3
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I need to multiply 3 lists of matrices (b.a.b) as the following code

a = {{{-17.8227277373099`, -1.6565234964560602`}, 
{-1.6565234954649242`, 
 5.298073701591974`}}, {{-17.812203521929003`, 
-1.5013126607114478`}, {-1.5013126574896714`, 
 4.384050851253119`}}, {{-17.801677045750512`, 
 -1.4055541329078751`}, {-1.405554138172727`, 
 3.869511752542245`}}};

b = {{{0.8409518416651456`, 0}, {0, 
 0.1274293000222242`}}, {{0.8409815693580924`, 0}, {0, 
 0.14187218616724442`}}, {{0.841011296000238`, 0}, {0, 
 0.15290209433231844`}}};

I used the following:

  mat = b.a.b

But, I think this way is not correct because I didn't get the result. Also, I make a test for the first matrices as the following code, that what I wanted to get for the whole matrices multiplication.

 a1 = {{-17.8227277373099`, -1.6565234964560602`}, 
{-1.6565234954649242`, 5.298073701591974`}};

b1 = {{0.8409518416651456`, 0}, {0, 0.1274293000222242`}};

 mat1 = b1.a1.b1


 {{-12.6042, -0.177516}, {-0.177516, 0.0860313}}

Thanks.
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2
  • 1
    $\begingroup$ Table[b[[i]].a[[i]].b[[i]], {i, 1, 3}] or #[[2]].#[[1]].#[[2]] & /@ Transpose[{a, b}]. $\endgroup$
    – corey979
    Mar 18, 2019 at 21:06
  • $\begingroup$ Thanks a lot corey979! $\endgroup$
    – Ghady
    Mar 19, 2019 at 0:30

2 Answers 2

8
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Using MapThread and Dot:

MapThread[Dot, {b, a, b}]
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1
  • $\begingroup$ Thank you very much, It is the easiest! $\endgroup$
    – Ghady
    Mar 19, 2019 at 0:33
6
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If you need it really fast, then use Compile:

n = 1000000;
a = RandomReal[{-1, 1}, {n, 2, 2}];
b = RandomReal[{-1, 1}, {n, 2, 2}];

cf = Compile[{{a, _Real, 2}, {b, _Real, 2}},
   b.a.b,
   RuntimeAttributes -> Listable,
   Parallelization -> True
   ];

MapThread[Dot, {b, a, b}]; // AbsoluteTiming // First
cf[a, b]; // AbsoluteTiming // First

1.46343

0.075722

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2
  • $\begingroup$ Thank you very much! $\endgroup$
    – Ghady
    Mar 19, 2019 at 0:31
  • $\begingroup$ You're welcome. $\endgroup$ Mar 19, 2019 at 8:00

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