|
Electrical conductivity
of saline solutions Estimates the parameters of an equation, by fitting
to experimental data. |
|
|
| x |
|
Vector of the independent variable
values. • |
| yT |
|
Dependent variable values. • |
| Model to fit |
|
Univariate polynomial or (below) partic. function. • |
| Parameters |
|
Initial guess for parameters (if polynomial,
descending power order). • |
| Scale factors |
|
Scale factors for parameters. • |
| Criterion |
∞ (minimax)
1
2 (min. sq.)
3 |
Criterion (power of
|ycalc−y|). |
| tol, maxit, mon |
(tol = 0 ⇒ εmach) |
Tolerance, max. num. of iterations, monitoring. |
| Graph sort |
|
Graph abscissa to sort by. |
| Graph |
|
Plots the initial or final graph. • |
| Show values ? |
|
Shows the graph coordinates. |
Estimates the parameters
of an underlying equation (model), starting from the given parameter values
(initial guesses). The model is:
either, in order to make it (in this context) as general as possible,
a polynomial, y = Σi pixi−1,
i = 1..n,
with n the number of (given) parameters, in descending power order;
or a particular function,
y = p1 −
p2 ⁄ (p3 + x).
The order of the polynomial is inferred from the number of given parameters,
e.g., a parabola if three parameters are given.
The Nelder-Mead ([1965]) algorithm is used to optimize fit.
A plot is shown for the experimental
and calculated points.
The base data are of electrical conductivity
(in mS/cm, millisiemens per centimeter) vs. concentration (fraction) from
generalfitting.xlsx, giving,
e.g., for NaCl ([DiVerdi, 2016]),
P(polynom.) ≅ (-2478.73, 1506.06, 0.92) and
P(partic.) ≅ (463, 121, 0.26).
Collaboration: colleague Prof. Jorge P. Correia,
Dept. of Chemistry and
Biochemistry,
Faculty of Sciences,
University of Lisbon. |
| References: |
Plate: ElectrConductSaline |
• DiVerdi, J. A.,
2016, Electrical conductivity of aqueous solutions.pdf,
Colorado State University, Fort Collins, CO., USA (accessed Mar-2016).
• Nelder, J. A.,
R. Mead, 1965,
"A simplex method for function minimization".pdf,
The Computer Journal, 7(4): 308–313.
• Wikipedia: Molar conductivity
• 1886-03-07: Taylor, Geoffrey Ingram (1975-06-27)
(Brook Taylor; 1788, Antoine Becquerel) |
