POTE tuning: Difference between revisions

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# Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is "weighted" by dividing through by the logarithms, so that V = [{{val|1 0 2/log2(5) -1/log2(7)}}, {{val|5/log2(3) 1/log2(5) 12/log2(7)}}]

# Find the matrix P = V*(VV*)^(-1~~), where V* is the transpose matrix~~.

# Find the matrix P = VT(VVT)-1.

# Find T = {{val|1 1 1 1}}P.

# Find the TE = {{val|1 1 1 1}}P.

# Find POTE = T/~~T[1]~~; in other words T scalar divided by ~~T[1], the first element of T~~.

# Find the TE octave: OTE = (TE*V)1, that is, the first entry of TE*V.

# Find the POTE = TE/OTE; in other words TE scalar divided by OTE.

If you carry out these operations, you should find

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* V ~ [{{val|1 0 0.861 -0.356}}, {{val|0 3.155 0.431 4.274}}]

* T ~ {{val|1.000902 0.317246}}

* TE ~ {{val|1.000902 0.317246}}

* POTE ~ {{val|1 0.3169600}}

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 # Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is "weighted" by dividing through by the logarithms, so that V = [{{val|1 0 2/log2(5) -1/log2(7)}}, {{val|5/log2(3) 1/log2(5) 12/log2(7)}}]
-# Find the matrix P = V*(VV*)^(-1), where V* is the transpose matrix.
+# Find the matrix P = V<sup>T</sup>(VV<sup>T</sup>)<sup>-1</sup>.
-# Find T = {{val|1 1 1 1}}P.
+# Find the TE = {{val|1 1 1 1}}P.
-# Find POTE = T/T[1]; in other words T scalar divided by T[1], the first element of T.
+# Find the TE octave: O<sub>TE</sub> = (TE*V)<sub>1</sub>, that is, the first entry of TE*V.
+# Find the POTE = TE/O<sub>TE</sub>; in other words TE scalar divided by O<sub>TE</sub>.
 If you carry out these operations, you should find
@@ Line 12: / Line 13: @@
 * V ~ [{{val|1 0 0.861 -0.356}}, {{val|0 3.155 0.431 4.274}}]
-* T ~ {{val|1.000902 0.317246}}
+* TE ~ {{val|1.000902 0.317246}}
 * POTE ~ {{val|1 0.3169600}}