    

 0.416606665      0.324635506      0.239433557      0.271107137      0.304715306      0.333829224      0.358776420      0.380251735      0.398895025      0.415270001      0.429880798      -6.52393579      -5.84947205      0.467720896      0.479777455      0.492111117      0.504699171      0.516976655      0.527697802      0.535157621      0.537844956      0.535157681      0.527697802      0.516976714      0.504699290      0.492111027      0.479777277      0.467720628      -5.84947205      -6.52393579      0.429880500      0.415270001      0.398895413      0.380252063      0.358776003      0.333829224      0.304715246      0.271106362      0.239433587      0.324635804      0.416606665    

 0.495766401      0.468931794      0.452914894      0.491556555      0.528390408      -12.8101072      -12.3052654      0.617275119      0.641844690      0.664552093      0.685565233      0.704941750      0.722658634      0.738638997      0.752775729      0.764953554      0.775063336      0.783014059      0.788738489      0.792190075      0.793342948      0.792190075      0.788738668      0.783013999      0.775063157      0.764953852      0.752775729      0.738638759      0.722658694      0.704941571      0.685565174      0.664552152      0.641844690      0.617275119      -12.3052645      -12.8101072      0.528390408      0.491556555      0.452914953      0.468931794      0.495766401  

0.512708426      0.525830388      0.552687049      0.580741763      0.609929502      0.640149713      0.671258569      0.703064799      0.735320449      0.767719150      0.799892545      0.831412077      0.861791074      0.890495777      0.916961849      0.940612555      0.960886896      0.977269113      0.989315629      0.996686459      0.999167860      0.996686459      0.989315629      0.977269113      0.960886896      0.940612555      0.916961849      0.890495777      0.861791074      0.831412077      0.799892545      0.767719150      0.735320449      0.703064799      0.671258569      0.640149713      0.609929502      0.580741763      0.552687049      0.525830388      0.512708426   

Answer 1

There appear to be unusually large values (perhaps indication of an asymptotic singularity?) along the lines y=x and y=-x.

You can see this in the data you posted. Consider for example, the first line:

  -31.3490391       6.68895245E-02   6.68859407E-02   ... -6.68895245E-02   31.3490391    

The first value is large and negative, followed by numbers which are small and positive. Near the end of the line the numbers are small and negative, while the last value is large and positive. Clearly, as it stands, this data is not going to produce a smoothly varying quiver plot.

If we remove these unusually large values:

data[np.abs(data) > 1] = np.nan
data2[np.abs(data2) > 1] = np.nan

then

import numpy as np
import matplotlib.pyplot as plt

data = np.genfromtxt('file1.dat')
data2 = np.genfromtxt('file2.dat')

data[np.abs(data) > 1] = np.nan
data2[np.abs(data2) > 1] = np.nan

N = 10
Fx = data[::N, ::N]
Fy = data2[::N, ::N]

nrows, ncols = Fx.shape
nx = 2
ny = 2
x = np.linspace(-nx, nx, ncols)
y = np.linspace(-ny, ny, nrows)
xi, yi = np.meshgrid(x, y, indexing='ij')

plt.axes([0.065, 0.065, 0.9, 0.9])
plt.quiver(xi, yi, Fx, Fy, alpha=.5)
plt.quiver(xi, yi, Fx, Fy, edgecolor='k', facecolor='none', linewidth=.5)

plt.show()

yields

---

data is a 2D array of shape (301, 301):

In [109]: data.shape
Out[109]: (301, 301)

If we slice data using data[::10] then the result has shape

In [113]: data[::10].shape
Out[113]: (31, 301)

Notice that only the first axis gets sliced. To slice both the first and second axes, use data[::10, ::10]:

In [114]: data[::10, ::10].shape
Out[114]: (31, 31)

See the docs for more on multidimensional slicing. Always pay attention to the shape of NumPy arrays. It is often the key to understanding NumPy operations.

---

Although plt.quiver can sometimes accept arrays of different shape, it is easiest to use plt.quiver by passing four arrays the the same shape. To ensure that xi, yi, Fx, Fy all have the same shape, slice data and data2 to form Fx and Fy first, and then build xi and yi to conform to the (common) shape of Fx of Fy:

nrows, ncols = Fx.shape
x = np.linspace(-nx, nx, ncols)
y = np.linspace(-ny, ny, nrows)

The third argument to np.linspace indicates the number of elements in the returned array.

Answer 2

First make sure the dimension for Fx and Fy is the same to avoid any confusion. Then generate the grid space dimension based on the data dimension. You can use np.linspace instead of np.arange as:

x = np.linspace(-nx, nx, Fx.shape[1])
y = np.linspace(-ny, ny, Fx.shape[0])

Update: The complete code looks like:

import numpy as np
import matplotlib.pyplot as plt

# Fxdata.dat contain Fx data while Fydata.dat is Fy downloaded from the provided link
Fx = np.genfromtxt('Fxdata.dat')
Fy = np.genfromtxt('Fydata.dat')

# input data dimensions 
num_Fx = Fx.shape[0]    # number of lines for the data in file1.dat
length_Fx = Fx.shape[1]  # length of each row for file1.dat 

nx = 15
ny = 15

# you can generate the grid points based on the dimensions of the input data
x = np.linspace(-nx, nx, length_Fx)
y = np.linspace(-ny, ny, num_Fx)

# grid points 
xi,yi=np.meshgrid(x,y)

#
plt.axes([0.065, 0.065, 0.9, 0.9])
plt.quiver(xi,yi,Fx,Fy, alpha=.5)
#plt.quiver(xi,yi,Fx,Fy, edgecolor='k',facecolor='none', linewidth=.5)

plt.show()

Not sure if it make sense now but the resulting plot looks like: