Basic harness for testing NIST problems.

Change-Id: I5baaa24dbf0506ceedf4a9be4ed17c84974d71a1

data/nist/Bennett5.dat

@@ -0,0 +1,214 @@
+NIST/ITL StRD
+Dataset Name:  Bennett5          (Bennett5.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  43)
+               Certified Values  (lines 41 to  48)
+               Data              (lines 61 to 214)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               superconductivity magnetization modeling.  The
+               response variable is magnetism, and the predictor
+               variable is the log of time in minutes.
+
+Reference:     Bennett, L., L. Swartzendruber, and H. Brown, 
+               NIST (1994).  
+               Superconductivity Magnetization Modeling.
+
+
+
+
+
+
+Data:          1 Response Variable  (y = magnetism)
+               1 Predictor Variable (x = log[time])
+               154 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               3 Parameters (b1 to b3)
+
+               y = b1 * (b2+x)**(-1/b3)  +  e
+
+ 
+ 
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   -2000       -1500        -2.5235058043E+03  2.9715175411E+02
+  b2 =      50          45         4.6736564644E+01  1.2448871856E+00
+  b3 =       0.8         0.85      9.3218483193E-01  2.0272299378E-02
+
+Residual Sum of Squares:                    5.2404744073E-04
+Residual Standard Deviation:                1.8629312528E-03
+Degrees of Freedom:                               151
+Number of Observations:                           154
+
+
+
+
+
+
+
+
+
+
+
+Data:   y               x
+     -34.834702E0      7.447168E0
+     -34.393200E0      8.102586E0
+     -34.152901E0      8.452547E0
+     -33.979099E0      8.711278E0
+     -33.845901E0      8.916774E0
+     -33.732899E0      9.087155E0
+     -33.640301E0      9.232590E0
+     -33.559200E0      9.359535E0
+     -33.486801E0      9.472166E0
+     -33.423100E0      9.573384E0
+     -33.365101E0      9.665293E0
+     -33.313000E0      9.749461E0
+     -33.260899E0      9.827092E0
+     -33.217400E0      9.899128E0
+     -33.176899E0      9.966321E0
+     -33.139198E0     10.029280E0
+     -33.101601E0     10.088510E0
+     -33.066799E0     10.144430E0
+     -33.035000E0     10.197380E0
+     -33.003101E0     10.247670E0
+     -32.971298E0     10.295560E0
+     -32.942299E0     10.341250E0
+     -32.916302E0     10.384950E0
+     -32.890202E0     10.426820E0
+     -32.864101E0     10.467000E0
+     -32.841000E0     10.505640E0
+     -32.817799E0     10.542830E0
+     -32.797501E0     10.578690E0
+     -32.774300E0     10.613310E0
+     -32.757000E0     10.646780E0
+     -32.733799E0     10.679150E0
+     -32.716400E0     10.710520E0
+     -32.699100E0     10.740920E0
+     -32.678799E0     10.770440E0
+     -32.661400E0     10.799100E0
+     -32.644001E0     10.826970E0
+     -32.626701E0     10.854080E0
+     -32.612202E0     10.880470E0
+     -32.597698E0     10.906190E0
+     -32.583199E0     10.931260E0
+     -32.568699E0     10.955720E0
+     -32.554298E0     10.979590E0
+     -32.539799E0     11.002910E0
+     -32.525299E0     11.025700E0
+     -32.510799E0     11.047980E0
+     -32.499199E0     11.069770E0
+     -32.487598E0     11.091100E0
+     -32.473202E0     11.111980E0
+     -32.461601E0     11.132440E0
+     -32.435501E0     11.152480E0
+     -32.435501E0     11.172130E0
+     -32.426800E0     11.191410E0
+     -32.412300E0     11.210310E0
+     -32.400799E0     11.228870E0
+     -32.392101E0     11.247090E0
+     -32.380501E0     11.264980E0
+     -32.366001E0     11.282560E0
+     -32.357300E0     11.299840E0
+     -32.348598E0     11.316820E0
+     -32.339901E0     11.333520E0
+     -32.328400E0     11.349940E0
+     -32.319698E0     11.366100E0
+     -32.311001E0     11.382000E0
+     -32.299400E0     11.397660E0
+     -32.290699E0     11.413070E0
+     -32.282001E0     11.428240E0
+     -32.273300E0     11.443200E0
+     -32.264599E0     11.457930E0
+     -32.256001E0     11.472440E0
+     -32.247299E0     11.486750E0
+     -32.238602E0     11.500860E0
+     -32.229900E0     11.514770E0
+     -32.224098E0     11.528490E0
+     -32.215401E0     11.542020E0
+     -32.203800E0     11.555380E0
+     -32.198002E0     11.568550E0
+     -32.189400E0     11.581560E0
+     -32.183601E0     11.594420E0
+     -32.174900E0     11.607121E0
+     -32.169102E0     11.619640E0
+     -32.163300E0     11.632000E0
+     -32.154598E0     11.644210E0
+     -32.145901E0     11.656280E0
+     -32.140099E0     11.668200E0
+     -32.131401E0     11.679980E0
+     -32.125599E0     11.691620E0
+     -32.119801E0     11.703130E0
+     -32.111198E0     11.714510E0
+     -32.105400E0     11.725760E0
+     -32.096699E0     11.736880E0
+     -32.090900E0     11.747890E0
+     -32.088001E0     11.758780E0
+     -32.079300E0     11.769550E0
+     -32.073502E0     11.780200E0
+     -32.067699E0     11.790730E0
+     -32.061901E0     11.801160E0
+     -32.056099E0     11.811480E0
+     -32.050301E0     11.821700E0
+     -32.044498E0     11.831810E0
+     -32.038799E0     11.841820E0
+     -32.033001E0     11.851730E0
+     -32.027199E0     11.861550E0
+     -32.024300E0     11.871270E0
+     -32.018501E0     11.880890E0
+     -32.012699E0     11.890420E0
+     -32.004002E0     11.899870E0
+     -32.001099E0     11.909220E0
+     -31.995300E0     11.918490E0
+     -31.989500E0     11.927680E0
+     -31.983700E0     11.936780E0
+     -31.977900E0     11.945790E0
+     -31.972099E0     11.954730E0
+     -31.969299E0     11.963590E0
+     -31.963501E0     11.972370E0
+     -31.957701E0     11.981070E0
+     -31.951900E0     11.989700E0
+     -31.946100E0     11.998260E0
+     -31.940300E0     12.006740E0
+     -31.937401E0     12.015150E0
+     -31.931601E0     12.023490E0
+     -31.925800E0     12.031760E0
+     -31.922899E0     12.039970E0
+     -31.917101E0     12.048100E0
+     -31.911301E0     12.056170E0
+     -31.908400E0     12.064180E0
+     -31.902599E0     12.072120E0
+     -31.896900E0     12.080010E0
+     -31.893999E0     12.087820E0
+     -31.888201E0     12.095580E0
+     -31.885300E0     12.103280E0
+     -31.882401E0     12.110920E0
+     -31.876600E0     12.118500E0
+     -31.873699E0     12.126030E0
+     -31.867901E0     12.133500E0
+     -31.862101E0     12.140910E0
+     -31.859200E0     12.148270E0
+     -31.856300E0     12.155570E0
+     -31.850500E0     12.162830E0
+     -31.844700E0     12.170030E0
+     -31.841801E0     12.177170E0
+     -31.838900E0     12.184270E0
+     -31.833099E0     12.191320E0
+     -31.830200E0     12.198320E0
+     -31.827299E0     12.205270E0
+     -31.821600E0     12.212170E0
+     -31.818701E0     12.219030E0
+     -31.812901E0     12.225840E0
+     -31.809999E0     12.232600E0
+     -31.807100E0     12.239320E0
+     -31.801300E0     12.245990E0
+     -31.798401E0     12.252620E0
+     -31.795500E0     12.259200E0
+     -31.789700E0     12.265750E0
+     -31.786800E0     12.272240E0

data/nist/BoxBOD.dat

@@ -0,0 +1,66 @@
+NIST/ITL StRD
+Dataset Name:  BoxBOD            (BoxBOD.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 66)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are described in detail in Box, Hunter and
+               Hunter (1978).  The response variable is biochemical
+               oxygen demand (BOD) in mg/l, and the predictor
+               variable is incubation time in days.
+
+
+Reference:     Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
+               Statistics for Experimenters.  
+               New York, NY: Wiley, pp. 483-487.
+
+
+
+
+
+Data:          1 Response  (y = biochemical oxygen demand)
+               1 Predictor (x = incubation time)
+               6 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               2 Parameters (b1 and b2)
+
+               y = b1*(1-exp[-b2*x])  +  e
+
+
+ 
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1           100           2.1380940889E+02  1.2354515176E+01
+  b2 =   1             0.75        5.4723748542E-01  1.0455993237E-01
+
+Residual Sum of Squares:                    1.1680088766E+03
+Residual Standard Deviation:                1.7088072423E+01
+Degrees of Freedom:                                4
+Number of Observations:                            6  
+
+
+
+
+
+
+
+
+
+
+
+
+Data:   y             x
+      109             1
+      149             2
+      149             3
+      191             5
+      213             7
+      224            10

data/nist/Chwirut1.dat

@@ -0,0 +1,274 @@
+NIST/ITL StRD
+Dataset Name:  Chwirut1          (Chwirut1.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  43)
+               Certified Values  (lines 41 to  48)
+               Data              (lines 61 to 274)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               ultrasonic calibration.  The response variable is
+               ultrasonic response, and the predictor variable is
+               metal distance.
+
+Reference:     Chwirut, D., NIST (197?).  
+               Ultrasonic Reference Block Study. 
+
+
+
+
+
+
+
+Data:          1 Response Variable  (y = ultrasonic response)
+               1 Predictor Variable (x = metal distance)
+               214 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+
+               y = exp[-b1*x]/(b2+b3*x)  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   0.1         0.15          1.9027818370E-01  2.1938557035E-02
+  b2 =   0.01        0.008         6.1314004477E-03  3.4500025051E-04
+  b3 =   0.02        0.010         1.0530908399E-02  7.9281847748E-04
+
+Residual Sum of Squares:                    2.3844771393E+03
+Residual Standard Deviation:                3.3616721320E+00
+Degrees of Freedom:                               211
+Number of Observations:                           214
+
+
+
+
+
+
+
+
+
+
+
+Data:  y            x
+     92.9000E0     0.5000E0
+     78.7000E0     0.6250E0
+     64.2000E0     0.7500E0
+     64.9000E0     0.8750E0
+     57.1000E0     1.0000E0
+     43.3000E0     1.2500E0
+     31.1000E0     1.7500E0
+     23.6000E0     2.2500E0
+     31.0500E0     1.7500E0
+     23.7750E0     2.2500E0
+     17.7375E0     2.7500E0
+     13.8000E0     3.2500E0
+     11.5875E0     3.7500E0
+      9.4125E0     4.2500E0
+      7.7250E0     4.7500E0
+      7.3500E0     5.2500E0
+      8.0250E0     5.7500E0
+     90.6000E0     0.5000E0
+     76.9000E0     0.6250E0
+     71.6000E0     0.7500E0
+     63.6000E0     0.8750E0
+     54.0000E0     1.0000E0
+     39.2000E0     1.2500E0
+     29.3000E0     1.7500E0
+     21.4000E0     2.2500E0
+     29.1750E0     1.7500E0
+     22.1250E0     2.2500E0
+     17.5125E0     2.7500E0
+     14.2500E0     3.2500E0
+      9.4500E0     3.7500E0
+      9.1500E0     4.2500E0
+      7.9125E0     4.7500E0
+      8.4750E0     5.2500E0
+      6.1125E0     5.7500E0
+     80.0000E0     0.5000E0
+     79.0000E0     0.6250E0
+     63.8000E0     0.7500E0
+     57.2000E0     0.8750E0
+     53.2000E0     1.0000E0
+     42.5000E0     1.2500E0
+     26.8000E0     1.7500E0
+     20.4000E0     2.2500E0
+     26.8500E0     1.7500E0
+     21.0000E0     2.2500E0
+     16.4625E0     2.7500E0
+     12.5250E0     3.2500E0
+     10.5375E0     3.7500E0
+      8.5875E0     4.2500E0
+      7.1250E0     4.7500E0
+      6.1125E0     5.2500E0
+      5.9625E0     5.7500E0
+     74.1000E0     0.5000E0
+     67.3000E0     0.6250E0
+     60.8000E0     0.7500E0
+     55.5000E0     0.8750E0
+     50.3000E0     1.0000E0
+     41.0000E0     1.2500E0
+     29.4000E0     1.7500E0
+     20.4000E0     2.2500E0
+     29.3625E0     1.7500E0
+     21.1500E0     2.2500E0
+     16.7625E0     2.7500E0
+     13.2000E0     3.2500E0
+     10.8750E0     3.7500E0
+      8.1750E0     4.2500E0
+      7.3500E0     4.7500E0
+      5.9625E0     5.2500E0
+      5.6250E0     5.7500E0
+     81.5000E0      .5000E0
+     62.4000E0      .7500E0
+     32.5000E0     1.5000E0
+     12.4100E0     3.0000E0
+     13.1200E0     3.0000E0
+     15.5600E0     3.0000E0
+      5.6300E0     6.0000E0
+     78.0000E0      .5000E0
+     59.9000E0      .7500E0
+     33.2000E0     1.5000E0
+     13.8400E0     3.0000E0
+     12.7500E0     3.0000E0
+     14.6200E0     3.0000E0
+      3.9400E0     6.0000E0
+     76.8000E0      .5000E0
+     61.0000E0      .7500E0
+     32.9000E0     1.5000E0
+     13.8700E0     3.0000E0
+     11.8100E0     3.0000E0
+     13.3100E0     3.0000E0
+      5.4400E0     6.0000E0
+     78.0000E0      .5000E0
+     63.5000E0      .7500E0
+     33.8000E0     1.5000E0
+     12.5600E0     3.0000E0
+      5.6300E0     6.0000E0
+     12.7500E0     3.0000E0
+     13.1200E0     3.0000E0
+      5.4400E0     6.0000E0
+     76.8000E0      .5000E0
+     60.0000E0      .7500E0
+     47.8000E0     1.0000E0
+     32.0000E0     1.5000E0
+     22.2000E0     2.0000E0
+     22.5700E0     2.0000E0
+     18.8200E0     2.5000E0
+     13.9500E0     3.0000E0
+     11.2500E0     4.0000E0
+      9.0000E0     5.0000E0
+      6.6700E0     6.0000E0
+     75.8000E0      .5000E0
+     62.0000E0      .7500E0
+     48.8000E0     1.0000E0
+     35.2000E0     1.5000E0
+     20.0000E0     2.0000E0
+     20.3200E0     2.0000E0
+     19.3100E0     2.5000E0
+     12.7500E0     3.0000E0
+     10.4200E0     4.0000E0
+      7.3100E0     5.0000E0
+      7.4200E0     6.0000E0
+     70.5000E0      .5000E0
+     59.5000E0      .7500E0
+     48.5000E0     1.0000E0
+     35.8000E0     1.5000E0
+     21.0000E0     2.0000E0
+     21.6700E0     2.0000E0
+     21.0000E0     2.5000E0
+     15.6400E0     3.0000E0
+      8.1700E0     4.0000E0
+      8.5500E0     5.0000E0
+     10.1200E0     6.0000E0
+     78.0000E0      .5000E0
+     66.0000E0      .6250E0
+     62.0000E0      .7500E0
+     58.0000E0      .8750E0
+     47.7000E0     1.0000E0
+     37.8000E0     1.2500E0
+     20.2000E0     2.2500E0
+     21.0700E0     2.2500E0
+     13.8700E0     2.7500E0
+      9.6700E0     3.2500E0
+      7.7600E0     3.7500E0
+      5.4400E0     4.2500E0
+      4.8700E0     4.7500E0
+      4.0100E0     5.2500E0
+      3.7500E0     5.7500E0
+     24.1900E0     3.0000E0
+     25.7600E0     3.0000E0
+     18.0700E0     3.0000E0
+     11.8100E0     3.0000E0
+     12.0700E0     3.0000E0
+     16.1200E0     3.0000E0
+     70.8000E0      .5000E0
+     54.7000E0      .7500E0
+     48.0000E0     1.0000E0
+     39.8000E0     1.5000E0
+     29.8000E0     2.0000E0
+     23.7000E0     2.5000E0
+     29.6200E0     2.0000E0
+     23.8100E0     2.5000E0
+     17.7000E0     3.0000E0
+     11.5500E0     4.0000E0
+     12.0700E0     5.0000E0
+      8.7400E0     6.0000E0
+     80.7000E0      .5000E0
+     61.3000E0      .7500E0
+     47.5000E0     1.0000E0
+     29.0000E0     1.5000E0
+     24.0000E0     2.0000E0
+     17.7000E0     2.5000E0
+     24.5600E0     2.0000E0
+     18.6700E0     2.5000E0
+     16.2400E0     3.0000E0
+      8.7400E0     4.0000E0
+      7.8700E0     5.0000E0
+      8.5100E0     6.0000E0
+     66.7000E0      .5000E0
+     59.2000E0      .7500E0
+     40.8000E0     1.0000E0
+     30.7000E0     1.5000E0
+     25.7000E0     2.0000E0
+     16.3000E0     2.5000E0
+     25.9900E0     2.0000E0
+     16.9500E0     2.5000E0
+     13.3500E0     3.0000E0
+      8.6200E0     4.0000E0
+      7.2000E0     5.0000E0
+      6.6400E0     6.0000E0
+     13.6900E0     3.0000E0
+     81.0000E0      .5000E0
+     64.5000E0      .7500E0
+     35.5000E0     1.5000E0
+     13.3100E0     3.0000E0
+      4.8700E0     6.0000E0
+     12.9400E0     3.0000E0
+      5.0600E0     6.0000E0
+     15.1900E0     3.0000E0
+     14.6200E0     3.0000E0
+     15.6400E0     3.0000E0
+     25.5000E0     1.7500E0
+     25.9500E0     1.7500E0
+     81.7000E0      .5000E0
+     61.6000E0      .7500E0
+     29.8000E0     1.7500E0
+     29.8100E0     1.7500E0
+     17.1700E0     2.7500E0
+     10.3900E0     3.7500E0
+     28.4000E0     1.7500E0
+     28.6900E0     1.7500E0
+     81.3000E0      .5000E0
+     60.9000E0      .7500E0
+     16.6500E0     2.7500E0
+     10.0500E0     3.7500E0
+     28.9000E0     1.7500E0
+     28.9500E0     1.7500E0

data/nist/Chwirut2.dat

@@ -0,0 +1,114 @@
+NIST/ITL StRD
+Dataset Name:  Chwirut2          (Chwirut2.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  43)
+               Certified Values  (lines 41 to  48)
+               Data              (lines 61 to 114)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               ultrasonic calibration.  The response variable is
+               ultrasonic response, and the predictor variable is
+               metal distance.
+
+
+
+Reference:     Chwirut, D., NIST (197?).  
+               Ultrasonic Reference Block Study. 
+
+
+
+
+
+Data:          1 Response  (y = ultrasonic response)
+               1 Predictor (x = metal distance)
+               54 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+
+               y = exp(-b1*x)/(b2+b3*x)  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   0.1         0.15          1.6657666537E-01  3.8303286810E-02
+  b2 =   0.01        0.008         5.1653291286E-03  6.6621605126E-04
+  b3 =   0.02        0.010         1.2150007096E-02  1.5304234767E-03
+
+Residual Sum of Squares:                    5.1304802941E+02
+Residual Standard Deviation:                3.1717133040E+00
+Degrees of Freedom:                                51
+Number of Observations:                            54
+
+
+
+
+
+
+
+
+
+ 
+
+Data:  y             x
+      92.9000E0     0.500E0
+      57.1000E0     1.000E0
+      31.0500E0     1.750E0
+      11.5875E0     3.750E0
+       8.0250E0     5.750E0
+      63.6000E0     0.875E0
+      21.4000E0     2.250E0
+      14.2500E0     3.250E0
+       8.4750E0     5.250E0
+      63.8000E0     0.750E0
+      26.8000E0     1.750E0
+      16.4625E0     2.750E0
+       7.1250E0     4.750E0
+      67.3000E0     0.625E0
+      41.0000E0     1.250E0
+      21.1500E0     2.250E0
+       8.1750E0     4.250E0
+      81.5000E0      .500E0
+      13.1200E0     3.000E0
+      59.9000E0      .750E0
+      14.6200E0     3.000E0
+      32.9000E0     1.500E0
+       5.4400E0     6.000E0
+      12.5600E0     3.000E0
+       5.4400E0     6.000E0
+      32.0000E0     1.500E0
+      13.9500E0     3.000E0
+      75.8000E0      .500E0
+      20.0000E0     2.000E0
+      10.4200E0     4.000E0
+      59.5000E0      .750E0
+      21.6700E0     2.000E0
+       8.5500E0     5.000E0
+      62.0000E0      .750E0
+      20.2000E0     2.250E0
+       7.7600E0     3.750E0
+       3.7500E0     5.750E0
+      11.8100E0     3.000E0
+      54.7000E0      .750E0
+      23.7000E0     2.500E0
+      11.5500E0     4.000E0
+      61.3000E0      .750E0
+      17.7000E0     2.500E0
+       8.7400E0     4.000E0
+      59.2000E0      .750E0
+      16.3000E0     2.500E0
+       8.6200E0     4.000E0
+      81.0000E0      .500E0
+       4.8700E0     6.000E0
+      14.6200E0     3.000E0
+      81.7000E0      .500E0
+      17.1700E0     2.750E0
+      81.3000E0      .500E0
+      28.9000E0     1.750E0

data/nist/DanWood.dat

@@ -0,0 +1,66 @@
+NIST/ITL StRD
+Dataset Name:  DanWood           (DanWood.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 66)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data and model are described in Daniel and Wood
+               (1980), and originally published in E.S.Keeping, 
+               "Introduction to Statistical Inference," Van Nostrand
+               Company, Princeton, NJ, 1962, p. 354.  The response
+               variable is energy radieted from a carbon filament
+               lamp per cm**2 per second, and the predictor variable
+               is the absolute temperature of the filament in 1000
+               degrees Kelvin.
+
+Reference:     Daniel, C. and F. S. Wood (1980).
+               Fitting Equations to Data, Second Edition. 
+               New York, NY:  John Wiley and Sons, pp. 428-431.
+
+
+Data:          1 Response Variable  (y = energy)
+               1 Predictor Variable (x = temperature)
+               6 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               2 Parameters (b1 and b2)
+
+               y  = b1*x**b2  +  e
+
+
+ 
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1           0.7           7.6886226176E-01  1.8281973860E-02
+  b2 =   5           4             3.8604055871E+00  5.1726610913E-02
+ 
+Residual Sum of Squares:                    4.3173084083E-03
+Residual Standard Deviation:                3.2853114039E-02
+Degrees of Freedom:                                4
+Number of Observations:                            6 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Data:  y              x
+      2.138E0        1.309E0
+      3.421E0        1.471E0
+      3.597E0        1.490E0
+      4.340E0        1.565E0
+      4.882E0        1.611E0
+      5.660E0        1.680E0

data/nist/ENSO.dat

@@ -0,0 +1,228 @@
+NIST/ITL StRD
+Dataset Name:  ENSO              (ENSO.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  49)
+               Certified Values  (lines 41 to  54)
+               Data              (lines 61 to 228)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   The data are monthly averaged atmospheric pressure 
+               differences between Easter Island and Darwin, 
+               Australia.  This difference drives the trade winds in 
+               the southern hemisphere.  Fourier analysis of the data
+               reveals 3 significant cycles.  The annual cycle is the
+               strongest, but cycles with periods of approximately 44
+               and 26 months are also present.  These cycles
+               correspond to the El Nino and the Southern Oscillation.
+               Arguments to the SIN and COS functions are in radians.
+
+Reference:     Kahaner, D., C. Moler, and S. Nash, (1989). 
+               Numerical Methods and Software.  
+               Englewood Cliffs, NJ: Prentice Hall, pp. 441-445.
+
+Data:          1 Response  (y = atmospheric pressure)
+               1 Predictor (x = time)
+               168 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               9 Parameters (b1 to b9)
+
+               y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 
+                      + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
+                      + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 )  + e
+ 
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   11.0        10.0          1.0510749193E+01  1.7488832467E-01
+  b2 =    3.0         3.0          3.0762128085E+00  2.4310052139E-01
+  b3 =    0.5         0.5          5.3280138227E-01  2.4354686618E-01
+  b4 =   40.0        44.0          4.4311088700E+01  9.4408025976E-01
+  b5 =   -0.7        -1.5         -1.6231428586E+00  2.8078369611E-01
+  b6 =   -1.3         0.5          5.2554493756E-01  4.8073701119E-01
+  b7 =   25.0        26.0          2.6887614440E+01  4.1612939130E-01
+  b8 =   -0.3        -0.1          2.1232288488E-01  5.1460022911E-01
+  b9 =    1.4         1.5          1.4966870418E+00  2.5434468893E-01
+
+Residual Sum of Squares:                    7.8853978668E+02
+Residual Standard Deviation:                2.2269642403E+00
+Degrees of Freedom:                               159
+Number of Observations:                           168
+
+
+
+
+
+Data:   y          x
+    12.90000    1.000000
+    11.30000    2.000000
+    10.60000    3.000000
+    11.20000    4.000000
+    10.90000    5.000000
+    7.500000    6.000000
+    7.700000    7.000000
+    11.70000    8.000000
+    12.90000    9.000000
+    14.30000   10.000000
+    10.90000    11.00000
+    13.70000    12.00000
+    17.10000    13.00000
+    14.00000    14.00000
+    15.30000    15.00000
+    8.500000    16.00000
+    5.700000    17.00000
+    5.500000    18.00000
+    7.600000    19.00000
+    8.600000    20.00000
+    7.300000    21.00000
+    7.600000    22.00000
+    12.70000    23.00000
+    11.00000    24.00000
+    12.70000    25.00000
+    12.90000    26.00000
+    13.00000    27.00000
+    10.90000    28.00000
+   10.400000    29.00000
+   10.200000    30.00000
+    8.000000    31.00000
+    10.90000    32.00000
+    13.60000    33.00000
+   10.500000    34.00000
+    9.200000    35.00000
+    12.40000    36.00000
+    12.70000    37.00000
+    13.30000    38.00000
+   10.100000    39.00000
+    7.800000    40.00000
+    4.800000    41.00000
+    3.000000    42.00000
+    2.500000    43.00000
+    6.300000    44.00000
+    9.700000    45.00000
+    11.60000    46.00000
+    8.600000    47.00000
+    12.40000    48.00000
+   10.500000    49.00000
+    13.30000    50.00000
+   10.400000    51.00000
+    8.100000    52.00000
+    3.700000    53.00000
+    10.70000    54.00000
+    5.100000    55.00000
+   10.400000    56.00000
+    10.90000    57.00000
+    11.70000    58.00000
+    11.40000    59.00000
+    13.70000    60.00000
+    14.10000    61.00000
+    14.00000    62.00000
+    12.50000    63.00000
+    6.300000    64.00000
+    9.600000    65.00000
+    11.70000    66.00000
+    5.000000    67.00000
+    10.80000    68.00000
+    12.70000    69.00000
+    10.80000    70.00000
+    11.80000    71.00000
+    12.60000    72.00000
+    15.70000    73.00000
+    12.60000    74.00000
+    14.80000    75.00000
+    7.800000    76.00000
+    7.100000    77.00000
+    11.20000    78.00000
+    8.100000    79.00000
+    6.400000    80.00000
+    5.200000    81.00000
+    12.00000    82.00000
+   10.200000    83.00000
+    12.70000    84.00000
+   10.200000    85.00000
+    14.70000    86.00000
+    12.20000    87.00000
+    7.100000    88.00000
+    5.700000    89.00000
+    6.700000    90.00000
+    3.900000    91.00000
+    8.500000    92.00000
+    8.300000    93.00000
+    10.80000    94.00000
+    16.70000    95.00000
+    12.60000    96.00000
+    12.50000    97.00000
+    12.50000    98.00000
+    9.800000    99.00000
+    7.200000   100.00000
+    4.100000   101.00000
+    10.60000   102.00000
+   10.100000   103.00000
+   10.100000   104.00000
+    11.90000   105.00000
+    13.60000    106.0000
+    16.30000    107.0000
+    17.60000    108.0000
+    15.50000    109.0000
+    16.00000    110.0000
+    15.20000    111.0000
+    11.20000    112.0000
+    14.30000    113.0000
+    14.50000    114.0000
+    8.500000    115.0000
+    12.00000    116.0000
+    12.70000    117.0000
+    11.30000    118.0000
+    14.50000    119.0000
+    15.10000    120.0000
+   10.400000    121.0000
+    11.50000    122.0000
+    13.40000    123.0000
+    7.500000    124.0000
+   0.6000000    125.0000
+   0.3000000    126.0000
+    5.500000    127.0000
+    5.000000    128.0000
+    4.600000    129.0000
+    8.200000    130.0000
+    9.900000    131.0000
+    9.200000    132.0000
+    12.50000    133.0000
+    10.90000    134.0000
+    9.900000    135.0000
+    8.900000    136.0000
+    7.600000    137.0000
+    9.500000    138.0000
+    8.400000    139.0000
+    10.70000    140.0000
+    13.60000    141.0000
+    13.70000    142.0000
+    13.70000    143.0000
+    16.50000    144.0000
+    16.80000    145.0000
+    17.10000    146.0000
+    15.40000    147.0000
+    9.500000    148.0000
+    6.100000    149.0000
+   10.100000    150.0000
+    9.300000    151.0000
+    5.300000    152.0000
+    11.20000    153.0000
+    16.60000    154.0000
+    15.60000    155.0000
+    12.00000    156.0000
+    11.50000    157.0000
+    8.600000    158.0000
+    13.80000    159.0000
+    8.700000    160.0000
+    8.600000    161.0000
+    8.600000    162.0000
+    8.700000    163.0000
+    12.80000    164.0000
+    13.20000    165.0000
+    14.00000    166.0000
+    13.40000    167.0000
+    14.80000    168.0000

data/nist/Eckerle4.dat

@@ -0,0 +1,95 @@
+NIST/ITL StRD
+Dataset Name:  Eckerle4          (Eckerle4.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 43)
+               Certified Values  (lines 41 to 48)
+               Data              (lines 61 to 95)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               circular interference transmittance.  The response
+               variable is transmittance, and the predictor variable
+               is wavelength.
+
+
+Reference:     Eckerle, K., NIST (197?).  
+               Circular Interference Transmittance Study.
+
+
+
+
+
+
+Data:          1 Response Variable  (y = transmittance)
+               1 Predictor Variable (x = wavelength)
+               35 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+
+               y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
+
+
+
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =     1           1.5         1.5543827178E+00  1.5408051163E-02
+  b2 =    10           5           4.0888321754E+00  4.6803020753E-02
+  b3 =   500         450           4.5154121844E+02  4.6800518816E-02
+
+Residual Sum of Squares:                    1.4635887487E-03
+Residual Standard Deviation:                6.7629245447E-03
+Degrees of Freedom:                                32
+Number of Observations:                            35
+
+
+
+
+
+
+
+
+
+
+
+Data:  y                x
+      0.0001575E0    400.000000E0
+      0.0001699E0    405.000000E0
+      0.0002350E0    410.000000E0
+      0.0003102E0    415.000000E0
+      0.0004917E0    420.000000E0
+      0.0008710E0    425.000000E0
+      0.0017418E0    430.000000E0
+      0.0046400E0    435.000000E0
+      0.0065895E0    436.500000E0
+      0.0097302E0    438.000000E0
+      0.0149002E0    439.500000E0
+      0.0237310E0    441.000000E0
+      0.0401683E0    442.500000E0
+      0.0712559E0    444.000000E0
+      0.1264458E0    445.500000E0
+      0.2073413E0    447.000000E0
+      0.2902366E0    448.500000E0
+      0.3445623E0    450.000000E0
+      0.3698049E0    451.500000E0
+      0.3668534E0    453.000000E0
+      0.3106727E0    454.500000E0
+      0.2078154E0    456.000000E0
+      0.1164354E0    457.500000E0
+      0.0616764E0    459.000000E0
+      0.0337200E0    460.500000E0
+      0.0194023E0    462.000000E0
+      0.0117831E0    463.500000E0
+      0.0074357E0    465.000000E0
+      0.0022732E0    470.000000E0
+      0.0008800E0    475.000000E0
+      0.0004579E0    480.000000E0
+      0.0002345E0    485.000000E0
+      0.0001586E0    490.000000E0
+      0.0001143E0    495.000000E0
+      0.0000710E0    500.000000E0

data/nist/Gauss1.dat

@@ -0,0 +1,310 @@
+NIST/ITL StRD
+Dataset Name:  Gauss1            (Gauss1.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  48)
+               Certified Values  (lines 41 to  53)
+               Data              (lines 61 to 310)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   The data are two well-separated Gaussians on a 
+               decaying exponential baseline plus normally 
+               distributed zero-mean noise with variance = 6.25.
+
+Reference:     Rust, B., NIST (1996).
+
+
+
+
+
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               250 Observations
+               Lower Level of Difficulty
+               Generated Data
+ 
+Model:         Exponential Class
+               8 Parameters (b1 to b8) 
+ 
+               y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+                                   + b6*exp( -(x-b7)**2 / b8**2 ) + e
+ 
+ 
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =    97.0        94.0         9.8778210871E+01  5.7527312730E-01
+  b2 =     0.009       0.0105      1.0497276517E-02  1.1406289017E-04
+  b3 =   100.0        99.0         1.0048990633E+02  5.8831775752E-01
+  b4 =    65.0        63.0         6.7481111276E+01  1.0460593412E-01
+  b5 =    20.0        25.0         2.3129773360E+01  1.7439951146E-01
+  b6 =    70.0        71.0         7.1994503004E+01  6.2622793913E-01
+  b7 =   178.0       180.0         1.7899805021E+02  1.2436988217E-01
+  b8 =    16.5        20.0         1.8389389025E+01  2.0134312832E-01
+
+Residual Sum of Squares:                    1.3158222432E+03
+Residual Standard Deviation:                2.3317980180E+00
+Degrees of Freedom:                               242
+Number of Observations:                           250
+
+
+
+
+ 
+
+Data:   y          x
+    97.62227    1.000000
+    97.80724    2.000000
+    96.62247    3.000000
+    92.59022    4.000000
+    91.23869    5.000000
+    95.32704    6.000000
+    90.35040    7.000000
+    89.46235    8.000000
+    91.72520    9.000000
+    89.86916   10.000000
+    86.88076    11.00000
+    85.94360    12.00000
+    87.60686    13.00000
+    86.25839    14.00000
+    80.74976    15.00000
+    83.03551    16.00000
+    88.25837    17.00000
+    82.01316    18.00000
+    82.74098    19.00000
+    83.30034    20.00000
+    81.27850    21.00000
+    81.85506    22.00000
+    80.75195    23.00000
+    80.09573    24.00000
+    81.07633    25.00000
+    78.81542    26.00000
+    78.38596    27.00000
+    79.93386    28.00000
+    79.48474    29.00000
+    79.95942    30.00000
+    76.10691    31.00000
+    78.39830    32.00000
+    81.43060    33.00000
+    82.48867    34.00000
+    81.65462    35.00000
+    80.84323    36.00000
+    88.68663    37.00000
+    84.74438    38.00000
+    86.83934    39.00000
+    85.97739    40.00000
+    91.28509    41.00000
+    97.22411    42.00000
+    93.51733    43.00000
+    94.10159    44.00000
+   101.91760    45.00000
+    98.43134    46.00000
+    110.4214    47.00000
+    107.6628    48.00000
+    111.7288    49.00000
+    116.5115    50.00000
+    120.7609    51.00000
+    123.9553    52.00000
+    124.2437    53.00000
+    130.7996    54.00000
+    133.2960    55.00000
+    130.7788    56.00000
+    132.0565    57.00000
+    138.6584    58.00000
+    142.9252    59.00000
+    142.7215    60.00000
+    144.1249    61.00000
+    147.4377    62.00000
+    148.2647    63.00000
+    152.0519    64.00000
+    147.3863    65.00000
+    149.2074    66.00000
+    148.9537    67.00000
+    144.5876    68.00000
+    148.1226    69.00000
+    148.0144    70.00000
+    143.8893    71.00000
+    140.9088    72.00000
+    143.4434    73.00000
+    139.3938    74.00000
+    135.9878    75.00000
+    136.3927    76.00000
+    126.7262    77.00000
+    124.4487    78.00000
+    122.8647    79.00000
+    113.8557    80.00000
+    113.7037    81.00000
+    106.8407    82.00000
+    107.0034    83.00000
+   102.46290    84.00000
+    96.09296    85.00000
+    94.57555    86.00000
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data/nist/Gauss2.dat

@@ -0,0 +1,310 @@
+NIST/ITL StRD
+Dataset Name:  Gauss2            (Gauss2.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  48)
+               Certified Values  (lines 41 to  53)
+               Data              (lines 61 to 310)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   The data are two slightly-blended Gaussians on a 
+               decaying exponential baseline plus normally 
+               distributed zero-mean noise with variance = 6.25. 
+
+Reference:     Rust, B., NIST (1996). 
+
+
+
+
+
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               250 Observations
+               Lower Level of Difficulty
+               Generated Data
+
+Model:         Exponential Class
+               8 Parameters (b1 to b8)
+
+               y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) 
+                                   + b6*exp( -(x-b7)**2 / b8**2 ) + e
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =    96.0        98.0         9.9018328406E+01  5.3748766879E-01
+  b2 =     0.009       0.0105      1.0994945399E-02  1.3335306766E-04
+  b3 =   103.0       103.0         1.0188022528E+02  5.9217315772E-01
+  b4 =   106.0       105.0         1.0703095519E+02  1.5006798316E-01
+  b5 =    18.0        20.0         2.3578584029E+01  2.2695595067E-01
+  b6 =    72.0        73.0         7.2045589471E+01  6.1721965884E-01
+  b7 =   151.0       150.0         1.5327010194E+02  1.9466674341E-01
+  b8 =    18.0        20.0         1.9525972636E+01  2.6416549393E-01
+
+Residual Sum of Squares:                    1.2475282092E+03
+Residual Standard Deviation:                2.2704790782E+00
+Degrees of Freedom:                               242
+Number of Observations:                           250
+
+
+
+
+
+ 
+Data:   y          x
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+    97.76344    2.000000
+    96.56705    3.000000
+    92.52037    4.000000
+    91.15097    5.000000
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data/nist/Gauss3.dat

@@ -0,0 +1,310 @@
+NIST/ITL StRD
+Dataset Name:  Gauss3            (Gauss3.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  48)
+               Certified Values  (lines 41 to  53)
+               Data              (lines 61 to 310)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   The data are two strongly-blended Gaussians on a 
+               decaying exponential baseline plus normally 
+               distributed zero-mean noise with variance = 6.25.
+
+Reference:     Rust, B., NIST (1996).
+
+
+
+
+
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               250 Observations
+               Average Level of Difficulty
+               Generated Data
+
+Model:         Exponential Class
+               8 Parameters (b1 to b8)
+
+               y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+                                   + b6*exp( -(x-b7)**2 / b8**2 ) + e
+ 
+ 
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =    94.9        96.0         9.8940368970E+01  5.3005192833E-01
+  b2 =     0.009       0.0096      1.0945879335E-02  1.2554058911E-04
+  b3 =    90.1        80.0         1.0069553078E+02  8.1256587317E-01
+  b4 =   113.0       110.0         1.1163619459E+02  3.5317859757E-01
+  b5 =    20.0        25.0         2.3300500029E+01  3.6584783023E-01
+  b6 =    73.8        74.0         7.3705031418E+01  1.2091239082E+00
+  b7 =   140.0       139.0         1.4776164251E+02  4.0488183351E-01
+  b8 =    20.0        25.0         1.9668221230E+01  3.7806634336E-01
+
+Residual Sum of Squares:                    1.2444846360E+03  
+Residual Standard Deviation:                2.2677077625E+00
+Degrees of Freedom:                               242
+Number of Observations:                           250
+
+
+
+
+
+
+Data:   y          x
+    97.58776    1.000000
+    97.76344    2.000000
+    96.56705    3.000000
+    92.52037    4.000000
+    91.15097    5.000000
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+    107.3192    136.0000
+    106.9000    137.0000
+    109.6526    138.0000
+    107.1602    139.0000
+    108.2509    140.0000
+   104.96310    141.0000
+    109.3601    142.0000
+    107.6696    143.0000
+    99.77286    144.0000
+   104.96440    145.0000
+    106.1376    146.0000
+    106.5816    147.0000
+   100.12860    148.0000
+   101.66910    149.0000
+    96.44254    150.0000
+    97.34169    151.0000
+    96.97412    152.0000
+    90.73460    153.0000
+    93.37949    154.0000
+    82.12331    155.0000
+    83.01657    156.0000
+    78.87360    157.0000
+    74.86971    158.0000
+    72.79341    159.0000
+    65.14744    160.0000
+    67.02127    161.0000
+    60.16136    162.0000
+    57.13996    163.0000
+    54.05769    164.0000
+    50.42265    165.0000
+    47.82430    166.0000
+    42.85748    167.0000
+    42.45495    168.0000
+    38.30808    169.0000
+    36.95794    170.0000
+    33.94543    171.0000
+    34.19017    172.0000
+    31.66097    173.0000
+    23.56172    174.0000
+    29.61143    175.0000
+    23.88765    176.0000
+    22.49812    177.0000
+    24.86901    178.0000
+    17.29481    179.0000
+    18.09291    180.0000
+    15.34813    181.0000
+    14.77997    182.0000
+    13.87832    183.0000
+    12.88891    184.0000
+    16.20763    185.0000
+    16.29024    186.0000
+    15.29712    187.0000
+    14.97839    188.0000
+    12.11330    189.0000
+    14.24168    190.0000
+    12.53824    191.0000
+    15.19818    192.0000
+    11.70478    193.0000
+    15.83745    194.0000
+   10.035850    195.0000
+    9.307574    196.0000
+    12.86800    197.0000
+    8.571671    198.0000
+    11.60415    199.0000
+    12.42772    200.0000
+    11.23627    201.0000
+    11.13198    202.0000
+    7.761117    203.0000
+    6.758250    204.0000
+    14.23375    205.0000
+    10.63876    206.0000
+    8.893581    207.0000
+    11.55398    208.0000
+    11.57221    209.0000
+    11.58347    210.0000
+    9.724857    211.0000
+    11.43854    212.0000
+    11.22636    213.0000
+   10.170150    214.0000
+    12.50765    215.0000
+    6.200494    216.0000
+    9.018902    217.0000
+    10.80557    218.0000
+    13.09591    219.0000
+    3.914033    220.0000
+    9.567723    221.0000
+    8.038338    222.0000
+   10.230960    223.0000
+    9.367358    224.0000
+    7.695937    225.0000
+    6.118552    226.0000
+    8.793192    227.0000
+    7.796682    228.0000
+    12.45064    229.0000
+    10.61601    230.0000
+    6.001000    231.0000
+    6.765096    232.0000
+    8.764652    233.0000
+    4.586417    234.0000
+    8.390782    235.0000
+    7.209201    236.0000
+   10.012090    237.0000
+    7.327461    238.0000
+    6.525136    239.0000
+    2.840065    240.0000
+   10.323710    241.0000
+    4.790035    242.0000
+    8.376431    243.0000
+    6.263980    244.0000
+    2.705892    245.0000
+    8.362109    246.0000
+    8.983507    247.0000
+    3.362469    248.0000
+    1.182678    249.0000
+    4.875312    250.0000

data/nist/Hahn1.dat

@@ -0,0 +1,296 @@
+NIST/ITL StRD
+Dataset Name:  Hahn1             (Hahn1.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  47)
+               Certified Values  (lines 41 to  52)
+               Data              (lines 61 to 296)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               the thermal expansion of copper.  The response 
+               variable is the coefficient of thermal expansion, and
+               the predictor variable is temperature in degrees 
+               kelvin.
+
+
+Reference:     Hahn, T., NIST (197?). 
+               Copper Thermal Expansion Study.
+
+
+
+
+
+Data:          1 Response  (y = coefficient of thermal expansion)
+               1 Predictor (x = temperature, degrees kelvin)
+               236 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Rational Class (cubic/cubic)
+               7 Parameters (b1 to b7)
+
+               y = (b1+b2*x+b3*x**2+b4*x**3) /
+                   (1+b5*x+b6*x**2+b7*x**3)  +  e
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   10           1            1.0776351733E+00  1.7070154742E-01
+  b2 =   -1          -0.1         -1.2269296921E-01  1.2000289189E-02
+  b3 =    0.05        0.005        4.0863750610E-03  2.2508314937E-04
+  b4 =   -0.00001    -0.000001    -1.4262662514E-06  2.7578037666E-07
+  b5 =   -0.05       -0.005       -5.7609940901E-03  2.4712888219E-04
+  b6 =    0.001       0.0001       2.4053735503E-04  1.0449373768E-05
+  b7 =   -0.000001   -0.0000001   -1.2314450199E-07  1.3027335327E-08
+
+Residual Sum of Squares:                    1.5324382854E+00 
+Residual Standard Deviation:                8.1803852243E-02
+Degrees of Freedom:                               229
+Number of Observations:                           236
+
+
+
+
+
+
+  
+Data:   y              x
+        .591E0         24.41E0  
+       1.547E0         34.82E0  
+       2.902E0         44.09E0  
+       2.894E0         45.07E0  
+       4.703E0         54.98E0  
+       6.307E0         65.51E0  
+       7.03E0          70.53E0  
+       7.898E0         75.70E0  
+       9.470E0         89.57E0  
+       9.484E0         91.14E0  
+      10.072E0         96.40E0  
+      10.163E0         97.19E0  
+      11.615E0        114.26E0  
+      12.005E0        120.25E0  
+      12.478E0        127.08E0  
+      12.982E0        133.55E0  
+      12.970E0        133.61E0  
+      13.926E0        158.67E0  
+      14.452E0        172.74E0  
+      14.404E0        171.31E0  
+      15.190E0        202.14E0  
+      15.550E0        220.55E0  
+      15.528E0        221.05E0  
+      15.499E0        221.39E0  
+      16.131E0        250.99E0  
+      16.438E0        268.99E0  
+      16.387E0        271.80E0  
+      16.549E0        271.97E0  
+      16.872E0        321.31E0  
+      16.830E0        321.69E0  
+      16.926E0        330.14E0  
+      16.907E0        333.03E0  
+      16.966E0        333.47E0  
+      17.060E0        340.77E0  
+      17.122E0        345.65E0  
+      17.311E0        373.11E0  
+      17.355E0        373.79E0  
+      17.668E0        411.82E0  
+      17.767E0        419.51E0  
+      17.803E0        421.59E0  
+      17.765E0        422.02E0  
+      17.768E0        422.47E0  
+      17.736E0        422.61E0  
+      17.858E0        441.75E0  
+      17.877E0        447.41E0  
+      17.912E0        448.7E0   
+      18.046E0        472.89E0  
+      18.085E0        476.69E0  
+      18.291E0        522.47E0  
+      18.357E0        522.62E0  
+      18.426E0        524.43E0  
+      18.584E0        546.75E0  
+      18.610E0        549.53E0  
+      18.870E0        575.29E0  
+      18.795E0        576.00E0  
+      19.111E0        625.55E0  
+        .367E0         20.15E0  
+        .796E0         28.78E0  
+       0.892E0         29.57E0  
+       1.903E0         37.41E0  
+       2.150E0         39.12E0  
+       3.697E0         50.24E0  
+       5.870E0         61.38E0  
+       6.421E0         66.25E0  
+       7.422E0         73.42E0  
+       9.944E0         95.52E0  
+      11.023E0        107.32E0  
+      11.87E0         122.04E0  
+      12.786E0        134.03E0  
+      14.067E0        163.19E0  
+      13.974E0        163.48E0  
+      14.462E0        175.70E0  
+      14.464E0        179.86E0  
+      15.381E0        211.27E0  
+      15.483E0        217.78E0  
+      15.59E0         219.14E0  
+      16.075E0        262.52E0  
+      16.347E0        268.01E0  
+      16.181E0        268.62E0  
+      16.915E0        336.25E0  
+      17.003E0        337.23E0  
+      16.978E0        339.33E0  
+      17.756E0        427.38E0  
+      17.808E0        428.58E0  
+      17.868E0        432.68E0  
+      18.481E0        528.99E0  
+      18.486E0        531.08E0  
+      19.090E0        628.34E0  
+      16.062E0        253.24E0  
+      16.337E0        273.13E0  
+      16.345E0        273.66E0  
+      16.388E0        282.10E0  
+      17.159E0        346.62E0  
+      17.116E0        347.19E0  
+      17.164E0        348.78E0  
+      17.123E0        351.18E0  
+      17.979E0        450.10E0  
+      17.974E0        450.35E0  
+      18.007E0        451.92E0  
+      17.993E0        455.56E0  
+      18.523E0        552.22E0  
+      18.669E0        553.56E0  
+      18.617E0        555.74E0  
+      19.371E0        652.59E0  
+      19.330E0        656.20E0  
+       0.080E0         14.13E0  
+       0.248E0         20.41E0  
+       1.089E0         31.30E0  
+       1.418E0         33.84E0  
+       2.278E0         39.70E0  
+       3.624E0         48.83E0  
+       4.574E0         54.50E0  
+       5.556E0         60.41E0  
+       7.267E0         72.77E0  
+       7.695E0         75.25E0  
+       9.136E0         86.84E0  
+       9.959E0         94.88E0  
+       9.957E0         96.40E0  
+      11.600E0        117.37E0  
+      13.138E0        139.08E0  
+      13.564E0        147.73E0  
+      13.871E0        158.63E0  
+      13.994E0        161.84E0  
+      14.947E0        192.11E0  
+      15.473E0        206.76E0  
+      15.379E0        209.07E0  
+      15.455E0        213.32E0  
+      15.908E0        226.44E0  
+      16.114E0        237.12E0  
+      17.071E0        330.90E0  
+      17.135E0        358.72E0  
+      17.282E0        370.77E0  
+      17.368E0        372.72E0  
+      17.483E0        396.24E0  
+      17.764E0        416.59E0  
+      18.185E0        484.02E0  
+      18.271E0        495.47E0  
+      18.236E0        514.78E0  
+      18.237E0        515.65E0  
+      18.523E0        519.47E0  
+      18.627E0        544.47E0  
+      18.665E0        560.11E0  
+      19.086E0        620.77E0  
+       0.214E0         18.97E0  
+       0.943E0         28.93E0  
+       1.429E0         33.91E0  
+       2.241E0         40.03E0  
+       2.951E0         44.66E0  
+       3.782E0         49.87E0  
+       4.757E0         55.16E0  
+       5.602E0         60.90E0  
+       7.169E0         72.08E0  
+       8.920E0         85.15E0  
+      10.055E0         97.06E0  
+      12.035E0        119.63E0  
+      12.861E0        133.27E0  
+      13.436E0        143.84E0  
+      14.167E0        161.91E0  
+      14.755E0        180.67E0  
+      15.168E0        198.44E0  
+      15.651E0        226.86E0  
+      15.746E0        229.65E0  
+      16.216E0        258.27E0  
+      16.445E0        273.77E0  
+      16.965E0        339.15E0  
+      17.121E0        350.13E0  
+      17.206E0        362.75E0  
+      17.250E0        371.03E0  
+      17.339E0        393.32E0  
+      17.793E0        448.53E0  
+      18.123E0        473.78E0  
+      18.49E0         511.12E0  
+      18.566E0        524.70E0  
+      18.645E0        548.75E0  
+      18.706E0        551.64E0  
+      18.924E0        574.02E0  
+      19.1E0          623.86E0  
+       0.375E0         21.46E0  
+       0.471E0         24.33E0  
+       1.504E0         33.43E0  
+       2.204E0         39.22E0  
+       2.813E0         44.18E0  
+       4.765E0         55.02E0  
+       9.835E0         94.33E0  
+      10.040E0         96.44E0  
+      11.946E0        118.82E0  
+      12.596E0        128.48E0  
+      13.303E0        141.94E0  
+      13.922E0        156.92E0  
+      14.440E0        171.65E0  
+      14.951E0        190.00E0  
+      15.627E0        223.26E0  
+      15.639E0        223.88E0  
+      15.814E0        231.50E0  
+      16.315E0        265.05E0  
+      16.334E0        269.44E0  
+      16.430E0        271.78E0  
+      16.423E0        273.46E0  
+      17.024E0        334.61E0  
+      17.009E0        339.79E0  
+      17.165E0        349.52E0  
+      17.134E0        358.18E0  
+      17.349E0        377.98E0  
+      17.576E0        394.77E0  
+      17.848E0        429.66E0  
+      18.090E0        468.22E0  
+      18.276E0        487.27E0  
+      18.404E0        519.54E0  
+      18.519E0        523.03E0  
+      19.133E0        612.99E0  
+      19.074E0        638.59E0  
+      19.239E0        641.36E0  
+      19.280E0        622.05E0  
+      19.101E0        631.50E0  
+      19.398E0        663.97E0  
+      19.252E0        646.9E0   
+      19.89E0         748.29E0  
+      20.007E0        749.21E0  
+      19.929E0        750.14E0  
+      19.268E0        647.04E0  
+      19.324E0        646.89E0  
+      20.049E0        746.9E0   
+      20.107E0        748.43E0  
+      20.062E0        747.35E0  
+      20.065E0        749.27E0  
+      19.286E0        647.61E0  
+      19.972E0        747.78E0  
+      20.088E0        750.51E0  
+      20.743E0        851.37E0  
+      20.83E0         845.97E0  
+      20.935E0        847.54E0  
+      21.035E0        849.93E0  
+      20.93E0         851.61E0  
+      21.074E0        849.75E0  
+      21.085E0        850.98E0  
+      20.935E0        848.23E0  

data/nist/Kirby2.dat

@@ -0,0 +1,211 @@
+NIST/ITL StRD
+Dataset Name:  Kirby2            (Kirby2.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to  45)
+               Certified Values  (lines 41 to  50)
+               Data              (lines 61 to 211)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               scanning electron microscope line with standards.
+
+
+Reference:     Kirby, R., NIST (197?).  
+               Scanning electron microscope line width standards.
+
+
+
+
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               151 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Rational Class (quadratic/quadratic)
+               5 Parameters (b1 to b5)
+
+               y = (b1 + b2*x + b3*x**2) /
+                   (1 + b4*x + b5*x**2)  +  e
+
+ 
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =    2           1.5          1.6745063063E+00  8.7989634338E-02
+  b2 =   -0.1        -0.15        -1.3927397867E-01  4.1182041386E-03
+  b3 =    0.003       0.0025       2.5961181191E-03  4.1856520458E-05
+  b4 =   -0.001      -0.0015      -1.7241811870E-03  5.8931897355E-05
+  b5 =    0.00001     0.00002      2.1664802578E-05  2.0129761919E-07
+
+Residual Sum of Squares:                    3.9050739624E+00
+Residual Standard Deviation:                1.6354535131E-01
+Degrees of Freedom:                               146
+Number of Observations:                           151
+
+
+
+
+
+
+
+
+
+Data:   y             x
+       0.0082E0      9.65E0
+       0.0112E0     10.74E0
+       0.0149E0     11.81E0
+       0.0198E0     12.88E0
+       0.0248E0     14.06E0
+       0.0324E0     15.28E0
+       0.0420E0     16.63E0
+       0.0549E0     18.19E0
+       0.0719E0     19.88E0
+       0.0963E0     21.84E0
+       0.1291E0     24.00E0
+       0.1710E0     26.25E0
+       0.2314E0     28.86E0
+       0.3227E0     31.85E0
+       0.4809E0     35.79E0
+       0.7084E0     40.18E0
+       1.0220E0     44.74E0
+       1.4580E0     49.53E0
+       1.9520E0     53.94E0
+       2.5410E0     58.29E0
+       3.2230E0     62.63E0
+       3.9990E0     67.03E0
+       4.8520E0     71.25E0
+       5.7320E0     75.22E0
+       6.7270E0     79.33E0
+       7.8350E0     83.56E0
+       9.0250E0     87.75E0
+      10.2670E0     91.93E0
+      11.5780E0     96.10E0
+      12.9440E0    100.28E0
+      14.3770E0    104.46E0
+      15.8560E0    108.66E0
+      17.3310E0    112.71E0
+      18.8850E0    116.88E0
+      20.5750E0    121.33E0
+      22.3200E0    125.79E0
+      22.3030E0    125.79E0
+      23.4600E0    128.74E0
+      24.0600E0    130.27E0
+      25.2720E0    133.33E0
+      25.8530E0    134.79E0
+      27.1100E0    137.93E0
+      27.6580E0    139.33E0
+      28.9240E0    142.46E0
+      29.5110E0    143.90E0
+      30.7100E0    146.91E0
+      31.3500E0    148.51E0
+      32.5200E0    151.41E0
+      33.2300E0    153.17E0
+      34.3300E0    155.97E0
+      35.0600E0    157.76E0
+      36.1700E0    160.56E0
+      36.8400E0    162.30E0
+      38.0100E0    165.21E0
+      38.6700E0    166.90E0
+      39.8700E0    169.92E0
+      40.0300E0    170.32E0
+      40.5000E0    171.54E0
+      41.3700E0    173.79E0
+      41.6700E0    174.57E0
+      42.3100E0    176.25E0
+      42.7300E0    177.34E0
+      43.4600E0    179.19E0
+      44.1400E0    181.02E0
+      44.5500E0    182.08E0
+      45.2200E0    183.88E0
+      45.9200E0    185.75E0
+      46.3000E0    186.80E0
+      47.0000E0    188.63E0
+      47.6800E0    190.45E0
+      48.0600E0    191.48E0
+      48.7400E0    193.35E0
+      49.4100E0    195.22E0
+      49.7600E0    196.23E0
+      50.4300E0    198.05E0
+      51.1100E0    199.97E0
+      51.5000E0    201.06E0
+      52.1200E0    202.83E0
+      52.7600E0    204.69E0
+      53.1800E0    205.86E0
+      53.7800E0    207.58E0
+      54.4600E0    209.50E0
+      54.8300E0    210.65E0
+      55.4000E0    212.33E0
+      56.4300E0    215.43E0
+      57.0300E0    217.16E0
+      58.0000E0    220.21E0
+      58.6100E0    221.98E0
+      59.5800E0    225.06E0
+      60.1100E0    226.79E0
+      61.1000E0    229.92E0
+      61.6500E0    231.69E0
+      62.5900E0    234.77E0
+      63.1200E0    236.60E0
+      64.0300E0    239.63E0
+      64.6200E0    241.50E0
+      65.4900E0    244.48E0
+      66.0300E0    246.40E0
+      66.8900E0    249.35E0
+      67.4200E0    251.32E0
+      68.2300E0    254.22E0
+      68.7700E0    256.24E0
+      69.5900E0    259.11E0
+      70.1100E0    261.18E0
+      70.8600E0    264.02E0
+      71.4300E0    266.13E0
+      72.1600E0    268.94E0
+      72.7000E0    271.09E0
+      73.4000E0    273.87E0
+      73.9300E0    276.08E0
+      74.6000E0    278.83E0
+      75.1600E0    281.08E0
+      75.8200E0    283.81E0
+      76.3400E0    286.11E0
+      76.9800E0    288.81E0
+      77.4800E0    291.08E0
+      78.0800E0    293.75E0
+      78.6000E0    295.99E0
+      79.1700E0    298.64E0
+      79.6200E0    300.84E0
+      79.8800E0    302.02E0
+      80.1900E0    303.48E0
+      80.6600E0    305.65E0
+      81.2200E0    308.27E0
+      81.6600E0    310.41E0
+      82.1600E0    313.01E0
+      82.5900E0    315.12E0
+      83.1400E0    317.71E0
+      83.5000E0    319.79E0
+      84.0000E0    322.36E0
+      84.4000E0    324.42E0
+      84.8900E0    326.98E0
+      85.2600E0    329.01E0
+      85.7400E0    331.56E0
+      86.0700E0    333.56E0
+      86.5400E0    336.10E0
+      86.8900E0    338.08E0
+      87.3200E0    340.60E0
+      87.6500E0    342.57E0
+      88.1000E0    345.08E0
+      88.4300E0    347.02E0
+      88.8300E0    349.52E0
+      89.1200E0    351.44E0
+      89.5400E0    353.93E0
+      89.8500E0    355.83E0
+      90.2500E0    358.32E0
+      90.5500E0    360.20E0
+      90.9300E0    362.67E0
+      91.2000E0    364.53E0
+      91.5500E0    367.00E0
+      92.2000E0    371.30E0

data/nist/Lanczos1.dat

@@ -0,0 +1,84 @@
+NIST/ITL StRD
+Dataset Name:  Lanczos1          (Lanczos1.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 46)
+               Certified Values  (lines 41 to 51)
+               Data              (lines 61 to 84)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are taken from an example discussed in
+               Lanczos (1956).  The data were generated to 14-digits
+               of accuracy using
+               f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) 
+                                     + 1.5576*exp(-5*x).
+
+
+Reference:     Lanczos, C. (1956).
+               Applied Analysis.
+               Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               24 Observations
+               Average Level of Difficulty
+               Generated Data
+
+Model:         Exponential Class
+               6 Parameters (b1 to b6)
+
+               y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
+
+
+ 
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1.2         0.5           9.5100000027E-02  5.3347304234E-11
+  b2 =   0.3         0.7           1.0000000001E+00  2.7473038179E-10
+  b3 =   5.6         3.6           8.6070000013E-01  1.3576062225E-10
+  b4 =   5.5         4.2           3.0000000002E+00  3.3308253069E-10
+  b5 =   6.5         4             1.5575999998E+00  1.8815731448E-10
+  b6 =   7.6         6.3           5.0000000001E+00  1.1057500538E-10
+
+Residual Sum of Squares:                    1.4307867721E-25
+Residual Standard Deviation:                8.9156129349E-14
+Degrees of Freedom:                                18
+Number of Observations:                            24
+
+
+
+
+
+
+
+
+Data:   y                   x
+       2.513400000000E+00  0.000000000000E+00
+       2.044333373291E+00  5.000000000000E-02
+       1.668404436564E+00  1.000000000000E-01
+       1.366418021208E+00  1.500000000000E-01
+       1.123232487372E+00  2.000000000000E-01
+       9.268897180037E-01  2.500000000000E-01
+       7.679338563728E-01  3.000000000000E-01
+       6.388775523106E-01  3.500000000000E-01
+       5.337835317402E-01  4.000000000000E-01
+       4.479363617347E-01  4.500000000000E-01
+       3.775847884350E-01  5.000000000000E-01
+       3.197393199326E-01  5.500000000000E-01
+       2.720130773746E-01  6.000000000000E-01
+       2.324965529032E-01  6.500000000000E-01
+       1.996589546065E-01  7.000000000000E-01
+       1.722704126914E-01  7.500000000000E-01
+       1.493405660168E-01  8.000000000000E-01
+       1.300700206922E-01  8.500000000000E-01
+       1.138119324644E-01  9.000000000000E-01
+       1.000415587559E-01  9.500000000000E-01
+       8.833209084540E-02  1.000000000000E+00
+       7.833544019350E-02  1.050000000000E+00
+       6.976693743449E-02  1.100000000000E+00
+       6.239312536719E-02  1.150000000000E+00

data/nist/Lanczos2.dat

@@ -0,0 +1,84 @@
+NIST/ITL StRD
+Dataset Name:  Lanczos2          (Lanczos2.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 46)
+               Certified Values  (lines 41 to 51)
+               Data              (lines 61 to 84)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are taken from an example discussed in
+               Lanczos (1956).  The data were generated to 6-digits
+               of accuracy using
+               f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) 
+                                     + 1.5576*exp(-5*x).
+
+
+Reference:     Lanczos, C. (1956).
+               Applied Analysis.
+               Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               24 Observations
+               Average Level of Difficulty
+               Generated Data
+ 
+Model:         Exponential Class
+               6 Parameters (b1 to b6)
+ 
+               y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
+ 
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1.2         0.5           9.6251029939E-02  6.6770575477E-04
+  b2 =   0.3         0.7           1.0057332849E+00  3.3989646176E-03
+  b3 =   5.6         3.6           8.6424689056E-01  1.7185846685E-03
+  b4 =   5.5         4.2           3.0078283915E+00  4.1707005856E-03
+  b5 =   6.5         4             1.5529016879E+00  2.3744381417E-03
+  b6 =   7.6         6.3           5.0028798100E+00  1.3958787284E-03
+
+Residual Sum of Squares:                    2.2299428125E-11
+Residual Standard Deviation:                1.1130395851E-06
+Degrees of Freedom:                                18
+Number of Observations:                            24
+
+
+
+
+
+
+
+
+Data:   y            x
+       2.51340E+00  0.00000E+00
+       2.04433E+00  5.00000E-02
+       1.66840E+00  1.00000E-01
+       1.36642E+00  1.50000E-01
+       1.12323E+00  2.00000E-01
+       9.26890E-01  2.50000E-01
+       7.67934E-01  3.00000E-01
+       6.38878E-01  3.50000E-01
+       5.33784E-01  4.00000E-01
+       4.47936E-01  4.50000E-01
+       3.77585E-01  5.00000E-01
+       3.19739E-01  5.50000E-01
+       2.72013E-01  6.00000E-01
+       2.32497E-01  6.50000E-01
+       1.99659E-01  7.00000E-01
+       1.72270E-01  7.50000E-01
+       1.49341E-01  8.00000E-01
+       1.30070E-01  8.50000E-01
+       1.13812E-01  9.00000E-01
+       1.00042E-01  9.50000E-01
+       8.83321E-02  1.00000E+00
+       7.83354E-02  1.05000E+00
+       6.97669E-02  1.10000E+00
+       6.23931E-02  1.15000E+00

data/nist/Lanczos3.dat

@@ -0,0 +1,84 @@
+NIST/ITL StRD
+Dataset Name:  Lanczos3          (Lanczos3.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 46)
+               Certified Values  (lines 41 to 51)
+               Data              (lines 61 to 84)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are taken from an example discussed in
+               Lanczos (1956).  The data were generated to 5-digits
+               of accuracy using
+               f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) 
+                                     + 1.5576*exp(-5*x).
+
+
+Reference:     Lanczos, C. (1956).
+               Applied Analysis.
+               Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
+
+
+
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               24 Observations
+               Lower Level of Difficulty
+               Generated Data
+ 
+Model:         Exponential Class
+               6 Parameters (b1 to b6)
+ 
+               y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1.2         0.5           8.6816414977E-02  1.7197908859E-02
+  b2 =   0.3         0.7           9.5498101505E-01  9.7041624475E-02
+  b3 =   5.6         3.6           8.4400777463E-01  4.1488663282E-02
+  b4 =   5.5         4.2           2.9515951832E+00  1.0766312506E-01
+  b5 =   6.5         4             1.5825685901E+00  5.8371576281E-02
+  b6 =   7.6         6.3           4.9863565084E+00  3.4436403035E-02
+
+Residual Sum of Squares:                    1.6117193594E-08
+Residual Standard Deviation:                2.9923229172E-05
+Degrees of Freedom:                                18
+Number of Observations:                            24
+
+
+
+
+
+
+
+
+Data:   y           x
+       2.5134E+00  0.00000E+00
+       2.0443E+00  5.00000E-02
+       1.6684E+00  1.00000E-01
+       1.3664E+00  1.50000E-01
+       1.1232E+00  2.00000E-01
+       0.9269E+00  2.50000E-01
+       0.7679E+00  3.00000E-01
+       0.6389E+00  3.50000E-01
+       0.5338E+00  4.00000E-01
+       0.4479E+00  4.50000E-01
+       0.3776E+00  5.00000E-01
+       0.3197E+00  5.50000E-01
+       0.2720E+00  6.00000E-01
+       0.2325E+00  6.50000E-01
+       0.1997E+00  7.00000E-01
+       0.1723E+00  7.50000E-01
+       0.1493E+00  8.00000E-01
+       0.1301E+00  8.50000E-01
+       0.1138E+00  9.00000E-01
+       0.1000E+00  9.50000E-01
+       0.0883E+00  1.00000E+00
+       0.0783E+00  1.05000E+00
+       0.0698E+00  1.10000E+00
+       0.0624E+00  1.15000E+00

data/nist/MGH09.dat

@@ -0,0 +1,71 @@
+NIST/ITL StRD
+Dataset Name:  MGH09             (MGH09.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 44)
+               Certified Values  (lines 41 to 49)
+               Data              (lines 61 to 71)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   This problem was found to be difficult for some very 
+               good algorithms.  There is a local minimum at (+inf,
+               -14.07..., -inf, -inf) with final sum of squares 
+               0.00102734....
+
+               See More, J. J., Garbow, B. S., and Hillstrom, K. E. 
+               (1981).  Testing unconstrained optimization software.
+               ACM Transactions on Mathematical Software. 7(1): 
+               pp. 17-41.
+
+Reference:     Kowalik, J.S., and M. R. Osborne, (1978).  
+               Methods for Unconstrained Optimization Problems.  
+               New York, NY:  Elsevier North-Holland.
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               11 Observations
+               Higher Level of Difficulty
+               Generated Data
+ 
+Model:         Rational Class (linear/quadratic)
+               4 Parameters (b1 to b4)
+ 
+               y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e
+ 
+
+ 
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   25          0.25          1.9280693458E-01  1.1435312227E-02
+  b2 =   39          0.39          1.9128232873E-01  1.9633220911E-01
+  b3 =   41.5        0.415         1.2305650693E-01  8.0842031232E-02
+  b4 =   39          0.39          1.3606233068E-01  9.0025542308E-02
+
+Residual Sum of Squares:                    3.0750560385E-04
+Residual Standard Deviation:                6.6279236551E-03
+Degrees of Freedom:                                7
+Number of Observations:                           11
+ 
+ 
+
+
+
+
+
+ 
+ 
+ 
+Data:  y               x
+       1.957000E-01    4.000000E+00
+       1.947000E-01    2.000000E+00
+       1.735000E-01    1.000000E+00
+       1.600000E-01    5.000000E-01
+       8.440000E-02    2.500000E-01
+       6.270000E-02    1.670000E-01
+       4.560000E-02    1.250000E-01
+       3.420000E-02    1.000000E-01
+       3.230000E-02    8.330000E-02
+       2.350000E-02    7.140000E-02
+       2.460000E-02    6.250000E-02

data/nist/MGH10.dat

@@ -0,0 +1,76 @@
+NIST/ITL StRD
+Dataset Name:  MGH10             (MGH10.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 43)
+               Certified Values  (lines 41 to 48)
+               Data              (lines 61 to 76)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   This problem was found to be difficult for some very
+               good algorithms.
+
+               See More, J. J., Garbow, B. S., and Hillstrom, K. E. 
+               (1981).  Testing unconstrained optimization software.
+               ACM Transactions on Mathematical Software. 7(1): 
+               pp. 17-41.
+
+Reference:     Meyer, R. R. (1970).  
+               Theoretical and computational aspects of nonlinear 
+               regression.  In Nonlinear Programming, Rosen, 
+               Mangasarian and Ritter (Eds).  
+               New York, NY: Academic Press, pp. 465-486.
+
+Data:          1 Response  (y)
+               1 Predictor (x)
+               16 Observations
+               Higher Level of Difficulty
+               Generated Data
+ 
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+ 
+               y = b1 * exp[b2/(x+b3)]  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =        2         0.02       5.6096364710E-03  1.5687892471E-04
+  b2 =   400000      4000          6.1813463463E+03  2.3309021107E+01
+  b3 =    25000       250          3.4522363462E+02  7.8486103508E-01
+
+Residual Sum of Squares:                    8.7945855171E+01
+Residual Standard Deviation:                2.6009740065E+00
+Degrees of Freedom:                                13
+Number of Observations:                            16
+
+
+
+
+
+
+
+
+
+
+
+Data:  y               x
+      3.478000E+04    5.000000E+01
+      2.861000E+04    5.500000E+01
+      2.365000E+04    6.000000E+01
+      1.963000E+04    6.500000E+01
+      1.637000E+04    7.000000E+01
+      1.372000E+04    7.500000E+01
+      1.154000E+04    8.000000E+01
+      9.744000E+03    8.500000E+01
+      8.261000E+03    9.000000E+01
+      7.030000E+03    9.500000E+01
+      6.005000E+03    1.000000E+02
+      5.147000E+03    1.050000E+02
+      4.427000E+03    1.100000E+02
+      3.820000E+03    1.150000E+02
+      3.307000E+03    1.200000E+02
+      2.872000E+03    1.250000E+02

data/nist/MGH17.dat

@@ -0,0 +1,93 @@
+NIST/ITL StRD
+Dataset Name:  MGH17             (MGH17.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 45)
+               Certified Values  (lines 41 to 50)
+               Data              (lines 61 to 93)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   This problem was found to be difficult for some very
+               good algorithms.
+
+               See More, J. J., Garbow, B. S., and Hillstrom, K. E.
+               (1981).  Testing unconstrained optimization software.
+               ACM Transactions on Mathematical Software. 7(1):
+               pp. 17-41.
+
+Reference:     Osborne, M. R. (1972).  
+               Some aspects of nonlinear least squares 
+               calculations.  In Numerical Methods for Nonlinear 
+               Optimization, Lootsma (Ed).  
+               New York, NY:  Academic Press, pp. 171-189.
+ 
+Data:          1 Response  (y)
+               1 Predictor (x)
+               33 Observations
+               Average Level of Difficulty
+               Generated Data
+
+Model:         Exponential Class
+               5 Parameters (b1 to b5)
+
+               y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03
+  b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01
+  b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01
+  b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04
+  b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04
+
+Residual Sum of Squares:                    5.4648946975E-05
+Residual Standard Deviation:                1.3970497866E-03
+Degrees of Freedom:                                28
+Number of Observations:                            33
+
+
+
+
+
+
+
+
+
+Data:  y               x
+      8.440000E-01    0.000000E+00
+      9.080000E-01    1.000000E+01
+      9.320000E-01    2.000000E+01
+      9.360000E-01    3.000000E+01
+      9.250000E-01    4.000000E+01
+      9.080000E-01    5.000000E+01
+      8.810000E-01    6.000000E+01
+      8.500000E-01    7.000000E+01
+      8.180000E-01    8.000000E+01
+      7.840000E-01    9.000000E+01
+      7.510000E-01    1.000000E+02
+      7.180000E-01    1.100000E+02
+      6.850000E-01    1.200000E+02
+      6.580000E-01    1.300000E+02
+      6.280000E-01    1.400000E+02
+      6.030000E-01    1.500000E+02
+      5.800000E-01    1.600000E+02
+      5.580000E-01    1.700000E+02
+      5.380000E-01    1.800000E+02
+      5.220000E-01    1.900000E+02
+      5.060000E-01    2.000000E+02
+      4.900000E-01    2.100000E+02
+      4.780000E-01    2.200000E+02
+      4.670000E-01    2.300000E+02
+      4.570000E-01    2.400000E+02
+      4.480000E-01    2.500000E+02
+      4.380000E-01    2.600000E+02
+      4.310000E-01    2.700000E+02
+      4.240000E-01    2.800000E+02
+      4.200000E-01    2.900000E+02
+      4.140000E-01    3.000000E+02
+      4.110000E-01    3.100000E+02
+      4.060000E-01    3.200000E+02

data/nist/Misra1a.dat

@@ -0,0 +1,74 @@
+NIST/ITL StRD
+Dataset Name:  Misra1a           (Misra1a.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 74)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study regarding
+               dental research in monomolecular adsorption.  The
+               response variable is volume, and the predictor
+               variable is pressure.
+
+Reference:     Misra, D., NIST (1978).  
+               Dental Research Monomolecular Adsorption Study.
+
+ 
+
+
+
+
+
+Data:          1 Response Variable  (y = volume)
+               1 Predictor Variable (x = pressure)
+               14 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               2 Parameters (b1 and b2)
+
+               y = b1*(1-exp[-b2*x])  +  e
+
+
+ 
+          Starting values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   500         250           2.3894212918E+02  2.7070075241E+00
+  b2 =     0.0001      0.0005      5.5015643181E-04  7.2668688436E-06
+
+Residual Sum of Squares:                    1.2455138894E-01
+Residual Standard Deviation:                1.0187876330E-01
+Degrees of Freedom:                                12
+Number of Observations:                            14
+
+
+
+
+
+
+
+
+
+
+
+
+Data:   y               x
+      10.07E0      77.6E0
+      14.73E0     114.9E0
+      17.94E0     141.1E0
+      23.93E0     190.8E0
+      29.61E0     239.9E0
+      35.18E0     289.0E0
+      40.02E0     332.8E0
+      44.82E0     378.4E0
+      50.76E0     434.8E0
+      55.05E0     477.3E0
+      61.01E0     536.8E0
+      66.40E0     593.1E0
+      75.47E0     689.1E0
+      81.78E0     760.0E0

data/nist/Misra1b.dat

@@ -0,0 +1,74 @@
+NIST/ITL StRD
+Dataset Name:  Misra1b           (Misra1b.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 74)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study regarding
+               dental research in monomolecular adsorption.  The
+               response variable is volume, and the predictor
+               variable is pressure.
+
+Reference:     Misra, D., NIST (1978).  
+               Dental Research Monomolecular Adsorption Study.
+
+
+
+
+
+
+
+Data:          1 Response  (y = volume)
+               1 Predictor (x = pressure)
+               14 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               2 Parameters (b1 and b2)
+
+               y = b1 * (1-(1+b2*x/2)**(-2))  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   500         300           3.3799746163E+02  3.1643950207E+00
+  b2 =     0.0001      0.0002      3.9039091287E-04  4.2547321834E-06
+ 
+Residual Sum of Squares:                    7.5464681533E-02
+Residual Standard Deviation:                7.9301471998E-02
+Degrees of Freedom:                                12
+Number of Observations:                            14
+
+
+
+
+
+
+
+
+
+
+ 
+ 
+Data:   y               x
+      10.07E0      77.6E0
+      14.73E0     114.9E0
+      17.94E0     141.1E0
+      23.93E0     190.8E0
+      29.61E0     239.9E0
+      35.18E0     289.0E0
+      40.02E0     332.8E0
+      44.82E0     378.4E0
+      50.76E0     434.8E0
+      55.05E0     477.3E0
+      61.01E0     536.8E0
+      66.40E0     593.1E0
+      75.47E0     689.1E0
+      81.78E0     760.0E0

data/nist/Misra1c.dat

@@ -0,0 +1,74 @@
+NIST/ITL StRD
+Dataset Name:  Misra1c           (Misra1c.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 74)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study regarding
+               dental research in monomolecular adsorption.  The
+               response variable is volume, and the predictor
+               variable is pressure.
+
+Reference:     Misra, D., NIST (1978).  
+               Dental Research Monomolecular Adsorption.
+
+
+
+
+
+
+
+Data:          1 Response  (y = volume)
+               1 Predictor (x = pressure)
+               14 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               2 Parameters (b1 and b2)
+
+               y = b1 * (1-(1+2*b2*x)**(-.5))  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   500         600           6.3642725809E+02  4.6638326572E+00
+  b2 =     0.0001      0.0002      2.0813627256E-04  1.7728423155E-06
+  
+Residual Sum of Squares:                    4.0966836971E-02
+Residual Standard Deviation:                5.8428615257E-02
+Degrees of Freedom:                                12
+Number of Observations:                            14
+ 
+
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+  
+  
+  
+Data:   y            x 
+      10.07E0      77.6E0
+      14.73E0     114.9E0
+      17.94E0     141.1E0
+      23.93E0     190.8E0
+      29.61E0     239.9E0
+      35.18E0     289.0E0
+      40.02E0     332.8E0
+      44.82E0     378.4E0
+      50.76E0     434.8E0
+      55.05E0     477.3E0
+      61.01E0     536.8E0
+      66.40E0     593.1E0
+      75.47E0     689.1E0
+      81.78E0     760.0E0

data/nist/Misra1d.dat

@@ -0,0 +1,74 @@
+NIST/ITL StRD
+Dataset Name:  Misra1d           (Misra1d.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 42)
+               Certified Values  (lines 41 to 47)
+               Data              (lines 61 to 74)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study regarding
+               dental research in monomolecular adsorption.  The
+               response variable is volume, and the predictor
+               variable is pressure.
+
+Reference:     Misra, D., NIST (1978).  
+               Dental Research Monomolecular Adsorption Study.
+
+
+
+
+
+
+
+Data:          1 Response  (y = volume)
+               1 Predictor (x = pressure)
+               14 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               2 Parameters (b1 and b2)
+
+               y = b1*b2*x*((1+b2*x)**(-1))  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   500         450           4.3736970754E+02  3.6489174345E+00
+  b2 =     0.0001      0.0003      3.0227324449E-04  2.9334354479E-06
+
+Residual Sum of Squares:                    5.6419295283E-02
+Residual Standard Deviation:                6.8568272111E-02
+Degrees of Freedom:                                12
+Number of Observations:                            14
+
+
+
+
+
+
+
+
+
+
+
+
+Data:   y            x
+      10.07E0      77.6E0
+      14.73E0     114.9E0
+      17.94E0     141.1E0
+      23.93E0     190.8E0
+      29.61E0     239.9E0
+      35.18E0     289.0E0
+      40.02E0     332.8E0
+      44.82E0     378.4E0
+      50.76E0     434.8E0
+      55.05E0     477.3E0
+      61.01E0     536.8E0
+      66.40E0     593.1E0
+      75.47E0     689.1E0
+      81.78E0     760.0E0

data/nist/Nelson.dat

@@ -0,0 +1,188 @@
+NIST/ITL StRD
+Dataset Name:  Nelson            (Nelson.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 43)
+               Certified Values  (lines 41 to 48)
+               Data              (lines 61 to 188)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a study involving
+               the analysis of performance degradation data from
+               accelerated tests, published in IEEE Transactions
+               on Reliability.  The response variable is dialectric
+               breakdown strength in kilo-volts, and the predictor
+               variables are time in weeks and temperature in degrees
+               Celcius.
+
+
+Reference:     Nelson, W. (1981).  
+               Analysis of Performance-Degradation Data.  
+               IEEE Transactions on Reliability.
+               Vol. 2, R-30, No. 2, pp. 149-155.
+
+Data:          1 Response   ( y = dialectric breakdown strength) 
+               2 Predictors (x1 = time; x2 = temperature)
+               128 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+
+               log[y] = b1 - b2*x1 * exp[-b3*x2]  +  e
+
+
+
+          Starting values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =    2           2.5          2.5906836021E+00  1.9149996413E-02
+  b2 =    0.0001      0.000000005  5.6177717026E-09  6.1124096540E-09
+  b3 =   -0.01       -0.05        -5.7701013174E-02  3.9572366543E-03
+
+Residual Sum of Squares:                    3.7976833176E+00
+Residual Standard Deviation:                1.7430280130E-01
+Degrees of Freedom:                               125
+Number of Observations:                           128
+
+
+
+
+
+
+
+
+
+
+
+Data:   y              x1            x2
+      15.00E0         1E0         180E0
+      17.00E0         1E0         180E0
+      15.50E0         1E0         180E0
+      16.50E0         1E0         180E0
+      15.50E0         1E0         225E0
+      15.00E0         1E0         225E0
+      16.00E0         1E0         225E0
+      14.50E0         1E0         225E0
+      15.00E0         1E0         250E0
+      14.50E0         1E0         250E0
+      12.50E0         1E0         250E0
+      11.00E0         1E0         250E0
+      14.00E0         1E0         275E0
+      13.00E0         1E0         275E0
+      14.00E0         1E0         275E0
+      11.50E0         1E0         275E0
+      14.00E0         2E0         180E0
+      16.00E0         2E0         180E0
+      13.00E0         2E0         180E0
+      13.50E0         2E0         180E0
+      13.00E0         2E0         225E0
+      13.50E0         2E0         225E0
+      12.50E0         2E0         225E0
+      12.50E0         2E0         225E0
+      12.50E0         2E0         250E0
+      12.00E0         2E0         250E0
+      11.50E0         2E0         250E0
+      12.00E0         2E0         250E0
+      13.00E0         2E0         275E0
+      11.50E0         2E0         275E0
+      13.00E0         2E0         275E0
+      12.50E0         2E0         275E0
+      13.50E0         4E0         180E0
+      17.50E0         4E0         180E0
+      17.50E0         4E0         180E0
+      13.50E0         4E0         180E0
+      12.50E0         4E0         225E0
+      12.50E0         4E0         225E0
+      15.00E0         4E0         225E0
+      13.00E0         4E0         225E0
+      12.00E0         4E0         250E0
+      13.00E0         4E0         250E0
+      12.00E0         4E0         250E0
+      13.50E0         4E0         250E0
+      10.00E0         4E0         275E0
+      11.50E0         4E0         275E0
+      11.00E0         4E0         275E0
+       9.50E0         4E0         275E0
+      15.00E0         8E0         180E0
+      15.00E0         8E0         180E0
+      15.50E0         8E0         180E0
+      16.00E0         8E0         180E0
+      13.00E0         8E0         225E0
+      10.50E0         8E0         225E0
+      13.50E0         8E0         225E0
+      14.00E0         8E0         225E0
+      12.50E0         8E0         250E0
+      12.00E0         8E0         250E0
+      11.50E0         8E0         250E0
+      11.50E0         8E0         250E0
+       6.50E0         8E0         275E0
+       5.50E0         8E0         275E0
+       6.00E0         8E0         275E0
+       6.00E0         8E0         275E0
+      18.50E0        16E0         180E0
+      17.00E0        16E0         180E0
+      15.30E0        16E0         180E0
+      16.00E0        16E0         180E0
+      13.00E0        16E0         225E0
+      14.00E0        16E0         225E0
+      12.50E0        16E0         225E0
+      11.00E0        16E0         225E0
+      12.00E0        16E0         250E0
+      12.00E0        16E0         250E0
+      11.50E0        16E0         250E0
+      12.00E0        16E0         250E0
+       6.00E0        16E0         275E0
+       6.00E0        16E0         275E0
+       5.00E0        16E0         275E0
+       5.50E0        16E0         275E0
+      12.50E0        32E0         180E0
+      13.00E0        32E0         180E0
+      16.00E0        32E0         180E0
+      12.00E0        32E0         180E0
+      11.00E0        32E0         225E0
+       9.50E0        32E0         225E0
+      11.00E0        32E0         225E0
+      11.00E0        32E0         225E0
+      11.00E0        32E0         250E0
+      10.00E0        32E0         250E0
+      10.50E0        32E0         250E0
+      10.50E0        32E0         250E0
+       2.70E0        32E0         275E0
+       2.70E0        32E0         275E0
+       2.50E0        32E0         275E0
+       2.40E0        32E0         275E0
+      13.00E0        48E0         180E0
+      13.50E0        48E0         180E0
+      16.50E0        48E0         180E0
+      13.60E0        48E0         180E0
+      11.50E0        48E0         225E0
+      10.50E0        48E0         225E0
+      13.50E0        48E0         225E0
+      12.00E0        48E0         225E0
+       7.00E0        48E0         250E0
+       6.90E0        48E0         250E0
+       8.80E0        48E0         250E0
+       7.90E0        48E0         250E0
+       1.20E0        48E0         275E0
+       1.50E0        48E0         275E0
+       1.00E0        48E0         275E0
+       1.50E0        48E0         275E0
+      13.00E0        64E0         180E0
+      12.50E0        64E0         180E0
+      16.50E0        64E0         180E0
+      16.00E0        64E0         180E0
+      11.00E0        64E0         225E0
+      11.50E0        64E0         225E0
+      10.50E0        64E0         225E0
+      10.00E0        64E0         225E0
+       7.27E0        64E0         250E0
+       7.50E0        64E0         250E0
+       6.70E0        64E0         250E0
+       7.60E0        64E0         250E0
+       1.50E0        64E0         275E0
+       1.00E0        64E0         275E0
+       1.20E0        64E0         275E0
+       1.20E0        64E0         275E0

data/nist/Rat42.dat

@@ -0,0 +1,69 @@
+NIST/ITL StRD
+Dataset Name:  Rat42             (Rat42.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 43)
+               Certified Values  (lines 41 to 48)
+               Data              (lines 61 to 69)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   This model and data are an example of fitting
+               sigmoidal growth curves taken from Ratkowsky (1983).
+               The response variable is pasture yield, and the
+               predictor variable is growing time.
+
+
+Reference:     Ratkowsky, D.A. (1983).  
+               Nonlinear Regression Modeling.
+               New York, NY:  Marcel Dekker, pp. 61 and 88.
+
+
+
+
+
+Data:          1 Response  (y = pasture yield)
+               1 Predictor (x = growing time)
+               9 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               3 Parameters (b1 to b3)
+
+               y = b1 / (1+exp[b2-b3*x])  +  e
+
+
+
+          Starting Values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   100         75            7.2462237576E+01  1.7340283401E+00
+  b2 =     1          2.5          2.6180768402E+00  8.8295217536E-02
+  b3 =     0.1        0.07         6.7359200066E-02  3.4465663377E-03
+
+Residual Sum of Squares:                    8.0565229338E+00
+Residual Standard Deviation:                1.1587725499E+00
+Degrees of Freedom:                                6
+Number of Observations:                            9 
+
+
+
+
+
+
+
+
+
+
+
+Data:   y              x
+       8.930E0        9.000E0
+      10.800E0       14.000E0
+      18.590E0       21.000E0
+      22.330E0       28.000E0
+      39.350E0       42.000E0
+      56.110E0       57.000E0
+      61.730E0       63.000E0
+      64.620E0       70.000E0
+      67.080E0       79.000E0

data/nist/Rat43.dat

@@ -0,0 +1,75 @@
+NIST/ITL StRD
+Dataset Name:  Rat43             (Rat43.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 44)
+               Certified Values  (lines 41 to 49)
+               Data              (lines 61 to 75)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   This model and data are an example of fitting  
+               sigmoidal growth curves taken from Ratkowsky (1983).  
+               The response variable is the dry weight of onion bulbs 
+               and tops, and the predictor variable is growing time. 
+
+
+Reference:     Ratkowsky, D.A. (1983).  
+               Nonlinear Regression Modeling.
+               New York, NY:  Marcel Dekker, pp. 62 and 88.
+
+
+
+
+
+Data:          1 Response  (y = onion bulb dry weight)
+               1 Predictor (x = growing time)
+               15 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Exponential Class
+               4 Parameters (b1 to b4)
+
+               y = b1 / ((1+exp[b2-b3*x])**(1/b4))  +  e
+
+
+
+          Starting Values                  Certified Values
+ 
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   100         700           6.9964151270E+02  1.6302297817E+01
+  b2 =    10           5           5.2771253025E+00  2.0828735829E+00
+  b3 =     1           0.75        7.5962938329E-01  1.9566123451E-01
+  b4 =     1           1.3         1.2792483859E+00  6.8761936385E-01
+ 
+Residual Sum of Squares:                    8.7864049080E+03
+Residual Standard Deviation:                2.8262414662E+01
+Degrees of Freedom:                                9
+Number of Observations:                           15 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Data:   y          x
+      16.08E0     1.0E0
+      33.83E0     2.0E0
+      65.80E0     3.0E0
+      97.20E0     4.0E0
+     191.55E0     5.0E0
+     326.20E0     6.0E0
+     386.87E0     7.0E0
+     520.53E0     8.0E0
+     590.03E0     9.0E0
+     651.92E0    10.0E0
+     724.93E0    11.0E0
+     699.56E0    12.0E0
+     689.96E0    13.0E0
+     637.56E0    14.0E0
+     717.41E0    15.0E0

data/nist/Roszman1.dat

@@ -0,0 +1,85 @@
+NIST/ITL StRD
+Dataset Name:  Roszman1          (Roszman1.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 44)
+               Certified Values  (lines 41 to 49)
+               Data              (lines 61 to 85)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               quantum defects in iodine atoms.  The response
+               variable is the number of quantum defects, and the
+               predictor variable is the excited energy state.
+               The argument to the ARCTAN function is in radians.
+
+Reference:     Roszman, L., NIST (19??).  
+               Quantum Defects for Sulfur I Atom.
+
+
+
+
+
+
+Data:          1 Response  (y = quantum defect)
+               1 Predictor (x = excited state energy)
+               25 Observations
+               Average Level of Difficulty
+               Observed Data
+
+Model:         Miscellaneous Class
+               4 Parameters (b1 to b4)
+
+               pi = 3.141592653589793238462643383279E0
+               y =  b1 - b2*x - arctan[b3/(x-b4)]/pi  +  e
+
+
+          Starting Values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =      0.1         0.2         2.0196866396E-01  1.9172666023E-02
+  b2 =     -0.00001    -0.000005   -6.1953516256E-06  3.2058931691E-06
+  b3 =   1000        1200           1.2044556708E+03  7.4050983057E+01
+  b4 =   -100        -150          -1.8134269537E+02  4.9573513849E+01
+
+Residual Sum of Squares:                    4.9484847331E-04
+Residual Standard Deviation:                4.8542984060E-03
+Degrees of Freedom:                                 21
+Number of Observations:                             25
+
+
+
+
+
+
+
+
+
+
+Data:   y           x
+       0.252429    -4868.68
+       0.252141    -4868.09
+       0.251809    -4867.41
+       0.297989    -3375.19
+       0.296257    -3373.14
+       0.295319    -3372.03
+       0.339603    -2473.74
+       0.337731    -2472.35
+       0.333820    -2469.45
+       0.389510    -1894.65
+       0.386998    -1893.40
+       0.438864    -1497.24
+       0.434887    -1495.85
+       0.427893    -1493.41
+       0.471568    -1208.68
+       0.461699    -1206.18
+       0.461144    -1206.04
+       0.513532     -997.92
+       0.506641     -996.61
+       0.505062     -996.31
+       0.535648     -834.94
+       0.533726     -834.66
+       0.568064     -710.03
+       0.612886     -530.16
+       0.624169     -464.17

data/nist/Thurber.dat

@@ -0,0 +1,97 @@
+NIST/ITL StRD
+Dataset Name:  Thurber           (Thurber.dat)
+
+File Format:   ASCII
+               Starting Values   (lines 41 to 47)
+               Certified Values  (lines 41 to 52)
+               Data              (lines 61 to 97)
+
+Procedure:     Nonlinear Least Squares Regression
+
+Description:   These data are the result of a NIST study involving
+               semiconductor electron mobility.  The response 
+               variable is a measure of electron mobility, and the 
+               predictor variable is the natural log of the density.
+
+
+Reference:     Thurber, R., NIST (197?).  
+               Semiconductor electron mobility modeling.
+
+
+
+
+
+
+Data:          1 Response Variable  (y = electron mobility)
+               1 Predictor Variable (x = log[density])
+               37 Observations
+               Higher Level of Difficulty
+               Observed Data
+
+Model:         Rational Class (cubic/cubic)
+               7 Parameters (b1 to b7)
+
+               y = (b1 + b2*x + b3*x**2 + b4*x**3) / 
+                   (1 + b5*x + b6*x**2 + b7*x**3)  +  e
+
+
+          Starting Values                  Certified Values
+
+        Start 1     Start 2           Parameter     Standard Deviation
+  b1 =   1000        1300          1.2881396800E+03  4.6647963344E+00
+  b2 =   1000        1500          1.4910792535E+03  3.9571156086E+01
+  b3 =    400         500          5.8323836877E+02  2.8698696102E+01
+  b4 =     40          75          7.5416644291E+01  5.5675370270E+00
+  b5 =      0.7         1          9.6629502864E-01  3.1333340687E-02
+  b6 =      0.3         0.4        3.9797285797E-01  1.4984928198E-02
+  b7 =      0.03        0.05       4.9727297349E-02  6.5842344623E-03
+
+Residual Sum of Squares:                    5.6427082397E+03
+Residual Standard Deviation:                1.3714600784E+01
+Degrees of Freedom:                                30
+Number of Observations:                            37
+
+
+
+
+
+
+
+Data:   y             x
+      80.574E0      -3.067E0
+      84.248E0      -2.981E0
+      87.264E0      -2.921E0
+      87.195E0      -2.912E0
+      89.076E0      -2.840E0
+      89.608E0      -2.797E0
+      89.868E0      -2.702E0
+      90.101E0      -2.699E0
+      92.405E0      -2.633E0
+      95.854E0      -2.481E0
+     100.696E0      -2.363E0
+     101.060E0      -2.322E0
+     401.672E0      -1.501E0
+     390.724E0      -1.460E0
+     567.534E0      -1.274E0
+     635.316E0      -1.212E0
+     733.054E0      -1.100E0
+     759.087E0      -1.046E0
+     894.206E0      -0.915E0
+     990.785E0      -0.714E0
+    1090.109E0      -0.566E0
+    1080.914E0      -0.545E0
+    1122.643E0      -0.400E0
+    1178.351E0      -0.309E0
+    1260.531E0      -0.109E0
+    1273.514E0      -0.103E0
+    1288.339E0       0.010E0
+    1327.543E0       0.119E0
+    1353.863E0       0.377E0
+    1414.509E0       0.790E0
+    1425.208E0       0.963E0
+    1421.384E0       1.006E0
+    1442.962E0       1.115E0
+    1464.350E0       1.572E0
+    1468.705E0       1.841E0
+    1447.894E0       2.047E0
+    1457.628E0       2.200E0

examples/CMakeLists.txt

@@ -32,6 +32,9 @@ IF (${GFLAGS})
   ADD_EXECUTABLE(quadratic quadratic.cc)
   TARGET_LINK_LIBRARIES(quadratic ceres)
 
+  ADD_EXECUTABLE(nist nist.cc)
+  TARGET_LINK_LIBRARIES(nist ceres)
+
   ADD_EXECUTABLE(quadratic_auto_diff quadratic_auto_diff.cc)
   TARGET_LINK_LIBRARIES(quadratic_auto_diff ceres)
 

examples/nist.cc

@@ -0,0 +1,415 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+//
+// NIST non-linear regression problems solved using Ceres.
+//
+// The data was obtained from
+// http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml, where more
+// background on these problems can also be found.
+//
+// Currently not all problems are solved successfully. Some of the
+// failures are due to convergence to a local minimum, and some fail
+// because of numerical issues.
+//
+// TODO(sameeragarwal): Fix numerical issues so that all the problems
+// converge and then look at convergence to the wrong solution issues.
+
+#include <iostream>
+#include <fstream>
+#include "ceres/ceres.h"
+#include "ceres/split.h"
+#include "gflags/gflags.h"
+#include "glog/logging.h"
+#include "Eigen/Core"
+
+DEFINE_string(nist_data_dir, "", "Directory containing the NIST non-linear"
+              "regression examples");
+
+using Eigen::Dynamic;
+using Eigen::RowMajor;
+typedef Eigen::Matrix<double, Dynamic, 1> Vector;
+typedef Eigen::Matrix<double, Dynamic, Dynamic, RowMajor> Matrix;
+
+bool GetAndSplitLine(std::ifstream& ifs, std::vector<std::string>* pieces) {
+  pieces->clear();
+  char buf[256];
+  ifs.getline(buf, 256);
+  ceres::SplitStringUsing(std::string(buf), " ", pieces);
+  return true;
+}
+
+void SkipLines(std::ifstream& ifs, int num_lines) {
+  char buf[256];
+  for (int i = 0; i < num_lines; ++i) {
+    ifs.getline(buf, 256);
+  }
+}
+
+class NISTProblem {
+ public:
+  explicit NISTProblem(const std::string& filename) {
+    std::ifstream ifs(filename.c_str(), std::ifstream::in);
+
+    std::vector<std::string> pieces;
+    SkipLines(ifs, 24);
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumResponses = std::atoi(pieces[1].c_str());
+
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumPredictors = std::atoi(pieces[0].c_str());
+
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumObservations = std::atoi(pieces[0].c_str());
+
+    SkipLines(ifs, 4);
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumParameters = std::atoi(pieces[0].c_str());
+    SkipLines(ifs, 8);
+
+    // Get the first line of initial and final parameter values to
+    // determine the number of tries.
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumTries = pieces.size() - 4;
+
+    predictor_.resize(kNumObservations, kNumPredictors);
+    response_.resize(kNumObservations, kNumResponses);
+    initial_parameters_.resize(kNumTries, kNumParameters);
+    final_parameters_.resize(1, kNumParameters);
+
+    // Parse the line for parameter b1.
+    int parameter_id = 0;
+    for (int i = 0; i < kNumTries; ++i) {
+      initial_parameters_(i, parameter_id) = std::atof(pieces[i + 2].c_str());
+    }
+    final_parameters_(0, parameter_id) = std::atof(pieces[2 + kNumTries].c_str());
+
+    // Parse the remaining parameter lines.
+    for (int parameter_id = 1; parameter_id < kNumParameters; ++parameter_id) {
+     GetAndSplitLine(ifs, &pieces);
+     // b2, b3, ....
+     for (int i = 0; i < kNumTries; ++i) {
+       initial_parameters_(i, parameter_id) = std::atof(pieces[i + 2].c_str());
+     }
+     final_parameters_(0, parameter_id) = std::atof(pieces[2 + kNumTries].c_str());
+    }
+
+    // Read the observations.
+    SkipLines(ifs, 20 - kNumParameters);
+    for (int i = 0; i < kNumObservations; ++i) {
+      GetAndSplitLine(ifs, &pieces);
+      // Response.
+      for (int j = 0; j < kNumResponses; ++j) {
+        response_(i, j) =  std::atof(pieces[j].c_str());
+      }
+
+      // Predictor variables.
+      for (int j = 0; j < kNumPredictors; ++j) {
+        predictor_(i, j) =  std::atof(pieces[j + kNumResponses].c_str());
+      }
+    }
+  }
+
+  Matrix initial_parameters(int start) const { return initial_parameters_.row(start); }
+  Matrix final_parameters() const  { return final_parameters_; }
+  Matrix predictor()        const { return predictor_;         }
+  Matrix response()         const { return response_;          }
+  int predictor_size()      const { return predictor_.cols();  }
+  int num_observations()    const { return predictor_.rows();  }
+  int response_size()       const { return response_.cols();   }
+  int num_parameters()      const { return initial_parameters_.cols(); }
+  int num_starts()          const { return initial_parameters_.rows(); }
+
+ private:
+  Matrix predictor_;
+  Matrix response_;
+  Matrix initial_parameters_;
+  Matrix final_parameters_;
+};
+
+#define NIST_BEGIN(CostFunctionName) \
+  struct CostFunctionName { \
+    CostFunctionName(const double* const x, \
+                     const double* const y) \
+        : x_(*x), y_(*y) {} \
+    double x_; \
+    double y_; \
+    template <typename T> \
+    bool operator()(const T* const b, T* residual) const { \
+    const T y(y_); \
+    const T x(x_); \
+      residual[0] = y - (
+
+#define NIST_END ); return true; }};
+
+// y = b1 * (b2+x)**(-1/b3)  +  e
+NIST_BEGIN(Bennet5)
+  b[0] * pow(b[1] + x, T(-1.0) / b[2])
+NIST_END
+
+// y = b1*(1-exp[-b2*x])  +  e
+NIST_BEGIN(BoxBOD)
+  b[0] * (T(1.0) - exp(-b[1] * x))
+NIST_END
+
+// y = exp[-b1*x]/(b2+b3*x)  +  e
+NIST_BEGIN(Chwirut)
+  exp(-b[0] * x) / (b[1] + b[2] * x)
+NIST_END
+
+// y  = b1*x**b2  +  e
+NIST_BEGIN(DanWood)
+  b[0] * pow(x, b[1])
+NIST_END
+
+// y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+//     + b6*exp( -(x-b7)**2 / b8**2 ) + e
+NIST_BEGIN(Gauss)
+  b[0] * exp(-b[1] * x) +
+  b[2] * exp(-pow((x - b[3])/b[4], 2)) +
+  b[5] * exp(-pow((x - b[6])/b[7],2))
+NIST_END
+
+// y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
+NIST_BEGIN(Lanczos)
+  b[0] * exp(-b[1] * x) + b[2] * exp(-b[3] * x) + b[4] * exp(-b[5] * x)
+NIST_END
+
+// y = (b1+b2*x+b3*x**2+b4*x**3) /
+//     (1+b5*x+b6*x**2+b7*x**3)  +  e
+NIST_BEGIN(Hahn1)
+  (b[0] + b[1] * x + b[2] * x * x + b[3] * x * x * x) /
+  (T(1.0) + b[4] * x + b[5] * x * x + b[6] * x * x * x)
+NIST_END
+
+// y = (b1 + b2*x + b3*x**2) /
+//    (1 + b4*x + b5*x**2)  +  e
+NIST_BEGIN(Kirby2)
+  (b[0] + b[1] * x + b[2] * x * x) /
+  (T(1.0) + b[3] * x + b[4] * x * x)
+NIST_END
+
+// y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e
+NIST_BEGIN(MGH09)
+  b[0] * (x * x + x * b[1]) / (x * x + x * b[2] + b[3])
+NIST_END
+
+// y = b1 * exp[b2/(x+b3)]  +  e
+NIST_BEGIN(MGH10)
+  b[0] * exp(b[1] / (x + b[2]))
+NIST_END
+
+// y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]
+NIST_BEGIN(MGH17)
+  b[0] + b[1] * exp(-x * b[3]) + b[2] * exp(-x * b[4])
+NIST_END
+
+// y = b1*(1-exp[-b2*x])  +  e
+NIST_BEGIN(Misra1a)
+  b[0] * (T(1.0) - exp(-b[1] * x))
+NIST_END
+
+// y = b1 * (1-(1+b2*x/2)**(-2))  +  e
+NIST_BEGIN(Misra1b)
+  b[0] * (T(1.0) - T(1.0)/ ((T(1.0) + b[1] * x / 2.0) * (T(1.0) + b[1] * x / 2.0)))
+NIST_END
+
+// y = b1 * (1-(1+2*b2*x)**(-.5))  +  e
+NIST_BEGIN(Misra1c)
+  b[0] * (T(1.0) - pow(T(1.0) + T(2.0) * b[1] * x, 0.5))
+NIST_END
+
+// y = b1*b2*x*((1+b2*x)**(-1))  +  e
+NIST_BEGIN(Misra1d)
+  b[0] * b[1] * x / (T(1.0) + b[1] * x)
+NIST_END
+
+const double kPi = 3.141592653589793238462643383279;
+// pi = 3.141592653589793238462643383279E0
+// y =  b1 - b2*x - arctan[b3/(x-b4)]/pi  +  e
+NIST_BEGIN(Roszman1)
+  b[0] - b[1] * x - atan2(b[2], (x - b[3]))/T(kPi)
+NIST_END
+
+// y = b1 / (1+exp[b2-b3*x])  +  e
+NIST_BEGIN(Rat42)
+  b[0] / (T(1.0) + exp(b[1] - b[2] * x))
+NIST_END
+
+// y = b1 / ((1+exp[b2-b3*x])**(1/b4))  +  e
+NIST_BEGIN(Rat43)
+  b[0] / pow(T(1.0) + exp(b[1] - b[2] * x), T(1.0) / b[4])
+NIST_END
+
+// y = (b1 + b2*x + b3*x**2 + b4*x**3) /
+//    (1 + b5*x + b6*x**2 + b7*x**3)  +  e
+NIST_BEGIN(Thurber)
+  (b[0] + b[1] * x + b[2] * x * x  + b[3] * x * x * x) /
+  (T(1.0) + b[4] * x + b[5] * x * x + b[6] * x * x * x)
+NIST_END
+
+// y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
+//        + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
+//        + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 )  + e
+NIST_BEGIN(ENSO)
+  b[0] + b[1] * cos(T(2.0 * kPi) * x / T(12.0)) +
+         b[2] * sin(T(2.0 * kPi) * x / T(12.0)) +
+         b[4] * cos(T(2.0 * kPi) * x / b[3]) +
+         b[5] * sin(T(2.0 * kPi) * x / b[3]) +
+         b[7] * cos(T(2.0 * kPi) * x / b[6]) +
+         b[8] * sin(T(2.0 * kPi) * x / b[6])
+NIST_END
+
+// y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
+NIST_BEGIN(Eckerle4)
+  b[0] / b[1] * exp(T(-0.5) * pow((x - b[2])/b[1], 2))
+NIST_END
+
+struct Nelson {
+ public:
+  Nelson(const double* const x, const double* const y)
+      : x1_(x[0]), x2_(x[1]), y_(y[0]) {}
+
+  template <typename T>
+  bool operator()(const T* const b, T* residual) const {
+    // log[y] = b1 - b2*x1 * exp[-b3*x2]  +  e
+    residual[0] = T(log(y_)) - (b[0] - b[1] * T(x1_) * exp(-b[2] * T(x2_)));
+    return true;
+  }
+
+ private:
+  double x1_;
+  double x2_;
+  double y_;
+};
+
+template <typename Model, int num_residuals, int num_parameters>
+void RegressionDriver(const std::string& filename,
+                      const ceres::Solver::Options& options) {
+  NISTProblem nist_problem(FLAGS_nist_data_dir + filename);
+  CHECK_EQ(num_residuals, nist_problem.response_size());
+  CHECK_EQ(num_parameters, nist_problem.num_parameters());
+
+  Matrix predictor = nist_problem.predictor();
+  Matrix response = nist_problem.response();
+  Matrix final_parameters = nist_problem.final_parameters();
+  std::vector<ceres::Solver::Summary> summaries(nist_problem.num_starts() + 1);
+
+  // Each NIST problem comes with multiple starting points, so we
+  // construct the problem from scratch for each case and solve it.
+  for (int start = 0; start < nist_problem.num_starts(); ++start) {
+    Matrix initial_parameters = nist_problem.initial_parameters(start);
+    ceres::Problem problem;
+
+    for (int i = 0; i < nist_problem.num_observations(); ++i) {
+      problem.AddResidualBlock(
+          new ceres::AutoDiffCostFunction<Model, num_residuals, num_parameters>(
+              new Model(predictor.data() + nist_problem.predictor_size() * i,
+                        response.data() + nist_problem.response_size() * i)),
+          NULL,
+          initial_parameters.data());
+    }
+
+    Solve(options, &problem, &summaries[start]);
+  }
+
+  // Ugly hack to get the objective function value at the certified
+  // optimal parameter values.
+  Matrix initial_parameters = nist_problem.final_parameters();
+  ceres::Problem problem;
+  for (int i = 0; i < nist_problem.num_observations(); ++i) {
+    problem.AddResidualBlock(
+        new ceres::AutoDiffCostFunction<Model, num_residuals, num_parameters>(
+            new Model(predictor.data() + nist_problem.predictor_size() * i,
+                      response.data() + nist_problem.response_size() * i)),
+        NULL,
+        initial_parameters.data());
+  }
+  Solve(options, &problem, &summaries.back());
+  double certified_cost = summaries.back().initial_cost;
+
+  std::cout << filename << std::endl;
+  for (int i = 0; i < nist_problem.num_starts(); ++i) {
+    std::cout << "start " << i + 1 << ": "
+              << " relative difference : "
+              << (summaries[i].final_cost - certified_cost) / certified_cost
+              << " termination: "
+              << ceres::SolverTerminationTypeToString(summaries[i].termination_type)
+              << std::endl;
+  }
+}
+
+int main(int argc, char** argv) {
+  google::ParseCommandLineFlags(&argc, &argv, true);
+  google::InitGoogleLogging(argv[0]);
+
+  // TODO(sameeragarwal): Test more combinations of non-linear and
+  // linear solvers.
+  ceres::Solver::Options options;
+  options.linear_solver_type = ceres::DENSE_QR;
+  options.max_num_iterations = 2000;
+  options.function_tolerance *= 1e-10;
+  options.gradient_tolerance *= 1e-10;
+  options.parameter_tolerance *= 1e-10;
+
+  std::cout << "Lower Difficulty\n";
+  RegressionDriver<Misra1a,  1, 2>("Misra1a.dat",  options);
+  RegressionDriver<Chwirut,  1, 3>("Chwirut1.dat", options);
+  RegressionDriver<Chwirut,  1, 3>("Chwirut2.dat", options);
+  RegressionDriver<Lanczos,  1, 6>("Lanczos3.dat", options);
+  RegressionDriver<Gauss,    1, 8>("Gauss1.dat",   options);
+  RegressionDriver<Gauss,    1, 8>("Gauss2.dat",   options);
+  RegressionDriver<DanWood,  1, 2>("DanWood.dat",  options);
+  RegressionDriver<Misra1b,  1, 2>("Misra1b.dat",  options);
+
+  std::cout << "\nAverage Difficulty\n";
+  RegressionDriver<Kirby2,   1, 5>("Kirby2.dat",   options);
+  RegressionDriver<Hahn1,    1, 7>("Hahn1.dat",    options);
+  RegressionDriver<Nelson,   1, 3>("Nelson.dat",   options);
+  RegressionDriver<MGH17,    1, 5>("MGH17.dat",    options);
+  RegressionDriver<Lanczos,  1, 6>("Lanczos1.dat", options);
+  RegressionDriver<Lanczos,  1, 6>("Lanczos2.dat", options);
+  RegressionDriver<Gauss,    1, 8>("Gauss3.dat",   options);
+  RegressionDriver<Misra1c,  1, 2>("Misra1c.dat",  options);
+  RegressionDriver<Misra1d,  1, 2>("Misra1d.dat",  options);
+  RegressionDriver<Roszman1, 1, 4>("Roszman1.dat", options);
+  RegressionDriver<ENSO,     1, 9>("ENSO.dat",     options);
+
+  std::cout << "\nHigher Difficulty\n";
+  RegressionDriver<MGH09,    1, 4>("MGH09.dat",    options);
+  RegressionDriver<Thurber,  1, 7>("Thurber.dat",  options);
+  RegressionDriver<BoxBOD,   1, 2>("BoxBOD.dat",   options);
+  RegressionDriver<Rat42,    1, 3>("Rat42.dat",    options);
+  RegressionDriver<MGH10,    1, 3>("MGH10.dat",    options);
+  RegressionDriver<Eckerle4, 1, 3>("Eckerle4.dat", options);
+  RegressionDriver<Rat43,    1, 4>("Rat43.dat",    options);
+  RegressionDriver<Bennet5,  1, 3>("Bennett5.dat", options);
+
+  return 0;
+};

internal/ceres/split.h

@@ -0,0 +1,21 @@
+// Copyright 2011 Google Inc. All Rights Reserved.
+// Author: keir@google.com (Keir Mierle)
+
+#ifndef CERES_INTERNAL_SPLIT_H_
+#define VISION_OPTIMIZATION_LEAST_SQUARES_INTERNAL_SPLIT_H_
+
+#include <string>
+#include <vector>
+#include "ceres/internal/port.h"
+
+namespace ceres {
+
+// Split a string using one or more character delimiters, presented as a
+// nul-terminated c string. Append the components to 'result'. If there are
+// consecutive delimiters, this function skips over all of them.
+void SplitStringUsing(const string& full, const char* delim,
+                      vector<string>* res);
+
+}  // namespace ceres
+
+#endif  // CERES_INTERNAL_SPLIT_H_