Re: Could this be improved?

*To*: mathgroup at smc.vnet.net*Subject*: [mg21776] Re: Could this be improved?*From*: Tom Burton <tburton at brahea.com>*Date*: Thu, 27 Jan 2000 22:56:57 -0500 (EST)*Organization*: Brahea, Inc.*References*: <86mdpv$2f3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 26 Jan 2000 04:12:31 -0500, in comp.soft-sys.math.mathematica you wrote: >I wrote the following code which works correctly. I was wondering, however, >if there was a way of doing the same thing that had more of a Mathematica >approach. I am new to Mathematica and am still trying to get a grasp on how >to program effectively within the environment. > >myMtx[v_] := Module[ > {nCols, nRows, vPadded, c}, > nCols = Length[v]; > nRows = 2nCols - 1; > c = ZeroMatrix[nRows, nCols]; > vPadded = PadRight[v, nRows, 0]; > For[i = 1, i <= nCols, i++, > c[[All, i]] = vPadded; > vPadded = RotateRight[vPadded] > ]; > c > ] Here is your function on a small vector, In[72]:= myMtx[{a, b, c}] Out[72]= {{a, 0, 0}, {b, a, 0}, {c, b, a}, {0, c, b}, {0, 0, c}} and on a large one. In[70]:= Timing[y = myMtx[Range[1000]]; Out[70]= {1.562 Second, Null} In[71]:=Dimensions[y] Out[71]={1999, 1000} Here is a modification that lets the NestList function do the work of repeated rotation and accumulation of the results. In[74]:= myMatrix1[v_List] := With[{n = Length[v] - 1}, Transpose[NestList[RotateRight, PadRight[v, 2*n + 1, 0], n]] ] In[78]:= myMatrix1[{a, b, c}] Out[78]= {{a, 0, 0}, {b, a, 0}, {c, b, a}, {0, c, b}, {0, 0, c}} It runs about three times faster and is far easier to read, once you get used to NestList. In[76]:= Timing[y = myMatrix1[Range[1000]]; ] Out[76]={0.481 Second, Null} In[77]:= Dimensions[y] Out[77]= {1999, 1000} If NestList seems a bit strange, try the Table function: myMatrix2[v_List] := With[{n = Length[v] - 1}, With[{pv = PadRight[v, 2*n+1, 0]}, Transpose[Table[RotateRight[pv, j], {j,0,n}]] ]] myMatrix2 is at least as fast and perhaps easier to read at first than myMatrix1. An important facet of "the Mathematica approach" is to let a function like Table or NestList assemble a result all at once, rather than declaring space for the result (e.g., with ZeroMatrix) and then filling it incrementally. Tom Burton