notebooks/vector_field.ipynb

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   "source": [
    "#Plot a vector field\n",
    "\n",
    "First let's look at a simple vector field plot. It requires four parameters `x`, `y`, `dx` and `dy`, where `dx` and `dy` determine the endpoints of the arrows attached to the points with coordinates given in `x` and `y`."
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      "text/plain": [
       "#<GnuplotRB::Plot:0x000000025a0d28 @datasets=Hamster::Vector[#<GnuplotRB::Dataset:0x000000025a0ad0 @type=:datablock, @data=#<GnuplotRB::Datablock:0x000000025a0a58 @stored_in_file=false, @data=\"0 0 1.0 0.0\\n1 0 0.9510565162951535 0.0\\n2 0 0.8090169943749475 0.0\\n3 0 0.5877852522924731 0.0\\n4 0 0.30901699437494745 0.0\\n5 0 6.123233995736766e-17 0.0\\n6 0 -0.30901699437494734 0.0\\n7 0 -0.587785252292473 0.0\\n8 0 -0.8090169943749473 0.0\\n9 0 -0.9510565162951535 0.0\\n0 1 1.0 0.3090169943749474\\n1 1 0.9510565162951535 0.3090169943749474\\n2 1 0.8090169943749475 0.3090169943749474\\n3 1 0.5877852522924731 0.3090169943749474\\n4 1 0.30901699437494745 0.3090169943749474\\n5 1 6.123233995736766e-17 0.3090169943749474\\n6 1 -0.30901699437494734 0.3090169943749474\\n7 1 -0.587785252292473 0.3090169943749474\\n8 1 -0.8090169943749473 0.3090169943749474\\n9 1 -0.9510565162951535 0.3090169943749474\\n0 2 1.0 0.5877852522924731\\n1 2 0.9510565162951535 0.5877852522924731\\n2 2 0.8090169943749475 0.5877852522924731\\n3 2 0.5877852522924731 0.5877852522924731\\n4 2 0.30901699437494745 0.5877852522924731\\n5 2 6.123233995736766e-17 0.5877852522924731\\n6 2 -0.30901699437494734 0.5877852522924731\\n7 2 -0.587785252292473 0.5877852522924731\\n8 2 -0.8090169943749473 0.5877852522924731\\n9 2 -0.9510565162951535 0.5877852522924731\\n0 3 1.0 0.8090169943749475\\n1 3 0.9510565162951535 0.8090169943749475\\n2 3 0.8090169943749475 0.8090169943749475\\n3 3 0.5877852522924731 0.8090169943749475\\n4 3 0.30901699437494745 0.8090169943749475\\n5 3 6.123233995736766e-17 0.8090169943749475\\n6 3 -0.30901699437494734 0.8090169943749475\\n7 3 -0.587785252292473 0.8090169943749475\\n8 3 -0.8090169943749473 0.8090169943749475\\n9 3 -0.9510565162951535 0.8090169943749475\\n0 4 1.0 0.9510565162951535\\n1 4 0.9510565162951535 0.9510565162951535\\n2 4 0.8090169943749475 0.9510565162951535\\n3 4 0.5877852522924731 0.9510565162951535\\n4 4 0.30901699437494745 0.9510565162951535\\n5 4 6.123233995736766e-17 0.9510565162951535\\n6 4 -0.30901699437494734 0.9510565162951535\\n7 4 -0.587785252292473 0.9510565162951535\\n8 4 -0.8090169943749473 0.9510565162951535\\n9 4 -0.9510565162951535 0.9510565162951535\\n0 5 1.0 1.0\\n1 5 0.9510565162951535 1.0\\n2 5 0.8090169943749475 1.0\\n3 5 0.5877852522924731 1.0\\n4 5 0.30901699437494745 1.0\\n5 5 6.123233995736766e-17 1.0\\n6 5 -0.30901699437494734 1.0\\n7 5 -0.587785252292473 1.0\\n8 5 -0.8090169943749473 1.0\\n9 5 -0.9510565162951535 1.0\\n0 6 1.0 0.9510565162951536\\n1 6 0.9510565162951535 0.9510565162951536\\n2 6 0.8090169943749475 0.9510565162951536\\n3 6 0.5877852522924731 0.9510565162951536\\n4 6 0.30901699437494745 0.9510565162951536\\n5 6 6.123233995736766e-17 0.9510565162951536\\n6 6 -0.30901699437494734 0.9510565162951536\\n7 6 -0.587785252292473 0.9510565162951536\\n8 6 -0.8090169943749473 0.9510565162951536\\n9 6 -0.9510565162951535 0.9510565162951536\\n0 7 1.0 0.8090169943749475\\n1 7 0.9510565162951535 0.8090169943749475\\n2 7 0.8090169943749475 0.8090169943749475\\n3 7 0.5877852522924731 0.8090169943749475\\n4 7 0.30901699437494745 0.8090169943749475\\n5 7 6.123233995736766e-17 0.8090169943749475\\n6 7 -0.30901699437494734 0.8090169943749475\\n7 7 -0.587785252292473 0.8090169943749475\\n8 7 -0.8090169943749473 0.8090169943749475\\n9 7 -0.9510565162951535 0.8090169943749475\\n0 8 1.0 0.5877852522924732\\n1 8 0.9510565162951535 0.5877852522924732\\n2 8 0.8090169943749475 0.5877852522924732\\n3 8 0.5877852522924731 0.5877852522924732\\n4 8 0.30901699437494745 0.5877852522924732\\n5 8 6.123233995736766e-17 0.5877852522924732\\n6 8 -0.30901699437494734 0.5877852522924732\\n7 8 -0.587785252292473 0.5877852522924732\\n8 8 -0.8090169943749473 0.5877852522924732\\n9 8 -0.9510565162951535 0.5877852522924732\\n0 9 1.0 0.3090169943749475\\n1 9 0.9510565162951535 0.3090169943749475\\n2 9 0.8090169943749475 0.3090169943749475\\n3 9 0.5877852522924731 0.3090169943749475\\n4 9 0.30901699437494745 0.3090169943749475\\n5 9 6.123233995736766e-17 0.3090169943749475\\n6 9 -0.30901699437494734 0.3090169943749475\\n7 9 -0.587785252292473 0.3090169943749475\\n8 9 -0.8090169943749473 0.3090169943749475\\n9 9 -0.9510565162951535 0.3090169943749475\">, @options=Hamster::Hash[:with => \"vectors\"]>], @options=Hamster::Hash[:key => false, :title => \"Vector Field\"], @already_plotted=true, @cmd=\"plot \", @terminal=#<GnuplotRB::Terminal:0x00000002588110 @cmd=\"gnuplot 2>&1\", @current_datablock=0, @err_array=[], @in=#<IO:fd 23>>>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "require 'gnuplotrb'\n",
    "include GnuplotRB\n",
    "include Math\n",
    "\n",
    "x = Array.new(10) { (0..9).to_a }.flatten\n",
    "y = (0..9).map { |i| Array.new(10) {i} }.flatten\n",
    "dx = x.zip(y).map { |p| cos(p[0].to_f*PI/10.0) }\n",
    "dy = x.zip(y).map { |p| sin(p[1].to_f*PI/10.0) }\n",
    "\n",
    "Plot.new([[x,y,dx,dy], with: 'vectors'], \n",
    "         key: false, title: 'Vector Field')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Colored arrows\n",
    "\n",
    "Now, color the arrows according to their slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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@options=Hamster::Hash[:key => false, :title => \"Vector Field\", :tics => false], @already_plotted=true, @cmd=\"plot \", @terminal=#<GnuplotRB::Terminal:0x0000000252e1b0 @cmd=\"gnuplot 2>&1\", @current_datablock=0, @err_array=[], @in=#<IO:fd 27>>>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#the slopes of the vectors on the logistic scale\n",
    "col = dx.zip(dy).map do |p| \n",
    "  p[0]==0 ? 1.0 : 1.0 / (1.0 + Math::exp(-p[1].to_f / p[0].to_f))\n",
    "end\n",
    "\n",
    "Plot.new([[x,y,dx,dy,col], with: 'vectors', filled: true, lc: 'palette'],\n",
    "         key: false, tics: false, title: 'Vector Field')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##3D vector field\n",
    "\n",
    "Vector fields may be visualized in 3D as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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9 9 1.0 0.3090169943749475 -0.9510565162951535 0.5766453024931508\\n1 9 9 0.9510565162951535 0.3090169943749475 -0.9510565162951535 0.5805227496880025\\n2 9 9 0.8090169943749475 0.3090169943749475 -0.9510565162951535 0.5943471932933198\\n3 9 9 0.5877852522924731 0.3090169943749475 -0.9510565162951535 0.6284869125079644\\n4 9 9 0.30901699437494745 0.3090169943749475 -0.9510565162951535 0.7310585786300049\\n5 9 9 6.123233995736766e-17 0.3090169943749475 -0.9510565162951535 1.0\\n6 9 9 -0.30901699437494734 0.3090169943749475 -0.9510565162951535 0.26894142136999505\\n7 9 9 -0.587785252292473 0.3090169943749475 -0.9510565162951535 0.3715130874920355\\n8 9 9 -0.8090169943749473 0.3090169943749475 -0.9510565162951535 0.40565280670668025\\n9 9 9 -0.9510565162951535 0.3090169943749475 -0.9510565162951535 0.41947725031199745\">, @options=Hamster::Hash[:with => \"vectors\", :lc => \"palette\", :filled => true]>], @options=Hamster::Hash[:key => false, :title => \"3D Vector Field\", :tics => false], @already_plotted=true, @cmd=\"splot \", @terminal=#<GnuplotRB::Terminal:0x0000000201ad18 @cmd=\"gnuplot 2>&1\", @current_datablock=0, @err_array=[], @in=#<IO:fd 31>>>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx = ([x] * 10).flatten\n",
    "yy = ([y] * 10).flatten\n",
    "zz = (0..9).map { |i| Array.new(100) {i} }.flatten\n",
    "dxx = xx.zip(yy, zz).map { |p| cos(p[0].to_f*PI/10.0) }\n",
    "dyy = xx.zip(yy, zz).map { |p| sin(p[1].to_f*PI/10.0) }\n",
    "dzz = xx.zip(yy, zz).map { |p| cos(p[2].to_f*PI/10.0) }\n",
    "color = dxx.zip(dyy, dzz).map do |p| \n",
    "  p[0]==0 ? 1.0 : 1.0 / (1.0 + exp(-p[1].to_f / p[0].to_f))\n",
    "end\n",
    "Splot.new(\n",
    "  [[xx,yy,zz,dxx,dyy,dzz,color], with: 'vectors', filled: true, lc: 'palette'],\n",
    "  key: false,\n",
    "  tics: false,\n",
    "  title: '3D Vector Field'\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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   "language": "ruby",
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   "file_extension": "rb",
   "mimetype": "application/x-ruby",
   "name": "ruby",
   "version": "2.1.2"
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