MaplePrimes - comments on Post, Sparse Matrix-Vector product using evaluation

MaplePrimes - comments on Post, Sparse Matrix-Vector product using evaluation http://www.mapleprimes.com/posts/42963-Sparse-MatrixVector-Product-Using-Evaluation en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 13:23:09 GMT Tue, 09 Jun 2026 13:23:09 GMT The latest comments added to the Post, Sparse Matrix-Vector product using evaluation http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Sparse Matrix-Vector product using evaluation http://www.mapleprimes.com/posts/42963-Sparse-MatrixVector-Product-Using-Evaluation Sparse Matrix-Vector Product: Application and Timing Comparison http://www.mapleprimes.com/posts/42963-Sparse-MatrixVector-Product-Using-Evaluation?ref=Feed:MaplePrimes:Sparse Matrix-Vector product using evaluation:Comments#comment79966 This is an interesting technique. To see a benefit, I presume, the multiplication by the matrix must be done repeatedly for different vectors, otherwise the start-up cost is prohibitive. An obvious application is Matrix-Matrix multiplication. I put together a small procedure to test this: <pre> MatrixMultiply := proc(A,B) local m,n,p,X,Ax,i,j,x,col; uses LinearAlgebra:-LA_Main; m := op([1,1],A); (n,p) := op(1,B); X := rtable( 1..n , i -> x[i] , 'subtype' = 'Vector'['column'] ); Ax := convert(MatrixVectorMultiply(A, X, 'outputoptions' = []) , list); for j to p do for i to m do x[i] := B[i,j]; end do; col[j] := eval(Ax); x := 'x'; end do; rtable( 1..m, 1..p , ListTools:-Transpose([seq](col[j],j=1..p)) , 'subtype' = 'Matrix' ); end proc: </pre> Timing Here is a direct comparison with Matrix multiplication using the LA:-Main subpackage (to avoid the minor overhead of type checking, etc): <pre> with(LinearAlgebra): (m,n,p) := (100,100,1000); B := RandomMatrix(n,p): A := RandomMatrix(m,n,density=1): time(MatrixMultiply(A,B)); time(LinearAlgebra:-LA_Main:-MatrixMatrixMultiply(A,B,'inplace'=false,'outputoptions'=[])); A := RandomMatrix(m,n,density=1/10): time(MatrixMultiply(A,B)); time(LinearAlgebra:-LA_Main:-MatrixMatrixMultiply(A,B,'inplace'=false,'outputoptions'=[])); A := RandomMatrix(m,n,density=1/100): time(MatrixMultiply(A,B)); time(LinearAlgebra:-LA_Main:-MatrixMatrixMultiply(A,B,'inplace'=false,'outputoptions'=[])); </pre> The times were<pre> density MatrixMultiply LA_Main ------------------------------------ 1 5.340 4.269 1/10 0.910 3.949 1/100 0.450 3.840 </pre> For dense Matrices there is a minor penalty to this technique. For sparse Matrices there can be a considerable time saving. Follow up I corrected a bug in the code. A for-loop over an rtable, in the previous version, for v in B[1..-1,j] is not guaranteed to loop sequentially through the elements. It gets all the elements, but not necessarily in order of increasing index. If the selected element were not equal to B[i,j], then an incorrect result would be returned. There was no clear change in the execution time. The latest comments added to the Post, Sparse Matrix-Vector product using evaluation 79966 Thu, 13 Apr 2006 18:50:59 Z Joe Riel Joe Riel Actually I was thinking... http://www.mapleprimes.com/posts/42963-Sparse-MatrixVector-Product-Using-Evaluation?ref=Feed:MaplePrimes:Sparse Matrix-Vector product using evaluation:Comments#comment86535 Actually I was thinking more along the lines of using this as a new matrix data structure... The latest comments added to the Post, Sparse Matrix-Vector product using evaluation 86535 Fri, 28 Apr 2006 10:32:00 Z roman_pearce roman_pearce