Numpy linalg

How to transpose higher dimension arrays

http://jameshensman.wordpress.com/2010/06/14/multiple-matrix-multiplication-in-numpy/

Faster dot product using BLAS

http://www.huyng.com/posts/faster-numpy-dot-product/

http://stackoverflow.com/questions/5990577/speeding-up-numpy-dot

http://wiki.scipy.org/PerformanceTips

http://thread.gmane.org/gmane.comp.python.numeric.general/28135/

Multi dot

http://wiki.scipy.org/Cookbook/MultiDot

Einsum

http://chintaksheth.wordpress.com/2013/07/31/numpy-the-tricks-of-the-trade-part-ii/

http://stackoverflow.com/questions/14758283/is-there-a-numpy-scipy-dot-product-calculating-only-the-diagonal-entries-of-the

a = np.arange(4).reshape(2,2)
print a
print "np.einsum('ii', a), row i multiplied downwards"
print np.einsum('ii', a)

print "np.einsum('ij', a), same matrix ?"
print np.einsum('ij', a)

print "np.einsum('ji', a), transpose"
print np.einsum('ji', a)

print "np.einsum('ij,jk', a, a), dot product"
print np.einsum('ij,jk', a, a)
print np.dot(a, a)

Ellipsis broadcasting in numpy.einsum

http://stackoverflow.com/questions/16591696/ellipsis-broadcasting-in-numpy-einsum

http://comments.gmane.org/gmane.comp.python.numeric.general/53705

http://stackoverflow.com/questions/118370/how-do-you-use-the-ellipsis-slicing-syntax-in-python

http://stackoverflow.com/questions/772124/what-does-the-python-ellipsis-object-do

"..." Is designed to mean at this point, insert as many full slices (:) to extend the multi-dimensional slice to all dimensions.

print ""
a = np.arange(4).reshape(2,2)
print "a is"
print a
print "dot a"
print np.dot(a, a)
# Expand one axis in start, and tile up 2 times.
a2 = np.tile(a[None,:], (2, 1, 1))
print "a2 shape", a2.shape
print "einsum dot product over higher dimensions"
a2_e = np.einsum('...ij,...jk', a2, a2)
print a2_e

# Expand one axis in start, and tile up 2 times.
a3 = np.tile(a2[None,:], (2, 1, 1, 1))
print "a3 shape", a3.shape
print "einsum dot product over higher dimensions"
a3_e = np.einsum('...ij,...jk', a3, a3)
print a3_e

# With Ellipsis and axis notation
a = np.arange(4).reshape(2,2)
a = np.arange(4).reshape(2,2)
print "a is"
print a
print "dot a"
print np.dot(a, a)
# Expand one axis in start, and tile up 2 times.
a2 = np.tile(a[None,:], (2, 1, 1))
print "a2 shape", a2.shape
print "einsum dot product over higher dimensions"
a2_e = np.einsum(a2, [Ellipsis, 0, 1], a2, [Ellipsis, 1, 2])
print a2_e
 
# Expand one axis in start, and tile up 2 times.
a3 = np.tile(a2[None,:], (2, 1, 1, 1))
print "a3 shape", a3.shape
print "einsum dot product over higher dimensions"
a3_e =  np.einsum(a3, [Ellipsis, 0, 1], a3, [Ellipsis, 1, 2])
print a3_e