Short Notes on Wavelets - Revision history

Admin: /* numpy Version */

2017-02-27T11:11:09Z

‎numpy Version

Admin at 11:09, 27 February 2017

2017-02-27T11:09:14Z

Admin at 09:50, 27 February 2017

2017-02-27T09:50:34Z

Admin: /* Integer Haar Wavelets, Python implementation */

2017-02-24T15:02:56Z

‎Integer Haar Wavelets, Python implementation

Admin: /* Using numpy array's */

2017-02-24T15:01:44Z

‎Using numpy array's

Admin: Undo revision 296 by Admin (talk)

2017-02-24T14:14:39Z

Undo revision 296 by Admin (talk)

Admin: /* Integer Haar Wavelets, Python implementation */

2017-02-24T14:11:43Z

‎Integer Haar Wavelets, Python implementation

Admin: Created page with "== Integer Haar Wavelets, Python implementation == This is a trivial implementation of Haar integer-to-integer wavelets. Note that resulting values typically use 1 more bit t..."

2017-02-24T13:14:45Z

Created page with "== Integer Haar Wavelets, Python implementation == This is a trivial implementation of Haar integer-to-integer wavelets. Note that resulting values typically use 1 more bit t..."

New page

== Integer Haar Wavelets, Python implementation ==

This is a trivial implementation of Haar integer-to-integer wavelets.
Note that resulting values typically use 1 more bit than original ones - if source values are in [0..N) interval, then resulting values are in (-N, N) interval.

=== Using Lists ===

<pre>def haar_int_fwd_1d(d):
if len(d) == 1:
return d
even = d[::2]
odd = d[1::2]
hp = [j - i for i, j in zip(even, odd)]
lp = [i + (w >> 1) + (w % 2) for i, w in zip(even, hp)]
return haar_int_fwd_1d(lp) + hp

def haar_int_inv_1d(d):
if len(d) == 1:
return d
even = haar_int_inv_1d(d[:len(d) >> 1])
odd = d[len(d) >> 1:]
lp = [i - (j >> 1) - (j % 2) for i, j in zip(even, odd)]
hp = [i + j for i, j in zip(lp, odd)]
return [x for t in zip(lp, hp) for x in t]</pre>

=== Using numpy array's ===

TBP

← Older revision		Revision as of 11:11, 27 February 2017
Line 57:		Line 57:

	==== numpy Version ====		==== numpy Version ====
		+
		+	This is highly '''un'''-optimized - it creates copy for each step of transformation, and both directions of transformation use ''np.apply_along_axis'', which I suspect builds the new array row by row.
		+
		+	Both versions could be parallelised and made into in-place transforms. Enjoy!

	<pre>def haar_int_fwd_2d_np(d):		<pre>def haar_int_fwd_2d_np(d):

@@ Line 1: / Line 1: @@
 == Integer Haar Wavelets, Python implementation ==
 === 1D Case ===
@@ Line 54: / Line 58: @@
 ==== numpy Version ====
-TBP
+<pre>def haar_int_fwd_2d_np(d):

@@ Line 1: / Line 1: @@
 == Integer Haar Wavelets, Python implementation ==
 This is a trivial implementation of Haar integer-to-integer wavelets.
@@ Line 7: / Line 9: @@
 Note that resulting values typically use 1 more bit than original ones - if source values are in [0..N) interval, then resulting values are in (-N, N) interval.
-=== Using Lists ===
+==== Using Lists ====
 <pre>def haar_int_fwd_1d(d):
@@ Line 27: / Line 29: @@
      return [x for t in zip(lp, hp) for x in t]</pre>
-=== Using numpy array's ===
+==== Using numpy Array's ====
 <pre>import numpy as np
@@ Line 45: / Line 47: @@
      even = lp - (hp >> 1) - (hp % 2)
      return np.ravel(np.column_stack((even, even + hp)))</pre>

← Older revision		Revision as of 15:01, 24 February 2017
Line 26:		Line 26:
	=== Using numpy array's ===		=== Using numpy array's ===

−	~~TBP~~	+	<pre>def haar_int_fwd_1d_np(d):
		+	if len(d) == 1:
		+	return d
		+	hp = d[1::2] - d[::2]
		+	lp = d[::2] + (hp >> 1) + (hp % 2)
		+	return np.concatenate((haar_int_fwd_1d_np(lp), hp))
		+
		+	def haar_int_inv_1d_np(d):
		+	if len(d) == 1:
		+	return d
		+	lp = haar_int_inv_1d_np(d[:len(d) >> 1])
		+	hp = d[len(d) >> 1:]
		+	even = lp - (hp >> 1) - (hp % 2)
		+	return np.ravel(np.column_stack((even, even + hp)))</pre>

@@ Line 2: / Line 2: @@
 This is a trivial implementation of Haar integer-to-integer wavelets.
 Note that resulting values typically use 1 more bit than original ones - if source values are in [0..N) interval, then resulting values are in (-N, N) interval.
@@ Line 26: / Line 29: @@
 === Using numpy array's ===
-<pre>def haar_int_fwd_1d_np(d):
+<pre>import numpy as np
      if len(d) == 1:
          return d