[R] elementwise matrix multiplication with a special structure

[eugen pircalabelu]

Hello R users,
I have the following annoying matrix multiplication and I do not know how to avoid the nested loops, so maybe someone can help me with some ideas. I have searched the forum for past posts but nothing came up.Here it is:
 aa=matrix(1:9,3,3) bb=matrix(seq(10,90,by=10),3,3) cc=matrix(seq(100,900, by=100),3,3) dd=NULL 
for(r in 1:3){    for(c in 1:3){        for(j in 1:3){            for(k in 1:3){dd=c(dd,aa[j,k]*bb[r,j]*cc[k,c])}}}}dd [1]   1000   8000  21000   8000  40000  96000  21000  84000 189000   4000[11]  20000  42000  32000 100000 192000  84000 210000 378000   7000  32000[21]  63000  56000 160000 288000 147000 336000 567000   2000  16000  42000[31]  10000  50000 120000  24000  96000 216000   8000  40000  84000  40000[41] 125000 240000  96000 240000 432000  14000  64000 126000  70000 200000[51] 360000 168000 384000 648000   3000  24000  63000  12000  60000 144000[61]  27000 108000 243000  12000  60000 126000  48000 150000 288000 108000[71] 270000 486000  21000  96000 189000  84000 240000 432000 189000 432000[81] 729000
What I want to obtain is the content of the vector dd in an efficient (fast) and clever way.Thank you very much and have a great day ahead!Eugen

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