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MathGroup Archive 2006

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Re: Zero times a variable in numerical calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68394] Re: Zero times a variable in numerical calculations
  • From: "Maurits Haverkort" <Haverkort at ph2.uni-koeln.de>
  • Date: Thu, 3 Aug 2006 06:07:27 -0400 (EDT)
  • References: <a02020013-1047-ppc-D86740659B534E4384129C036A76A845@QuarkNew.local>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Bill and others who answered my question.

Chop[0.0 a] indeed works and returns nicely 0 however I still have some 
problems when using this on Sparse Arrays.

I define:
M = SparseArray[{{1, 1} -> a, {2, 2} -> 1.0, {3, 3} -> 1.0, {2, 3} -> b, {3, 
2} -> b, {_, _} -> 0}, {3, 3}];
and
T = SparseArray[{{1, 1} -> 1.0, {2, 2} -> -Sqrt[0.5], {3, 3} -> Sqrt[0.5], 
{2, 3} -> Sqrt[0.5], {3, 2} -> Sqrt[0.5], {_, _} -> 0}, {3, 3}];
I calculate T.M.T This should result in a sparse array with 3 nonzero 
elements. (a,1-b and 1+b on the diagonal).
However
T.M.T=SparseArray[<5>, {3, 3}]
(T.M.T)[[3,2]]=0. (0.707107 + 0.707107 b)
and
(T.M.T)[[2,3]]=0.707107 (0.707107- 0.707107 b) + 0.707107 (-0.707107 + 
0.707107 b)

Chop works almost as
Chop[T.M.T]=SparseArray[<5>, {3, 3}]
But
Chop[T.M.T][[3,2]]=0
However
Chop[T.M.T][[2,3]]=0.707107 (0.707107 - 0.707107 b) + 0.707107 (-0.707107 + 
0.707107 b)

Simplify does nothing. i.e.
Simplify[T.M.T]=T.M.T

Chop[Simplify[Normal[T.M.T]]]
does what I want, but does not work with sparse arrays and in between all 
elements become large expressions so I run out of memory.

Thanks in advance,
Maurits Haverkort

(P.S. Mathematica 5.2 under Linux (Redhat) 1 Gb and Windows XP, 512Mb, the 
matrix size I aim for is 646*646, however I curently can't evaluate a 
134*134 matrix)

----- Original Message ----- 
From: "Bill Rowe" <readnewsciv at earthlink.net>
To: mathgroup at smc.vnet.net
Subject: [mg68394] Re: Zero times a variable in numerical calculations


On 8/2/06 at 10:49 AM, Haverkort at ph2.uni-koeln.de (Maurits Haverkort)
wrote:

>2) What is the fastest way to multiply a numerical matrix times a
>half numerical half analytical sparse matrix, whereby the result is
>band diagonal. (The current result has 0. a + 0. b + 0. c + 0. d +
>0. e + 0. f on all places where it should be zero.)

How are you defining the sparse matrix?

If I do

In[17]:=
a=SparseArray[{{1, 2} -> Random[], {3, 4} -> Random[]},
  {5, 5}];

followed by

In[18]:=
Normal@a

Out[18]=
{{0, 0.49847100218212825, 0, 0, 0}, {0, 0, 0, 0, 0},
  {0, 0, 0, 0.009744974537243703, 0}, {0, 0, 0, 0, 0},
  {0, 0, 0, 0, 0}}


I see the zero elements are exact 0's not inexact 0's. Which means the 
matrix multiplication will be evaluating 0 a etc which will evaluate to 0.
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