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matrix - Time-efficient manipulation (zeroing) of expression


I have huge matrices in the form of


mtx1 = {{24+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8]},{24+24 FF[5,10] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[7,8] GG[7,8]},{24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]+24 FF[7,8] GG[7,8],24+24 FF[5,10] GG[5,10]+24 FF[6,9] GG[5,10]+24 FF[7,8] GG[5,10]+24 FF[5,10] GG[6,9]+24 FF[6,9] GG[6,9]+24 FF[7,8] GG[6,9]+24 FF[5,10] GG[7,8]+24 FF[6,9] GG[7,8]}};

but the matrices I use are much bigger. Now I want to get rid of each term that contains FF[___] or GG[___]. Both always come together, therefore I used


mtx2 = mtx1 /. FF[___] -> 0; 

(* mtx2={{24, 24, 24}, {24, 24, 24}, {24, 24, 24}} *)

and got the desired result in mtx2. Unfortunatly it turns out that this zeroing is extremly time-consuming. For my huge matrices, it takes on the order of 100 seconds.


Question:


Is there a more time-efficient way to zero all FF[___]-terms in mtx1?


Comparison:


I compare several approaches, for a big 3 big test-matrix. The approaches also include the construction of the matrix.


my original approach



  • {174.8417751, 65.4913582, 25.3878123} seconds



Coefficient-Creation of Matrix



  • {134.4920621, 51.4260521sec, 19.6079772} seconds


belisarius' Block-evaluation methode



  • {82.3675688, 31.5639078, 12.3822025} seconds


eldo's Join/Partition




  • {77.8615328, 29.0973367, 11.2742769} seconds


kguler's Block-evaluation



  • {75.8906436, 29.1315892, 11.6544345} seconds


Mr.Wizard's mtx1[[All, All, 1]]



  • {75.5589726, 29.0378220, 11.9491954} seconds



Edit


The full problem, including the matrix-creation is posted here: Time-efficient creation of matrix



Answer



For the example you gave FF[___] and GG[___] are the only non-number terms, therefore by polynomial sort order you could use simply:


mtx1[[All, All, 1]]


{{24, 24, 24}, {24, 24, 24}, {24, 24, 24}}


I shall now look at your newer question where I anticipate a more representative example.


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