exp_2o_decay {OptimModel}

Five-parameter second-order exponential decay, gradient, starting values, and back-calculation functions

Description

Five-parameter second-order exponential decay, gradient, starting values, and back-calculation functions.

Usage

 
        exp_2o_decay(theta, x)

Arguments

theta

Vector of five parameters: (A, B, k1, k2, p). See details.

x

Vector of concentrations.

Details

The five-parameter exponential decay model is given by:

y = A + B\times P\times \exp(-K1 \times x) + B\times (1 - P)\times \exp(-K2\times x)

The parameter vector is (A, B, k1, k2, p) where A = \min y (min y value), A+B = \max y (max y value), K1 = \exp(k1) which is the shape parameter for first term, K2 = \exp(k2) which is the shape parameter for second term, and P = 1/(1+\exp(p)) which is the proportion of signal from the first term.

Value

Let N = length(x). Then

• exp_2o_decay(theta, x) returns a numeric vector of length N.

• attr(exp_2o_decay, "gradient")(theta, x) returns an N x 5 matrix.

• attr(exp_2o_decay, "start")(x, y) returns a numeric vector of length 5 with starting values for (A, B, k1, k2, p).

• attr(exp_2o_decay, "backsolve")(theta, y) returns a numeric vector of length = length(y).

Author(s)

Steven Novick

See Also

optim_fit, rout_fitter

Examples

set.seed(123L)
x = 2^(-4:4)
theta = c(25, 75, log(3), log(1.2), 1/(1+exp(.7)))
y = exp_2o_decay(theta, x) + rnorm( length(x), mean=0, sd=1 )
attr(exp_2o_decay, "gradient")(theta, x)
attr(exp_2o_decay, "start")(x, y)
attr(exp_2o_decay, "backsolve")(theta, 38)