def fOdeDx(theta, x):
theta = vector(theta)
x = matrix(x)
resultDx = np.zeros(
shape=[np.shape(x)[0],
np.shape(x)[1],
np.shape(x)[1]])
P = (x[:, 0])
M = (x[:, 1])
H = (x[:, 2])
expMminusP = np.exp(M - P)
dP = -np.power(1 + np.exp(2 * P), -2) * np.exp(2 * P) * 2
resultDx[:, 0, 0] = -theta[1] * expMminusP
resultDx[:, 1, 0] = theta[1] * expMminusP
resultDx[:, 2, 0] = -theta[0] * np.exp(H)
resultDx[:, 0, 1] = theta[4] * np.multiply(np.exp(-M), dP)
resultDx[:, 1, 1] = -theta[4] * np.exp(-M) / (1 + np.exp(2 * P))
resultDx[:, 0, 2] = -theta[0] * np.exp(P) + theta[5] * np.multiply(
np.exp(-H), dP)
resultDx[:, 2, 2] = -theta[5] * np.exp(-H) / (1 + np.exp(2 * P))
return ArmaCube(resultDx.T.copy())
def fOde(theta, x):
theta = vector(theta)
x = matrix(x)
V = x[:, 0]
R = x[:, 1]
Vdt = theta[2] * (V - pow(V, 3) / 3.0 + R)
Rdt = -1.0 / theta[2] * (V - theta[0] + theta[1] * R)
result = np.stack([Vdt, Rdt], axis=1)
return ArmaMatrix(result.T.copy())
def fOdeDx(theta, x):
theta = vector(theta)
x = matrix(x)
resultDx = np.zeros(
shape=[np.shape(x)[0],
np.shape(x)[1],
np.shape(x)[1]])
V = x[:, 0]
R = x[:, 1]
resultDx[:, 0, 0] = theta[2] * (1 - np.square(V))
resultDx[:, 1, 0] = theta[2]
resultDx[:, 0, 1] = -1.0 / theta[2]
resultDx[:, 1, 1] = -1.0 * theta[1] / theta[2]
return ArmaCube(resultDx.T.copy())
def fOde(theta, x):
theta = vector(theta)
x = matrix(x)
P = np.exp(x[:, 0])
M = np.exp(x[:, 1])
H = np.exp(x[:, 2])
PMHdt = np.zeros(shape=np.shape(x))
PMHdt[:, 0] = -theta[0] * H + theta[1] * M / P - theta[2]
PMHdt[:, 1] = -theta[3] + theta[4] / (1 + np.square(P)) / M
PMHdt[:,
2] = -theta[0] * P + theta[5] / (1 +
np.square(P)) / H - theta[6]
return ArmaMatrix(PMHdt.T.copy())
def fOdeDtheta(theta, x):
theta = vector(theta)
x = matrix(x)
resultDtheta = np.zeros(
shape=[np.shape(x)[0],
np.shape(theta)[0],
np.shape(x)[1]])
V = x[:, 0]
R = x[:, 1]
resultDtheta[:, 2, 0] = V - pow(V, 3) / 3.0 + R
resultDtheta[:, 0, 1] = 1.0 / theta[2]
resultDtheta[:, 1, 1] = -R / theta[2]
resultDtheta[:, 2, 1] = 1.0 / pow(
theta[2], 2) * (V - theta[0] + theta[1] * R)
return ArmaCube(resultDtheta.T.copy())
def fOdeDtheta(theta, x):
theta = vector(theta)
x = matrix(x)
resultDtheta = np.zeros(
shape=[np.shape(x)[0],
np.shape(theta)[0],
np.shape(x)[1]])
P = (x[:, 0])
M = (x[:, 1])
H = (x[:, 2])
resultDtheta[:, 0, 0] = -np.exp(H)
resultDtheta[:, 1, 0] = np.exp(M - P)
resultDtheta[:, 2, 0].fill(-1)
resultDtheta[:, 3, 1].fill(-1)
resultDtheta[:, 4, 1] = np.exp(-M) / (1 + np.exp(2 * P))
resultDtheta[:, 0, 2] = -np.exp(P)
resultDtheta[:, 5, 2] = np.exp(-H) / (1 + np.exp(2 * P))
resultDtheta[:, 6, 2].fill(-1)
return ArmaCube(resultDtheta.T.copy())
def fOde(theta, x):
theta = vector(theta)
x = matrix(x)
return theta * x
def test_solve_fn(self):
fn_system = OdeSystem()
def fOde(theta, x):
theta = vector(theta)
x = matrix(x)
V = x[:, 0]
R = x[:, 1]
Vdt = theta[2] * (V - pow(V, 3) / 3.0 + R)
Rdt = -1.0 / theta[2] * (V - theta[0] + theta[1] * R)
result = np.stack([Vdt, Rdt], axis=1)
return ArmaMatrix(result.T.copy())
def fOdeDx(theta, x):
theta = vector(theta)
x = matrix(x)
resultDx = np.zeros(
shape=[np.shape(x)[0],
np.shape(x)[1],
np.shape(x)[1]])
V = x[:, 0]
R = x[:, 1]
resultDx[:, 0, 0] = theta[2] * (1 - np.square(V))
resultDx[:, 1, 0] = theta[2]
resultDx[:, 0, 1] = -1.0 / theta[2]
resultDx[:, 1, 1] = -1.0 * theta[1] / theta[2]
return ArmaCube(resultDx.T.copy())
def fOdeDtheta(theta, x):
theta = vector(theta)
x = matrix(x)
resultDtheta = np.zeros(
shape=[np.shape(x)[0],
np.shape(theta)[0],
np.shape(x)[1]])
V = x[:, 0]
R = x[:, 1]
resultDtheta[:, 2, 0] = V - pow(V, 3) / 3.0 + R
resultDtheta[:, 0, 1] = 1.0 / theta[2]
resultDtheta[:, 1, 1] = -R / theta[2]
resultDtheta[:, 2, 1] = 1.0 / pow(
theta[2], 2) * (V - theta[0] + theta[1] * R)
return ArmaCube(resultDtheta.T.copy())
fn_system.fOde = fOde
fn_system.fOdeDx = fOdeDx
fn_system.fOdeDtheta = fOdeDtheta
fn_system.thetaLowerBound = ArmaVector(np.array([0, 0, 0]))
fn_system.thetaUpperBound = ArmaVector(
np.array([np.inf, np.inf, np.inf]))
fn_system.name = "FN"
fn_system.thetaSize = 3
ydataV = [
-0.86, -0.26, 2.14, 1.94, 1.63, 1.75, 1.92, 1.39, 1.29, 1.59, 0.63,
0.78, -1.59, -1.92, -1.56, -1.58, -1.26, -1.34, -0.62, -0.39, 1.58,
2.29, 1.69, 1.61, 1.88, 1.57, 1.28, 1.09, 1.21, 0.1, -1.66, -2.05,
-1.55, -1.81, -1.72, -0.98, -0.77, -0.09, 1.87, 2.18, 1.67
]
ydataR = [
0.94, 0.87, 0.62, 0.44, 0.07, 0.02, -0.55, -0.09, -0.66, -0.73,
-0.73, -0.63, -0.85, -0.55, 0.01, 0.43, 0.4, 0.57, 0.64, 1.26,
1.09, 0.46, 0.13, 0.14, -0.3, -0.53, -0.5, -0.35, -1.03, -1.02,
-0.6, -0.61, -0.05, 0.31, 0.82, 0.85, 0.64, 1.31, 0.78, 0.47, 0.35
]
ydata = np.stack([np.array(ydataV), np.array(ydataR)], axis=1)
tvecFull = np.linspace(0, 20, num=81)
yFull = np.ndarray([81, 2])
yFull.fill(np.nan)
yFull[np.linspace(0, 80, num=41).astype(int), :] = ydata
result_solver = solveMagiPy(
yFull=ArmaMatrix(yFull).t(),
odeModel=fn_system,
tvecFull=ArmaVector(tvecFull),
sigmaExogenous=ArmaVector(np.ndarray(0)),
phiExogenous=ArmaMatrix(np.ndarray([0, 0])),
xInitExogenous=ArmaMatrix(np.ndarray([0, 0])),
thetaInitExogenous=ArmaVector(np.ndarray(0)),
muExogenous=ArmaMatrix(np.ndarray([0, 0])),
dotmuExogenous=ArmaMatrix(np.ndarray([0, 0])),
priorTemperatureLevel=1.0,
priorTemperatureDeriv=1.0,
priorTemperatureObs=1.0,
kernel="generalMatern",
nstepsHmc=100,
burninRatioHmc=0.5,
niterHmc=1000,
stepSizeFactorHmc=0.1,
nEpoch=1,
bandSize=20,
useFrequencyBasedPrior=True,
useBand=True,
useMean=False,
useScalerSigma=False,
useFixedSigma=False,
verbose=True)
phiUsed = matrix(result_solver.phiAllDimensions)
samplesCpp = matrix(result_solver.llikxthetasigmaSamples.slice(0))
def test_solve_hes1log(self):
hes1_system = OdeSystem()
def fOde(theta, x):
theta = vector(theta)
x = matrix(x)
P = np.exp(x[:, 0])
M = np.exp(x[:, 1])
H = np.exp(x[:, 2])
PMHdt = np.zeros(shape=np.shape(x))
PMHdt[:, 0] = -theta[0] * H + theta[1] * M / P - theta[2]
PMHdt[:, 1] = -theta[3] + theta[4] / (1 + np.square(P)) / M
PMHdt[:,
2] = -theta[0] * P + theta[5] / (1 +
np.square(P)) / H - theta[6]
return ArmaMatrix(PMHdt.T.copy())
def fOdeDx(theta, x):
theta = vector(theta)
x = matrix(x)
resultDx = np.zeros(
shape=[np.shape(x)[0],
np.shape(x)[1],
np.shape(x)[1]])
P = (x[:, 0])
M = (x[:, 1])
H = (x[:, 2])
expMminusP = np.exp(M - P)
dP = -np.power(1 + np.exp(2 * P), -2) * np.exp(2 * P) * 2
resultDx[:, 0, 0] = -theta[1] * expMminusP
resultDx[:, 1, 0] = theta[1] * expMminusP
resultDx[:, 2, 0] = -theta[0] * np.exp(H)
resultDx[:, 0, 1] = theta[4] * np.multiply(np.exp(-M), dP)
resultDx[:, 1, 1] = -theta[4] * np.exp(-M) / (1 + np.exp(2 * P))
resultDx[:, 0, 2] = -theta[0] * np.exp(P) + theta[5] * np.multiply(
np.exp(-H), dP)
resultDx[:, 2, 2] = -theta[5] * np.exp(-H) / (1 + np.exp(2 * P))
return ArmaCube(resultDx.T.copy())
def fOdeDtheta(theta, x):
theta = vector(theta)
x = matrix(x)
resultDtheta = np.zeros(
shape=[np.shape(x)[0],
np.shape(theta)[0],
np.shape(x)[1]])
P = (x[:, 0])
M = (x[:, 1])
H = (x[:, 2])
resultDtheta[:, 0, 0] = -np.exp(H)
resultDtheta[:, 1, 0] = np.exp(M - P)
resultDtheta[:, 2, 0].fill(-1)
resultDtheta[:, 3, 1].fill(-1)
resultDtheta[:, 4, 1] = np.exp(-M) / (1 + np.exp(2 * P))
resultDtheta[:, 0, 2] = -np.exp(P)
resultDtheta[:, 5, 2] = np.exp(-H) / (1 + np.exp(2 * P))
resultDtheta[:, 6, 2].fill(-1)
return ArmaCube(resultDtheta.T.copy())
hes1_system.fOde = fOde
hes1_system.fOdeDx = fOdeDx
hes1_system.fOdeDtheta = fOdeDtheta
hes1_system.thetaLowerBound = ArmaVector(
np.array([0, 0, 0, 0, 0, 0, 0]))
hes1_system.thetaUpperBound = ArmaVector(
np.array([np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf]))
hes1_system.name = "Hes1-log"
hes1_system.thetaSize = 7
ydataP = [
0.74, 0.78, 1.86, 1.86, 2.2, 1.93, 1.47, 1.03, 0.36, 0.88, 1.68,
1.97, 2.15, 1.85, 1.8, 1.47, 0.71
]
ydataM = [
0.91, 0.82, 0.71, -0.11, 0.08, -0.45, -0.05, 0.2, 0.88, 1.09, 0.3,
0.35, 0.25, -0.23, -0.51, -0.09
]
yFull = np.ndarray([33, 3])
yFull.fill(np.nan)
yFull[np.linspace(0, 32, num=17).astype(int), 0] = ydataP
yFull[np.linspace(1, 31, num=16).astype(int), 1] = ydataM
tvecFull = np.linspace(0, 240, num=33)
result_solver = solveMagiPy(
yFull=ArmaMatrix(yFull).t(),
odeModel=hes1_system,
tvecFull=ArmaVector(tvecFull),
sigmaExogenous=ArmaVector(np.array([0.15, 0.15, 0.15])),
phiExogenous=ArmaMatrix(np.ndarray([0, 0])),
xInitExogenous=ArmaMatrix(np.ndarray([0, 0])),
thetaInitExogenous=ArmaVector(np.ndarray(0)),
muExogenous=ArmaMatrix(np.ndarray([0, 0])),
dotmuExogenous=ArmaMatrix(np.ndarray([0, 0])),
priorTemperatureLevel=1.0,
priorTemperatureDeriv=1.0,
priorTemperatureObs=1.0,
kernel="generalMatern",
nstepsHmc=100,
burninRatioHmc=0.5,
niterHmc=1000,
stepSizeFactorHmc=0.1,
nEpoch=1,
bandSize=20,
useFrequencyBasedPrior=True,
useBand=True,
useMean=False,
useScalerSigma=False,
useFixedSigma=True,
verbose=True)
phiUsed = matrix(result_solver.phiAllDimensions)
samplesCpp = matrix(result_solver.llikxthetasigmaSamples.slice(0))