least_square_fit_3d.adb
fit poly to  1 degree polynomial
a^ 0 b^ 0 c^ 0

a^ 1 b^ 0 c^ 0
a^ 0 b^ 1 c^ 0
a^ 0 b^ 0 c^ 1

C(  1)=  3.0318E+01
C(  2)= -1.3188E+01
C(  3)=  4.0330E+01
C(  4)= -1.0789E+01
check_3d k=100, xmin= -1.350E+00, xmax=  1.620E+00
       ymin= -9.757E-01, ymax=  9.999E-01
       zmin= -4.918E-02, zmax=  1.000E+00
       umin=  2.852E+00, umax=  4.962E+01
max= 3.5556E+00 at   1, xbad=-1.350E+00, ybad=-9.757E-01, zbad= 2.190E-01, ubad= 2.852E+00
rms_err=  1.2565E+00, avg_err=  1.0935E+00, max_err=  3.5556E+00

fit poly to  2 degree polynomial
a^ 0 b^ 0 c^ 0

a^ 1 b^ 0 c^ 0
a^ 0 b^ 1 c^ 0
a^ 0 b^ 0 c^ 1

a^ 2 b^ 0 c^ 0
a^ 1 b^ 1 c^ 0
a^ 1 b^ 0 c^ 1
a^ 0 b^ 2 c^ 0
a^ 0 b^ 1 c^ 1
a^ 0 b^ 0 c^ 2

C(  1)=  2.2030E+02
C(  2)= -3.7629E+01
C(  3)=  8.2518E+01
C(  4)= -3.7527E+02
C(  5)= -7.5466E+01
C(  6)= -1.4746E+02
C(  7)= -2.8029E+01
C(  8)=  2.2225E+02
C(  9)=  9.1392E+00
C( 10)=  1.7297E+02
check_3d k=100, xmin= -1.350E+00, xmax=  1.620E+00
       ymin= -9.757E-01, ymax=  9.999E-01
       zmin= -4.918E-02, zmax=  1.000E+00
       umin=  2.852E+00, umax=  4.962E+01
max= 5.4909E-04 at 100, xbad= 1.620E+00, ybad= 9.988E-01, zbad=-4.918E-02, ubad= 4.749E+01
rms_err=  1.5435E-04, avg_err=  1.3007E-04, max_err=  5.4909E-04

fit poly to  3 degree polynomial
a^ 0 b^ 0 c^ 0

a^ 1 b^ 0 c^ 0
a^ 0 b^ 1 c^ 0
a^ 0 b^ 0 c^ 1

a^ 2 b^ 0 c^ 0
a^ 1 b^ 1 c^ 0
a^ 1 b^ 0 c^ 1
a^ 0 b^ 2 c^ 0
a^ 0 b^ 1 c^ 1
a^ 0 b^ 0 c^ 2

a^ 3 b^ 0 c^ 0
a^ 2 b^ 1 c^ 0
a^ 2 b^ 0 c^ 1
a^ 1 b^ 2 c^ 0
a^ 1 b^ 1 c^ 1
a^ 1 b^ 0 c^ 2
a^ 0 b^ 3 c^ 0
a^ 0 b^ 2 c^ 1
a^ 0 b^ 1 c^ 2
a^ 0 b^ 0 c^ 3

C(  1)=  2.3550E+01
C(  2)=  3.0598E+01
C(  3)= -1.1970E+00
C(  4)= -1.0054E+01
C(  5)=  3.7298E+00
C(  6)= -1.6640E+00
C(  7)=  1.3211E+01
C(  8)= -5.4156E+00
C(  9)= -2.4167E+00
C( 10)=  6.2189E+00
C( 11)= -4.1924E+00
C( 12)=  1.0764E+00
C( 13)=  3.6484E+00
C( 14)=  1.2672E+01
C( 15)=  1.4134E+01
C( 16)=  1.5654E+01
C( 17)= -2.9764E+01
C( 18)= -1.8125E+00
C( 19)= -2.9849E+01
C( 20)= -1.7147E+00
check_3d k=100, xmin= -1.350E+00, xmax=  1.620E+00
       ymin= -9.757E-01, ymax=  9.999E-01
       zmin= -4.918E-02, zmax=  1.000E+00
       umin=  2.852E+00, umax=  4.962E+01
max= 2.9466E-07 at   1, xbad=-1.350E+00, ybad=-9.757E-01, zbad= 2.190E-01, ubad= 2.852E+00
rms_err=  9.7664E-08, avg_err=  8.2754E-08, max_err=  2.9466E-07