User:Tom Allen/ta/AddendumX06P10

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GX06P1000E.png


... 4th order partial derivatives continuous at the y2 axis ... 


load 'plot'

pd 'reset'

pU0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_
pd 'itemcolor red'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.15p1 0.15p1 0"_)*10"_
pd 'itemcolor green'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.35p1 0.35p1 0"_)*10"_
pd 'itemcolor purple'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_
pd 'itemcolor pink'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.65p1 0.65p1 0"_)*10"_
pd 'itemcolor purple'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.85p1 0.85p1 0"_)*10"_
pd 'itemcolor green'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_
pd 'itemcolor red'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

pd 'itemcolor blue'
pd (((0.8704"_)@]"0);]"0) pTsteps _ _4 4 160
pd (((1.3235"_)@]"0);]"0) pTsteps _ _4 4 160

pd 'itemcolor black'
pd (((0.9675"_)@]"0);]"0) pTsteps _ _9 7 160
pd (((1.2832"_)@]"0);]"0) pTsteps _ _9 7 160

pd 'canvas plot.html 666 500'

'finished' 1!:2[2


JX06P1000E.png


GX06P1001C.png 


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

pU0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

vSgDd2=:pU0([([(0{])@E1cn yRef@hkyX06B),:@(S03yH{]))]

Initx =:  0.9510 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:128"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,48000"_)*InitInt
pdDX     =:vSgD@vS''

pdDXpt1=:(i.@(4096000"_){]) pdDX
pdDXpt1 arrayPut   'pdDXpt1'
        arrayClose 'pdDXpt1'

pdDXpt2=:((4096000+i.@(2048001"_)){]) pdDX
pdDXpt2 arrayPut   'pdDXpt2'
        arrayClose 'pdDXpt2'

'finished' 1!:2[2



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

                      arrayOpen  'pdDXpt1'
pdDXpt1=:4096000 8 4  arrayGet   'pdDXpt1'   NB. ... shape required ...
                      arrayClose 'pdDXpt1'

                      arrayOpen  'pdDXpt2'
pdDXpt2=:2048001 8 4  arrayGet   'pdDXpt2'   NB. ... shape required ...
                      arrayClose 'pdDXpt2'

pdDX=:pdDXpt1,pdDXpt2

pdDXpt1=:0
pdDXpt2=:0

'finished' 1!:2[2



load 'plot'

pd 'reset'

pd 'itemcolor blue'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDX

pd 'itemcolor Black'
pd ((1.0*cos@]"0);1.0*sin@]"0) pTsteps _ 0p1 2p1 160

pd 'itemcolor yellow'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(96000"_){]) pdDX

pd 'aspect 1'
pd 'canvas plot.html 666 500'

'finished' 1!:2[2


JX06P1001J.png 


load 'plot'

pd 'reset'

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 'itemcolor green'
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDX

pd 'canvas plot.html 1332 1000'

'finished' 1!:2[2


JX06P1002K.png


... 4th order partial derivatives not continuous at the y2 axis ... 


load 'plot'

pd 'reset'

pU0=:,:@(0.05 1 2 7 1 1 1 _0.1 0"_)

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_
pd 'itemcolor red'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.15p1 0.15p1 0"_)*10"_
pd 'itemcolor green'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.35p1 0.35p1 0"_)*10"_
pd 'itemcolor purple'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_
pd 'itemcolor pink'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.65p1 0.65p1 0"_)*10"_
pd 'itemcolor purple'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.85p1 0.85p1 0"_)*10"_
pd 'itemcolor green'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_
pd 'itemcolor red'
pd (pU0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX06B zfyc"_ 1))]) pTtotal xCpts''

pd 'itemcolor blue'
pd (((0.8360"_)@]"0);]"0) pTsteps _ _4 4 160
pd (((1.3660"_)@]"0);]"0) pTsteps _ _4 4 160

pd (((1.0940"_)@]"0);]"0) pTsteps _ _4 4 160

pd 'canvas plot.html 666 500'

'finished' 1!:2[2


JX06P1003H.png


GX06P1002C.png 


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

pU0=:,:@(0.05 1 2 7 1 1 1 _0.1 0"_)

vSgDd2=:pU0([([(0{])@E1cn yRef@hkyX06B),:@(S03yH{]))]

Initx =:  0.9430 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:128"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,48000"_)*InitInt
pdDY     =:vSgD@vS''

pdDYpt1=:(i.@(4096000"_){]) pdDY
pdDYpt1 arrayPut   'pdDYpt1'
        arrayClose 'pdDYpt1'

pdDYpt2=:((4096000+i.@(2048001"_)){]) pdDY
pdDYpt2 arrayPut   'pdDYpt2'
        arrayClose 'pdDYpt2'

'finished' 1!:2[2



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

                      arrayOpen  'pdDYpt1'
pdDYpt1=:4096000 8 4  arrayGet   'pdDYpt1'   NB. ... shape required ...
                      arrayClose 'pdDYpt1'

                      arrayOpen  'pdDYpt2'
pdDYpt2=:2048001 8 4  arrayGet   'pdDYpt2'   NB. ... shape required ...
                      arrayClose 'pdDYpt2'

pdDY=:pdDYpt1,pdDYpt2

pdDYpt1=:0
pdDYpt2=:0

'finished' 1!:2[2



load 'plot'

pd 'reset'

pd 'itemcolor blue'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDY

pd 'itemcolor Black'
pd ((1.0*cos@]"0);1.0*sin@]"0) pTsteps _ 0p1 2p1 160

pd 'itemcolor yellow'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(84000"_){]) pdDY

pd 'aspect 1'
pd 'canvas plot.html 666 500'

'finished' 1!:2[2


JX06P1004C.png


GX06P1003E.png 


load 'plot'

pd 'reset'

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 'itemcolor green'
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDY

pd 'canvas plot.html 1332 1000'

'finished' 1!:2[2


JX06P1005C.png


Download: File:LX06P1000E.txt
Download: File:LX06P1001C.txt
Download: File:LX06P1002C.txt
Download: File:LX06P1003E.txt


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