Numpy linalg
How to transpose higher dimension arrays
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
Einsum
http://chintaksheth.wordpress.com/2013/07/31/numpy-the-tricks-of-the-trade-part-ii/
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
Stride tricks
http://chintaksheth.wordpress.com/2013/07/31/numpy-the-tricks-of-the-trade-part-ii/
http://stackoverflow.com/questions/4936620/using-strides-for-an-efficient-moving-average-filter
http://www.rigtorp.se/2011/01/01/rolling-statistics-numpy.html
http://wiki.scipy.org/Cookbook/GameOfLifeStrides
http://wiki.scipy.org/Cookbook/SegmentAxis
Simple, with window 3
row, col = 3, 5
x=np.arange(row*col).reshape((row, col))
print "shape is:", x.shape
print x
window = 3
# Shape should end out in tuple.
shape = tuple([row, col - window + 1, window])
print "stride shape is:", shape
# Get strides
x_str = x.strides
print "strides is", x_str
# Get itemsize, Length of one array element in bytes. Depends on dtype. float64=8, complex128=16.
x_itz = x.itemsize
print "itemsize is", x_str
# Again, strides should be in tuple.
# Strides tuble is a way to tell, how far is to next element.
# Next element is first to next row in bytes = col * itemsize
# and then how many bytes to next element in the row.
cut_strides = tuple(list(x_str) + [x_itz])
print "cut strides are", cut_strides
cut_strides_cal = tuple([col*x_itz] + [x_itz] + [x_itz])
print "Can be calculated as [col*x_itz] + [x_itz]:", cut_strides_cal
y = as_strided(x, shape=shape, strides=cut_strides)
print y
And then
from numpy.lib.stride_tricks import as_strided
import numpy as np
NE, NS, NM, NO, ND, Row, Col = 1, 2, 2, 1, 2, 2, 2
mat = np.arange(NE*NS*NM*NO*ND*Row*Col).reshape(NE, NS, NM, NO, ND, Row, Col)
print "mat is:"
for ei in range(NE):
for si in range(NS):
for mi in range(NM):
for oi in range(NO):
for di in range(ND):
print("ei:%i, si:%i, mi:%i, oi:%i, di:%i"%(ei, si, mi, oi, di))
print(mat[ei, si, mi, oi, di])
size = mat.itemsize
print "itemsize is:"
print size
strides = mat.strides
print "strides is"
print strides