qpcR_functions {qpcR}R Documentation

The nonlinear models implemented in qpcR

Description

A summary of all available models implemented in this package.

Usage

l5
l4
l3
b5
b4
b3
w4
w3
baro5
expGrowth 

Details

The following nonlinear models are implemented:

l5:

f(x) = c + frac{d-c}{(1+exp(b(log(x)-log(e))))^f}

l4:

f(x) = c + frac{d-c}{1+exp(b(log(x)-log(e)))}

l3:

f(x) = frac{d}{1+exp(b(log(x)-log(e)))}

b5:

f(x) = c + frac{d-c}{(1+exp(b(x-e)))^f}

b4:

f(x) = c + frac{d-c}{1+exp(b(x-e))}

b3:

f(x) = frac{d}{1+exp(b(x-e))}

w4:

f(x) = c + (d-c) exp(-exp(b(log(x)-log(e))))

w3:

f(x) = d exp(-exp(b(log(x)-log(e))))

expGrowth:

f(x) = a * exp(b * x) + c

baro5:

f(x) = c + frac{d-c}{1+fexp(b1(log(x)-log(e))) + (1-f)exp(b2(log(x)-log(e)))}

with

f = frac{1}{1 + exp((2b1b2/|b1+b2|)(log(x)-log(e)))}

The functions are defined as a list containing the following items:

$expr the function as an expression for the fitting procedure.
$fct the function defined as f(x, parm).
$ssfct the self-starter function.
$d1 the first derivative function.
$d2 the second derivative function.
$inv the inverse function.
$expr.grad the function as an expression for gradient calculation.
$inv.grad the inverse functions as an expression for gradient calculation.
$parnames the parameter names.
$name the function name.
$type the function type as a character string.

Author(s)

Andrej-Nikolai Spiess

Examples

m1 <- pcrfit(reps, 1, 2, b3)
m2 <- pcrfit(reps, 1, 2, b5)
m3 <- pcrfit(reps, 1, 2, w4)

## get the second derivative
## curve of m2
d2 <- b5$d2(m2$DATA[, 1], coef(m2))
plot(m2)
lines(d2, col = 2)  

[Package qpcR version 1.2-4 Index]