Re: Special Matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg28345] Re: Special Matrix*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Thu, 12 Apr 2001 02:18:08 -0400 (EDT)*Organization*: University of Washington*References*: <9ah5nq$ps0@smc.vnet.net> <9ajmap$s9e@smc.vnet.net> <9b0sso$rq@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Allan, I was thinking about your method a bit more, and came up with the alternative PM3. In[1]:= PM1[n_]:=Block[{mat=Table[1,{n},{n}]}, mat[[{1,-1},All]]=0; mat[[All,{1,-1}]]=0; mat] PM2[n_]:=PadLeft[Table[1,{n-2},{n-2}],{n,n},0,{1,1}] PM3[n_]:=Block[{mat=IdentityMatrix[n]}, mat[[All,All]]=1; mat[[{1,-1},All]]=0; mat[[All,{1,-1}]]=0; mat] Basically, as I said before, the Table construct is quite slow. However, instead of using PadLeft to construct the table of 1's as I described in my last post, why not use your method to construct the table of 1's? So, that's the change in PM3. The result is quite a bit faster, witness: In[4]:= Do[r1=PM1[1000],{10}]//Timing Do[r2=PM2[1000],{10}]//Timing Do[r3=PM3[1000],{10}]//Timing r1===r2===r3 Out[4]= {11.688 Second, Null} Out[5]= {13.421 Second, Null} Out[6]= {2.469 Second, Null} Out[7]= True So, the fastest way (so far) to create a matrix of 1's is to create a dummy matrix (IdentityMatrix[n]) and then to change all the entries to 1. Carl Woll Physics Dept U of Washington "Allan Hayes" <hay at haystack.demon.co.uk> wrote in message news:9b0sso$rq at smc.vnet.net... > Souvik, > Here is another way > > PM1[n]:= > Block[{mat= Table[1,{n},{n}]},mat[[{1,-1},All]]=0;mat[[All,{1,-1}]]=0;mat] > > It seems to be slightly quicker than Carl Woll's (which itself appears to be > the fastest of the posting so far) > > PM2[n_]:=PadLeft[Table[1,{n-2},{n-2}],{n,n},0,{1,1}] > > n=2000; > > M1= PM1[n];//Timing > > {8.18 Second,Null} > > M2= PM2[n];//Timing > > {10.71 Second,Null} > > Check > > M1===M2 > > True > > -- > Allan > --------------------- > Allan Hayes > Mathematica Training and Consulting > Leicester UK > www.haystack.demon.co.uk > hay at haystack.demon.co.uk > Voice: +44 (0)116 271 4198 > Fax: +44 (0)870 164 0565 > > "Souvik Banerjee" <s-banerjee at nwu.edu> wrote in message > news:9ajmap$s9e at smc.vnet.net... > > Not sure if the shortest but it works: > > > > CreateMatrix[n_] := > > Block[{r,c,m}, > > Needs["LinearAlgebra`MatrixManipulation`"]; > > r = ZeroMatrix[1, n]; m = Table[1, {n - 2}, {n - 2}]; > > c = ZeroMatrix[n - 2, 1]; > > BlockMatrix[{{r}, {c, m, c}, {r}}] > > ] > > > > The bottleneck seems to be the Table[] operations. If there is a built in > > function to create a matrix with a constant element then it will speed > this > > up. > > > > -Souvik > > > > > > Yoram Pollack <syftech at saad.org.il> wrote in message > > news:9ah5nq$ps0 at smc.vnet.net... > > > Hello > > > I am trying to create a "n x n" matrix with "1" in every position exept > in > > > first and last row, and first and last coulumn, where "0" is needed. In > > > other words: sqare matrix full of "1" sorounded by "0". > > > What will be the fastest and shortest way to do it? > > > > > > Thanks > > > Yoram > > > > > > > > > > > > > > > > > >