User:Tom Allen/TensorExperimentsB12

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...

...

...

... 5.75p1+0.2000000000000/1.75/628/2 ...

... 6.25p1+0.1622043454706/1.75/628/2 ...


vSgDd2M=.[([(0{])@(([mcn xRef)smx"2 1[(ydx((0|:[)smx])"2 1 B2kCEr1+SBkCEr1)yRef)hkxI),:@(S03xH{])
vSgDd2 =.gXB(-@(([([(0{])@ch2k xRef@hkxI),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+-@vSgDd2M)]

Initds2=.(gXB([(0{])@mcv xRef@hkxI),:@Initx)+/^:2@:*(]*/])@Initdx

gXcw   =:  1.5  0  _  _               _"_
gXpAll =:  1    1  1  6.49877559482  _1"_
gXq2All=:  1    1  1  6.49877559482   _"_
gXq3All=:  0    0  1  1               0"_
gXq4All=:  1    1  1  1               _"_
gXq5All=:  2    0  1  1              _2"_
gXq6All=:  1    1  1  0               _"_
gXq7All=:  1    1  3  1              _2"_

Initx =:   (5.75p1+0.20) , 0.5p1 ,  1p1  , 1.75p1"_
Initdx=:  (0             , 0     , _0.01 , 0     "_)*%@(2"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*2"_
pdDA      =:vSgD@vS''

vSgDd2 =.gXB(-@(([([(0{])@ch2k xRef@hkxI),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initx =:   (6.25p1+0.1622043454706) , 0.5p1 , 1p1  , 1.75p1"_
Initdx=:  (0                        , 0     , 0.01 , 0     "_)*%@(2"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*2"_
pdDB      =:vSgD@vS''


load 'plot'

NB. ... using pdDA and pdDB from above ...

pd vSgDplot pdDA
pd vSgDplot pdDB

pd 'pdf'
pd 'show'


Egraphic1200.jpg
... geodesics ...


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

NB. ... using pdDA and pdDB from above ...

   $pdDA
1257 8 4

   $pdDB
1257 8 4

NB. ... x0 ...

   *./ (0=]) ((2^_42)qtsz]) ((5.75p1+0.20           )-]) cx0"1@:((S00xL{])"2) pdDA
1
   *./ (0=]) ((2^_43)qtsz]) ((6.25p1+0.1622043454706)-]) cx0"1@:((S00xL{])"2) pdDB
1

NB. ... x1 ...

   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDA
1
   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDB
1

NB. ... x2 decreases/increases continuously ...

   *./ (0<]) (2- /\]) cx2"1@:((S00xL{])"2) pdDA
1
   *./ (0<]) (2-~/\]) cx2"1@:((S00xL{])"2) pdDB
1

NB. ... x3 ...

   *./ (0=]) ((2^_48)qtsz]) (1.75p1-]) cx3"1@:((S00xL{])"2) pdDA
1
   *./ (0=]) ((2^_47)qtsz]) (1.75p1-]) cx3"1@:((S00xL{])"2) pdDB
1


...

...

...


GTEB1200C.jpg


load 'plot'

r=.({.+(1&{-{.)*(i.&>:%])@{:) _1.5 1.5 161

pd (];0.2*(6 o.])-1:) r
pd (];0.2*(5 o.])   ) r

pd 'pdf'
pd 'show'


Egraphic1201.jpg
... cosh and sinh ...


vSgDd2M=.[((0.2*(6 o.])-1:)@((0{])-12"_),0,0,0:)(S03xH{])

vSgDd2 =.gXT(-@(([([(0{])@ch2k xRef@hkxF),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+-@vSgDd2M)]

Initds2=.(gXT([(0{])@mcv xRef@hkxF),:@Initx)+/^:2@:*(]*/])@Initdx

gXcw  =:  1.5  0  _  _  _"_
gXpAll=:  0    0  0  0  0"_

Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*1"_

pdDA=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(2"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*2"_

pdDB=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(4"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*4"_

pdDC=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(8"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*8"_

pdDD=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(16"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*16"_

pdDE=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(32"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*32"_

pdDF=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(64"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*64"_

pdDG=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(128"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*128"_

pdDH=:vSgD@vS''


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(256"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*256"_

pdDI=:vSgD@vS''


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

NB. ... x0 ...

   9!:11 [6

   ,.@:(<./@:(cx0"1)@:((S00xL{])"2)&>) pdDA;pdDB;pdDC;pdDD;pdDE;pdDF;pdDG;pdDH;pdDI
11.9101
11.9569
11.9789
11.9895
11.9948
11.9974
11.9987
11.9994
11.9997

   ,.@:(>./@:(cx0"1)@:((S00xL{])"2)&>) pdDA;pdDB;pdDC;pdDD;pdDE;pdDF;pdDG;pdDH;pdDI
13.4352
13.4117
13.4002
13.3946
13.3918
13.3904
13.3897
13.3894
13.3892

NB. ... x1 ...

   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDA
1
   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDB
1
   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDI
1

NB. ... x2 decreases continuously ...

   *./ (0<]) (2-/\]) cx2"1@:((S00xL{])"2) pdDA
1
   *./ (0<]) (2-/\]) cx2"1@:((S00xL{])"2) pdDB
1
   *./ (0<]) (2-/\]) cx2"1@:((S00xL{])"2) pdDI
1

NB. ... x3 ...

   *./ (0=]) cx3"1@:((S00xL{])"2) pdDA
1
   *./ (0=]) cx3"1@:((S00xL{])"2) pdDB
1
   *./ (0=]) cx3"1@:((S00xL{])"2) pdDI
1


load 'plot'

pd vSgDplot pdDA
pd vSgDplot pdDB
pd vSgDplot pdDI

pd 'pdf'
pd 'show'


Egraphic1202.jpg
... patterns (x0/x2) ...


load 'plot'

pd (-@cx2"1;cx0"1)@:((S00xL{])"2) pdDA
pd (-@cx2"1;cx0"1)@:((S00xL{])"2) pdDB
pd (-@cx2"1;cx0"1)@:((S00xL{])"2) pdDI

pd 'pdf'
pd 'show'


Egraphic1203.jpg
... x0 ...


...

...

...


vSgDd2M=.[((0.2*(6 o.])-1:)@((0{])-12"_),0,0,0:)(S03xH{])

vSgDd2 =.gXT(-@(([([(0{])@ch2k xRef@hkxF),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+-@vSgDd2M)]

Initds2=.(gXT([(0{])@mcv xRef@hkxF),:@Initx)+/^:2@:*(]*/])@Initdx

gXcw  =:  1.5  0  _  _  _"_
gXpAll=:  0    0  0  0  0"_


Initx =:  12 , 0.5p1 ,  1p1  , 0"_
Initdx=: ( 0 , 0     , _0.01 , 0"_)*%@(96"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,12000"_)*96"_

pdDX=:vSgD@vS''


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

   $pdDX
1152001 8 4

NB. ... x0 ...

   9!:11 [6

   <./@:(cx0"1)@:((S00xL{])"2) pdDX
11.9795

   >./@:(cx0"1)@:((S00xL{])"2) pdDX
13.3987

NB. ... x1 ...

   *./ (0=]) (0.50p1-]) cx1"1@:((S00xL{])"2) pdDX
1

NB. ... x2 decreases continuously ...

   *./ (0<]) (2-/\]) cx2"1@:((S00xL{])"2) pdDX
1

NB. ... x3 ...

   *./ (0=]) cx3"1@:((S00xL{])"2) pdDX
1


load 'plot'

pd vSgDplot pdDX

pd 'pdf'
pd 'show'


Egraphic1204.jpg
... pattern (x0/x2) ...


load 'plot'

pd (-@cx2"1;cx0"1)@:((S00xL{])"2) (i.@(1152000"_){]) pdDX

pd 'pdf 459 360'
pd 'show'


Egraphic1205.jpg
... x0 ...



Download: File:LTEB1200C.txt




Download MoinMoin source: File:TensorExperimentsB12.ijs