test_gaulegf2D.c running 
calling gaulegf(-1.000000, 2.000000, xx, wx, n) 
n=1, equivalent h=3.000000 
xx[1]=0.500000, wx[1]=3.000000 

calling gaulegf(-2.000000, 1.500000, yy, wy, n) 
n=1, equivalent h=3.500000 
yy[1]=-0.250000, wy[1]=3.500000 

calling gaulegf(-1.000000, 2.000000, xx, wx, n) 
n=2, equivalent h=1.500000 
xx[1]=-0.366025, wx[1]=1.500000 
xx[2]=1.366025, wx[2]=1.500000 

calling gaulegf(-2.000000, 1.500000, yy, wy, n) 
n=2, equivalent h=1.750000 
yy[1]=-1.260363, wy[1]=1.750000 
yy[2]=0.760363, wy[2]=1.750000 

calling gaulegf(-1.000000, 2.000000, xx, wx, n) 
n=3, equivalent h=1.000000 
xx[1]=-0.661895, wx[1]=0.833333 
xx[2]=0.500000, wx[2]=1.333333 
xx[3]=1.661895, wx[3]=0.833333 

calling gaulegf(-2.000000, 1.500000, yy, wy, n) 
n=3, equivalent h=1.166667 
yy[1]=-1.605544, wy[1]=0.972222 
yy[2]=-0.250000, wy[2]=1.555556 
yy[3]=1.105544, wy[3]=0.972222 

calling gaulegf(-1.000000, 2.000000, xx, wx, n) 
n=4, equivalent h=0.750000 
xx[1]=-0.791704, wx[1]=0.521782 
xx[2]=-0.009972, wx[2]=0.978218 
xx[3]=1.009972, wx[3]=0.978218 
xx[4]=1.791704, wx[4]=0.521782 

calling gaulegf(-2.000000, 1.500000, yy, wy, n) 
n=4, equivalent h=0.875000 
yy[1]=-1.756989, wy[1]=0.608746 
yy[2]=-0.844967, wy[2]=1.141254 
yy[3]=0.344967, wy[3]=1.141254 
yy[4]=1.256989, wy[4]=0.608746 

calling gaulegf(-1.000000, 2.000000, xx, wx, n) 
n=5, equivalent h=0.600000 
xx[1]=-0.859270, wx[1]=0.355390 
xx[2]=-0.307704, wx[2]=0.717943 
xx[3]=0.500000, wx[3]=0.853333 
xx[4]=1.307704, wx[4]=0.717943 
xx[5]=1.859270, wx[5]=0.355390 

calling gaulegf(-2.000000, 1.500000, yy, wy, n) 
n=5, equivalent h=0.700000 
yy[1]=-1.835815, wy[1]=0.414622 
yy[2]=-1.192321, wy[2]=0.837600 
yy[3]=-0.250000, wy[3]=0.995556 
yy[4]=0.692321, wy[4]=0.837600 
yy[5]=1.335815, wy[5]=0.414622 

f12(x,y)=x+2.0*y+3.0 
n=1, n^2=1, area=31.500000 
n=2, n^2=4, area=31.500000 
n=3, n^2=9, area=31.500000 
n=4, n^2=16, area=31.500000 
n=5, n^2=25, area=31.500000 

f22(x,y)=x*x+2.0*y*y+3.0*x*y+4.0*x+5.0*y+6.0; 
n=1, n^2=1, area=70.875000 
n=2, n^2=4, area=100.187500 
n=3, n^2=9, area=100.187500 
n=4, n^2=16, area=100.187500 
n=5, n^2=25, area=100.187500 

f32(x,y)=x*x*x+2.0*y*y*y+3.0*x*x*y+4.0*x*y*y+ 
         5.0*x*x+6.0*y*y+7.0*x*y+8.0*x+9.0*y+10.0 
n=1, n^2=1, area=131.578125 
n=2, n^2=4, area=246.531250 
n=3, n^2=9, area=246.531250 
n=4, n^2=16, area=246.531250 
n=5, n^2=25, area=246.531250 
f42(x,y)=x*x*x*x+2.0*y*y*y*y+3.0*x*x*x*y+4.0*x*x*y*y+ 
         5.0*x*x*x*y+6.0*x*x*x+7.0*y*y*y+8.0*x*x*y+ 
         9.0*x*y*y+10.0*x*x+11.0*y*y+12.0*x*y+13.0*x+ 
         14.0*y+15.0 
n=1, n^2=1, area=209.917969 
n=2, n^2=4, area=522.520833 
n=3, n^2=9, area=544.753125 
n=4, n^2=16, area=544.753125 
n=5, n^2=25, area=544.753125 

fe2(x,y)=exp(x+y) 
n=1, n^2=1, area=13.482267 
n=2, n^2=4, area=29.337044 
n=3, n^2=9, area=30.489045 
n=4, n^2=16, area=30.516173 
n=5, n^2=25, area=30.516515 

phi(x,2,3,xg)*phi(y,2,3,yg) 
n=1, n^2=1,  area=3.322266 
n=2, n^2=4,  area=5.906250 
n=3, n^2=9,  area=3.366562 
n=4, n^2=16,  area=4.050000 
n=5, n^2=25,  area=4.050000 
n=6, n^2=36,  area=4.050000 
n=7, n^2=49,  area=4.050000 

phi(x,2,3,xg)*phi(y,2,3,yg]*f12(x,y) 
n=1, n^2=1, area=9.966797 
n=2, n^2=4, area=32.484375 
n=3, n^2=9, area=15.415312 
n=4, n^2=16, area=19.743750 
n=5, n^2=25, area=19.743750 
n=6, n^2=36, area=19.743750 
n=7, n^2=49, area=19.743750 
n=8, n^2=64, area=19.743750 
n=9, n^2=81, area=19.743750 

phi(x,2,3,xg)*phi(y,2,3,yg)*f22(x,y) 
n=1, n^2=1, area=22.425293 
n=2, n^2=4, area=119.109375 
n=3, n^2=9, area=58.161797 
n=4, n^2=16, area=65.270089 
n=5, n^2=25, area=68.090625 
n=6, n^2=36, area=68.090625 
n=7, n^2=49, area=68.090625 
n=8, n^2=64, area=68.090625 
n=9, n^2=81, area=68.090625 

phi(x,2,3,xg)*phi(y,2,3,yg)*f32(x,y) 
n=1, n^2=1, area=41.632141 
n=2, n^2=4, area=324.290039 
n=3, n^2=9, area=167.737869 
n=4, n^2=16, area=164.995915 
n=5, n^2=25, area=179.465625 
n=6, n^2=36, area=179.465625 
n=7, n^2=49, area=179.465625 
n=8, n^2=64, area=179.465625 
n=9, n^2=81, area=179.465625 

phi(x,2,3,xg)*phi(y,2,3,yg)*f42(x,y) 
n=1, n^2=1, area=66.419357 
n=2, n^2=4, area=781.768066 
n=3, n^2=9, area=452.867164 
n=4, n^2=16, area=383.721099 
n=5, n^2=25, area=427.049749 
n=6, n^2=36, area=431.372940 
n=7, n^2=49, area=431.372940 
n=8, n^2=64, area=431.372940 
n=9, n^2=81, area=431.372940 

phi(x,2,3,xg)*phi(y,2,3,yg)*fe2(x,y) 
n=1, n^2=1, area=4.265874 
n=2, n^2=4, area=46.281644 
n=3, n^2=9, area=27.888595 
n=4, n^2=16, area=23.861047 
n=5, n^2=25, area=25.759823 
n=6, n^2=36, area=26.201766 
n=7, n^2=49, area=26.238316 
n=8, n^2=64, area=26.239942 
n=9, n^2=81, area=26.239987 
n=10, n^2=100, area=26.239988 
n=11, n^2=121, area=26.239988 

phi(x,3,5,xg)*phi(y,3,5,yg) 
n=1, n^2=1,  area=3.604889 
n=2, n^2=4,  area=0.082050 
n=3, n^2=9,  area=3.880819 
n=4, n^2=16,  area=5.135257 
n=5, n^2=25,  area=2.262140 
n=6, n^2=36,  area=3.281513 
n=7, n^2=49,  area=3.281513 

phi(x,3,5,xg)*phi(y,3,5,yg]*f12(x,y) 
n=1, n^2=1, area=10.814667 
n=2, n^2=4, area=0.392668 
n=3, n^2=9, area=15.914917 
n=4, n^2=16, area=23.792916 
n=5, n^2=25, area=9.104393 
n=6, n^2=36, area=14.201257 
n=7, n^2=49, area=14.201257 
n=8, n^2=64, area=14.201257 
n=9, n^2=81, area=14.201257 

phi(x,3,5,xg)*phi(y,3,5,yg)*f22(x,y) 
n=1, n^2=1, area=24.333000 
n=2, n^2=4, area=1.467132 
n=3, n^2=9, area=62.084198 
n=4, n^2=16, area=89.847309 
n=5, n^2=25, area=36.844690 
n=6, n^2=36, area=46.849475 
n=7, n^2=49, area=51.019636 
n=8, n^2=64, area=51.019636 
n=9, n^2=81, area=51.019636 

phi(x,3,5,xg)*phi(y,3,5,yg)*f32(x,y) 
n=1, n^2=1, area=45.173764 
n=2, n^2=4, area=3.932417 
n=3, n^2=9, area=174.081643 
n=4, n^2=16, area=243.388036 
n=5, n^2=25, area=105.675006 
n=6, n^2=36, area=116.656862 
n=7, n^2=49, area=135.020009 
n=8, n^2=64, area=135.020009 
n=9, n^2=81, area=135.020009 

phi(x,3,5,xg)*phi(y,3,5,yg)*f42(x,y) 
n=1, n^2=1, area=72.069615 
n=2, n^2=4, area=9.447085 
n=3, n^2=9, area=470.679164 
n=4, n^2=16, area=636.880960 
n=5, n^2=25, area=306.211807 
n=6, n^2=36, area=282.399965 
n=7, n^2=49, area=339.864675 
n=8, n^2=64, area=346.225046 
n=9, n^2=81, area=346.225046 

phi(x,3,5,xg)*phi(y,3,5,yg)*fe2(x,y) 
n=1, n^2=1, area=4.628769 
n=2, n^2=4, area=0.559832 
n=3, n^2=9, area=29.033473 
n=4, n^2=16, area=40.030702 
n=5, n^2=25, area=19.742851 
n=6, n^2=36, area=18.071552 
n=7, n^2=49, area=21.077505 
n=8, n^2=64, area=21.703138 
n=9, n^2=81, area=21.754022 
n=10, n^2=100, area=21.756281 
n=11, n^2=121, area=21.756344