### * Completing jskip formula for LD that is analogous to the jskip formula for

`UD matrix format.`
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commit d04ea8cbea
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math/symmetrix-array-index.PY

#### 24 math/symmetrix-array-index.PY Unescape Escape View File

 `@ -40,6 +40,28 @@ Note:` ` {m}` ` SUM a = 1 + 2 + ... + m = m(m+1)/2` ` {a=1}` `"""` ``` ``` `"""` `Update 20120124: the jskip formula can be written in similar fashion to` `the 'UD' array format, as shown below.` ``` ``` `The endpoint of the array index is N(N+1)/2 .` `The (negative) offset of the j index from the rightmost column is` `dj = (N + 1 - j).` `Note: dj is 1 on the rightmost column.` ``` ``` `So, the jskip is given by:` ``` ``` `N(N+1)/2 - (N+1-j)(N+2-j) / 2 =` ` = [ N**2 + N - ( N**2 + 3N - 2jN + 2 - 3j + j**2 ) ] / 2` ` = ( -2N + 2jN - 2 + 3j - j**2 ) / 2` ` = (j-1)N + (j-2)(j-1)/2` ` >>> the same formula as before.` ``` ``` ``` ``` ``` ``` ``` ``` `"""` ``` ``` `import numpy` `@ -175,7 +197,7 @@ def Hack2_LD_enc_dec(N):` ` #print "%3d %3d | %6d | %3d %3d" % (i,j, ij, ii,jj)` ` print "%3d %3d | %6d %6d | %3d %3d // %8.4f" % (` ` i,j,` ` ij, LDsize-ij,` ` ij, (LDsize-ij) * 2,` ` ii,jj,` ` jj2)` ``` ```
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