Bayesian Inference with PyMC3. Compilation error. - python-2.7

Question

The following two codes do a simple bayesian inference in python using PyMC3. While the first code for exponential model compiles and run perfectly fine, the second one for a simple ode model, gives an error. I do not understand why one is working and the other is not. Please help.
Code #1
import numpy as np
import pymc3 as pm
def f(a,b,x,c):
return a * np.exp(b*x)+c
#Generating Data with error
a, b = 5, 0.2
xdata = np.linspace(0, 10, 21)
ydata = f(a, b, xdata,0.5)
yerror = 5 * np.random.rand(len(xdata))
ydata += np.random.normal(0.0, np.sqrt(yerror))
model = pm.Model()
with model:
alpha = pm.Uniform('alpha', lower=a/2, upper=2*a)
beta = pm.Uniform('beta', lower=b/2, upper=2*b)
mu = f(alpha, beta, xdata,0.5)
Y_obs = pm.Normal('Y_obs', mu=mu, sd=yerror, observed=ydata)
trace = pm.sample(100, tune = 50, nchains = 1)
Code #2
import numpy as np
import pymc3 as pm
def solver(I, a, T, dt):
"""Solve u'=-a*u, u(0)=I, for t in (0,T] with steps of dt."""
dt = float(dt) # avoid integer division
N = int(round(T/dt)) # no of time intervals
print N
T = N*dt # adjust T to fit time step dt
u = np.zeros(N+1) # array of u[n] values
t = np.linspace(0, T, N+1) # time mesh
u[0] = I # assign initial condition
for n in range(0, N): # n=0,1,...,N-1
u[n+1] = (1 - a*dt)*u[n]
return np.ravel(u)
# Generating data
ydata = solver(1,1.7,10,0.1)
yerror = 5 * np.random.rand(101)
ydata += np.random.normal(0.0, np.sqrt(yerror))
model = pm.Model()
with model:
alpha = pm.Uniform('alpha', lower = 1.0, upper = 2.5)
mu = solver(1,alpha,10,0.1)
Y_obs = pm.Normal('Y_obs', mu=mu, sd=yerror, observed=ydata)
trace = pm.sample(100, nchains=1)
The error is
Traceback (most recent call last):
File "1.py", line 27, in <module>
mu = solver(1,alpha,10,0.1)
File "1.py", line 16, in solver
u[n+1] = (1 - a*dt)*u[n]
ValueError: setting an array element with a sequence.
Please help.

Answer 1

The error is in this line:
mu = solver(1,alpha,10,0.1)
You are trying to pass alpha as a value, but alpha is a pymc3 distribution. The function solver only works when you provide a number in the second argument.
The code #1 works because this function
def f(a,b,x,c):
return a * np.exp(b*x)+c
returns a number.