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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Ages and transit time distribution from Century
This notebook shows how to use the LAPM package to compute system level metrics for the Century model.
Step1:  In the second line above, we imported also the linear_autonomous_pool_model module which contains most of the functions required for the examples in this notebook.
We will create now a compartmental representation of Century using the original parameter values described in Parton et al. (1987).
Step2:  Other useful system diagnostics are
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Python Code:
from sympy import *
from LAPM import *
from LAPM.linear_autonomous_pool_model import LinearAutonomousPoolModel
Explanation: Ages and transit time distribution from Century
This notebook shows how to use the LAPM package to compute system level metrics for the Century model.
End of explanation
B=Matrix([[-2.927714,   0,  0,   0,  0,  0,  0.000000],
           [0, -14.560,  0,   0,  0,  0,  0],
           [0,   0, -3.6211195,   0,  0,  0,  0],
           [0,   0,  0, -18.20,  0,  0,  0],
           [1.449218, 6.552, 1.4665534, 8.19, -3.731, 0.082992,  0.003042],
           [0.204940, 0,  0.2534784,   0,  2.193828, -0.1976,  0],
           [0,   0,  0,   0,  0.014924,  0.005928, -0.006760]])
u=Matrix(7,1,[3.58800, 18.97804, 4.68, 24.75396, 0, 0, 0])
M=LinearAutonomousPoolModel(u, B, True)
M.A_expected_value
Explanation: In the second line above, we imported also the linear_autonomous_pool_model module which contains most of the functions required for the examples in this notebook.
We will create now a compartmental representation of Century using the original parameter values described in Parton et al. (1987).
End of explanation
M.A_quantile(0.5) # Median (50% quantile) of the system age distribution
M.T_expected_value #Mean transit time
M.T_quantile(0.95) # Median (50% quantile) of the transit time distribution
M.a_expected_value # Mean age vector of individual pools
M.a_quantile(0.95) # 95% quantile of individual pools
M.a_quantile(0.05) # 5% quantiles of individual pools
Explanation: Other useful system diagnostics are:
End of explanation
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