wzelik

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13 years, 337 days

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These are replies submitted by wzelik

@mmcdara 

Besides the execution time, something else will worry me. When I import more amount of data as a DataFrame, I see a distinct delay in characters refresh. It looks like the typed characters appear with an apparent and frustrating delay of even a few seconds.

Also, you're right, DataFrame logic is quite similar to native R.
So I really regret that it doesn't work as well in Maple as it does in R.
In certain types of analysis, DataFrame would be very helpful.

wzelik

in relation to my question...

Data from Excel: 150 000 rows x 13 columns (in attachment).

Example task: count the "single" value in the fifth column (name: "Married_Single").

Import via ImportMatrix() - 0.813 s

t := time();
sel := select(t -> data[t, 5] = "single", [$ (1 .. op([1, 1], data))]);
Statistics:-Count(data[sel, 5]);
time() - t;
# time = 0.047 s, result = 134638 

 

Import to DataFrame via Import() - 41.563s 

t := time();
Statistics:-Count(data[`=`~(data[Married_Single], "single")][Married_Single]);
time() - t;
#time = 2.48 s, result = 134638 

 

wzelik

150kX13_LOAN.xlsx

 

Maple Flow Team,

Maple Flow 2022.2 - big step forward in performance.

I keep my fingers crossed for the development of Maple Flow.

wzelik

@mmcdara 
Including you😀

I appreciate

wzelik

@acer 

It's a little bit complicated but really fast.

Calculation on my XPS 9710 in Maple 2022.2  takes 0.2 s for 50 000 samples.

Thank you.

wzelik

@mmcdara 

It seems that your procedure proposition is much more efficient than the preliminary mine.

The execution time is almost twice as short as mine (11.6 s for 50 000 samples), but still, the calculation time is quite far from the solution in Mathcad Prime 8.0.

Anyway, thank you for your effort

@mmcdara 

Thank you,

As you are probably aware, it was not my intention to use the well-known and documented conjugate prior method.

In fact, I wanted to reproduce by Maple the results I got a few months ago using the mcmcPack packages in R (https://cran.r-project.org/web/packages/MCMCpack/), where I used the MCbinomialbeta function to compute the posterior distribution.

Of course, I know the exact solution you gave, Beta(23,3), from the method of the conjugate prior. So I could easily compare the results. At the same time, I watched the trace plot and tried to observe the ratio calculated by following the procedure:

rep := <seq(0, N-burning)>:
for i to numelems(rep) - 1 do
    if evalb(samp[i + 1] = samp[i]) then 
        rep[i] := 1; 
    else     rep[i] := 0; 
    end if;
end do;
add(rep);
ratio := 1 - evalf(add(rep)/N);
 

wzelik

@Carl Love 

Thank you for your prompt reply.

I have tested, samp:=mcmcBinomialBeta(21, 1, 4, 2, 0.5, 50000, 500, 0.1) # timeCalc = 20.56 s

a, b - parameters of Beta distribution, type: Integer,

n, k - parameters of Binomial distribution, type: Integer,

init - initial value, type float,

N - number of samples, type Integer,

burn - reject first burn value samples, type: Integer,

thin - adjust results if needed.

with(Statistics):

Mean(samp); # 0.884957164100278
Quantile(samp, 0.025); # 0.742018607354109
Quantile(samp, 0.975);0.975124932511784


plots:-pointplot(<seq([n, samp(n)], n = 1 .. numelems(samp))>, axes = boxed, font = [Helvetica, Bold, 10], gridlines = true, colour = red, size = [500, 300], symbol = diagonalcross);

Histogram(samp, averageshifted = 4, style = polygon, color = "LightSlateGrey", font = [Helvetica, Bold, 10])

Thank you once again.

wzelik

@Preben Alsholm 

Thank you. It seems that your nested solution works very well.

wz

@Carl Love 

 

wz

Hi,

 

Question is the same...

...but I saw that previous version of test.mw was not correct.

I need value from internal procedure of module.

 

wz

 

test.mw

@Carl Love 

please edit startup code

 

wz

@Preben Alsholm

Thank you very much.

My target is, to solve multilayer (different thermal diffusivity for each layer) heat transfer problem by reducing PDE to ODE form, ans solve system of ODE describing by matrix way as you wrote

As you see I have had more basic problem, than I expect :-)

Is there a way to avoid this instability and to solve this problem for each t?

wzel

 

 


Maybe problem is conected with yestardays update of MaplePrimes?

This time I put the contents...


restart

 

General rule:
rho*`&delta;x`*cp*dT__i/dt = lambda*(`T__i-1`-T__i)/`&delta;x`-lambda*(T__i-`T__i+1`)/`&delta;x`

where:

rho - density of material,

`&delta;x` - distance beetween node,

cp - heat capacity,

lambda - thermal conduction,

T - temperature

t - time,

 

 

n := 20:

 

L := .3:

`&delta;x` := L/(n-1):

for i to n do eq || i := isolate(node || i, diff(T[i](t), t)) end do:

sys := {seq(eq || i, i = 1 .. n)}:

ic := {seq(T[i](0) = 298, i = 1 .. n)}:

func := seq(T[i](t), i = 1 .. n):

sol := dsolve(`union`(sys, ic), {func}, numeric);

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 20, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .679123214198435, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 4 ) = (Array(1..53, {(1) = 20, (2) = 20, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0}, datatype = integer[4])), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 6 ) = (Array(1..20, {(1) = 298.0, (2) = 298.0, (3) = 298.0, (4) = 298.0, (5) = 298.0, (6) = 298.0, (7) = 298.0, (8) = 298.0, (9) = 298.0, (10) = 298.0, (11) = 298.0, (12) = 298.0, (13) = 298.0, (14) = 298.0, (15) = 298.0, (16) = 298.0, (17) = 298.0, (18) = 298.0, (19) = 298.0, (20) = 298.0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = T[1](t), Y[2] = T[2](t), Y[3] = T[3](t), Y[4] = T[4](t), Y[5] = T[5](t), Y[6] = T[6](t), Y[7] = T[7](t), Y[8] = T[8](t), Y[9] = T[9](t), Y[10] = T[10](t), Y[11] = T[11](t), Y[12] = T[12](t), Y[13] = T[13](t), Y[14] = T[14](t), Y[15] = T[15](t), Y[16] = T[16](t), Y[17] = T[17](t), Y[18] = T[18](t), Y[19] = T[19](t), Y[20] = T[20](t)]`; YP[1] := 28.14814815-0.2392592593e-1*Y[1]+0.3820105823e-2*Y[2]; YP[2] := 0.3820105823e-2*Y[1]-0.7640211646e-2*Y[2]+0.3820105823e-2*Y[3]; YP[3] := 0.3820105823e-2*Y[2]-0.7640211646e-2*Y[3]+0.3820105823e-2*Y[4]; YP[4] := 0.3820105823e-2*Y[3]-0.7640211646e-2*Y[4]+0.3820105823e-2*Y[5]; YP[5] := 0.3820105823e-2*Y[4]-0.7640211646e-2*Y[5]+0.3820105823e-2*Y[6]; YP[6] := 0.3820105823e-2*Y[5]-0.7640211646e-2*Y[6]+0.3820105823e-2*Y[7]; YP[7] := 0.3820105823e-2*Y[6]-0.7640211646e-2*Y[7]+0.3820105823e-2*Y[8]; YP[8] := 0.3820105823e-2*Y[7]-0.7640211646e-2*Y[8]+0.3820105823e-2*Y[9]; YP[9] := 0.3820105823e-2*Y[8]-0.7640211646e-2*Y[9]+0.3820105823e-2*Y[10]; YP[10] := 0.3820105823e-2*Y[9]-0.7640211646e-2*Y[10]+0.3820105823e-2*Y[11]; YP[11] := 0.3820105823e-2*Y[10]-0.7640211646e-2*Y[11]+0.3820105823e-2*Y[12]; YP[12] := 0.3820105823e-2*Y[11]-0.7640211646e-2*Y[12]+0.3820105823e-2*Y[13]; YP[13] := 0.3820105823e-2*Y[12]-0.7640211646e-2*Y[13]+0.3820105823e-2*Y[14]; YP[14] := 0.3820105823e-2*Y[13]-0.7640211646e-2*Y[14]+0.3820105823e-2*Y[15]; YP[15] := 0.3820105823e-2*Y[14]-0.7640211646e-2*Y[15]+0.3820105823e-2*Y[16]; YP[16] := 0.3820105823e-2*Y[15]-0.7640211646e-2*Y[16]+0.3820105823e-2*Y[17]; YP[17] := 0.3820105823e-2*Y[16]-0.7640211646e-2*Y[17]+0.3820105823e-2*Y[18]; YP[18] := 0.3820105823e-2*Y[17]-0.7640211646e-2*Y[18]+0.3820105823e-2*Y[19]; YP[19] := 0.3820105823e-2*Y[18]-0.7640211646e-2*Y[19]+0.3820105823e-2*Y[20]; YP[20] := 0.3820105823e-2*Y[19]-0.3015873019e-2*Y[20]-.2396613757; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 11 ) = (Array(1..6, 0..20, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (1, 13) = .0, (1, 14) = .0, (1, 15) = .0, (1, 16) = .0, (1, 17) = .0, (1, 18) = .0, (1, 19) = .0, (1, 20) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (2, 13) = .0, (2, 14) = .0, (2, 15) = .0, (2, 16) = .0, (2, 17) = .0, (2, 18) = .0, (2, 19) = .0, (2, 20) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (3, 13) = .0, (3, 14) = .0, (3, 15) = .0, (3, 16) = .0, (3, 17) = .0, (3, 18) = .0, (3, 19) = .0, (3, 20) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (4, 13) = .0, (4, 14) = .0, (4, 15) = .0, (4, 16) = .0, (4, 17) = .0, (4, 18) = .0, (4, 19) = .0, (4, 20) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (5, 13) = .0, (5, 14) = .0, (5, 15) = .0, (5, 16) = .0, (5, 17) = .0, (5, 18) = .0, (5, 19) = .0, (5, 20) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (6, 13) = .0, (6, 14) = .0, (6, 15) = .0, (6, 16) = .0, (6, 17) = .0, (6, 18) = .0, (6, 19) = .0, (6, 20) = .0}, datatype = float[8], order = C_order)), ( 8 ) = ([Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = 22.156613758114002, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = -0.10800005334488105e-9}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..20, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1, (9) = .1, (10) = .1, (11) = .1, (12) = .1, (13) = .1, (14) = .1, (15) = .1, (16) = .1, (17) = .1, (18) = .1, (19) = .1, (20) = .1}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, 1..20, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (1, 13) = .0, (1, 14) = .0, (1, 15) = .0, (1, 16) = .0, (1, 17) = .0, (1, 18) = .0, (1, 19) = .0, (1, 20) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (2, 13) = .0, (2, 14) = .0, (2, 15) = .0, (2, 16) = .0, (2, 17) = .0, (2, 18) = .0, (2, 19) = .0, (2, 20) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (3, 13) = .0, (3, 14) = .0, (3, 15) = .0, (3, 16) = .0, (3, 17) = .0, (3, 18) = .0, (3, 19) = .0, (3, 20) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (4, 13) = .0, (4, 14) = .0, (4, 15) = .0, (4, 16) = .0, (4, 17) = .0, (4, 18) = .0, (4, 19) = .0, (4, 20) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (5, 13) = .0, (5, 14) = .0, (5, 15) = .0, (5, 16) = .0, (5, 17) = .0, (5, 18) = .0, (5, 19) = .0, (5, 20) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (6, 13) = .0, (6, 14) = .0, (6, 15) = .0, (6, 16) = .0, (6, 17) = .0, (6, 18) = .0, (6, 19) = .0, (6, 20) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (7, 13) = .0, (7, 14) = .0, (7, 15) = .0, (7, 16) = .0, (7, 17) = .0, (7, 18) = .0, (7, 19) = .0, (7, 20) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (8, 13) = .0, (8, 14) = .0, (8, 15) = .0, (8, 16) = .0, (8, 17) = .0, (8, 18) = .0, (8, 19) = .0, (8, 20) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (9, 13) = .0, (9, 14) = .0, (9, 15) = .0, (9, 16) = .0, (9, 17) = .0, (9, 18) = .0, (9, 19) = .0, (9, 20) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (10, 13) = .0, (10, 14) = .0, (10, 15) = .0, (10, 16) = .0, (10, 17) = .0, (10, 18) = .0, (10, 19) = .0, (10, 20) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (11, 13) = .0, (11, 14) = .0, (11, 15) = .0, (11, 16) = .0, (11, 17) = .0, (11, 18) = .0, (11, 19) = .0, (11, 20) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0, (12, 13) = .0, (12, 14) = .0, (12, 15) = .0, (12, 16) = .0, (12, 17) = .0, (12, 18) = .0, (12, 19) = .0, (12, 20) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (13, 12) = .0, (13, 13) = .0, (13, 14) = .0, (13, 15) = .0, (13, 16) = .0, (13, 17) = .0, (13, 18) = .0, (13, 19) = .0, (13, 20) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (14, 12) = .0, (14, 13) = .0, (14, 14) = .0, (14, 15) = .0, (14, 16) = .0, (14, 17) = .0, (14, 18) = .0, (14, 19) = .0, (14, 20) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (15, 12) = .0, (15, 13) = .0, (15, 14) = .0, (15, 15) = .0, (15, 16) = .0, (15, 17) = .0, (15, 18) = .0, (15, 19) = .0, (15, 20) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (16, 12) = .0, (16, 13) = .0, (16, 14) = .0, (16, 15) = .0, (16, 16) = .0, (16, 17) = .0, (16, 18) = .0, (16, 19) = .0, (16, 20) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (17, 12) = .0, (17, 13) = .0, (17, 14) = .0, (17, 15) = .0, (17, 16) = .0, (17, 17) = .0, (17, 18) = .0, (17, 19) = .0, (17, 20) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (18, 12) = .0, (18, 13) = .0, (18, 14) = .0, (18, 15) = .0, (18, 16) = .0, (18, 17) = .0, (18, 18) = .0, (18, 19) = .0, (18, 20) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (19, 12) = .0, (19, 13) = .0, (19, 14) = .0, (19, 15) = .0, (19, 16) = .0, (19, 17) = .0, (19, 18) = .0, (19, 19) = .0, (19, 20) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (20, 12) = .0, (20, 13) = .0, (20, 14) = .0, (20, 15) = .0, (20, 16) = .0, (20, 17) = .0, (20, 18) = .0, (20, 19) = .0, (20, 20) = .0}, datatype = float[8], order = C_order), Array(1..20, 1..20, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (1, 13) = .0, (1, 14) = .0, (1, 15) = .0, (1, 16) = .0, (1, 17) = .0, (1, 18) = .0, (1, 19) = .0, (1, 20) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (2, 13) = .0, (2, 14) = .0, (2, 15) = .0, (2, 16) = .0, (2, 17) = .0, (2, 18) = .0, (2, 19) = .0, (2, 20) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (3, 13) = .0, (3, 14) = .0, (3, 15) = .0, (3, 16) = .0, (3, 17) = .0, (3, 18) = .0, (3, 19) = .0, (3, 20) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (4, 13) = .0, (4, 14) = .0, (4, 15) = .0, (4, 16) = .0, (4, 17) = .0, (4, 18) = .0, (4, 19) = .0, (4, 20) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (5, 13) = .0, (5, 14) = .0, (5, 15) = .0, (5, 16) = .0, (5, 17) = .0, (5, 18) = .0, (5, 19) = .0, (5, 20) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (6, 13) = .0, (6, 14) = .0, (6, 15) = .0, (6, 16) = .0, (6, 17) = .0, (6, 18) = .0, (6, 19) = .0, (6, 20) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (7, 13) = .0, (7, 14) = .0, (7, 15) = .0, (7, 16) = .0, (7, 17) = .0, (7, 18) = .0, (7, 19) = .0, (7, 20) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (8, 13) = .0, (8, 14) = .0, (8, 15) = .0, (8, 16) = .0, (8, 17) = .0, (8, 18) = .0, (8, 19) = .0, (8, 20) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (9, 13) = .0, (9, 14) = .0, (9, 15) = .0, (9, 16) = .0, (9, 17) = .0, (9, 18) = .0, (9, 19) = .0, (9, 20) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (10, 13) = .0, (10, 14) = .0, (10, 15) = .0, (10, 16) = .0, (10, 17) = .0, (10, 18) = .0, (10, 19) = .0, (10, 20) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (11, 13) = .0, (11, 14) = .0, (11, 15) = .0, (11, 16) = .0, (11, 17) = .0, (11, 18) = .0, (11, 19) = .0, (11, 20) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0, (12, 13) = .0, (12, 14) = .0, (12, 15) = .0, (12, 16) = .0, (12, 17) = .0, (12, 18) = .0, (12, 19) = .0, (12, 20) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (13, 12) = .0, (13, 13) = .0, (13, 14) = .0, (13, 15) = .0, (13, 16) = .0, (13, 17) = .0, (13, 18) = .0, (13, 19) = .0, (13, 20) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (14, 12) = .0, (14, 13) = .0, (14, 14) = .0, (14, 15) = .0, (14, 16) = .0, (14, 17) = .0, (14, 18) = .0, (14, 19) = .0, (14, 20) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (15, 12) = .0, (15, 13) = .0, (15, 14) = .0, (15, 15) = .0, (15, 16) = .0, (15, 17) = .0, (15, 18) = .0, (15, 19) = .0, (15, 20) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (16, 12) = .0, (16, 13) = .0, (16, 14) = .0, (16, 15) = .0, (16, 16) = .0, (16, 17) = .0, (16, 18) = .0, (16, 19) = .0, (16, 20) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (17, 12) = .0, (17, 13) = .0, (17, 14) = .0, (17, 15) = .0, (17, 16) = .0, (17, 17) = .0, (17, 18) = .0, (17, 19) = .0, (17, 20) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (18, 12) = .0, (18, 13) = .0, (18, 14) = .0, (18, 15) = .0, (18, 16) = .0, (18, 17) = .0, (18, 18) = .0, (18, 19) = .0, (18, 20) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (19, 12) = .0, (19, 13) = .0, (19, 14) = .0, (19, 15) = .0, (19, 16) = .0, (19, 17) = .0, (19, 18) = .0, (19, 19) = .0, (19, 20) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (20, 12) = .0, (20, 13) = .0, (20, 14) = .0, (20, 15) = .0, (20, 16) = .0, (20, 17) = .0, (20, 18) = .0, (20, 19) = .0, (20, 20) = .0}, datatype = float[8], order = C_order), Array(1..20, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 0, (20) = 0}, datatype = integer[4]), Array(1..20, {(1) = 298.0, (2) = 298.0, (3) = 298.0, (4) = 298.0, (5) = 298.0, (6) = 298.0, (7) = 298.0, (8) = 298.0, (9) = 298.0, (10) = 298.0, (11) = 298.0, (12) = 298.0, (13) = 298.0, (14) = 298.0, (15) = 298.0, (16) = 298.0, (17) = 298.0, (18) = 298.0, (19) = 298.0, (20) = 298.0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order), Array(1..20, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0}, datatype = float[8], order = C_order)]), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 13 ) = (), ( 12 ) = (), ( 20 ) = ([]), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = T[1](t), Y[2] = T[2](t), Y[3] = T[3](t), Y[4] = T[4](t), Y[5] = T[5](t), Y[6] = T[6](t), Y[7] = T[7](t), Y[8] = T[8](t), Y[9] = T[9](t), Y[10] = T[10](t), Y[11] = T[11](t), Y[12] = T[12](t), Y[13] = T[13](t), Y[14] = T[14](t), Y[15] = T[15](t), Y[16] = T[16](t), Y[17] = T[17](t), Y[18] = T[18](t), Y[19] = T[19](t), Y[20] = T[20](t)]`; YP[1] := 28.14814815-0.2392592593e-1*Y[1]+0.3820105823e-2*Y[2]; YP[2] := 0.3820105823e-2*Y[1]-0.7640211646e-2*Y[2]+0.3820105823e-2*Y[3]; YP[3] := 0.3820105823e-2*Y[2]-0.7640211646e-2*Y[3]+0.3820105823e-2*Y[4]; YP[4] := 0.3820105823e-2*Y[3]-0.7640211646e-2*Y[4]+0.3820105823e-2*Y[5]; YP[5] := 0.3820105823e-2*Y[4]-0.7640211646e-2*Y[5]+0.3820105823e-2*Y[6]; YP[6] := 0.3820105823e-2*Y[5]-0.7640211646e-2*Y[6]+0.3820105823e-2*Y[7]; YP[7] := 0.3820105823e-2*Y[6]-0.7640211646e-2*Y[7]+0.3820105823e-2*Y[8]; YP[8] := 0.3820105823e-2*Y[7]-0.7640211646e-2*Y[8]+0.3820105823e-2*Y[9]; YP[9] := 0.3820105823e-2*Y[8]-0.7640211646e-2*Y[9]+0.3820105823e-2*Y[10]; YP[10] := 0.3820105823e-2*Y[9]-0.7640211646e-2*Y[10]+0.3820105823e-2*Y[11]; YP[11] := 0.3820105823e-2*Y[10]-0.7640211646e-2*Y[11]+0.3820105823e-2*Y[12]; YP[12] := 0.3820105823e-2*Y[11]-0.7640211646e-2*Y[12]+0.3820105823e-2*Y[13]; YP[13] := 0.3820105823e-2*Y[12]-0.7640211646e-2*Y[13]+0.3820105823e-2*Y[14]; YP[14] := 0.3820105823e-2*Y[13]-0.7640211646e-2*Y[14]+0.3820105823e-2*Y[15]; YP[15] := 0.3820105823e-2*Y[14]-0.7640211646e-2*Y[15]+0.3820105823e-2*Y[16]; YP[16] := 0.3820105823e-2*Y[15]-0.7640211646e-2*Y[16]+0.3820105823e-2*Y[17]; YP[17] := 0.3820105823e-2*Y[16]-0.7640211646e-2*Y[17]+0.3820105823e-2*Y[18]; YP[18] := 0.3820105823e-2*Y[17]-0.7640211646e-2*Y[18]+0.3820105823e-2*Y[19]; YP[19] := 0.3820105823e-2*Y[18]-0.7640211646e-2*Y[19]+0.3820105823e-2*Y[20]; YP[20] := 0.3820105823e-2*Y[19]-0.3015873019e-2*Y[20]-.2396613757; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 18 ) = ([]), ( 19 ) = (0)  ] ))  ] ); _y0 := Array(0..20, {(1) = 0., (2) = 298., (3) = 298., (4) = 298., (5) = 298., (6) = 298., (7) = 298., (8) = 298., (9) = 298., (10) = 298., (11) = 298., (12) = 298., (13) = 298., (14) = 298., (15) = 298., (16) = 298., (17) = 298., (18) = 298., (19) = 298., (20) = 298.}); _vmap := array( 1 .. 20, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 5 ) = (5), ( 4 ) = (4), ( 7 ) = (7), ( 6 ) = (6), ( 10 ) = (10), ( 11 ) = (11), ( 8 ) = (8), ( 9 ) = (9), ( 15 ) = (15), ( 14 ) = (14), ( 13 ) = (13), ( 12 ) = (12), ( 20 ) = (20), ( 16 ) = (16), ( 17 ) = (17), ( 18 ) = (18), ( 19 ) = (19)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 10 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 10 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _src = 0 and 10 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-10, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; _dat[4][26] := _EnvDSNumericSaveDigits; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, T[1](t), T[2](t), T[3](t), T[4](t), T[5](t), T[6](t), T[7](t), T[8](t), T[9](t), T[10](t), T[11](t), T[12](t), T[13](t), T[14](t), T[15](t), T[16](t), T[17](t), T[18](t), T[19](t), T[20](t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(1)

t1 := 3600:

Y1 := [seq(rhs(op(sol(t1))[i]), i = 2 .. n+1)]:

X1 := [seq(i*`&delta;x`, i = 0 .. n-1)]:

t2 := 5*3600:

Y2 := [seq(rhs(op(sol(t2))[i]), i = 2 .. n+1)]:

X2 := [seq(i*`&delta;x`, i = 0 .. n-1)]:

 

plot(X1, Y1)

 

NULL

 

plot(X2, Y2)

 

NULL

 

 


Download HT_one_layer.mw

HT_one_layer.mw

Hi,

I'm sorry but I don't know why "404" error appears.

 Trying once again,

 

wzel

 

 

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