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tomleslie

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These are answers submitted by tomleslie

Depending on which animation you want...

tomleslie 13876
December 30 2019
0 0

you might consider the attached

> 

SOLNSuy[1, 1] := 2.5872902469406659197*10^(-20)-.65694549571241255901*y+1.9708364871372376767*y^2-1.3138909914248251176*y^3-1.6010739356637904911*10^(-19)*y^4:
SOLNSuy[2, 1] := -4.002204462000*10^(-20)-1.7879176897079605225*y+5.3637530691192141414*y^2-3.5758353794044226250*y^3-6.8309939211286845440*10^(-12)*y^4:
SOLNSuy[3, 1] := -1.1953264450000*10^(-19)-3.2481690589079594122*y+9.7445071767154794599*y^2-6.4963381177952273213*y^3-1.2292726248071398400*10^(-11)*y^4:
SOLNSuy[4, 1] := -2.6720465500000*10^(-19)-4.9239979672954025921*y+14.771993901873204315*y^2-9.8479959345587718955*y^3-1.9029826928878336000*10^(-11)*y^4:
SOLNSuy[5, 1] := 3.416928541000*10^(-20)-6.7268498492441931137*y+20.180549547714413714*y^2-13.453699698443639810*y^3-2.6580790570532587008*10^(-11)*y^4:
SOLNSuy[6, 1] := -2.554122292000*10^(-20)-8.5884528335125514887*y+25.765358500514014457*y^2-17.176905666966875698*y^3-3.4587270427710613504*10^(-11)*y^4:
SOLNSuy[7, 1] := -9.206107680000*10^(-20)-10.456823708331499352*y+31.370471124965259849*y^2-20.913647416590986491*y^3-4.2774005353527132160*10^(-11)*y^4:
SOLNSuy[8, 1] := 1.9644186790000*10^(-19)-12.293003938471349390*y+36.879011815379230436*y^2-24.586007876856948223*y^3-5.0932823222176363520*10^(-11)*y^4:
SOLNSuy[9, 1] := -3.775112769000*10^(-19)-14.068404975282556550*y+42.205214925807397100*y^2-28.136809950465931724*y^3-5.8908824448577377280*10^(-11)*y^4:
SOLNSuy[10, 1] := 1.146281780000*10^(-19)-15.762658869974768890*y+47.287976609878780960*y^2-31.525317739837422477*y^3-6.6589592851037286400*10^(-11)*y^4:
plots:- display
        ( [ seq
            ( plots[animate]
              ( plot,
                [SOLNSuy[i, 1], y = 0 .. x, color=ColorTools:-Color("HSV", [0.1*i, 0.6, 0.6])],
                x=0..1
              ),
              i=1..10
            )
          ]
       );

 
> 

 

> 

 


 

Download simplt.mw

How I'd do it...

tomleslie 13876
December 29 2019
1 0

is in the attached.

You have to appreciate that when you define the function v(), the expression diff(r(t),t) will not be evaluated until the function v() is called with an argument. When you supply a numeric argument, (eg 2) Maple will attempt to compute diff(r(2), 2), whihc is obviously not good.

By defining a function using the unapply(argument1, argument2) command, both argument1 and argument2 will be evaluated before the function is created. Thus v:=unapply(diff(r(t),t), t) will evaluate the derivative of 'r(t)', with respect to the variable 't' and create the appropriate function v() which can then be called with either numeric or symbolic arguments.

See the attached

> 

  restart;
> 

  r := t -> Vector([5*cos(Pi*t), 5*sin(Pi*t)]):
  v:= unapply(diff(r(t),t), t):
> 

  r(t);
  v(t);
  r(2);
  v(2);

Vector(2, {(1) = 5*cos(Pi*t), (2) = 5*sin(Pi*t)})

  

Vector(2, {(1) = -5*Pi*sin(Pi*t), (2) = 5*Pi*cos(Pi*t)})

  

Vector(2, {(1) = 5, (2) = 0})

  

Vector[column](%id = 18446744074326969030)

 (1)
> 

 

Download deffun.mw

Am I missing something?...

tomleslie 13876
December 23 2019
1 5

or does the code in the attached achieve what you want (quickly?)

> 

  restart;
  with(LinearAlgebra):
#
# Generate a (random) 64*64 binary matrix
#
  A:=RandomMatrix(64, 64, generator=rand(0..1)):
  r:=8:
  n := upperbound(A)[1]/r:
  B := Matrix(n, n, 0):
  for i to n do
      for j to n do
          B[i, j] := SubMatrix(A, [(i-1)*r+1 .. i*r], [(j-1)*r+1 .. j*r])
      end do;
  end do;
 
> 

#
# Get the determinants for all the subMatrices in B
#
  Determinant~([entries(B,`nolist`)]);

[3, 0, -1, 0, 1, 2, 0, -2, 0, 0, 2, -2, 0, -2, -3, 0, 6, 4, 0, 0, 0, 3, 0, 2, -2, 0, 1, 6, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 2, 0, 1, -5, 0, 0, 0, -1, 0, 0, -2, 0, -5, 2, -2, 0, -6, -1, 0, 0, 2, 0, -3, -1]

 (1)
> 

#
# Are any determinants 0?
#
  member(0, %);

true

 (2)
> 

 


 

Download doDets.mw

 

Hmmm...

tomleslie 13876
December 21 2019
0 0

Since you don't provide code for the procedure "Eadd()" it is difficult to perform meaningful debug. So the following is just some observations

  1. You could make life much easier for responders here (and yourself) by using the big green up-arrow in the Mapleprimes toolbar to upload a complete worksheet which exhibits whatever problem you are having
  2. In the code 'snip' you do supply, the calls to Eadd() contain the name 'x' which is not defined in the calling procedure Weil()'. This is not necessarily an error, since it may (implicitly) be a global variable, which is either assigned to something at the top-level, or (if unassigned) will be regarded as a global (unassigned) name
  3. If I make up a "toy" example for the procedure Eadd(), which returns a 1-D indexable entity, then the procedure Weil() executes correctly (see the attached)
  4. To view variable values during debugging, just type the variable name into the text box of the debugger window and click the 'execute' button. There is also nothing wrong with sticking a few printf() statements into troublesome code (as I have demonstrated  in the attached). This is a very crude "debugging" technique, but I'm sure we've all done it!
  5. Maple will not "save" the values (which values??) from a procedure unless you specifically instruct it to do so somehow - eg by including them as a list in the procedure's return statement. You could also get these from the interactive debugger by examining them within the debugger (see bullet 4 above) and checking the "Copy Results on exit" box in the debugger window
> 

  restart;
> 

  WeilP:=proc(m, P1, P2, Q1, Q2, f, p)
              local S1, S2, gP, gQ, temp, PS1, PS2, QS1, QS2;
              if   [P1,P2] = [Q1, Q2] mod p
              then return 1 ;
              else # [S1, S2] := EAdd( f, x, P1, P2, Q1, Q2);
                   temp := EAdd( f, x, p, P1, P2, Q1, Q2);
                 #
                 # Crude debug! Use print statements to check
                 # what Eadd() is returning
                 #
                   printf("%a\n", temp);
                   S1:=temp[1];
                   S2:=temp[2];
                   temp := EAdd( f, x, p, P1, P2, S1, -S2);   #represents P-S
                   printf("%a\n", temp); 
                   PS1:= temp[1];
                   PS2:=temp[2];
                   temp := EAdd( f, x, p, Q1, Q2, S1, S2);    #Q+S
                   printf("%a\n", temp);
                   QS1:=temp[1];
                   QS2:=temp[2];
                 # gP:=Weil( m, P1,P2, f, p );
                 # gQ:=Weil( m, Q1,Q2, f, p );
                   return 0
                 # return Normal(  ( Eval(gP, { x=QS1, y=QS2 } ) * Eval(gQ, {x=S1, y= -S2} ) )  / ( Eval(gP, { x=PS1, y=PS2 } ) * Eval(gQ, {x=S1, y= -S2} ) )   )  mod p;    # ( f_P(Q+S) f_Q(-S)  ) / ( f_Q(P-S) f_P(S)  )
             end if ;
         end proc:
#
# OP does not supply 'Eadd' so just
# insert something which *ought* to
# make WeilP at least 'execute'
#
  EAdd:= proc( a0, a1, a2)
               return <a1, a2>:
         end proc:
  WeilP( 3, 4, 5, 6, 7, 8, 9);

Vector(2, [x,9])
Vector(2, [x,9])
Vector(2, [x,9])

  

0

 (1)
> 

 

Download DBGstuff.mw

Use stoperror()...

tomleslie 13876
December 20 2019
0 0

As in the toy example attached. NB I can't show the the "output" of the second execution - because this "output" is an interactive debugger, 'stopped. at the appropriate point.

Read the help page at ?stoperror for more info

> 

  restart;
  f := proc(x)
            local a;
            a := x;
            g(x);
            x^2
       end proc:
  g := proc(x)
            cos(x);
            1/x;
            sin(x);
       end proc:
> 

#
# This will "error". It will return the name of the
# procedure in which the error occurred and the
# "source of the error"
#
  f(0);

Error, (in g) numeric exception: division by zero

  
> 

#
# This will start the interactive debugger at the point
# where any error occurs. Debugger window will show
# procedure name and the statement/number where the error
# occurred
#
  stoperror(`all`):
  f(0);
> 

 

Download basicDBG.mw

Maybe like this?...

tomleslie 13876
December 18 2019
2 7

assuminng that you want all the curves on the same graph

> 

restart; with(plots); ha := 15; alp := (1/180)*(5*3.14); rkVals := [5, 10, 15, 20]; f := 1-x^2+c[1]*(-x^3+x^2)+c[2]*(-x^4+x^2); eq1 := diff(f, `$`(x, 3))+2*alp*rk*f*(diff(f, `$`(x, 1)))+(4-ha)*alp^2*(diff(f, `$`(x, 1))); eq2 := collect(expand(eq1), c); a[1] := subs(x = 1/6, eq2); a[2] := subs(x = 2*(1/6), eq2); plts := NULL; colors := [red, green, blue, black]; for j to numelems(rkVals) do rk := rkVals[j]; p := fsolve({a[1], a[2]}); plts := plts, plot(eval(eq2, p), x = 0 .. 1, color = colors[j]) end do; plots:-display([plts])

 
> 

 

Download plotLoop.mw

use...

tomleslie 13876
December 17 2019
2 1

display(Array(...))

as in the attached

arrplt.mw

(which for some reason won't display inline on this page, but will work within Maple!)

 

 





 

Observation...

tomleslie 13876
December 17 2019
1 1

@Carl Love 

The plot you suggest, ie

plot3d(sin(x)*cos(y), x= -Pi..Pi, y= -Pi..Pi, grid= [300,300]);

may contain "more" data points, but I'm not convinced it is a relevant comparison. The time-consuming part *seems* to be the amount of calculation whihc has to be performed on the data points one has. In the OP's case, this is strongly influenced by the number/type of options in the plot3d() command.

See the attached for some fairly impressive usage statistics

Note On my machine, after the CodeTools:-Usage() command returns its statistics, it still takes significant further time for the plot windows to appear and the plots to render.

> 

  restart;
> 

#
# Some random "large" plot, whose render time is to be used
# as a reference
#
  plotsetup(window);
  CodeTools:-Usage(plot3d(sin(x)*cos(y), x= -Pi..Pi, y= -Pi..Pi, grid= [300,300]));
  plotsetup(default);

memory used=4.03MiB, alloc change=1.00MiB, cpu time=63.00ms, real time=61.00ms, gc time=0ns

  
> 

  restart;
> 

  M:=LinearAlgebra:-RandomMatrix(500,70):
  plotsetup(window);
#
# Plot random matrix with a lot of options
#
  CodeTools:-Usage(plots:-matrixplot(M, style=surface,axes=normal, lightmodel=light2, labels=["n","d","C"], heights=histogram, gap=  0.00000000000000000001, colorscheme=["xyzcoloring", (x,y,z)->x*y*z]));
#
# Same random matrix with "minimal" options
#
  CodeTools:-Usage(plots:-matrixplot(M, axes=normal, labels=["n","d","C"], heights=histogram ));
  plotsetup(default);

memory used=5.61GiB, alloc change=443.49MiB, cpu time=113.90s, real time=43.18s, gc time=94.74s

memory used=402.85MiB, alloc change=163.21MiB, cpu time=3.82s, real time=2.99s, gc time=1.11s

  
> 

 


 

Download pltTimes.mw

 

How I'd do it...

tomleslie 13876
December 16 2019
0 0

As CarlLove has said, ArrayInterpolation may not be the best starting point

Consider the attached

  1. A spline fit of degree 1, is just simple linear interpolation - which is what the ArrayInterprolation() command uses by default, and why the first answer in the attached agrees with that obtained elsewhere on this thread
  2. Increasing the degree of the spline interpolating polynomials, changes the result (slightly)
  3. Although I have shown results for interpolating polynomials up to order 10, I normally wouldn't recommend using orders higher than 3. The higher the order of the interpolating polynomial, the more likely it is that something will go numerically apeshit (for example, look at the final result obtianed for a 10-th order fit)
> 

Digits:=16:
with(CurveFitting):
for j from 1 by 1 to 10 do
    fsolve( Spline( [-149, 208, 567, 925, 1283, 1642, 2000],
                    [257.184, 230.4, 184.3, 138.2, 92.2, 46.1, 0],
                    x,
                   degree=j
                  )
            -153.25
          );
od;

808.1258134490237

  

807.8493501622970

  

806.0299587919305

  

805.0141030420970

  

805.9961318934920

  

805.8224749509850

  

806.6904136778054

  

806.6659595099449

  

807.1167393131392

  

-2017.872466327373

 (1)
> 

 


 

Download fitSpl.mw

Use the zip() command...

tomleslie 13876
December 16 2019
1 0

which is probably the "best" way for your specific example - see the attached.

There are several other ways to achieve the same thing!!

(I'd avoid using the name 'D' for anything in Maple because (by default) it representss the differential operator)

> 

  restart;
  A:=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]:
  B:=[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]:
#
# Symbolic solution
#
  C:=zip( (x,y)->x*E/4*Pi*y, A, B);
#
# Evaluate the above for a specific value
# of E
#
  CC:=eval(C, E=5);
#
# Get a floating point solution
#
  CCC:=evalf~(CC);

[(5/2)*E*Pi, 10*E*Pi, (45/2)*E*Pi, 40*E*Pi, (125/2)*E*Pi, 90*E*Pi, (245/2)*E*Pi, 160*E*Pi, (405/2)*E*Pi, 250*E*Pi]

  

[(25/2)*Pi, 50*Pi, (225/2)*Pi, 200*Pi, (625/2)*Pi, 450*Pi, (1225/2)*Pi, 800*Pi, (2025/2)*Pi, 1250*Pi]

  

[39.26990818, 157.0796327, 353.4291736, 628.3185308, 981.7477044, 1413.716694, 1924.225501, 2513.274123, 3180.862562, 3926.990818]

 (1)
> 

#
# OR
#
# Initialize
#
  restart;
  A:=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]:
  B:=[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]:
#
# By specifying E as a 'float', then all
# subsequent calculations which contain
# E will be evaluated as 'floats'
#
  E:=5.0:
  C:=zip( (x,y)->x*E/4*Pi*y, A, B);

[39.26990818, 157.0796327, 353.4291735, 628.3185308, 981.7477045, 1413.716694, 1924.225501, 2513.274125, 3180.862562, 3926.990818]

 (2)
> 

 


 

Download useZip.mw

One way...

tomleslie 13876
December 13 2019
1 1

is shown in the attached - but I can think of a few others!!

> 

  restart;
  p:=piecewise( t-2*Pi*trunc(t/(2*Pi))<=Pi,
                Pi,
                (2*Pi-t+2*Pi*trunc(t/(2*Pi)))
              );
  plot(p, t=0..20*Pi, size=[1000,200]);

p := piecewise(t-2*Pi*trunc(t/(2*Pi)) <= Pi, Pi, 2*Pi-t+2*Pi*trunc(t/(2*Pi)))

  

 
> 

 

Download perPW.mw

 

Explanation is in the attached file...

tomleslie 13876
December 13 2019
1 1

Relevant comments are highlighted in the attached

The only thing that bothers me about the explanation in the attached is what is reported when an even doesn't fire! I would have expected some kind of "warning" or NULL answer, rather than returning "t=0, x(t)=0"

If you think about this explanation for long enough, then it should be obvious why reversing the order of events always works! First time through the "offending" loop the 'sol' procedure will been evaluated from t=0 to t=1, so the event at t=0.5 is available. Second time throught the loop the 'sol' procedure has been evaluated from t=0 to t=0.5, so the event at t=0.3 is available - and so on

> 

  restart;
> 

  interface(version);

`Standard Worksheet Interface, Maple 2019.2, Windows 7, November 26 2019 Build ID 1435526`

 (1)
> 

  sys := { diff(x(t), t) = 1, x(0) = 0 }:
  evs := [ [x(t)-0.1, none],  [x(t)-0.3, none], [x(t)-0.5, none] ]:
  sol := dsolve(sys, numeric, events=evs);
  plots:-odeplot(sol, [t, x(t)], t=0..0.5, gridlines=true);

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 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([Array(1..4, 1..21, {(1, 1) = 1.0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = 1.0, (1, 8) = undefined, (1, 9) = -.1, (1, 10) = 1.0, (1, 11) = undefined, (1, 12) = undefined, (1, 13) = undefined, (1, 14) = undefined, (1, 15) = undefined, (1, 16) = undefined, (1, 17) = undefined, (1, 18) = undefined, (1, 19) = undefined, (1, 20) = undefined, (1, 21) = undefined, (2, 1) = 2.0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = 1.0, (2, 8) = undefined, (2, 9) = -.3, (2, 10) = 1.0, (2, 11) = undefined, (2, 12) = undefined, (2, 13) = undefined, (2, 14) = undefined, (2, 15) = undefined, (2, 16) = undefined, (2, 17) = undefined, (2, 18) = undefined, (2, 19) = undefined, (2, 20) = undefined, (2, 21) = undefined, (3, 1) = 3.0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = 1.0, (3, 8) = undefined, (3, 9) = -.5, (3, 10) = 1.0, (3, 11) = undefined, (3, 12) = undefined, (3, 13) = undefined, (3, 14) = undefined, (3, 15) = undefined, (3, 16) = undefined, (3, 17) = undefined, (3, 18) = undefined, (3, 19) = undefined, (3, 20) = undefined, (3, 21) = undefined, (4, 1) = 3.0, (4, 2) = .0, (4, 3) = 100.0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = undefined, (4, 9) = undefined, (4, 10) = 0.10e-6, (4, 11) = undefined, (4, 12) = .0, (4, 13) = undefined, (4, 14) = .0, (4, 15) = .0, (4, 16) = undefined, (4, 17) = undefined, (4, 18) = undefined, (4, 19) = undefined, (4, 20) = undefined, (4, 21) = undefined}, datatype = float[8], order = C_order), proc (t, Y, Ypre, n, EA) EA[1, 7+2*n] := Y[1]-.1; EA[1, 8+2*n] := 1; EA[2, 7+2*n] := Y[1]-.3; EA[2, 8+2*n] := 1; EA[3, 7+2*n] := Y[1]-.5; EA[3, 8+2*n] := 1; 0 end proc, proc (e, t, Y, Ypre) return 0 end proc, Array(1..3, 1..2, {(1, 1) = undefined, (1, 2) = undefined, (2, 1) = undefined, (2, 2) = undefined, (3, 1) = undefined, (3, 2) = undefined}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (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) = 3, (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, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.5047658755841546e-2, (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)), ( 6 ) = (Array(1..1, {(1) = .0}, datatype = float[8], order = C_order)), ( 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)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 1.0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = x(t)]`; YP[1] := 1; 0 end proc, -1, 0, 0, 0, 0, proc (t, Y, Ypre, n, EA) EA[1, 7+2*n] := Y[1]-.1; EA[1, 8+2*n] := 1; EA[2, 7+2*n] := Y[1]-.3; EA[2, 8+2*n] := 1; EA[3, 7+2*n] := Y[1]-.5; EA[3, 8+2*n] := 1; 0 end proc, proc (e, t, Y, Ypre) return 0 end proc, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = x(t)]`; YP[1] := 1; 0 end proc, -1, 0, 0, 0, 0, proc (t, Y, Ypre, n, EA) EA[1, 7+2*n] := Y[1]-.1; EA[1, 8+2*n] := 1; EA[2, 7+2*n] := Y[1]-.3; EA[2, 8+2*n] := 1; EA[3, 7+2*n] := Y[1]-.5; EA[3, 8+2*n] := 1; 0 end proc, proc (e, t, Y, Ypre) return 0 end proc, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..1, {(1) = 0.}); _vmap := array( 1 .. 1, [( 1 ) = (1) ] ); _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); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `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 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] < 100 and 100 <= _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 100 <= _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] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; 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] < 100 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 _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _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 _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _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]-100, 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 _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _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]-100, 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]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _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, x(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 := 1; _ndsol := _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

  

 
> 

# times that fired the events
#
# Technically this is not an "initialization".
# In order to obtain the result at t=1, Maple
# has to "run" the solution module "sol" from
# t=0 to t=1. During this process any events
# which are "fired" will be recorded and can
# be accessed
#
  sol(1); # initialization
  sol(eventfired=[1]);
  sol(eventfired=[2]);
  sol(eventfired=[3]);
 

[t = 1., x(t) = HFloat(1.0)]

  

[HFloat(0.1)]

  

[HFloat(0.3)]

  

[HFloat(0.49999999999999994)]

 (2)
> 

# Same times computed  within a loop
#
# Does the same as above - the solution has
# still be evaluaetd between t=0 and t=1 and
# any events which are "fired" are recorded
# and can be accessed
#

  for i from 1 to 3 do
      te := op(sol(eventfired=[i]));
  end do;

HFloat(0.1)

  

HFloat(0.3)

  

HFloat(0.49999999999999994)

 (3)
> 

# Values of x(t) computed  within a loop
#
# Why are calues for events 2 and 3 wrong ?
  for i from 1 to 3 do
    #
    # First time through this loop the 'sol'
    # procedure has been evaluated above
    # between t=0 and t=1 so all "fired"
    # events can be accessed
    #
      te := op(sol(eventfired=[i]));
    #
    # Now the 'sol' procedure will be
    # re-initialized and re-evaluated
    # between t=0 and t=te, ie t=0 and
    # t=0.1. Since the stopping point for
    # this evaluation is t=0.1, then any
    # evaents which occur after this time
    # will not be accessible in the next
    # iteration of the loop. After all, if
    # you have run the procedure from t=0.0
    # to t=0.1, then you would not expect
    # to fire an eveent at t=0.3 - would you?
    #
      xe := sol(te);
  end do;

HFloat(0.1)

  

[t = HFloat(0.1), x(t) = HFloat(0.1)]

  

HFloat(0.0)

  

[t = HFloat(0.0), x(t) = HFloat(0.0)]

  

HFloat(0.0)

  

[t = HFloat(0.0), x(t) = HFloat(0.0)]

 (4)
> 

 


 

Download events.mw

Pretty simple...

tomleslie 13876
December 13 2019
1 1

See the attached - Note that you will have to change the file path in the ExcelTools:-Import() to something appropriate for where you have the data stored

> 

restart:
with(DiscreteTransforms):
data := ExcelTools:-Import("C:/Users/TomLeslie/Desktop/rr.xlsx"):
plots:-listplot(abs~(FourierTransform(data[..,2])), axis[1]=[mode=log], size=[1200, 400]);
plots:-listplot(abs~(FourierTransform(data[..,2]))^~2, axis[1]=[mode=log], size=[1200, 400]);

 

 
> 

 


 

Download dfts.mw

Numerous syntax errors...

tomleslie 13876
December 12 2019
1 1

which I found too painful to debug using 2-D math input. Using 1D input in worksheet mode (IMO the easiest way to understand/debug) the attached shows the calculation I think you are trying to

> 

  restart;
> 

  pde := ((diff(C(x, t), t) = k*diff(C(x, t), x, x)) assuming (0 < x and x < h__1, 0 < t));
  bc1 := ((C(h__1, t) = C1) assuming (0 < t));
  bc2 := C(x, 0) = C2;
  bc3 := ((D[1](C)(0, t) = 0) assuming (0 <= t));
  ans:=pdsolve([pde, bc1, bc2, bc3]);

diff(C(x, t), t) = k*(diff(diff(C(x, t), x), x))

  

C(h__1, t) = C1

  

C(x, 0) = C2

  

(D[1](C))(0, t) = 0

  

C(x, t) = Sum(-4*cos((1/2)*Pi*csgn(1/h__1)*x*(1+2*n)/h__1)*exp(-(1/4)*k*Pi^2*(1+2*n)^2*t/h__1^2)*(-1)^n*(C1-C2)/((1+2*n)*Pi), n = 0 .. infinity)+C1

 (1)
> 

  h__1, h__2 := 7*10^(-6), 250*10^(-6);
  E__1, E__2, nu__1, nu__2 := 1.13*10^9, 130*10^9, 0.32, 0.28;
  `E__1`, `E__2` := E__1/(1 - nu__1), E__2/(1 - nu__2);
  C1 := 8.23*10^(-3);
  C2 := 20.58*10^(-3);
  alpha := beta*(rhs(ans) - C2)/C2:
  kappa__T0 := 0:
  kappa__T:=kappa__T0+6*alpha* (E__1*h__1^2 - E__2*h__2^2)^2/(E__1*E__2*h__1*h__2(h__1 + h__2)) + 4*(h__1 + h__2);
 

7/1000000, 1/4000

  

1130000000., 130000000000, .32, .28

  

1661764706., 0.1805555556e12

  

0.8230000000e-2

  

0.2058000000e-1

  

257/250000+0.7070708340e-1*beta*(Sum(0.1572450838e-1*cos((500000/7)*Pi*x*(1+2*n))*exp(-(250000000000/49)*k*Pi^2*(1+2*n)^2*t)*(-1)^n/(1+2*n), n = 0 .. infinity)-0.1235000000e-1)

 (2)
> 

#
# 1D plot of kappa_T with fixed 'x'
#
  plot(eval(kappa__T, [x=5.0, beta=0.078, k=3*10^(-12)]), t = 0 .. 20);
#
# 2D plot of kappa_T  as function of (x,t)
#
  plot3d(eval(kappa__T, [beta=0.078, k=3*10^(-12)]), t = 0 .. 20, x=0..10)

 

 
> 

 


 

Download pdeProb.mw

Specify tickmarks for both axes...

tomleslie 13876
December 09 2019
1 0

as in the attached

> 

  restart;
  with(GraphTheory):
> 

  G := SpecialGraphs[DodecahedronGraph]():
  DrawGraph(G);
  A := AdjacencyMatrix(G):
  plots:-sparsematrixplot(A, size=[900,900]);

 

 
> 

  S := [$1..20] =~ StringTools:-Char~(96 +~  [$1..20]):
  plots:-sparsematrixplot(A, axis[1]=[tickmarks=[S]],axis[2]=[tickmarks=[S]], size=[900,900])

 
> 

 

> 

 

> 

 

> 

 

Download ticks.mw

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