from IPython.core.display import Image 
Image(url='http://labrosa.ee.columbia.edu/crucialpython/logo.png', width=600) 

# Get our pylab mise en place going
import numpy as np
import matplotlib.pyplot as plt

# I'll make up a time series of sequential data
# 
x = np.arange(8 * 16)

# And print it
print x

frame_length = 8

x_framed = np.reshape(x, (-1, frame_length))

print x_framed

hop_length = frame_length / 2

num_frames = 1 + (len(x) - frame_length) / hop_length

x_framed_overlap = np.zeros( (num_frames, frame_length), dtype=int )

for t in range(num_frames):
    x_framed_overlap[t, :] = x[t*hop_length:t*hop_length + frame_length]
    
print x_framed_overlap

from numpy.lib import stride_tricks

# Ok, it's a linear index, so it's both F- and C-contiguous
# Next, let's see how big each item in x is.  This is provided by the `itemsize` field
print x.itemsize, x.dtype

# Now, we're ready to set up our fake frmaed data

# Each row advances by `hop_length` entries, times the number of bytes in each entry
row_stride = x.itemsize * hop_length

# Columns are still contiguous, and only advance by one entry
col_stride = x.itemsize

# as_strided will construct a new view of the data in x, using the shape and stride parameters we supply
x_framed_strided = stride_tricks.as_strided(x, 
                                            shape=(num_frames, frame_length), 
                                            strides=(row_stride, col_stride))

print x_framed_strided

# What if we want our frames vertical instead?  Just swap the row and column strides

x_framed_strided_column = stride_tricks.as_strided(x, 
                                            shape=(num_frames, frame_length), 
                                            strides=(col_stride, row_stride))

print x_framed_strided_column