Description of fast matrix multiplication algorithm: ⟨22×24×32:9331⟩

Algorithm type

3⁢X16⁢Y16⁢Z16+4⁢X14⁢Y16⁢Z14+2⁢X8⁢Y24⁢Z8+2⁢X8⁢Y16⁢Z16+4⁢X8⁢Y16⁢Z8+2⁢X8⁢Y8⁢Z14+82⁢X8⁢Y8⁢Z8+8⁢X8⁢Y8⁢Z6+24⁢X7⁢Y8⁢Z7+8⁢X6⁢Y8⁢Z8+8⁢X6⁢Y8⁢Z6+36⁢X4⁢Y12⁢Z4+36⁢X4⁢Y8⁢Z8+72⁢X4⁢Y8⁢Z4+36⁢X4⁢Y4⁢Z8+6⁢X2⁢Y2⁢Z12+12⁢X4⁢Y4⁢Z7+8⁢X4⁢Y4⁢Z6+4⁢X2⁢Y4⁢Z8+6⁢X6⁢Y2⁢Z4+720⁢X4⁢Y4⁢Z4+4⁢X2⁢Y6⁢Z4+2⁢X2⁢Y2⁢Z8+48⁢X4⁢Y4⁢Z3+48⁢X3⁢Y4⁢Z4+18⁢X6⁢Y2⁢Z2+24⁢X4⁢Y4⁢Z2+2⁢X4⁢Y2⁢Z4+48⁢X3⁢Y4⁢Z3+228⁢X2⁢Y6⁢Z2+262⁢X2⁢Y4⁢Z4+18⁢X2⁢Y2⁢Z6+6⁢X4⁢Y2⁢Z2+502⁢X2⁢Y4⁢Z2+292⁢X2⁢Y2⁢Z4+36⁢X⁢Y⁢Z6+48⁢X2⁢Y2⁢Z3+24⁢X⁢Y2⁢Z4+36⁢X3⁢Y⁢Z2+2186⁢X2⁢Y2⁢Z2+24⁢X⁢Y3⁢Z2+12⁢X⁢Y⁢Z4+108⁢X3⁢Y⁢Z+144⁢X2⁢Y2⁢Z+12⁢X2⁢Y⁢Z2+504⁢X⁢Y3⁢Z+708⁢X⁢Y2⁢Z2+108⁢X⁢Y⁢Z3+36⁢X2⁢Y⁢Z+1284⁢X⁢Y2⁢Z+456⁢X⁢Y⁢Z2+1020⁢X⁢Y⁢Z3X16Y16Z164X14Y16Z142X8Y24Z82X8Y16Z164X8Y16Z82X8Y8Z1482X8Y8Z88X8Y8Z624X7Y8Z78X6Y8Z88X6Y8Z636X4Y12Z436X4Y8Z872X4Y8Z436X4Y4Z86X2Y2Z1212X4Y4Z78X4Y4Z64X2Y4Z86X6Y2Z4720X4Y4Z44X2Y6Z42X2Y2Z848X4Y4Z348X3Y4Z418X6Y2Z224X4Y4Z22X4Y2Z448X3Y4Z3228X2Y6Z2262X2Y4Z418X2Y2Z66X4Y2Z2502X2Y4Z2292X2Y2Z436XYZ648X2Y2Z324XY2Z436X3YZ22186X2Y2Z224XY3Z212XYZ4108X3YZ144X2Y2Z12X2YZ2504XY3Z708XY2Z2108XYZ336X2YZ1284XY2Z456XYZ21020XYZ3*X^16*Y^16*Z^16+4*X^14*Y^16*Z^14+2*X^8*Y^24*Z^8+2*X^8*Y^16*Z^16+4*X^8*Y^16*Z^8+2*X^8*Y^8*Z^14+82*X^8*Y^8*Z^8+8*X^8*Y^8*Z^6+24*X^7*Y^8*Z^7+8*X^6*Y^8*Z^8+8*X^6*Y^8*Z^6+36*X^4*Y^12*Z^4+36*X^4*Y^8*Z^8+72*X^4*Y^8*Z^4+36*X^4*Y^4*Z^8+6*X^2*Y^2*Z^12+12*X^4*Y^4*Z^7+8*X^4*Y^4*Z^6+4*X^2*Y^4*Z^8+6*X^6*Y^2*Z^4+720*X^4*Y^4*Z^4+4*X^2*Y^6*Z^4+2*X^2*Y^2*Z^8+48*X^4*Y^4*Z^3+48*X^3*Y^4*Z^4+18*X^6*Y^2*Z^2+24*X^4*Y^4*Z^2+2*X^4*Y^2*Z^4+48*X^3*Y^4*Z^3+228*X^2*Y^6*Z^2+262*X^2*Y^4*Z^4+18*X^2*Y^2*Z^6+6*X^4*Y^2*Z^2+502*X^2*Y^4*Z^2+292*X^2*Y^2*Z^4+36*X*Y*Z^6+48*X^2*Y^2*Z^3+24*X*Y^2*Z^4+36*X^3*Y*Z^2+2186*X^2*Y^2*Z^2+24*X*Y^3*Z^2+12*X*Y*Z^4+108*X^3*Y*Z+144*X^2*Y^2*Z+12*X^2*Y*Z^2+504*X*Y^3*Z+708*X*Y^2*Z^2+108*X*Y*Z^3+36*X^2*Y*Z+1284*X*Y^2*Z+456*X*Y*Z^2+1020*X*Y*Z

Algorithm definition

The algorithm ⟨22×24×32:9331⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨11×12×16:1333⟩.

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.


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