Add reverse haar wavelet transform and tests

extra/math/haar/authors.txt

@@ -0,0 +1,2 @@
+Slava Pestov
+Aaron Schaefer

extra/math/haar/haar-tests.factor

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+USING: math.haar tools.test ;
+IN: math.haar.tests
+
+[ { 3 2 -1 -2 3 0 4 1 } ] [ { 7 1 6 6 3 -5 4 2 } haar ] unit-test
+[ { 7 1 6 6 3 -5 4 2 } ] [ { 3 2 -1 -2 3 0 4 1 } rev-haar ] unit-test

extra/math/haar/haar.factor

@@ -1,15 +1,30 @@
-! Haar wavelet transform -- http://dmr.ath.cx/gfx/haar/
-USING: sequences math kernel splitting grouping columns ;
+! Copyright (c) 2008 Slava Pestov, Aaron Schaefer.
+! See http://factorcode.org/license.txt for BSD license.
+USING: assocs columns grouping kernel math math.statistics math.vectors
+    sequences ;
 IN: math.haar
 
+! Haar Wavelet Transform -- http://dmr.ath.cx/gfx/haar/
+
+<PRIVATE
+
 : averages ( seq -- seq )
-    [ first2 + 2 / ] map ;
+    [ mean ] map ;
 
 : differences ( seq averages -- differences )
-    >r 0 <column> r> [ - ] 2map ;
+    [ 0 <column> ] dip v- ;
 
 : haar-step ( seq -- differences averages )
     2 group dup averages [ differences ] keep ;
 
+: rev-haar-step ( seq -- seq )
+    halves [ v+ ] [ v- ] 2bi zip concat ;
+
+PRIVATE>
+
 : haar ( seq -- seq )
     dup length 1 <= [ haar-step haar prepend ] unless ;
+
+: rev-haar ( seq -- seq )
+    dup length 2 > [ halves swap rev-haar prepend ] when rev-haar-step ;
+