least_square_fit_2d.adb
fit 1+2x+3y+4x^2+5xy+6y^2+7x^2y, to  1 degree polynomial
terms used to fit
x^0 y^0
x^ 1 y^ 0
x^ 0 y^ 1
C(  1)= -1.4671E+01
C(  2)=  2.2160E+01
C(  3)=  2.7173E+01
check_2d k= 25, xmin=  0.000E+00, xmax=  2.000E+00
ymin=  0.000E+00, ymax=  1.440E+00, zmin=  1.000E+00, zmax=  9.248E+01
max= 2.3704E+01 at  25, xbad= 2.000E+00, ybad= 1.440E+00, zbad= 9.248E+01
rms_err=  8.0059E+00, avg_err=  6.3220E+00, max_err=  2.3704E+01

fit 1+2x+3y+4x^2+5xy+6y^2+7x^2y, to  2 degree polynomial
terms used to fit
x^0 y^0
x^ 1 y^ 0
x^ 0 y^ 1
x^ 2 y^ 0
x^ 1 y^ 1
x^ 0 y^ 2
C(  1)=  3.2400E+00
C(  2)= -6.9600E+00
C(  3)= -5.0000E-01
C(  4)=  8.4800E+00
C(  5)=  1.9000E+01
C(  6)=  6.0000E+00
check_2d k= 25, xmin=  0.000E+00, xmax=  2.000E+00
ymin=  0.000E+00, ymax=  1.440E+00, zmin=  1.000E+00, zmax=  9.248E+01
max= 2.8000E+00 at  23, xbad= 1.000E+00, ybad= 1.440E+00, zbad= 4.104E+01
rms_err=  1.5037E+00, avg_err=  1.2544E+00, max_err=  2.8000E+00

fit 1+2x+3y+4x^2+5xy+6y^2+7x^2y, to  3 degree polynomial
terms used to fit
x^0 y^0
x^ 1 y^ 0
x^ 0 y^ 1
x^ 2 y^ 0
x^ 1 y^ 1
x^ 0 y^ 2
x^ 3 y^ 0
x^ 2 y^ 1
x^ 1 y^ 2
x^ 0 y^ 3
C(  1)=  1.0000E+00
C(  2)=  2.0000E+00
C(  3)=  3.0000E+00
C(  4)=  4.0000E+00
C(  5)=  5.0000E+00
C(  6)=  6.0000E+00
C(  7)= -6.6443E-13
C(  8)=  7.0000E+00
C(  9)= -8.1758E-14
C( 10)= -1.2704E-12
check_2d k= 25, xmin=  0.000E+00, xmax=  2.000E+00
ymin=  0.000E+00, ymax=  1.440E+00, zmin=  1.000E+00, zmax=  9.248E+01
max= 3.7548E-13 at   1, xbad= 0.000E+00, ybad= 0.000E+00, zbad= 1.000E+00
rms_err=  1.8508E-13, avg_err=  1.5546E-13, max_err=  3.7548E-13