Object Too Deep for Desired Array - scipy.integrate.odeint

Question

I've just started with Python yesterday, and I'm getting an error using scipy.integrate.odeint.

I've defined a function

def SIR(x, t, beta, gamma, mu, M):

which takes the numpy.array objects x, t, and M; and the scalar floats beta, gamma, and mu.

M is (60,60) in size, but I don't think this matters.

x and t are both nonsingleton, with x.shape being (180,) and t.shape being (5000,). I've tried giving them a singleton dimension, such that they have shapes (180,1) and (5000,1) respectively, but I still get the same error :

In [1]: run measles_age.py
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
/Library/Frameworks/EPD64.framework/Versions/7.3/lib/python2.7/site-packages/IPython/utils/py3compat.py in execfile(fname, *where)
    173             else:
    174                 filename = fname
--> 175             __builtin__.execfile(filename, *where)

/Users/qcaudron/Documents/SIR/measles_age.py in <module>()
    111 
    112 
--> 113         x = integrate.odeint(SIR, x0, t, args=(beta, gamma, mu, M));
    114 
    115 #       plot(t, x);


/Library/Frameworks/EPD64.framework/Versions/7.3/lib/python2.7/site-packages/scipy/integrate/odepack.py in odeint(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg)
    141     output = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu,
    142                              full_output, rtol, atol, tcrit, h0, hmax, hmin,
--> 143                              ixpr, mxstep, mxhnil, mxordn, mxords)
    144     if output[-1] < 0:
    145         print _msgs[output[-1]]

I get this error even when SIR just returns x, and if I strip all arguments apart from x and t from it :

def SIR(x, t):
    return x;

As you can see, the line causing the error is

x = integrate.odeint(SIR, x0, t, args=(beta, gamma, mu, M));

EDIT :

I've been asked to add the full code for the SIR method. Because it's relatively long, I've dropped the full .py script in a pastebin : http://pastebin.com/RphJbCHN

Thanks again.

Answer 1

I can reproduce your error in several ways.

The error occurs immediately if either the y0 argument or the t argument to odeint is not a 1-D array. In the code example posted on pastebin (referred to in a comment), t is reshaped like this:

t = np.arange(0, 520, 1);
t = t.reshape(len(t),1);

Delete the line that reshapes t. t must be a 1-D array, not a 2-D array with shape (len(t), 1).

For example...

In [177]: def SIR(x, t):
   .....:     return x
   .....: 

This works...

In [178]: x0 = [0.1, 0.2]

In [179]: odeint(SIR, x0, t=[0, 0.5, 1])
Out[179]: 
array([[ 0.1       ,  0.2       ],
       [ 0.16487213,  0.32974426],
       [ 0.27182822,  0.54365643]])

This results in the error:

In [180]: x0 = [[0.1, 0.2]]  # wrong shape

In [181]: odeint(SIR, x0, t=[0, 0.5, 1])
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-181-a37878f92395> in <module>()
----> 1 odeint(SIR, x0, t=[0, 0.5, 1])

/home/warren/anaconda/lib/python2.7/site-packages/scipy/integrate/odepack.pyc in odeint(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg)
    142     output = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu,
    143                              full_output, rtol, atol, tcrit, h0, hmax, hmin,
--> 144                              ixpr, mxstep, mxhnil, mxordn, mxords)
    145     if output[-1] < 0:
    146         print _msgs[output[-1]]

ValueError: object too deep for desired array

Check that the initial condition that you give to odeint (the second argument) is a 1-D numpy array (not a 2-D array with shape (1, 180) or (180, 1)).

I also get the 'object too deep...' error if SIR returns an array with the wrong shape. It must return a 1-D array, with the same shape as its first argument. Make sure it is truly 1-D, and not 2-D with shape (1, 180) or (180, 1).

Answer 2

From the tutorial it looks like the first argument to integrate.odeint() needs to be a function to operate on (in your case) x0 and t. Since your SIR() function only takes one argument, the operation is failing. It's possible that the size and/or shape of the results returned from SIR() are important in relation to the rest of the arguments.