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. -- To reply via email subtract one hundred and four