Name: testsuite::test_iaf_psp_peak - test of closed form expression for peak

Synopsis:

(test_iaf_psp_peak) run -&gt; compare expression with numerics


Description:

Several NEST neuron models have an alpha-shaped post-synaptic current (PSC). 
In these models the PSC is normalized to unit amplitude. Thus, a synaptic weight 
w leads to a PSC with amplitude w in units of pA. 
In order to adjust the amplitude of the post-synaptic potential (PSP) of a 
neuron model with an alpha-shaped post-synaptic current (PSC) to a particular 
amplitude we need to first find the location of the maximum tmax of the PSP. 
Here, this is done in two different ways: 
1. We numerically search for the root of the derivative of the PSP 
2. We used a closed form expression to compute the position of the maximum 
The test verifies that the methods lead to the same result. The test file 
test_iaf_psp_normalized shows how this value is used to specify w such that a 
PSP with a desired amplitude u in units of mV results. 
The closed form expression can be found by first transforming the expression 
d psp(t) / dt = 0 
into the normal form 
exp(s) = 1 + a * s, 
where s is the scaled time s=bt and a and b depend on the time constants 
a = tau_m/tau_alpha, b = 1/tau_alpha - 1/tau_m . 
The solution for s can then be expressed with the help of the Lambert W-function W 
which is the inverse of x=W*exp(W) and reads 
s = 1/a * ( -a W(-exp(-1/a)/a) - 1 )


References:

[1] Weisstein, Lambert W-function


Author:

July 2009, Diesmann


SeeAlso:

testsuite::test_lambertw
testsuite::test_iaf_psp_normalized
LambertWm1

Source:

/var/www/debian/nest/nest-simulator-2.20.0/testsuite/unittests/test_iaf_psp_peak.sli
