Roszman1: Quantum defects in iodine

In NISTnls: Nonlinear least squares examples from NIST

Description

The Roszman1 data frame has 25 rows and 2 columns of data on the number of quantum defects in iodine atoms at different energy states.

Format

This data frame contains the following columns:

y

A numeric vector of number of quantum defects.

x

A numeric vector of the excited energy state.

Details

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.

Source

Roszman, L., NIST (19??). Quantum Defects for Sulfur I Atom.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Roszman1)
Try(fm1 <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1,
           start = c(b1 = 0.1, b2 = -0.00001, b3 = 1000, b4 = -100),
           trace = TRUE))
Try(fm1a <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1,
           start = c(b1 = 0.1, b2 = -0.00001, b3 = 1000, b4 = -100),
           alg = "port", trace = TRUE))
Try(fm2 <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1,
           start = c(b1 = 0.2, b2 = -0.0000015, b3 = 1200, b4 = -150),
           trace = TRUE))
Try(fm2a <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1,
           start = c(b1 = 0.2, b2 = -0.0000015, b3 = 1200, b4 = -150),
           alg = "port", trace = TRUE))

Example output

0.5108107 :   1e-01 -1e-05  1e+03 -1e+02
0.000652679 :   2.057271e-01 -6.797293e-06  1.197851e+03 -1.498035e+02
0.0004948839 :   2.018532e-01 -6.180853e-06  1.205227e+03 -1.816681e+02
0.0004948485 :   2.019636e-01 -6.194580e-06  1.204477e+03 -1.813535e+02
0.0004948485 :   2.019685e-01 -6.195334e-06  1.204456e+03 -1.813429e+02
Nonlinear regression model
  model: y ~ b1 - b2 * x - atan(b3/(x - b4))/pi
   data: Roszman1
        b1         b2         b3         b4 
 2.020e-01 -6.195e-06  1.204e+03 -1.813e+02 
 residual sum-of-squares: 0.0004948

Number of iterations to convergence: 4 
Achieved convergence tolerance: 1.326e-06
  0:    0.25540537: 0.100000 -1.00000e-05  1000.00 -100.000
  1: 0.00032633951: 0.205727 -6.79729e-06  1197.85 -149.804
  2: 0.00024744197: 0.201853 -6.18085e-06  1205.23 -181.668
  3: 0.00024742424: 0.201964 -6.19458e-06  1204.48 -181.353
  4: 0.00024742424: 0.201969 -6.19533e-06  1204.46 -181.343
  5: 0.00024742424: 0.201969 -6.19535e-06  1204.46 -181.343
Nonlinear regression model
  model: y ~ b1 - b2 * x - atan(b3/(x - b4))/pi
   data: Roszman1
        b1         b2         b3         b4 
 2.020e-01 -6.195e-06  1.204e+03 -1.813e+02 
 residual sum-of-squares: 0.0004948

Algorithm "port", convergence message: relative convergence (4)
0.002608273 :   2.0e-01 -1.5e-06  1.2e+03 -1.5e+02
0.0004948902 :   2.018432e-01 -6.178783e-06  1.205202e+03 -1.817592e+02
0.0004948485 :   2.019638e-01 -6.194623e-06  1.204476e+03 -1.813527e+02
0.0004948485 :   2.019685e-01 -6.195331e-06  1.204456e+03 -1.813430e+02
Nonlinear regression model
  model: y ~ b1 - b2 * x - atan(b3/(x - b4))/pi
   data: Roszman1
        b1         b2         b3         b4 
 2.020e-01 -6.195e-06  1.204e+03 -1.813e+02 
 residual sum-of-squares: 0.0004948

Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.416e-06
  0:  0.0013041367: 0.200000 -1.50000e-06  1200.00 -150.000
  1: 0.00024744510: 0.201843 -6.17878e-06  1205.20 -181.759
  2: 0.00024742424: 0.201964 -6.19462e-06  1204.48 -181.353
  3: 0.00024742424: 0.201969 -6.19533e-06  1204.46 -181.343
  4: 0.00024742424: 0.201969 -6.19535e-06  1204.46 -181.343
Nonlinear regression model
  model: y ~ b1 - b2 * x - atan(b3/(x - b4))/pi
   data: Roszman1
        b1         b2         b3         b4 
 2.020e-01 -6.195e-06  1.204e+03 -1.813e+02 
 residual sum-of-squares: 0.0004948

Algorithm "port", convergence message: relative convergence (4)

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