Date: Jul 31, 2005 1:01 AM Author: Andrzej Kozlowski Subject: Add terms surrounded by zero together in matrix Here is a slightly improved version. (I just removed unnecessary

inner Blocks and a unnecessary conversion of the final expression to

List before applying Cases, which of course is never needed).

Andrzej Kozlowski

SumsOfTermsSurroundedByZero[AA_] :=

Block[{d, MakeNames, A = AA, p = First[Dimensions[

AA]], q = Last[Dimensions[AA]]},

MakeNames[1, 1] := A[[1, 1]] = Unique[z]*A[[1, 1]]; MakeNames[1,

i_] :=

A[[1, i]] = If[(d = Variables[A[[1, i - 1]]]) != {}, First[d]*A

[[1, i]],

Unique[z]*A[[1, i]]]; MakeNames[i_, 1] :=

A[[i, 1]] = Which[(d = Variables[A[[i - 1, 1]]]) != {},

First[

d]*A[[i, 1]], (d = Variables[A[[i - 1, 2]]]) != {}, First[d]*A

[[i, 1]],

True, Unique[z]*A[[i, 1]]]; MakeNames[i_, q] :=

A[[i, q]] = Which[(d = Variables[A[[i - 1, q - 1]]]) != {},

First[d]*A[[i, 5]], (d = Variables[A[[i - 1, q]]]) != {},

First[d]*A[[i, q]],

(d = Variables[A[[i, q - 1]]]) != {}, First[d]*A[[i, q]], True,

Unique[z]*A[[i, q]]]; MakeNames[i_, j_] :=

A[[i, j]] = Which[(d = Variables[A[[i - 1, j - 1]]]) != {},

First[d]*A[[i, j]], (

d = Variables[A[[i - 1, j]]]) != {}, First[d]*A[[i, j]],

(d = Variables[A[[i - 1, j + 1]]]) != {}, First[d]*A[[i, j]],

(d = Variables[A[[i, j - 1]]]) != {}, First[d]*A[[i, j]], True,

Unique[z]*A[[i, j]]]; Do[MakeNames[i, j], {i, p}, {j, q}];

Cases[Plus @@ Flatten[A], _?NumericQ, Infinity]]

On 29 Jul 2005, at 20:55, Andrzej Kozlowski wrote:

>

> On 29 Jul 2005, at 06:42, mchangun@gmail.com wrote:

>

>

>> Hi All,

>>

>> I think this is a rather tough problem to solve. I'm stumped and

>> would

>> really appreciated it if someone can come up with a solution.

>>

>> What i want to do is this. Suppose i have the following matrix:

>>

>> 0 0 0 1 0

>> 0 0 1 2 0

>> 0 0 0 2 1

>> 1 3 0 0 0

>> 0 0 0 0 0

>> 0 0 0 0 0

>> 0 0 1 1 0

>> 5 0 3 0 0

>> 0 0 0 0 0

>> 0 0 0 3 1

>>

>> I'd like to go through it and sum the elements which are

>> surrounded by

>> zeros. So for the above case, an output:

>>

>> [7 4 5 5 4]

>>

>> is required. The order in which the groups surrounded by zero is

>> summed does not matter.

>>

>> The elements are always integers greater than 0.

>>

>> Thanks for any help!

>>

>>

>>

>

>

> O.K., Here is a solution. I think the algorithm is rather nice but

> the implementation certainly isn't, with a nasty procedural Do

> loop, nested Blocks etc, but I can't really afford the time to try

> to make it nicer. Perhaps someone else will.

>

> Here is the function:

>

>

> SumsOfTermsSurroundedByZero[AA_] :=

> Block[{MakeNames, A = AA, p = First[Dimensions[AA]], q = Last

> [Dimensions[AA]]},

> MakeNames[1, 1] := A[[1,1]] = Unique[z]*A[[1,1]]; MakeNames[1,

> i_] :=

> A[[1,i]] = Block[{d}, If[(d = Variables[A[[1,i - 1]]]) != {},

> First[d]*A[[1,i]],

> Unique[z]*A[[1,i]]]]; MakeNames[i_, 1] :=

> A[[i,1]] = Block[{d}, Which[(d = Variables[A[[i - 1,1]]]) != {},

> First[d]*A[[i,1]], (d = Variables[A[[i - 1,2]]]) != {},

> First[d]*A[[i,1]],

> True, Unique[z]*A[[i,1]]]]; MakeNames[i_, q] :=

> A[[i,q]] = Block[{d}, Which[(d = Variables[A[[i - 1,q - 1]]]) !

> = {},

> First[d]*A[[i,5]], (d = Variables[A[[i - 1,q]]]) != {},

> First[d]*A[[i,q]],

> (d = Variables[A[[i,q - 1]]]) != {}, First[d]*A[[i,q]], True,

> Unique[z]*A[[i,q]]]]; MakeNames[i_, j_] :=

> A[[i,j]] = Block[{d}, Which[(d = Variables[A[[i - 1,j - 1]]]) !

> = {},

> First[d]*A[[i,j]], (d = Variables[A[[i - 1,j]]]) != {},

> First[d]*A[[i,j]],

> (d = Variables[A[[i - 1,j + 1]]]) != {}, First[d]*A[[i,j]],

> (d = Variables[A[[i,j - 1]]]) != {}, First[d]*A[[i,j]], True,

> Unique[z]*A[[i,j]]]]; Do[MakeNames[i, j], {i, p}, {j, q}];

> Cases[List @@ Plus @@ Flatten[A], _?NumericQ, Infinity]]

>

> Here is your matrix defined using proper Mathematica syntax:

>

> AA = {{0,0 , 0 , 1, 0}, {0, 0 , 1 , 2, 0}, {0, 0, 0, 2 , 1}, {1, 3,

> 0 , 0 , 0}, {0,

> 0, 0, 0 , 0}, {0 , 0, 0 , 0, 0}, {0, 0 , 1 , 1, 0}, {5 , 0, 3,

> 0 , 0}, {0,

> 0, 0, 0, 0}, {0, 0, 0, 3, 1}}

>

> And here is the solution:

>

> In[3]:=

> SumsOfTermsSurroundedByZero[AA]

>

> Out[3]=

> {7,4,5,5,4}

>

>

> I have not tested it on other examples but your own but it should

> work in all cases.

>

> Andrzej Kozlowski

>

>

>