User:Tom Allen/ta/AddendumX02P04

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GX02P0400C.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   mtA=:(bV0([Ocndc       yRef@hkyX02D)])                                 ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0(0|:])@([:(bV0([(0{])@Ocn       yRef@hkyX02D),:@])D.1])"_ 1]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_15)qteq[;])"2 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdc     yRef@hkyX02D)])                                 ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0(0|:])@([:(bV0([(0{])@Ocndc     yRef@hkyX02D),:@])D.1])"_ 1]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_12)qteq[;])"3 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdcdc   yRef@hkyX02D)])                                 ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0(0|:])@([:(bV0([(0{])@Ocndcdc   yRef@hkyX02D),:@])D.1])"_ 1]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_11)qteq[;])"4 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdcdcdc yRef@hkyX02D)])                                 ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0(0|:])@([:(bV0([(0{])@Ocndcdcdc yRef@hkyX02D),:@])D.1])"_ 1]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_07)qteq[;])"5 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0401C.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   mtA=:(bV0([Ocndc       zRef@hkyX02D)])                                                         ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0([(0|:])@([:(bV0([(0{])@Ocn       zRef@([hkyX02D bVyc"_ 1)),:@])D.1])"_ 1 bVzc"_ 1)]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
  
   mtA (((2^_44);2^_11)qteq[;])"2 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdc     zRef@hkyX02D)])                                                         ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0([(0|:])@([:(bV0([(0{])@Ocndc     zRef@([hkyX02D bVyc"_ 1)),:@])D.1])"_ 1 bVzc"_ 1)]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_10)qteq[;])"3 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdcdc   zRef@hkyX02D)])                                                         ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0([(0|:])@([:(bV0([(0{])@Ocndcdc   zRef@([hkyX02D bVyc"_ 1)),:@])D.1])"_ 1 bVzc"_ 1)]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_10)qteq[;])"4 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(bV0([Ocndcdcdcdc zRef@hkyX02D)])                                                         ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   mtB=:(bV0([(0|:])@([:(bV0([(0{])@Ocndcdcdc zRef@([hkyX02D bVyc"_ 1)),:@])D.1])"_ 1 bVzc"_ 1)]) ((2^_44)qtsz]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_08)qteq[;])"5 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0402C.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   *./^:3"3 (0=]) (bV0([ch2k       zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:4"4 (0=]) (bV0([ch2kdc     zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:5"5 (0=]) (bV0([ch2kdcdc   zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:6"6 (0=]) (bV0([ch2kdcdcdc zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0403C.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   (bV0([(([Ocn zRef)(((2^_44);2^_44)qteq[;])"1 zdy smx"2 1[Ocn yRef)hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   (bV0([(([Ocn yRef)(((2^_44);2^_44)qteq[;])"1 ydz smx"2 1[Ocn zRef)hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0404C.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_
   
NB. ... R is a tensor ...

   vA =:[R zRef
   vB0=:((0|:[)smx])"2 5
   vB1=:((0|:[)smx])"2 5
   vB2=:((0|:[)smx])"2 5
   vB3=:((0|:[)smx])"2 5
   vB4=:((   [)smx])"2 5
   vB =:[(zdy vB4 ydz vB3 ydz vB2 ydz vB1 ydz vB0 R)yRef

   (bV0([(vA(((2^_44);2^_36)qteq[;])"5 vB)hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0405D.png


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

NB. ... conservation of energy (y-coordinates) ...

   (0=]) ((2^_44)qtsz]) +/@((<0 1)|:])"2 (bV0([Ocndc yRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NB. ... conservation of energy (z-coordinates) ...

   (0=]) ((2^_44)qtsz]) +/@((<0 1)|:])"2 (bV0([Ocndc zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


... in y-coordinates the tensors for lowering and raising indices on tensors ...


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   (bV0([(mcv,mcn)yRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;1"_)pTRandom xCpts)''
1 0 0  0
0 1 0  0
0 0 1  0
0 0 0 _1

1 0 0  0
0 1 0  0
0 0 1  0
0 0 0 _1


... in z-coordinates the tensors for lowering and raising indices on tensors ...


NB. ... execute (ijx) ...

   bV0=:1 1 2 8 1 1 8 _8 0,:_0.90"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   (bV0([(mcv,mcn)zRef@hkyX02D)]) (bV0 zfyc"_ 1])@((0;1"_)pTRandom xCpts)''    NB. ... not "Special" ...
   1 0 0  _0.9
   0 1 0     0
   0 0 1     0
_0.9 0 0 _0.19

0.19 0 0  _0.9
   0 1 0     0
   0 0 1     0
_0.9 0 0    _1



Download: File:LX02P0400C.txt
Download: File:LX02P0401C.txt
Download: File:LX02P0402C.txt
Download: File:LX02P0403C.txt
Download: File:LX02P0404C.txt
Download: File:LX02P0405D.txt




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