haar_transform, a Python code which computes the Haar transform of data.
In the simplest case, the length of the data vector X is a power of 2. We now consider consecutive pairs of entries of X, and for I from 0 to (N/2)-1, we define:
S[I] = ( X[2*I] + X[2*I+1] ) / sqrt ( 2 )
D[I] = ( X[2*I] - X[2*I+1] ) / sqrt ( 2 )
We now replace X by the vector S concatenated with D. Assuming that (N/2)
is greater than 1, we repeat the operation on the (N/2) entries of S, and
so on, until we have reached a stage where our resultant S and D each contain
one entry.
The computer code and data files described and made available on this web page are distributed under the MIT license
haar_transform is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
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