surprising timings for multiplication of diagonalmatrix and full matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg124946] surprising timings for multiplication of diagonalmatrix and full matrix
• From: "Eric Michielssen" <emichiel at eecs.umich.edu>
• Date: Mon, 13 Feb 2012 03:42:38 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi,

I'd like to right multiply an n x n diagonal matrix (specified by a vector)
by an n x n full matrix.

I tried 3 ways

A. Brute force

B. Using my own routine in which I was hoping to avoid the (supposedly) n^3
cost of A.

diagtimesmat[diag_, mat_] := MapThread[Times, {diag, mat}];

C. The compiled version of B.

cdiagtimesmat =
Compile[{{diag, _Real, 1}, {mat, _Real, 2}},
Module[{}, MapThread[Times, {diag, mat}]],
CompilationTarget -> "C"];

I get weird timings.  For n=250:

n=250;nj=100;
asd=Table[RandomReal[],{n},{n}];
bsd=Table[RandomReal[],{n}];
x=Timing[Do[ed=DiagonalMatrix[bsd].asd,{nj}]][[1]]
y=Timing[Do[ed=diagtimesmat[bsd,asd],{nj}]][[1]]
z=Timing[Do[ed=cdiagtimesmat[bsd,asd],{nj}]][[1]]

Out[415]= 0.359
Out[416]= 6.037
Out[417]= 0.141

My own uncompiled routine is superslow!!!  There are warnings about arrays
being unpacked that I did not copy.

For n=500:

In[418]:= n = 500; nj = 100;
asd = Table[RandomReal[], {n}, {n}];
bsd = Table[RandomReal[], {n}];
x = Timing[Do[ed = DiagonalMatrix[bsd].asd, {nj}]][[1]]
y = Timing[Do[ed = diagtimesmat[bsd, asd], {nj}]][[1]]
z = Timing[Do[ed = cdiagtimesmat[bsd, asd], {nj}]][[1]]

Out[421]= 2.777
Out[422]= 1.31
Out[423]= 1.014

This is more reasonable. It remains a bit surprising that the routine that
only touches n^2 numbers is only twice as fast as the one that supposedly
touches n^3 ones.  Also, the compiled routine still does not achieve 100
MFlops on my laptop.

How can this behavior be explained?  What is the fastest way of doing this?
And how about multiplying a full matrix by a diagonal one?

Thanks!
Eric

Eric Michielssen
Department of Electrical Engineering and Computer Science
University of Michigan
1301 Beal Avenue
Ann Arbor, MI 48109
Ph: (734) 647 1793 -- Fax: (734) 647 2106

```

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