matrices are not aligned Error: Python SciPy fmin_bfgs

Question

Problem Synopsis: When attempting to use the scipy.optimize.fmin_bfgs minimization (optimization) function, the function throws a

derphi0 = np.dot(gfk, pk) ValueError: matrices are not aligned

error. According to my error checking this occurs at the very end of the first iteration through fmin_bfgs--just before any values are returned or any calls to callback.

Configuration: Windows Vista Python 3.2.2 SciPy 0.10 IDE = Eclipse with PyDev

Detailed Description: I am using the scipy.optimize.fmin_bfgs to minimize the cost of a simple logistic regression implementation (converting from Octave to Python/SciPy). Basically, the cost function is named cost_arr function and the gradient descent is in gradient_descent_arr function.

I have manually tested and fully verified that *cost_arr* and *gradient_descent_arr* work properly and return all values properly. I also tested to verify that the proper parameters are passed to the *fmin_bfgs* function. Nevertheless, when run, I get the ValueError: matrices are not aligned. According to the source review, the exact error occurs in the

def line_search_wolfe1 function in # Minpack's Wolfe line and scalar searches as supplied by the scipy packages.

Notably, if I use scipy.optimize.fmin instead, the fmin function runs to completion.

Exact Error:

File "D:\Users\Shannon\Programming\Eclipse\workspace\SBML\sbml\LogisticRegression.py", line 395, in fminunc_opt

optcost = scipy.optimize.fmin_bfgs(self.cost_arr, initialtheta, fprime=self.gradient_descent_arr, args=myargs, maxiter=maxnumit, callback=self.callback_fmin_bfgs, retall=True)   

File "C:\Python32x32\lib\site-packages\scipy\optimize\optimize.py", line 533, in fmin_bfgs old_fval,old_old_fval)
File "C:\Python32x32\lib\site-packages\scipy\optimize\linesearch.py", line 76, in line_search_wolfe1 derphi0 = np.dot(gfk, pk) ValueError: matrices are not aligned

I call the optimization function with: optcost = scipy.optimize.fmin_bfgs(self.cost_arr, initialtheta, fprime=self.gradient_descent_arr, args=myargs, maxiter=maxnumit, callback=self.callback_fmin_bfgs, retall=True)

I have spent a few days trying to fix this and cannot seem to determine what is causing the matrices are not aligned error.

ADDENDUM: 2012-01-08 I worked with this a lot more and seem to have narrowed the issues (but am baffled on how to fix them). First, fmin (using just fmin) works using these functions--cost, gradient. Second, the cost and the gradient functions both accurately return expected values when tested in a single iteration in a manual implementation (NOT using fmin_bfgs). Third, I added error code to optimize.linsearch and the error seems to be thrown at def line_search_wolfe1 in line: derphi0 = np.dot(gfk, pk). Here, according to my tests, scipy.optimize.optimize pk = [[ 12.00921659] [ 11.26284221]]pk type = and scipy.optimize.optimizegfk = [[-12.00921659] [-11.26284221]]gfk type = Note: according to my tests, the error is thrown on the very first iteration through fmin_bfgs (i.e., fmin_bfgs never even completes a single iteration or update).

I appreciate ANY guidance or insights.

My Code Below (logging, documentation removed): Assume theta = 2x1 ndarray (Actual: theta Info Size=(2, 1) Type = ) Assume X = 100x2 ndarray (Actual: X Info Size=(2, 100) Type = ) Assume y = 100x1 ndarray (Actual: y Info Size=(100, 1) Type = )

def cost_arr(self, theta, X, y):

    theta = scipy.resize(theta,(2,1))         

    m = scipy.shape(X)

    m = 1 / m[1] # Use m[1] because this is the length of X
    logging.info(__name__ + "cost_arr reports m = " + str(m))         

    z = scipy.dot(theta.T, X) # Must transpose the vector theta               

    hypthetax = self.sigmoid(z)

    yones = scipy.ones(scipy.shape(y))

    hypthetaxones = scipy.ones(scipy.shape(hypthetax))

    costright = scipy.dot((yones - y).T, ((scipy.log(hypthetaxones - hypthetax)).T))

    costleft = scipy.dot((-1 * y).T, ((scipy.log(hypthetax)).T))


def gradient_descent_arr(self, theta, X, y):

    theta = scipy.resize(theta,(2,1)) 

    m = scipy.shape(X)

    m = 1 / m[1] # Use m[1] because this is the length of X

    x = scipy.dot(theta.T, X) # Must transpose the vector theta

    sig = self.sigmoid(x)

    sig = sig.T - y

    grad = scipy.dot(X,sig)

    grad = m * grad

    return grad

def fminunc_opt_bfgs(self, initialtheta, X, y, maxnumit):
    myargs= (X,y)

    optcost = scipy.optimize.fmin_bfgs(self.cost_arr, initialtheta, fprime=self.gradient_descent_arr, args=myargs, maxiter=maxnumit, retall=True, full_output=True)

    return optcost

Answer 1

In case anyone else encounters this problem ....

1) ERROR 1: As noted in the comments, I incorrectly returned the value from my gradient as a multidimensional array (m,n) or (m,1). fmin_bfgs seems to require a 1d array output from the gradient (that is, you must return a (m,) array and NOT a (m,1) array. Use scipy.shape(myarray) to check the dimensions if you are unsure of the return value.

The fix involved adding:

grad = numpy.ndarray.flatten(grad)

just before returning the gradient from your gradient function. This "flattens" the array from (m,1) to (m,). fmin_bfgs can take this as input.

2) ERROR 2: Remember, the fmin_bfgs seems to work with NONlinear functions. In my case, the sample that I was initially working with was a LINEAR function. This appears to explain some of the anomalous results even after the flatten fix mentioned above. For LINEAR functions, fmin, rather than fmin_bfgs, may work better.

QED

Answer 2

As of current scipy version you need not pass fprime argument. It will compute the gradient for you without any issues. You can also use 'minimize' fn and pass method as 'bfgs' instead without providing gradient as argument.