def checkStability(parX, parY, parZ):
xSym, x = parX
ySym, y = parY
zSym, z = parZ
# Check stability of system at a point
labX = chSymtoLabel(xSym)
labY = chSymtoLabel(ySym)
labZ = chSymtoLabel(zSym)
data = defaults
data[labX] = x
data[labY] = y
data[labZ] = z
jac = computeJac(data)
w, v = LA.eig(jac)
if np.real(max(w)) < 0:
return 'stable'
else:
return 'unstable'
# Salinity
concEvapt = 0.7
concS = 0.8
concHyd = 1
decrS = 0.5
decrPrecip = 1
evaptS = -1
evaptM = 1.5
salts = {'concEvapt':concEvapt,'concHyd':concHyd, 'concS':concS, 'decrS':decrS,
'decrPrecip':decrPrecip,'evaptS':evaptS}
defaults = {**alphas, **betas, **mangs, **peats, **salts}
def stability(eigs):
# take in vector of eigenvalues
# tell if system stable or not (stable if all eigenvalues are less than zero)
reals = np.real(eigs)
if max(reals) < 0:
result = "Stable"
else:
result = "Unstable"
return result
J = computeJac(defaults)
w, v = LA.eig(J)
print(J)
print(np.max(w))
print(stability(w))
'volGrow':volGrow,'volP':volP,'volHyd':volHyd,'volPrecip':volPrecip,'eroM':eroM,\
'subsMort':subsMort,'subsHyd':subsHyd,'subsP':subsP,'concS':concS,\
'concEvapt':concEvapt,'concHyd':concHyd,'evaptM':evaptM,'evaptS':evaptS,\
'decrS':decrS,'decrPrecip':decrPrecip,'precipBeta':precipBeta}
eigs = [] #eigenvalue triplets
eigMax = [] # max Eigenvalue list
eigsV = [] #eigenvector triplets
stab = [] #stability (0,1)
determ = [] # determinant of Jacobian
traces = [] # trace of Jacobian
fixType = []
for j in tqdm(range(n)):
dataJ = {k: v[j] for (k, v) in data.items()}
jac = computeJac(dataJ)
w, v = LA.eig(jac)
det = LA.det(jac)
tr = np.trace(jac)
j2 = np.square(jac)
lamCoff = -0.5 * (tr**2 - np.trace(j2))
eigs.append(w)
eigMax.append(np.real(np.max(w)))
eigsV.append(v)
stab.append(stability(w))
determ.append(det)
traces.append(tr)
@author: Excalibur
"""
import numpy as np
import numpy.linalg as LA
from numpy import random
import matplotlib.pyplot as plt
from parameterDefaults import defaults
from jacobianSalt import computeJac
from parameterRanges import ranges
from tqdm import tqdm
dp = 0.01
param = 'betaA'
J1 = computeJac(defaults)
w1, v = LA.eig(J1)
#perturb = defaults
#perturb[param] = defaults[param] + dp
#J2 = computeJac(perturb)
#w2, v = LA.eig(J2)
#dw2 = w2-w1
#fracPar = defaults[param]/dp
#eigSens = [fracPar*dwi for dwi in dw2]
mangs = {
'propM', 'propS', 'growM', 'growS', 'drownHyd', 'drownM', 'stressM',