get_lb
Obtains scaled length at birth, given the scaled reserve density at birth
Contents
Syntax
[lb, info] = get_lb(p, eb, lb0)
Description
Obtains scaled length at birth, given the scaled reserve density at birth.
Input
- p: 3-vector with parameters: g, k, v_H^b (see below)
- eb: optional scalar with scaled reserve density at birth (default eb = 1)
- lb0: optional scalar with initial estimate for scaled length at birth (default lb0: lb for k = 1)
Output
- lb: scalar with scaled length at birth
- info: indicator equals 1 if successful, 0 otherwise
Remarks
The theory behind get_lb, get_tb and get_ue0 is discussed in Kooy2009b. Solves y(x_b) = y_b for lb with explicit solution for y(x) y(x) = x e_H/(1-kap) = x g u_H/ l^3 and y_b = x_b g u_H^b/ ((1-kap)l_b^3) d/dx y = r(x) - y s(x); with solution y(x) = v(x) \int r(x)/ v(x) dx and v(x) = exp(- \int s(x) dx). A Newton Raphson scheme is used with Euler integration, starting from an optional initial value. Replacement of Euler integration by ode23: get_lb1, but that function is much lower. Shooting method: get_lb2. Bisection method (via fzero): get_lb3. In case of no convergence, get_lb2 is run automatically as backup. Consider the application of get_lb_foetus for an alternative initial value.
Example of use
See mydata_ue0