CODEWITHSUNDEEP
pythonperformancenumpymatrixmultiplication
johnhenry
johnhenry

Reputation: 1333

np.dot for multiple product between 2D matrices

I have a code where I need to operate a lot of multiplications between matrices. The code is meant to be used for 2D matrices of arbitrary dimension n, which in principle could be very large, making the program very slow. So far, in order to operate the multiplications, I have always used np.dot, as in the following example

def getV(csi, e, e2, k):
    ktrans = k.transpose()
    v = np.dot(csi, ktrans)
    v = np.dot(v, e)
    v = np.dot(v, k)
    v = np.dot(v, csi)
    v = np.dot(v,  ktrans)
    e2trans = e2.transpose()
    v = np.dot(v, e2trans)
    v = np.dot(v, k)
    traceV = 2*v.trace()
    return traceV

where the output should be twice the trace of the product:

csi*ktrans*e*k*csi*ktrans*e2trans*k

(they are all matrices multiplied together). I am sure there is a faster way to make such a long product, possibly in one passage. Can someone explain how? I have tried but it seems that np.dot always needs just two matrices at any single passages.

Upvotes: 1

Views: 452

Answers (1)

user2379410
user2379410

Reputation:

Because of the properties of the trace this computation can be rewritten as follows, which reduces the number of matrix multiplications from 7 to 4:

def getV(csi, k, e, e2):
    temp = k.dot(csi).dot(k.T)
    trace_ = (temp.dot(e).dot(temp) * e2).sum()
    return 2 * trace_

Depending on your current setup, you could also try installing a different BLAS library or computing this on the graphics card instead of the CPU.

Upvotes: 3

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