Bennett5: Magentization modelling

In NISTnls: Nonlinear least squares examples from NIST

Description

The Bennett5 data frame has 154 rows and 2 columns of data from a magnetism study

Format

This data frame contains the following columns:

y

A numeric vector of magnetism values.

x

A numeric vector of log(time).

Details

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.

Source

Bennett, L., L. Swartzendruber, and H. Brown, NIST (1994). Superconductivity Magnetization Modeling.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Bennett5)
Try(fm1 <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5,
           start = c(b1 = -2000, b2 = 50, b3 = 0.8), trace = TRUE))
Try(fm1a <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5,
            start = c(b1 = -2000, b2 = 50, b3 = 0.8),
            trace = TRUE, alg = "port"))
Try(fm2 <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5,
           start = c(b1 = -1500, b2 = 45, b3 = 0.85), trace = TRUE))
Try(fm2a <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5,
            start = c(b1 = -1500, b2 = 45, b3 = 0.85),
            trace = TRUE, alg = "port"))
Try(fm3 <- nls(y ~ (b2+x)**(-1/b3), data = Bennett5, alg = "plinear",
           start = c( b2 = 50, b3 = 0.8), trace = TRUE))
Try(fm4 <- nls(y ~ (b2+x)**(-1/b3), data = Bennett5, alg = "plinear",
           start = c( b2 = 45, b3 = 0.8), trace = TRUE))

Example output

66022.45 :  -2e+03  5e+01  8e-01
15070.79 :  -696.188200   39.536827    1.144233
13459.72 :  -975.921572   41.883626    1.060434
11048.03 :  -1557.767158    45.073532     0.965179
1090.707 :  -2476.2346373    47.2667033     0.9201458
1.167839 :  -2516.1714512    46.6856866     0.9331823
0.000529635 :  -2523.3306699    46.7358712     0.9321957
0.0005240474 :  -2523.5169447    46.7366113     0.9321841
0.0005240474 :  -2523.502634    46.736551     0.932185
Nonlinear regression model
  model: y ~ b1 * (b2 + x)^(-1/b3)
   data: Bennett5
        b1         b2         b3 
-2523.5026    46.7366     0.9322 
 residual sum-of-squares: 0.000524

Number of iterations to convergence: 8 
Achieved convergence tolerance: 4.012e-06
  0:     33011.223: -2000.00  50.0000 0.800000
  1:     14207.092: -2337.05  42.7368 0.827049
  2:     14207.092: -2337.05  42.7368 0.827049
Error in nls(y ~ b1 * (b2 + x)^(-1/b3), data = Bennett5, start = c(b1 = -2000,  : 
  Convergence failure: false convergence (8)
57261.11 :  -1500.00    45.00     0.85
18191.49 :  -1914.654709    46.493945     1.070183
4.648938 :  -2117.5640555    45.8934937     0.9665484
4.529583 :  -2208.9330851    46.1001463     0.9577597
3.582768 :  -2281.6890728    46.2571880     0.9512474
2.630016 :  -2395.7790118    46.4946406     0.9415788
0.5043595 :  -2520.0216816    46.7360151     0.9320999
0.0005241062 :  -2523.4457988    46.7363146     0.9321891
0.0005240474 :  -2523.4725416    46.7364253     0.9321871
Nonlinear regression model
  model: y ~ b1 * (b2 + x)^(-1/b3)
   data: Bennett5
        b1         b2         b3 
-2523.4725    46.7364     0.9322 
 residual sum-of-squares: 0.000524

Number of iterations to convergence: 8 
Achieved convergence tolerance: 1.813e-06
  0:     28630.553: -1500.00  45.0000 0.850000
  1:     8882.2925: -2486.75  50.0783  1.01525
  2:     52.713095: -2178.15  45.9727 0.967433
  3:     17.038030: -2481.50  46.6935 0.932474
  4: 0.00035721769: -2523.50  46.7372 0.932180
  5: 0.00026202372: -2523.51  46.7366 0.932184
  6: 0.00026202372: -2523.50  46.7365 0.932186
  7: 0.00026202372: -2523.50  46.7365 0.932186
  8: 0.00026202372: -2523.50  46.7365 0.932186
  9: 0.00026202372: -2523.50  46.7365 0.932186
 10: 0.00026202372: -2523.50  46.7365 0.932186
Nonlinear regression model
  model: y ~ b1 * (b2 + x)^(-1/b3)
   data: Bennett5
        b1         b2         b3 
-2523.4958    46.7365     0.9322 
 residual sum-of-squares: 0.000524

Algorithm "port", convergence message: relative convergence (4)
0.5338162 :     50.000     0.800 -5550.004
0.01664294 :     46.2295866     0.9240461 -2597.4015615
0.0005268716 :     46.7023795     0.9325219 -2517.9434283
0.0005240474 :     46.7364600     0.9321863 -2523.4838167
0.0005240474 :     46.7365378     0.9321853 -2523.4993972
Nonlinear regression model
  model: y ~ (b2 + x)^(-1/b3)
   data: Bennett5
        b2         b3       .lin 
   46.7365     0.9322 -2523.4994 
 residual sum-of-squares: 0.000524

Number of iterations to convergence: 4 
Achieved convergence tolerance: 4.522e-07
2.075439 :     45.000     0.800 -4989.565
0.04921469 :     44.4445272     0.9418989 -2311.5374878
0.0005970986 :     46.5181967     0.9346334 -2484.8221569
0.000524054 :     46.7350160     0.9321995 -2523.2609288
0.0005240474 :     46.7365775     0.9321846 -2523.5088730
Nonlinear regression model
  model: y ~ (b2 + x)^(-1/b3)
   data: Bennett5
        b2         b3       .lin 
   46.7366     0.9322 -2523.5089 
 residual sum-of-squares: 0.000524

Number of iterations to convergence: 4 
Achieved convergence tolerance: 1.039e-06

NISTnls documentation built on May 2, 2019, 2:37 a.m.