I have the following:
n = 3;
m = 5;
ww = RandomReal[{0, 0.1}, {n, n}];
uu = RandomReal[{0, 1}, {m, n}];
pp = RandomReal[{0, 1}, {n, n}];
ss = RandomInteger[{0, 5}, {m, n}];
Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm,
pp // TableForm, ss // TableForm}}, Spacings -> {5, 2},
Dividers -> All]
where I would like to look at every element of matrix ss
and produce a matrix tt
, with zeroes at the locations in ss
which have zeroes, and in all other positions do the following:
tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])],
where Subscript[ww, m]
is the value at index
of ww
matrix and where Subscript[pp, m - 1]
is the value at index-1
of pp
matrix.
So for example if the first value ever read from matrix ss
happens to be 2, then value taken from matrix ww
would be from the row 2, but from pp
would be from row 1.
Also how to tell difference between a 0 as a valid value from within the matrix elements to end of matrix if I do not know the actual size of the matrix beforehand?
Given the data as above, tt matrix would be like this:
Answer
Two gaps in the information provided in the question : First, the elements of ss
cannot be greater than 3 (row dimension of ww
and pp
). Second, how do you process the case ss[[i, j]] = 1
? (Which row of pp
do you use?) You need to change the rule so that either ss does not contain any 1
s or treat the 1
s as you treat 0
s. In the following I restricted ss
to values in {0, 2, 3}
.
n = 3; m = 5;
ww = RandomReal[{0, 0.1}, {n, n}];
uu = RandomReal[{0, 1}, {m, n}];
pp = RandomReal[{0, 1}, {n, n}];
ss = RandomChoice[{0, 2, 3}, {m, n}];
Define tt
as
tt = SparseArray[{i_, j_} /; ss[[i, j]] != 0 :>
(-1/ww[[ss[[i, j]], j]]) Log[(1 - uu[[i, j]])/ pp[[ss[[i, j]] - 1, j]]], {m, n}]
With this,
Grid[Transpose@{{"ww", "uu", "pp", "ss", "tt"},
TableForm /@ {ww, uu, pp, ss, Normal[tt]}}, Spacings -> {5, 2}, Dividers -> All]
UPDATE: Incorporating OP's latest clarifications:
ww2 = Prepend[ww, {a, b, c}];
f2[i_, j_] := (-1/ww2[[ss[[i, j]] + 1, j]]) Log[(1 - uu[[i, j]])/pp[[ss[[i, j]], j]]];
tt2 = SparseArray[{i_, j_} /; ss[[i, j]] != 0 :> f2[i, j], {m, n}];
Grid[Transpose@{{"uu", "ww", "pp", "ss", "ww2", "tt2"},
TableForm /@ {uu, ww, pp, ss, ww2, Normal[tt2]}},
Spacings -> {5, 2},
Dividers -> {{All, {1 -> Thick, -1 -> Thick}},
{All, {5 -> Thick, 1 -> Thick, -1 -> Thick}}}]
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