IIRC matrix multiplication is non-associative, without parenthesis, J is post multiplication.
Or I was wrong. On Aug 20, 2014 5:26 PM, "Raul Miller" <[email protected]> wrote: > I think what you are asking about is: where do you put the parenthesis? > > That suggests: > > dX=: ((NbI-NbI mp CT mp NcI mp C mp NbI)mp W)+NbI mp CT mp NcI mp Wx > > In other words, you almost had it. > > Thanks, > > -- > Raul > > > > On Wed, Aug 20, 2014 at 3:43 AM, "Papp Erik Tamás" <[email protected]> > wrote: > > > Dear Forum, > > > > Can somebody help me to solve the folloving matrix equation? > > > > pps=:9!:11 NB. set print precision > > pps 20 > > mp=: +/ . * NB. Matrix product > > > > > > > NB.======================================================================================= > > NB. The following matrix equation have to be solve > > NB. dX=(NbI-NbI*CT*NcI*C*NbI)*W+NbI*CT*NcI*Wx > > > > > NB.======================================================================================= > > NB. BT = B transpose > > BT=:|:B > > NB. Nb = BT*B > > Nb=:BT mp B > > NB. NbI = Nb inverse > > NbI=:%.Nb > > NB. W = BT * l > > W=: BT mp l > > NB. C = [q0 q1 q2 q3 0] > > C=:1 5$q0,q1,q2,q3,0 > > NB. CT = C transpose > > CT=:|:C > > NB. Wx = (1-(q0^2)-(q1^2)-(q2^2)-(q3^2))%2 > > Wx=:(1-(q0^2)-(q1^2)-(q2^2)-(q3^2))%2 > > NB. Nc = C * Nb * CT > > Nc=:C mp Nb mp CT > > NB. NcI = Nc inverse > > NcI=:%.Nc > > > > > NB.======================================================================================= > > ]Nc=:C mp Nb mp CT > > 5736.3999999999996 > > > > ]Nc=:(C mp Nb) mp CT > > 5736.3999999999996 > > > > ]Nc=:C mp (Nb mp CT) > > 5736.3999999999996 > > > > > NB.======================================================================================= > > 12j3":B > > 4.700 4.700 20.700 4.700 _3.300 > > _4.700 _20.700 _11.300 _27.300 _8.000 > > 16.000 6.600 22.600 0.000 8.000 > > 2.200 12.200 8.200 _7.800 4.200 > > _2.200 _18.200 6.200 _9.800 2.000 > > 6.000 1.600 _2.400 10.000 8.000 > > 9.200 _0.800 15.200 19.200 1.200 > > _9.200 _5.200 _6.800 _2.800 _8.000 > > 6.000 _12.400 3.600 _10.000 _2.000 > > _10.300 _0.300 _24.300 _20.300 1.700 > > 10.300 14.300 13.700 17.700 12.000 > > _14.000 6.600 _17.400 10.000 _2.000 > > _5.800 _15.800 _19.800 4.200 _3.800 > > 5.800 29.800 _1.800 22.200 2.000 > > _14.000 _2.400 _6.400 _10.000 _12.000 > > > > $B > > 15 5 > > > > 12j3":BT > > 4.700 _4.700 16.000 2.200 _2.200 6.000 > > 9.200 _9.200 6.000 _10.300 10.300 _14.000 > > _5.800 5.800 _14.000 > > 4.700 _20.700 6.600 12.200 _18.200 1.600 > > _0.800 _5.200 _12.400 _0.300 14.300 6.600 > > _15.800 29.800 _2.400 > > 20.700 _11.300 22.600 8.200 6.200 _2.400 > > 15.200 _6.800 3.600 _24.300 13.700 _17.400 > > _19.800 _1.800 _6.400 > > 4.700 _27.300 0.000 _7.800 _9.800 10.000 > > 19.200 _2.800 _10.000 _20.300 17.700 10.000 > > 4.200 22.200 _10.000 > > _3.300 _8.000 8.000 4.200 2.000 8.000 > > 1.200 _8.000 _2.000 1.700 12.000 _2.000 > > _3.800 2.000 _12.000 > > > > $BT > > 5 15 > > > > 12j3":Nb > > 1222.600 623.600 1555.000 853.000 611.300 > > 623.600 2549.800 805.200 1754.000 602.300 > > 1555.000 805.200 2985.800 1034.600 602.300 > > 853.000 1754.000 1034.600 2936.600 602.300 > > 611.300 602.300 602.300 602.300 607.300 > > > > $Nb > > 5 5 > > > > 12j6":NbI > > 0.004533 0.000333 _0.001772 _0.000311 _0.002826 > > 0.000333 0.000749 _0.000128 _0.000382 _0.000573 > > _0.001772 _0.000128 0.001127 0.000039 0.000754 > > _0.000311 _0.000382 0.000039 0.000642 0.000016 > > _0.002826 _0.000573 0.000754 0.000016 0.004295 > > > > $NbI > > 5 5 > > > > 12j3":W > > _981.642 > > _1344.633 > > _1326.828 > > _1561.409 > > _610.603 > > > > $W > > 5 1 > > > > 12j3":C > > 0.500 0.500 0.500 0.500 0.000 > > > > $C > > 1 5 > > > > 12j3":CT > > 0.500 > > 0.500 > > 0.500 > > 0.500 > > 0.000 > > > > $CT > > 5 1 > > > > 12j3":Wx > > 0.500 > > > > $Wx > > 1 > > > > 12j3":Nc > > 5736.400 > > > > $Nc > > 1 1 > > > > NcI > > 0.00017432536085349698 > > > > $NcI > > 1 1 > > > > > > > NB.======================================================================================= > > NB. dX=(NbI-NbI*CT*NcI*C*NbI)*W+NbI*CT*NcI*Wx > > NB. dX=(NbI-NbI mp CT mp NcI mp C mp NbI) mp W+NbI mp CT mp NcI mp Wx > > > > > NB.======================================================================================= > > NB. solution step by step > > dX=:(NbI-NbI mp CT mp NcI mp C mp NbI) mp W+NbI mp CT mp NcI mp Wx > > NB. dX=f+i > > ]a=:NbI mp CT > > 0.0013909444659834052 > > 0.00028633175856724745 > > _0.00036699466085721166 > > _5.9456044547029092e_6 > > _0.0013142105194193007 > > > > ]b=:a mp NcI > > 2.4247689595973174e_7 > > 4.991488713605179e_8 > > _6.3976476685240161e_8 > > _1.0364696420582438e_9 > > _2.291002230352313e_7 > > > > ]c=:b mp C > > 1.2123844797986587e_7 1.2123844797986587e_7 1.2123844797986587e_7 > > 1.2123844797986587e_7 0 > > 2.4957443568025895e_8 2.4957443568025895e_8 2.4957443568025895e_8 > > 2.4957443568025895e_8 0 > > _3.1988238342620081e_8 _3.1988238342620081e_8 _3.1988238342620081e_8 > > _3.1988238342620081e_8 0 > > _5.1823482102912192e_10 _5.1823482102912192e_10 _5.1823482102912192e_10 > > _5.1823482102912192e_10 0 > > _1.1455011151761565e_7 _1.1455011151761565e_7 _1.1455011151761565e_7 > > _1.1455011151761565e_7 0 > > > > ]d=:c mp NbI > > 3.3727189656402491e_10 6.942883603207513e_11 _8.8987726198450762e_11 > > _1.441671712780783e_12 _3.1866568738641721e_10 > > 6.9428836032077935e_11 1.4292217412350897e_11 _1.8318497076221252e_11 > > _2.9677417531211663e_13 _6.5598669749826067e_11 > > _8.8987726198451706e_11 _1.8318497076220693e_11 2.3479025363938921e_11 > > 3.8037882477597397e_13 8.4078558655125846e_11 > > _1.4416717127807238e_12 _2.9677417531209235e_13 3.8037882477595918e_13 > > 6.1624385209859802e_15 1.3621393066516946e_12 > > _3.1866568738642073e_10 _6.5598669749824141e_11 8.4078558655125924e_11 > > 1.3621393066517597e_12 3.0108592311420753e_10 > > > > ]e=:NbI - d > > 0.0045328344164105271 0.00033293998348083668 _0.0017724766597981138 > > _0.00031140912439777367 _0.0028261600905336174 > > 0.00033293998348086812 0.00074882329681384913 _0.00012756882532661765 > > _0.00038153100293938686 _0.00057288268896462887 > > _0.0017724766597981279 _0.00012756882532660762 0.0011266169145724698 > > 3.9439332284661476e_5 0.00075421374633090137 > > _0.00031140912439777405 _0.00038153100293938501 3.9439332284660466e_5 > > 0.00064160958749499744 1.6408293152415618e_5 > > _0.0028261600905336603 _0.00057288268896460545 0.00075421374633090712 > > 1.6408293152416783e_5 0.0042952959863754138 > > > > ]f=:e mp W > > _0.33363012653942103 > > _0.21892822215417146 > > _0.10546286817415873 > > _0.24545184018518121 > > _0.1044605740131157 > > > > ]g=:NbI mp CT > > 0.0013909444659834052 > > 0.00028633175856724745 > > _0.00036699466085721166 > > _5.9456044547029092e_6 > > _0.0013142105194193007 > > > > ]h=:g mp NcI > > 2.4247689595973174e_7 > > 4.991488713605179e_8 > > _6.3976476685240161e_8 > > _1.0364696420582438e_9 > > _2.291002230352313e_7 > > > > ]i=:g mp Wx > > 0.00069547223299170258 0.00014316587928362372 _0.00018349733042860583 > > _2.9728022273514546e_6 _0.00065710525970965033 > > > > > > ]dX=:f + i NB. step by step solution > > _0.33293465430642932 > > _0.21878505627488784 > > _0.10564636550458734 > > _0.24545481298740857 > > _0.10511767927282535 > > > > > > > NB.======================================================================================= > > NB. VERSION 1 > > NB. dX=(NbI-NbI*CT*NcI*C*NbI)*W+NbI*CT*NcI*Wx > > NB. dX=((NbI-(((NbI*CT)*NcI)*C*NbI))*W)+((NbI*CT)*NcI*Wx) > > > > ]dX=:((NbI-(((NbI mp CT) mp NcI) mp C mp NbI)) mp W)+((NbI mp CT) mp > > NcI mp Wx) > > _0.33363000530097303 > > _0.2189281971967279 > > _0.10546290016239707 > > _0.24545184070341602 > > _0.10446068856322722 > > > > > NB.======================================================================================= > > NB. VERSION 2 > > NB. dX=(((NbI-(((NbI*CT)*NcI)*C)*NbI)*W)+(NbI*CT)*NcI)*Wx > > > > ]dX=:(((NbI-(((NbI mp CT) mp NcI) mp C) mp NbI) mp W)+(NbI mp CT) mp > > NcI) mp Wx > > _0.16681494203126254 _0.10946408611964216 _0.052731466075317708 > > _0.12272592061082542 _0.052230401556669366 > > > > > NB.======================================================================================= > > NB. VERSION 3 > > NB. dX=((NbI-(((NbI*CT)*NcI)*C)*NbI)*W)+(NbI*CT)*NcI*Wx > > > > ]dX=:((NbI-(((NbI mp CT) mp NcI) mp C) mp NbI) mp W)+(NbI mp CT) mp > NcI > > mp Wx > > _0.33363000530097303 > > _0.2189281971967279 > > _0.10546290016239707 > > _0.24545184070341602 > > _0.10446068856322722 > > > > > NB.======================================================================================= > > NB. VERSION 4 > > NB. dX=(NbI-NbI*CT*NcI*C*NbI)*W+NbI*CT*NcI*Wx > > NB. D=(NbI*CT)*NcI > > NB. dX=(NbI-D*C*NbI)*W+D*Wx > > NB. dX=((NbI-((D*C)*NbI))*W)+D*Wx > > > > ]dX=:(NbI-((D mp C) mp NbI)) mp W + D mp Wx[D=:(NbI mp CT) mp NcI > > _0.33363012560096128 > > _0.21892822202521539 > > _0.10546286851468895 > > _0.24545184023593167 > > _0.10446057488621374 > > > > > NB.======================================================================================= > > NB. VERSION 5 > > NB. dX=(NbI-NbI*CT*NcI*C*NbI)*W+NbI*CT*NcI*Wx > > NB. dX=:(NbI-NbI mp CT mp NcI mp C mp NbI) mp W+NbI mp CT mp NcI mp Wx > > > > ]dX=:(NbI-NbI mp CT mp NcI mp C mp NbI) mp W+NbI mp CT mp NcI mp Wx > > _0.33363012560096128 > > _0.21892822202521539 > > _0.10546286851468895 > > _0.24545184023593167 > > _0.10446057488621374 > > > > > > > NB.======================================================================================= > > > > NB. ORDER OF EVALUATION J Primer tell > > NB. J has a right-to-left order of evaluation. > > NB. J always parenthesies from right-to-left. > > NB. Remember: no verb precedence and right-to-left evaluation > > > > > > > NB.======================================================================================= > > NB. How can solve the above matrix equation? > > NB. > > NB. Can somebody tell me the right solution? > > NB. > > NB. Thanks, Erik > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
