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test_wpolyfit.m

## Tests for wpolyfit.
##
## Test cases are taken from the NIST Statistical Reference Datasets
##    http://www.itl.nist.gov/div898/strd/

## Author: Paul Kienzle
## This program is public domain

1;

function do_test(n,x,y,p,dp,varargin)
  [myp,s] = wpolyfit(x,y,n,varargin{:});
  %if length(varargin)==0, [myp,s] = polyfit(x,y,n); else return; end
  mydp = sqrt(sumsq(inv(s.R'))'/s.df)*s.normr;
  if length(varargin)>0, mydp = [mydp;0]; end %origin
  %[svdp,j,svddp] = svdfit(x,y,n);
  disp('parameter  certified value  rel. error');
  [myp(:), p, abs((myp(:)-p)./p)] %, svdp, abs((svdp-p)./p) ]
  disp('p-error    certified value  rel. error');
  [mydp(:), dp, abs((mydp(:) - dp)./dp)] %, svdp, abs((svddp - dp)./dp)]
  input('Press <Enter> to proceed to the next test');
endfunction

##          x         y          dy
data = [0.0013852  0.2144023  0.0020470
      0.0018469  0.2516856  0.0022868
      0.0023087  0.3070443  0.0026362
      0.0027704  0.3603186  0.0029670
      0.0032322  0.4260864  0.0033705
      0.0036939  0.4799956  0.0036983 ];
x=data(:,1); y=data(:,2); dy=data(:,3);
wpolyfit(x,y,dy,1);
disp('computing parameter uncertainty from monte carlo simulation...');
fflush(stdout);
n=100; p=zeros(2,n);
for i=1:n, p(:,i)=(polyfit(x,y+randn(size(y)).*dy,1)).'; end
printf("%15s %15s\n", "Coefficient", "Error");
printf("%15g %15g\n", [mean(p'); std(p')]);
input('Press <Enter> to see some sample regression lines: ');
t = [x(1), x(length(x))];
[p,s] = wpolyfit(x,y,dy,1); dp=sqrt(sumsq(inv(s.R'))'/s.df)*s.normr;
hold off; 
for i=1:15, plot(t,polyval(p(:)+randn(size(dp)).*dp,t),'-g;;'); hold on; end
errorbar(x,y,dy,"~b;;");
[yf,dyf]=polyconf(p,x,s,0.05,'ci');
plot(x,yf-dyf,"-r;;",x,yf+dyf,'-r;95% confidence interval;')
hold off;
input('Press <Enter> to continue with the tests: ');


##Procedure:     Linear Least Squares Regression
##Reference:     Filippelli, A., NIST.
##Model:         Polynomial Class
##               11 Parameters (B0,B1,...,B10)
##
##               y = B0 + B1*x + B2*(x**2) + ... + B9*(x**9) + B10*(x**10) + e

##Data:
##            y          x
data = [    0.8116   -6.860120914
            0.9072   -4.324130045
            0.9052   -4.358625055
            0.9039   -4.358426747
            0.8053   -6.955852379
            0.8377   -6.661145254
            0.8667   -6.355462942
            0.8809   -6.118102026
            0.7975   -7.115148017
            0.8162   -6.815308569
            0.8515   -6.519993057
            0.8766   -6.204119983
            0.8885   -5.853871964
            0.8859   -6.109523091
            0.8959   -5.79832982
            0.8913   -5.482672118
            0.8959   -5.171791386
            0.8971   -4.851705903
            0.9021   -4.517126416
            0.909    -4.143573228
            0.9139   -3.709075441
            0.9199   -3.499489089
            0.8692   -6.300769497
            0.8872   -5.953504836
            0.89     -5.642065153
            0.891    -5.031376979
            0.8977   -4.680685696
            0.9035   -4.329846955
            0.9078   -3.928486195
            0.7675   -8.56735134
            0.7705   -8.363211311
            0.7713   -8.107682739
            0.7736   -7.823908741
            0.7775   -7.522878745
            0.7841   -7.218819279
            0.7971   -6.920818754
            0.8329   -6.628932138
            0.8641   -6.323946875
            0.8804   -5.991399828
            0.7668   -8.781464495
            0.7633   -8.663140179
            0.7678   -8.473531488
            0.7697   -8.247337057
            0.77     -7.971428747
            0.7749   -7.676129393
            0.7796   -7.352812702
            0.7897   -7.072065318
            0.8131   -6.774174009
            0.8498   -6.478861916
            0.8741   -6.159517513
            0.8061   -6.835647144
            0.846    -6.53165267
            0.8751   -6.224098421
            0.8856   -5.910094889
            0.8919   -5.598599459
            0.8934   -5.290645224
            0.894    -4.974284616
            0.8957   -4.64454848
            0.9047   -4.290560426
            0.9129   -3.885055584
            0.9209   -3.408378962
            0.9219   -3.13200249
            0.7739   -8.726767166
            0.7681   -8.66695597
            0.7665   -8.511026475
            0.7703   -8.165388579
            0.7702   -7.886056648
            0.7761   -7.588043762
            0.7809   -7.283412422
            0.7961   -6.995678626
            0.8253   -6.691862621
            0.8602   -6.392544977
            0.8809   -6.067374056
            0.8301   -6.684029655
            0.8664   -6.378719832
            0.8834   -6.065855188
            0.8898   -5.752272167
            0.8964   -5.132414673
            0.8963   -4.811352704
            0.9074   -4.098269308
            0.9119   -3.66174277
            0.9228   -3.2644011];

##Certified values:
##                      p                       dP
target = [      -1467.48961422980         298.084530995537
                -2772.17959193342         559.779865474950
                -2316.37108160893         466.477572127796
                -1127.97394098372         227.204274477751
                -354.478233703349         71.6478660875927
                -75.1242017393757         15.2897178747400
                -10.8753180355343         2.23691159816033
                -1.06221498588947         0.221624321934227
                -0.670191154593408E-01    0.142363763154724E-01
                -0.246781078275479E-02    0.535617408889821E-03
                -0.402962525080404E-04    0.896632837373868E-05];
if 1
  disp("Filippelli, A.,  NIST.");
  do_test(10, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif

##Procedure:     Linear Least Squares Regression
##
##Reference:     Pontius, P., NIST. 
##               Load Cell Calibration.
##
##Model:         Quadratic Class
##               3 Parameters (B0,B1,B2)
##               y = B0 + B1*x + B2*(x**2)


##Data:       y             x
data = [ \
         .11019        150000
         .21956        300000
         .32949        450000
         .43899        600000
         .54803        750000
         .65694        900000
         .76562       1050000
         .87487       1200000
         .98292       1350000
        1.09146       1500000
        1.20001       1650000
        1.30822       1800000
        1.41599       1950000
        1.52399       2100000
        1.63194       2250000
        1.73947       2400000
        1.84646       2550000
        1.95392       2700000
        2.06128       2850000
        2.16844       3000000
         .11052        150000
         .22018        300000
         .32939        450000
         .43886        600000
         .54798        750000
         .65739        900000
         .76596       1050000
         .87474       1200000
         .98300       1350000
        1.09150       1500000
        1.20004       1650000
        1.30818       1800000
        1.41613       1950000
        1.52408       2100000
        1.63159       2250000
        1.73965       2400000
        1.84696       2550000
        1.95445       2700000
        2.06177       2850000
        2.16829       3000000 ];

##               Certified Regression Statistics
##
##                                          Standard Deviation
##                     Estimate             of Estimate
target = [ \
              0.673565789473684E-03    0.107938612033077E-03
              0.732059160401003E-06    0.157817399981659E-09
             -0.316081871345029E-14    0.486652849992036E-16 ];                

if 1
  disp("Pontius, P., NIST");
  do_test(2, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif



#Procedure:     Linear Least Squares Regression
#Reference:     Eberhardt, K., NIST.
#Model:         Linear Class
#               1 Parameter (B1)
#
#               y = B1*x + e

#Data:     y     x
data =[\
         130    60
         131    61
         132    62
         133    63
         134    64
         135    65
         136    66
         137    67
         138    68
         139    69
         140    70 ];


#               Certified Regression Statistics
#
#                                 Standard Deviation
#               Estimate             of Estimate
target = [ \
        0                    0
          2.07438016528926     0.165289256198347E-01 ];


if 1
  disp("Eberhardt, K., NIST");
  do_test(1, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)),'origin');
endif


#Reference:     Wampler, R. H. (1970). 
#               A Report of the Accuracy of Some Widely-Used Least 
#               Squares Computer Programs. 
#               Journal of the American Statistical Association, 65, 549-565.
#
#Model:         Polynomial Class
#               6 Parameters (B0,B1,...,B5)
#
#               y = B0 + B1*x + B2*(x**2) + B3*(x**3)+ B4*(x**4) + B5*(x**5)
#
#               Certified Regression Statistics
#
#                                          Standard Deviation
#     Parameter        Estimate               of Estimate
target = [\
                1.00000000000000        0.000000000000000
                1.00000000000000        0.000000000000000
                1.00000000000000        0.000000000000000
                1.00000000000000        0.000000000000000
                1.00000000000000        0.000000000000000
                1.00000000000000        0.000000000000000 ];

#Data:            y     x
data = [\
                 1     0
                 6     1
                63     2
               364     3
              1365     4
              3906     5
              9331     6
             19608     7
             37449     8
             66430     9
            111111    10
            177156    11
            271453    12
            402234    13
            579195    14
            813616    15
           1118481    16
           1508598    17
           2000719    18
           2613660    19
           3368421    20 ];

if 1
  disp("Wampler1");
  do_test(5, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif

##Reference:     Wampler, R. H. (1970). 
##               A Report of the Accuracy of Some Widely-Used Least 
##               Squares Computer Programs. 
##               Journal of the American Statistical Association, 65, 549-565.
##Model:         Polynomial Class
##               6 Parameters (B0,B1,...,B5)
##
##               y = B0 + B1*x + B2*(x**2) + B3*(x**3)+ B4*(x**4) + B5*(x**5)
##
##               Certified Regression Statistics
##                                       Standard Deviation
## Parameter         Estimate               of Estimate
target = [ \
                1.00000000000000         0.000000000000000
                0.100000000000000        0.000000000000000
                0.100000000000000E-01    0.000000000000000
                0.100000000000000E-02    0.000000000000000
                0.100000000000000E-03    0.000000000000000
                0.100000000000000E-04    0.000000000000000 ];


#Data:          y       x
data = [ \
            1.00000    0
            1.11111    1
            1.24992    2
            1.42753    3
            1.65984    4
            1.96875    5
            2.38336    6
            2.94117    7
            3.68928    8
            4.68559    9
            6.00000   10
            7.71561   11
            9.92992   12
           12.75603   13
           16.32384   14
           20.78125   15
           26.29536   16
           33.05367   17
           41.26528   18
           51.16209   19
           63.00000   20 ];

if 1
  disp("Wampler2");
  do_test(5, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif




##Reference:   Wampler, R. H. (1970). 
##             A Report of the Accuracy of Some Widely-Used Least 
##             Squares Computer Programs. 
##             Journal of the American Statistical Association, 65, 549-565.
##
##Model:       Polynomial Class
##             6 Parameters (B0,B1,...,B5)
##
##             y = B0 + B1*x + B2*(x**2) + B3*(x**3)+ B4*(x**4) + B5*(x**5)
##
##             Certified Regression Statistics
##
##                                        Standard Deviation
##   Parameter          Estimate             of Estimate
target = [\
                  1.00000000000000         2152.32624678170    
                  1.00000000000000         2363.55173469681    
                  1.00000000000000         779.343524331583    
                  1.00000000000000         101.475507550350    
                  1.00000000000000         5.64566512170752    
                  1.00000000000000         0.112324854679312    ];

#Data:           y      x
data = [ \
              760.     0
            -2042.     1
             2111.     2
            -1684.     3
             3888.     4
             1858.     5
            11379.     6
            17560.     7
            39287.     8
            64382.     9
           113159.    10
           175108.    11
           273291.    12
           400186.    13
           581243.    14
           811568.    15
          1121004.    16
          1506550.    17
          2002767.    18
          2611612.    19
          3369180.    20 ];
if 1
  disp("Wampler3");
  do_test(5, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif

##Model:         Polynomial Class
##               6 Parameters (B0,B1,...,B5)
##
##               y = B0 + B1*x + B2*(x**2) + B3*(x**3)+ B4*(x**4) + B5*(x**5)
##
##              Certified Regression Statistics
##
##                                          Standard Deviation
##     Parameter          Estimate             of Estimate
target = [\
                  1.00000000000000         215232.624678170
                  1.00000000000000         236355.173469681
                  1.00000000000000         77934.3524331583
                  1.00000000000000         10147.5507550350
                  1.00000000000000         564.566512170752
                  1.00000000000000         11.2324854679312 ];

#Data:            y     x
data = [\
              75901    0
            -204794    1
             204863    2
            -204436    3
             253665    4
            -200894    5
             214131    6
            -185192    7
             221249    8
            -138370    9
             315911   10
             -27644   11
             455253   12
             197434   13
             783995   14
             608816   15
            1370781   16
            1303798   17
            2205519   18
            2408860   19
            3444321   20 ];

if 1
  disp("Wampler4");
  do_test(5, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif



##Model:         Polynomial Class
##               6 Parameters (B0,B1,...,B5)
##
##               y = B0 + B1*x + B2*(x**2) + B3*(x**3)+ B4*(x**4) + B5*(x**5)
##
##               Certified Regression Statistics
##
##                                          Standard Deviation
##     Parameter          Estimate             of Estimate
target = [\
                  1.00000000000000         21523262.4678170
                  1.00000000000000         23635517.3469681
                  1.00000000000000         7793435.24331583
                  1.00000000000000         1014755.07550350
                  1.00000000000000         56456.6512170752
                  1.00000000000000         1123.24854679312 ];

##Data:            y     x
data = [ \
             7590001     0
           -20479994     1
            20480063     2
           -20479636     3
            25231365     4
           -20476094     5
            20489331     6
           -20460392     7
            18417449     8
           -20413570     9
            20591111    10
           -20302844    11
            18651453    12
           -20077766    13
            21059195    14
           -19666384    15
            26348481    16
           -18971402    17
            22480719    18
           -17866340    19
            10958421    20 ];
if 1
  disp("Wampler5");
  do_test(5, data(:,2),data(:,1),flipud(target(:,1)),flipud(target(:,2)));
endif

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