# Eckerle4: Circular interference data In NISTnls: Nonlinear least squares examples from NIST

## Description

The `Eckerle4` data frame has 35 rows and 2 columns giving transmittance as a function of wavelength.

## Format

This data frame contains the following columns:

y

A numeric vector of transmittance values.

x

A numeric vector of wavelengths.

## Details

These data are the result of a NIST study involving circular interference transmittance. The response variable is transmittance, and the predictor variable is wavelength.

## Source

Eckerle, K., NIST (197?). Circular Interference Transmittance Study.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val plot(y ~ x, data = Eckerle4) ## should fail - ridiculous starting value for b3 Try(fm1 <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, start = c(b1 = 1, b2 = 10, b3 = 500))) Try(fm1a <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, alg = "port", start = c(b1 = 1, b2 = 10, b3 = 500))) Try(fm2 <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, start = c(b1 = 1.5, b2 = 5, b3 = 450))) Try(fm2a <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, alg = "port", start = c(b1 = 1.5, b2 = 5, b3 = 450))) ## should fail - ridiculous starting value for b3 Try(fm3 <- nls(y ~ (1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, start = c(b2 = 10, b3 = 500), algorithm = "plinear")) Try(fm4 <- nls(y ~ (1/b2) * exp(-0.5*((x-b3)/b2)**2), Eckerle4, trace = TRUE, start = c(b2 = 5, b3 = 450), algorithm = "plinear")) ```

### Example output

```0.7223027 :    1  10 500
0.6999249 :    0.1164977  11.0440477 501.1919978
0.6948258 :    0.4043154  42.0375222 542.3624023
0.6935116 :    165.3319  7018.9224 17639.7963
Error in nls(y ~ (b1/b2) * exp(-0.5 * ((x - b3)/b2)^2), Eckerle4, trace = TRUE,  :
0:    0.36115133:  1.00000  10.0000  500.000
1:    0.34996243: 0.116498  11.0440  501.192
2:    0.34741292: 0.404315  42.0375  542.362
3:    0.29959768:  4.02960  179.578  421.407
4:    0.24739017:  12.0880  160.021  435.036
5:    0.24689459:  7.53998  97.9094  499.076
6:    0.24313543:  7.64688  92.2972  478.023
7:    0.24140992:  6.99697  83.0422  467.618
8:    0.23611339:  5.68742  63.2372  457.585
9:    0.12266011:  1.70829  10.8485  449.406
10:   0.084419610:  1.71448  8.87144  451.281
11:  0.0015330945:  1.60921  4.00755  451.545
12: 0.00073236009:  1.55375  4.08248  451.545
13: 0.00073179610:  1.55432  4.08852  451.541
14: 0.00073179437:  1.55438  4.08883  451.541
15: 0.00073179437:  1.55438  4.08883  451.541
Nonlinear regression model
model: y ~ (b1/b2) * exp(-0.5 * ((x - b3)/b2)^2)
data: Eckerle4
b1      b2      b3
1.554   4.089 451.541
residual sum-of-squares: 0.001464

Algorithm "port", convergence message: X-convergence (3)
0.05668291 :    1.5   5.0 450.0
0.00722609 :    1.563149   4.374689 451.974368
0.001525831 :    1.551040   4.091636 451.488425
0.001463731 :    1.554819   4.091467 451.541251
0.001463589 :    1.554395   4.088899 451.541108
0.001463589 :    1.554384   4.088839 451.541216
0.001463589 :    1.554383   4.088832 451.541218
Nonlinear regression model
model: y ~ (b1/b2) * exp(-0.5 * ((x - b3)/b2)^2)
data: Eckerle4
b1      b2      b3
1.554   4.089 451.541
residual sum-of-squares: 0.001464

Number of iterations to convergence: 6
Achieved convergence tolerance: 1.39e-06
0:   0.028341454:  1.50000  5.00000  450.000
1:  0.0036130449:  1.56315  4.37469  451.974
2: 0.00076291557:  1.55104  4.09164  451.488
3: 0.00073186561:  1.55482  4.09147  451.541
4: 0.00073179454:  1.55440  4.08890  451.541
5: 0.00073179437:  1.55438  4.08884  451.541
6: 0.00073179437:  1.55438  4.08883  451.541
Nonlinear regression model
model: y ~ (b1/b2) * exp(-0.5 * ((x - b3)/b2)^2)
data: Eckerle4
b1      b2      b3
1.554   4.089 451.541
residual sum-of-squares: 0.001464

Algorithm "port", convergence message: X-convergence (3)
0.6996961 :  1.000000e+01 5.000000e+02 2.599947e-03
0.699693 :   13.12231111 503.56476809   0.01632532
0.6996754 :   15.27996998 506.99922176   0.05166793
0.6995764 :   18.1827590 512.4698443   0.1679627
0.6990543 :   22.7767103 522.8167482   0.6327205
0.6963754 :   31.677045 547.551144   3.657081
0.6809651 :   56.14726 636.40852  87.57622
0.5864412 :     187.1014   1319.3595 374236.3999
0.5102738 :  -1.627890e+03 -1.597383e+04 -1.485301e+24
0.4985389 :  2.539069e+06 5.125588e+07 5.923357e+93
Error in nls(y ~ (1/b2) * exp(-0.5 * ((x - b3)/b2)^2), Eckerle4, trace = TRUE,  :
0.05086068 :    5.00000 450.00000   1.65696
0.004539377 :    4.471095 451.669974   1.621837
0.001478679 :    4.085508 451.514686   1.553734
0.001463615 :    4.089948 451.541333   1.554595
0.001463589 :    4.088856 451.541172   1.554387
0.001463589 :    4.088835 451.541217   1.554383
0.001463589 :    4.088832 451.541218   1.554383
Nonlinear regression model
model: y ~ (1/b2) * exp(-0.5 * ((x - b3)/b2)^2)
data: Eckerle4
b2      b3    .lin
4.089 451.541   1.554
residual sum-of-squares: 0.001464

Number of iterations to convergence: 6
Achieved convergence tolerance: 1.28e-06
```

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