Essays/Tensor Experiments/TensorExperiments23
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NB. ... script experimental.ijs ...
vSgDd2M=:[([(0{])@(mcn smx"2 1 B2kCEr1+SBkCEr1)xRef@hkxF),:@(S03xH{])
vSgDd2 =:gXT(-@(([([(0{])@ch2k xRef@hkxF),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)] NB. ... (+) divergence ...
NB. ... script experimental.ijs ...
S00xL =:00 00;00 01;00 02;00 03"_
S01dxL =:01 00;01 01;01 02;01 03"_
S02d1L =:02 00;02 01;02 02;02 03"_
S03xH =:03 00;03 01;03 02;03 03"_
S04dxH =:04 00;04 01;04 02;04 03"_
S05d1H =:05 00;05 01;05 02;05 03"_
S06ds =:(<06 00)"_
S07count =:07 00;07 01"_
S0700nmbr=:(<07 00)"_
S0701max =:(<07 01)"_
vS00=:''vS00xL `S00xL `]}]
vS01=:''vS01dxL `S01dxL `]}]
vS02=:''vS02d1L `S02d1L `]}]
vS06=:''vS06ds `S06ds `]}]
vS07=:''vS07count`S07count`]}]
vS =:vS07@vS06@vS02@vS01@vS00@(8 4$_"_)
vSgDxH =:''((S00xL{])+(S02d1L{])*S06ds{])`S03xH`]}]
vSgDdxH =:''((S02d1L{])*S06ds{])`S04dxH`]}]
vSgDd1H =:''((S02d1L{])+vSgDd2*S06ds{])`S05d1H`]}]
vSgDxHtoL =:''(S03xH{]) `S00xL `]}]
vSgDdxHtoL=:''(S04dxH{])`S01dxL`]}]
vSgDd1HtoL=:''(S05d1H{])`S02d1L`]}]
vSgDnmbr =:''(1+S0700nmbr{])`S0700nmbr`]}]
vSgD =:(vSgDnmbr@vSgDd1HtoL@vSgDdxHtoL@vSgDxHtoL@vSgDd1H@vSgDdxH@vSgDxH)`]@.((S0700nmbr{])=S0701max{])^:a:
vSgDplot=:<"1@(0|:])@:((((cx0*sin@cx1)*cos@cx2),(cx0*sin@cx1)*sin@cx2)@(S00xL{])"2)
NB. ... script experimental.ijs ...
Initds2=:(gXT([(0{])@mcv xRef@hkxF),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =:%:@|@Initds2
NB. ... script experimental.ijs ... Initd1=:Initdx%Initds
load 'plot'
NB. ... x coordinates ...
gXcw =: 1 0 _ _ _ "_
gXpAll=: 1 1 1 2 _0.6"_
Initx =: 5 , 0.5p1 , 1p1 , 0 "_
Initdx=: (0 , 0 , _0.01 , 0.220"_)*%@(128"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,160"_)*128"_
pd vSgDplot pdDA=:vSgD@vS''
gXcw =: 1 0 _ _ _ "_
gXpAll=: 1 1 1 2 _0.6"_
Initx =: 5 , 0.5p1 , 1p1 , 0 "_
Initdx=: (0 , 0 , _0.01 , 0.220"_)*%@(256"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,160"_)*256"_
pd vSgDplot pdDB=:vSgD@vS'' NB. ... convergence ...
NB. ... y coordinates ...
E3 =.+/"1@((<0 3)|:])"5@R
E1cv=.+/"1@((<0 1)|:])"3@(mcn([smx 0|:])"2 3 E3)
E1cn=.mcn smx"2 1 E1cv
hkyGmetric=.<@:>"1@(0|:])@:(((1 0 0 0,0 1 0 0,0 0 1 0,:0 0 0 _1"_);((3$4:)$0:);((4$4:)$0:);((5$4:)$0:);((6$4:)$0:);1$_"_)"_ 1)
hkyG =.(6$a:"_),(6$a:"_),hkyGmetric,(6$a:"_),<@:>"1@(0|:])@:(OyAXXS"_ 1),:6$a:"_
gXcw =: 1 0 _ _ _ "_
gXpAll=: 1 1 1 2 _0.6"_
Inity =: _5 , 0 , 0 , 0 "_
Initdy=: ( 0 , 0.16 , 0 , 0.7042"_)*%@(256"_)
Initds=.%:@|@((gXT([(0{])@mcv yRef@hkyG),:@Inity)+/^:2@:*(]*/])@Initdy)
vSgDd2=.gXT([([(0{])@E1cn yRef@hkyG),:@(S03xH{]))]
vS00xL =:Inity
vS01dxL =:0,0,0,0:
vS02d1L =:Initdy%Initds
vS06ds =:Initds
vS07count=:(0,50"_)*256"_
pd <"1@(0|:])@:((cy0,cy1)@(S00xL{])"2) pdDC=:vSgD@vS''
gXcw =: 1 0 _ _ _ "_
gXpAll=: 1 1 1 2 _0.6"_
Inity =: _5 , 0 , 0 , 0 "_
Initdy=: ( 0 , 0.16 , 0 , 0.7042"_)*%@(512"_)
Initds=.%:@|@((gXT([(0{])@mcv yRef@hkyG),:@Inity)+/^:2@:*(]*/])@Initdy)
vSgDd2=.gXT([([(0{])@E1cn yRef@hkyG),:@(S03xH{]))]
vS00xL =:Inity
vS01dxL =:0,0,0,0:
vS02d1L =:Initdy%Initds
vS06ds =:Initds
vS07count=:(0,50"_)*512"_
pd <"1@(0|:])@:((cy0,cy1)@(S00xL{])"2) pdDD=:vSgD@vS'' NB. ... convergence ...
pd 'pdf'
pd 'show'
... geodesics ...
load 'plot'
gXcw =. 1 0 _ _ _ "_
gXpAll=. 1 1 1 2 _0.6"_
pd (cy3"1@:((S00xL{])"2);(gXT([mcv xRef@hkxF)(S00xL{])"2)%:@|@:(+/^:2"2)@:*(]*/])"1@:((S01dxL{])"2)) }. pdDB
hkyGmetric=.<@:>"1@(0|:])@:(((1 0 0 0,0 1 0 0,0 0 1 0,:0 0 0 _1"_);((3$4:)$0:);((4$4:)$0:);((5$4:)$0:);((6$4:)$0:);1$_"_)"_ 1)
hkyG =.(6$a:"_),(6$a:"_),hkyGmetric,(6$a:"_),<@:>"1@(0|:])@:(OyAXXS"_ 1),:6$a:"_
pd (cy3"1@:((S00xL{])"2);(gXT([mcv yRef@hkyG)(S00xL{])"2)%:@|@:(+/^:2"2)@:*(]*/])"1@:((S01dxL{])"2)) }. pdDD
pd 'pdf'
pd 'show'
... 'curvature' resulting from Riemann-Christoffel tensor ...
NB. ... execute (ijx) ...
*./@(0<])@(2-~/\])@:(cx3@(S00xL{])"2) pdDA
1
*./@(0<])@(2-~/\])@:(cx3@(S00xL{])"2) pdDB
1
*./@(0<])@(2-~/\])@:(cy3@(S00xL{])"2) pdDC
1
*./@(0<])@(2-~/\])@:(cy3@(S00xL{])"2) pdDD
1
NB. ... execute (ijx) ...
*./ (0=]) ((2^_11)qtsz]) (]-0.5p1"_)@:(cx1@(S00xL{])"2) pdDA
1
*./ (0=]) ((2^_14)qtsz]) (]-0.5p1"_)@:(cx1@(S00xL{])"2) pdDB
1
*./ (0=]) (cy2@(S00xL{])"2) pdDC
1
*./ (0=]) (cy2@(S00xL{])"2) pdDD
1
Download: File:LTE2300C.txt
Download: File:LTE2301C.txt
Download: File:LTE2302C.txt
Download: File:LTE2303C.txt
Download: File:LTE2304C.txt
Download: File:LTE2305C.txt
Download MoinMoin source: File:TensorExperiments23.ijs
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