User:Tom Allen/TensorExperimentsR22
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vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 1 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,30000"_)*1"_
pdDA =:vSgD@vS''
pdDA arrayPut 'pdDA'
arrayClose 'pdDA'
Initx =: 0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0 , 0.04"_)*%@(2"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,15000"_)*2"_
pdDB =:vSgD@vS''
pdDB arrayPut 'pdDB'
arrayClose 'pdDB'
NB. ... execute (ijx) ...
arrayOpen 'pdDA'
pdDA=:30001 8 4 arrayGet 'pdDA' NB. ... shape required ...
arrayClose 'pdDA'
arrayOpen 'pdDB'
pdDB=:30001 8 4 arrayGet 'pdDB' NB. ... shape required ...
arrayClose 'pdDB'
load 'plot' pd vSgDplot pdDA pd vSgDplot pdDB pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd 'aspect 1' pd 'pdf' pd 'show'
... a geodesic ...
load 'plot'
pd (cx3"1;cx0"1)@:((S00xL{])"2) (i.@(30001"_){]) pdDA
pd (]"0;((0.94034"_)@]"0)) pTsteps _ 0 1302 160
pd (cx3"1;cx0"1)@:((S00xL{])"2) (i.@(30001"_){]) pdDB
pd (]"0;((0.92078"_)@]"0)) pTsteps _ 0 1302 160
pd 'pdf'
pd 'show'
... X0 with elapsed time along geodesic ...
load 'plot'
incy0=.(2-~/\])@:(cy0"1)
incy1=.(2-~/\])@:(cy1"1)
incy2=.(2-~/\])@:(cy2"1)
incy3=.(2-~/\])@:(cy3"1)
veloc=.(((incy0^2:)+incy1^2:)^0.5"_)%incy3
pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDA
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDA NB. ... incy2 is zero ...
pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDB
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDB NB. ... incy2 is zero ...
pd (]"0;((0.04417"_)@]"0)) pTsteps _ 0 1302 160
pd 'pdf'
pd 'show'
... velocity with elapsed time along geodesic ...
...
...
...
NB. ...
NB. ... the array pdDX can be generated in about 10 days ...
NB. ... on ...
NB. ... an Intel Core i5-6600k processor ...
NB. ...
vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 1 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(128"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,11250"_)*128"_
pdDX =:vSgD@vS''
pdDX arrayPut 'pdDX'
arrayClose 'pdDX'
NB. ... execute (ijx) ...
arrayOpen 'pdDX'
pdDX=:1440001 8 4 arrayGet 'pdDX' NB. ... shape required ...
arrayClose 'pdDX'
load 'plot' pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd vSgDplot pdDX pd 'aspect 1' pd 'pdf' pd 'show'
... a geodesic ...
... the motion of energy (+/-) in space ...
... generates ...
... geodesics which are generally not straight lines ...
... and ...
... this gives rise to some interesting patterns ...
load 'plot'
pd (cx3"1;cx0"1)@:((S00xL{])"2) pdDX
pd (]"0;((0.94"_)@]"0)) pTsteps _ 0 490 160
pd 'pdf'
pd 'show'
... x0 with elapsed time along geodesic ...
load 'plot'
incy0=.(2-~/\])@:(cy0"1)
incy1=.(2-~/\])@:(cy1"1)
incy2=.(2-~/\])@:(cy2"1)
incy3=.(2-~/\])@:(cy3"1)
veloc=.(((incy0^2:)+incy1^2:)^0.5"_)%incy3
pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDX
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDX NB. ... incy2 is zero ...
pd (]"0;((0.04837"_)@]"0)) pTsteps _ 0 490 160
pd 'pdf'
pd 'show'
... velocity with elapsed time along geodesic ...
