Re: Transforming matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg29688] Re: Transforming matrices
• From: "Orestis Vantzos" <atelesforos at hotmail.com>
• Date: Tue, 3 Jul 2001 04:40:43 -0400 (EDT)
• Organization: National Technical University of Athens, Greece
• References: <9hp4pa\$2ef\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```As far as I can see, you don't really transform the matrix as a whole, but
every row on its own as a vector.
So here is a function that does what you asked:

toRates[v_, r_] := Module[{p = Transpose[{Take[r, Length[v]], v /. 2 ->
1}]},
p = Split[p, #1[[2]] == #2[[2]] &];
p = Replace[
p, {L0 : {{_, 0} ..} :> 0[L0[[1, 1]], Length[L0]],
L1 : {{_, 1} ..} :> 1[L1[[-1, 1]], Length[L1]]}, 1];
p = p //. {L___, 1[n_, l1_], 0[m_, l2_], R___} /; n != m -> {L, 1[n,
l1],
0[n, l2], R};
Flatten[
Replace[p, {0[n_, l_] :> Table[n, {l}], 1[n_, l_] :> Table[0, {l}]},
1]]]

If M is your matrix and r is the vector of rates do this:
toRates[#,r]& /@ M
Orestis

PS.This probably will take a lot of time, no matter what you do. I hope you
don't do this transformation in a loop ;-)

"Michael Loop" <loopm at yahoo.com> wrote in message
news:9hp4pa\$2ef\$1 at smc.vnet.net...
> I am a relatively new user of Mathematica, and I am having some
> trouble transforming a matrix.  I would be appreciative of any advice.
> The problem is as follows.
>
> Given a randomly formed matrix of form:
>
> 0 0 1 2 2 2 0 0 0 0 0 0 1 2 0 1 2 2 2 0
> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>
> Each digit represents a different state, and therefore each digits
> position must be preserved.  I need to convert this matrix into a
> matrix of rates instead.  The zeros will be converted into constant
> rates dependent on their position, and the rate will continue until a
> 1 is reached.  Both 1 and 2 represent a rate of 0.  So given a vector
> of rates:
>
> 40 38, 37, 36, 33, 32, 31, 30, 27, 23, 22, 21, 20, 16, 14, 13, 12, 10,
> 9, 6
>
> I need to convert the first randomly generated matrix to look like:
>
> 40 40  0  0  0  0 32 32 32 32 32 32  0  0 16  0  0  0  0  9
> 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
> 40 40  0  0  0  0 32 32 32 32 32 32 32 32 32 32 32 32 32 32
>
> Besides the fact that the rate must stay constant until a 1 is
> reached, the other subtlety of my problem is that when a rate starts
> over after a 1 or 2, the new rate must begin in the position of the
> next zero, but the rate must come from the position of the last 1 or
> 2.  I can convert a matrix of this form on an individual basis using
> the Position and Table commands, but cannot find an efficient way of
> converting the matrix on a large scale.  The matrix I actually need to
> convert is 240*1000, so if anyone can think of an efficient way of
> doing this I would be grateful for your input.  Thank you.
>
> Micahel Loop
> Minneapolis, MN

```

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