Testing similarity of several datasets by producing a cross-correlation matrix

I am trying to compare several datasets and basically test, if they show the same feature, although this feature might be shifted, reversed or attenuated.
A very simple example below:

A = np.array([0., 0, 0, 1., 2., 3., 4., 3, 2, 1, 0, 0, 0])
B = np.array([0., 0, 0, 0, 0, 1, 2., 3., 4, 3, 2, 1, 0])
C = np.array([0., 0, 0, 1, 1.5, 2, 1.5, 1, 0, 0, 0, 0, 0])
D = np.array([0., 0, 0, 0, 0, -2, -4, -2, 0, 0, 0, 0, 0])
x = np.arange(0,len(A),1)

I thought the best way to do it would be to normalize these signals and get absolute values (their attenuation is not important for me at this stage, I am interested in the position… but I might be wrong, so I will welcome thoughts about this concept too) and calculate the area where they overlap. I am following up on this answer – the solution looked very elegant and simple, but I may be implementing it wrongly.

def normalize(sig):
    #ns = sig/max(np.abs(sig))
    ns = sig/sum(sig)
    return ns
a = normalize(A)
b = normalize(B)
c = normalize(C)
d = normalize(D)

which then look like this:

But then, when I try to implement the solution from the answer, I run into problems.

OLD

for c1,w1 in enumerate([a,b,c,d]):
    for c2,w2 in enumerate([a,b,c,d]):
        w1 = np.abs(w1)
        w2 = np.abs(w2)
        M[c1,c2] = integrate.trapz(min(np.abs(w2).any(),np.abs(w1).any()))
print M

Produces TypeError: 'numpy.bool_' object is not iterable or IndexError: list assignment index out of range. But I only included the .any() because without them, I was getting the ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all().

EDIT – NEW
(thanks @Kody King)

The new code is now:

M = np.zeros([4,4])
SH = np.zeros([4,4])
for c1,w1 in enumerate([a,b,c,d]):
    for c2,w2 in enumerate([a,b,c,d]):
        crossCorrelation = np.correlate(w1,w2, 'full')
        bestShift = np.argmax(crossCorrelation)

        # This reverses the effect of the padding.
        actualShift = bestShift - len(w2) + 1
        similarity = crossCorrelation[bestShift]

        M[c1,c2] = similarity
        SH[c1,c2] = actualShift
M = M/M.max()
print M, 'n', SH

And the output:

[[ 1.          1.          0.95454545  0.63636364]
 [ 1.          1.          0.95454545  0.63636364]
 [ 0.95454545  0.95454545  0.95454545  0.63636364]
 [ 0.63636364  0.63636364  0.63636364  0.54545455]] 
[[ 0. -2.  1.  0.]
 [ 2.  0.  3.  2.]
 [-1. -3.  0. -1.]
 [ 0. -2.  1.  0.]]

The matrix of shifts looks ok now, but the actual correlation matrix does not. I am really puzzled by the fact that the lowest correlation value is for correlating d with itself. What I would like to achieve now is that:

---

EDIT – UPDATE

Following on the advice, I used the recommended normalization formula (dividing the signal by its sum), but the problem wasn’t solved, just reversed. Now the correlation of d with d is 1, but all the other signals don’t correlate with themselves.

New output:

[[ 0.45833333  0.45833333  0.5         0.58333333]
 [ 0.45833333  0.45833333  0.5         0.58333333]
 [ 0.5         0.5         0.57142857  0.66666667]
 [ 0.58333333  0.58333333  0.66666667  1.        ]] 
[[ 0. -2.  1.  0.]
 [ 2.  0.  3.  2.]
 [-1. -3.  0. -1.]
 [ 0. -2.  1.  0.]]

---

1. The correlation value should be highest for correlating a signal with itself (i.e. to have the highest values on the main diagonal).
2. To get the correlation values in the range between 0 and 1, so as a result, I would have 1s on the main diagonal and other numbers (0.x) elsewhere.

I was hoping the M = M/M.max() would do the job, but only if condition no. 1 is fulfilled, which it currently isn’t.