tomleslie

6548 Reputation

17 Badges

10 years, 145 days

MaplePrimes Activity


These are answers submitted by tomleslie

on the nature of the quantity 'A' - some kind of table/matrix maybe?

First of all I suggest that you read the help page for the 'op()' command, and maybe consider the example in the attached

  restart;

  A:=LinearAlgebra:-RandomMatrix(8,2)

Matrix(8, 2, {(1, 1) = -93, (1, 2) = 8, (2, 1) = -76, (2, 2) = 69, (3, 1) = -72, (3, 2) = 99, (4, 1) = -2, (4, 2) = 29, (5, 1) = -32, (5, 2) = 44, (6, 1) = -74, (6, 2) = 92, (7, 1) = -4, (7, 2) = -31, (8, 1) = 27, (8, 2) = 67})

(1)

#
# So how does Maple represent this matrix internally.
#
# First show all of its operands
#
  op([0..-1],A);

Matrix, 8, 2, {(1, 1) = -93, (1, 2) = 8, (2, 1) = -76, (2, 2) = 69, (3, 1) = -72, (3, 2) = 99, (4, 1) = -2, (4, 2) = 29, (5, 1) = -32, (5, 2) = 44, (6, 1) = -74, (6, 2) = 92, (7, 1) = -4, (7, 2) = -31, (8, 1) = 27, (8, 2) = 67}, datatype = anything, storage = rectangular, order = Fortran_order, shape = []

(2)

#
# Now select the second operand of A
#
  op(2,A);

{(1, 1) = -93, (1, 2) = 8, (2, 1) = -76, (2, 2) = 69, (3, 1) = -72, (3, 2) = 99, (4, 1) = -2, (4, 2) = 29, (5, 1) = -32, (5, 2) = 44, (6, 1) = -74, (6, 2) = 92, (7, 1) = -4, (7, 2) = -31, (8, 1) = 27, (8, 2) = 67}

(3)

#
# Select the first operand from within the second operand
#
  op([2,1],A);

(1, 1) = -93

(4)

#
# Select the second operand from within the first operand of A
# from withing the second operand
#
  op([2,1,2],A);

-93

(5)

#
# So for the above Matrix A the three view range options
# would return
#
  0..op([2, 1, 2], A);
  0..op([2, 2, 2], A);
   min(0, A[..,2] )..max(A[..,2]);

0 .. -93

 

0 .. 8

 

-31 .. 99

(6)

 

Download ops.mw

Just solving the system in your original worksheet is pretty trivial - see the attached


 

restart;

eqs := diff(q(y), y, y) - A*q(y) = B*(P*y + c1),
       (1 + N)*diff(u(y), y, y) + N*diff(q(y), y) = P;
bcs := q(-sigma) = 0, q(sigma) = 0,
       u(-sigma) = 1, u(sigma) = -k;

diff(diff(q(y), y), y)-A*q(y) = B*(P*y+c1), (1+N)*(diff(diff(u(y), y), y))+N*(diff(q(y), y)) = P

 

q(-sigma) = 0, q(sigma) = 0, u(-sigma) = 1, u(sigma) = -k

(1)

  simplify~
  ( convert~
    ( dsolve
      ( [eqs, bcs],
        [q(y), u(y)]
      ),
      trigh
    )
  );

{q(y) = -B*(((P*y+c1)*sinh(A^(1/2)*sigma)-sinh(A^(1/2)*y)*P*sigma)*cosh(A^(1/2)*sigma)-cosh(A^(1/2)*y)*sinh(A^(1/2)*sigma)*c1)/(A*cosh(A^(1/2)*sigma)*sinh(A^(1/2)*sigma)), u(y) = (1/2)*(2*N*B*(P*sigma^2+c1*y)*cosh(A^(1/2)*sigma)^2+(((-P*sigma^3+((-k+1)*N+P*y^2-k+1)*sigma-y*(k+1)*(1+N))*A^(3/2)+A^(1/2)*B*N*P*sigma*(-sigma+y)*(sigma+y))*sinh(A^(1/2)*sigma)-2*B*N*cosh(A^(1/2)*y)*P*sigma^2)*cosh(A^(1/2)*sigma)-2*B*N*c1*(sinh(A^(1/2)*y)*sinh(A^(1/2)*sigma)*sigma+y))/(A^(3/2)*(1+N)*sigma*cosh(A^(1/2)*sigma)*sinh(A^(1/2)*sigma))}

(2)

 

 


 

Download odeSols.mw

 

In the attached, I have reproduced your calculations in a somewhat more organised and systematic way.

The worksheet reproduces the answers which you have already obtained

This suggests that your problem is not really a "Maple issue", but something wrong with the logic of your calculation - in other words it is a case of "garbage in = garbage out"

Anyhow, for what it is worth, you might want to read the comments in the attached very carefully

  restart;

  with(LinearAlgebra):
#
# increase 'rtablesiz' so that all entries
# in matrices will display
#
  interface(rtablesize=12):
#
# Decrease the display precision, for more
# compact output. Doesn't affect the accuracy
# with which calculations are performed, just
# helps to keep the output display a bit more
# "compact'
#
  interface(displayprecision=4):

#
# Specify some parameters
#
  L:= 1: x_1:= 4.8231: a_L:= 0.25:
  b_L:= 0.25: c_L:= 0.5:

#
# Define a 12*12 matrix - no idea where this comes
# from (or what it means)
#
  M1:= Matrix
       ( 12,
         [ [0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
           [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
           [sin(S_1), cos(S_1), sinh(S_1), cosh(S_1), 0, 0, 0, 0, 0, 0, 0, 0],
           [cos(S_1), -sin(S_1), cosh(S_1), sinh(S_1), -cos(S_1), sin(S_1), -cosh(S_1), -sinh(S_1), 0, 0, 0, 0],
           [-sin(S_1), -cos(S_1), sinh(S_1), cosh(S_1), sin(S_1), cos(S_1), -sinh(S_1), -cosh(S_1), 0, 0, 0, 0],
           [-cos(S_1), sin(S_1), cosh(S_1), sinh(S_1), cos(S_1), -sin(S_1), -cosh(S_1), -sinh(S_1), 0, 0, 0, 0],
           [0, 0, 0, 0, sin(S_2), cos(S_2), sinh(S_2), cosh(S_2), 0, 0, 0, 0],
           [0, 0, 0, 0, cos(S_2), -sin(S_2), cosh(S_2), sinh(S_2), -cos(S_2), sin(S_2), -cosh(S_2), -sinh(S_2)],
           [0, 0, 0, 0, -sin(S_2), -cos(S_2), sinh(S_2), cosh(S_2), sin(S_2), cos(S_2), -sinh(S_2), -cosh(S_2)],
           [0, 0, 0, 0, -cos(S_2), sin(S_2), cosh(S_2), sinh(S_2), cos(S_2), -sin(S_2), -cosh(S_2), -sinh(S_2)],
           [0, 0, 0, 0, 0, 0, 0, 0, -sin(S_3), -cos(S_3), sinh(S_3), cosh(S_3)],
           [0, 0, 0, 0, 0, 0, 0, 0, -cos(S_3), sin(S_3), cosh(S_3), sinh(S_3)]
         ]
       );

Matrix(12, 12, {(1, 1) = 0, (1, 2) = -1, (1, 3) = 0, (1, 4) = 1, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (2, 1) = -1, (2, 2) = 0, (2, 3) = 1, (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, (3, 1) = sin(S_1), (3, 2) = cos(S_1), (3, 3) = sinh(S_1), (3, 4) = cosh(S_1), (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (4, 1) = cos(S_1), (4, 2) = -sin(S_1), (4, 3) = cosh(S_1), (4, 4) = sinh(S_1), (4, 5) = -cos(S_1), (4, 6) = sin(S_1), (4, 7) = -cosh(S_1), (4, 8) = -sinh(S_1), (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (5, 1) = -sin(S_1), (5, 2) = -cos(S_1), (5, 3) = sinh(S_1), (5, 4) = cosh(S_1), (5, 5) = sin(S_1), (5, 6) = cos(S_1), (5, 7) = -sinh(S_1), (5, 8) = -cosh(S_1), (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (6, 1) = -cos(S_1), (6, 2) = sin(S_1), (6, 3) = cosh(S_1), (6, 4) = sinh(S_1), (6, 5) = cos(S_1), (6, 6) = -sin(S_1), (6, 7) = -cosh(S_1), (6, 8) = -sinh(S_1), (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = sin(S_2), (7, 6) = cos(S_2), (7, 7) = sinh(S_2), (7, 8) = cosh(S_2), (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = cos(S_2), (8, 6) = -sin(S_2), (8, 7) = cosh(S_2), (8, 8) = sinh(S_2), (8, 9) = -cos(S_2), (8, 10) = sin(S_2), (8, 11) = -cosh(S_2), (8, 12) = -sinh(S_2), (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = -sin(S_2), (9, 6) = -cos(S_2), (9, 7) = sinh(S_2), (9, 8) = cosh(S_2), (9, 9) = sin(S_2), (9, 10) = cos(S_2), (9, 11) = -sinh(S_2), (9, 12) = -cosh(S_2), (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = -cos(S_2), (10, 6) = sin(S_2), (10, 7) = cosh(S_2), (10, 8) = sinh(S_2), (10, 9) = cos(S_2), (10, 10) = -sin(S_2), (10, 11) = -cosh(S_2), (10, 12) = -sinh(S_2), (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) = -sin(S_3), (11, 10) = -cos(S_3), (11, 11) = sinh(S_3), (11, 12) = cosh(S_3), (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) = -cos(S_3), (12, 10) = sin(S_3), (12, 11) = cosh(S_3), (12, 12) = sinh(S_3)})

(1)

#
# One thing which the OP does is to substitute some "simple"
# functions of the unknown 'x' into the above matrix, and then
# plots the determinant of the result.
#
# No idea what the significance of this plot is: but for what
# it is worth - let's do it anyway
#
  plot
  ( Determinant
    ( eval
      ( M1,
        [ S_1 = x*L*a_L,
          S_2 = x*L*(a_L + b_L),
          S_3 = x*L*(a_L + b_L + c_L)
        ]
      )
    ),
    x=0..2*Pi
  );

 

###################################################################
#                                                                 #
# The following calculation makes no real sense to me at all, but #
# this reproduces the OP's worksheet hopefully in a somewhat      #
# clearer manner                                                  #
#                                                                 #
###################################################################

#
# Evaluate the above matrix with the unknowns S_1,
# S_2 and S_3 expressed in terms of parameter values
# defined earlier
#
# This is the same substitution as used in computation of the
# determinant above with the exception that  rather than using
# an unknown variable 'x', it uses the parameter x_1, with a
# value of 4.8231. (No idea where this value of 4,8321 comes from!!)
#
  M2:= eval( M1,
             [ S_1 = x_1*L*a_L,
               S_2 = x_1*L*(a_L + b_L),
               S_3 = x_1*L*(a_L + b_L + c_L)
             ]
           );

Matrix(12, 12, {(1, 1) = 0, (1, 2) = -1, (1, 3) = 0, (1, 4) = 1, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (2, 1) = -1, (2, 2) = 0, (2, 3) = 1, (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, (3, 1) = .9341, (3, 2) = .3570, (3, 3) = 1.5199, (3, 4) = 1.8194, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (4, 1) = .3570, (4, 2) = -.9341, (4, 3) = 1.8194, (4, 4) = 1.5199, (4, 5) = -.3570, (4, 6) = .9341, (4, 7) = -1.8194, (4, 8) = -1.5199, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (5, 1) = -.9341, (5, 2) = -.3570, (5, 3) = 1.5199, (5, 4) = 1.8194, (5, 5) = .9341, (5, 6) = .3570, (5, 7) = -1.5199, (5, 8) = -1.8194, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (6, 1) = -.3570, (6, 2) = .9341, (6, 3) = 1.8194, (6, 4) = 1.5199, (6, 5) = .3570, (6, 6) = -.9341, (6, 7) = -1.8194, (6, 8) = -1.5199, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = .6669, (7, 6) = -.7451, (7, 7) = 5.5308, (7, 8) = 5.6205, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = -.7451, (8, 6) = -.6669, (8, 7) = 5.6205, (8, 8) = 5.5308, (8, 9) = .7451, (8, 10) = .6669, (8, 11) = -5.6205, (8, 12) = -5.5308, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = -.6669, (9, 6) = .7451, (9, 7) = 5.5308, (9, 8) = 5.6205, (9, 9) = .6669, (9, 10) = -.7451, (9, 11) = -5.5308, (9, 12) = -5.6205, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = .7451, (10, 6) = .6669, (10, 7) = 5.6205, (10, 8) = 5.5308, (10, 9) = -.7451, (10, 10) = -.6669, (10, 11) = -5.6205, (10, 12) = -5.5308, (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) = .9939, (11, 10) = -.1105, (11, 11) = 62.1710, (11, 12) = 62.1790, (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) = -.1105, (12, 10) = -.9939, (12, 11) = 62.1790, (12, 12) = 62.1710})

(2)

#
# No more matrices to display so reset the display precisiion
#
  interface(displayprecision=-1):

#
# Idle curiosity (the OP doesn't do this in his original worksheet)
# but what happens if one looks for a solution of the complete
# linear system, defined by the above matrix M2 - solutions
# are identically zero - no idea if this is significant or not
#
  LinearSolve( M2, Vector(12, fill=0));

Vector(12, {(1) = -0., (2) = -0., (3) = 0., (4) = -0., (5) = -0., (6) = -0., (7) = 0., (8) = 0., (9) = 0., (10) = -0., (11) = -0., (12) = 0.})

(3)

#
# This is where it gets really weird. Rather than solving the
# complete 12 X 12 matrix M2 (whihc as shown above would be
# identically zero), the OP extracts the first eleven rows of
# the matrix M2, and uses this as a 12*11 coefficient matrix,
# and solves the matrix equation
#
#      M2[1..11,1..12] . x[1..11] = b[1..11]
#
# for the vector 'x', with the vector 'b' being identically 0
#
# Note that since the coefficient matrix is 11 X 12, the 11-element
# solution vector will contain a 'free' parameter
#
  sol:=LinearSolve( M2[1..11,..], Vector(11, fill=0));
 

Vector(12, {(1) = .10144366371771879*_t0[1], (2) = -.11438703694640917*_t0[1], (3) = .10144366371771879*_t0[1], (4) = -.11438703694640917*_t0[1], (5) = 0.709513414043042e-1*_t0[1], (6) = -.12603957118214704*_t0[1], (7) = .15105911639526973*_t0[1], (8) = -.1737777468223752*_t0[1], (9) = .21022728290544188*_t0[1], (10) = -.2816561313410131*_t0[1], (11) = -1.0039906216693695*_t0[1], (12) = _t0[1]})

(4)

#
# The OP seems to want the coefficients of the 'free' parameter in
# the above solution. Then taking these coefficients in blocks
# of four, use these to multiply a Vector of functions of x to
# generate some expressions which don't seem to bear much relation to
# anything which has gone before??!
#
   terms:= Vector( [ sin(x_1*x), cos(x_1*x), sinh(x_1*x), cosh(x_1*x)]):
   pltEqs:= Vector( [ seq( Transpose(sol/~indets(sol)[])[j..j+3].terms,
                          j=1..9, 4
                        )
                   ]
                 );
#
# But plot them anyway
#
   plot( convert(pltEqs,list),
         x = 0 .. 1,
         color = [blue, green, red]
       );

Vector(3, {(1) = .10144366371771879*sin(4.8231*x)-.11438703694640917*cos(4.8231*x)+.10144366371771879*sinh(4.8231*x)-.11438703694640917*cosh(4.8231*x), (2) = 0.709513414043042e-1*sin(4.8231*x)-.12603957118214704*cos(4.8231*x)+.15105911639526973*sinh(4.8231*x)-.1737777468223752*cosh(4.8231*x), (3) = .21022728290544188*sin(4.8231*x)-.2816561313410131*cos(4.8231*x)-1.0039906216693695*sinh(4.8231*x)+cosh(4.8231*x)})

 

 

NULL

 

 

NULL


 

Download oddPlots.mw

it is difficult to provide detailed help. I can only suggest that you read the help for the command

StringTools:-DecodeEntities()

to see if it meets your requirements

maybe something like the attached?

  restart;
  with(plots):
  T:=Array([[1,2],[1.5,1]]):
  display
  ( [ seq
      ( seq
        ( plot3d
          ( T[i,j],
            x=i-1..i,
            y=j-1..j,
            shading=zhue,
            style=surface,
            axes=normal,
            view=[0..2,0..2,0..2]
          ),
          i=1..2
        ),
        j=1..2
      )
    ]
  );

 

 

Download arrplot2.mw

 

 

but maybe  something in the attached worksheet will help.

You can extract the final animation to a GIF by rightclicking it and using Export->GIF

  restart;
  with(plots): with(plottools): with(ColorTools): with(combinat):

#
# Number of terms in the fibonacci sequence. Ajust
# as required
#
  N:=24:
#
# A couple of utilities
#
  g:= k-> round~( convert( op(1, a[k])[-1,..], list)):
  h:= k-> round~( convert( op(1, a[k])[1,..], list)):
#
# Initialise the first arc and rectangle
#
  a[1]:= arc( [0,0], fibonacci(1),0..Pi/2):
  r[1]:= rectangle( g(1), h(1)):

#
# Loop through all subsequent arc sections and
# rectangles
#
  for j from 2 by 1 to N do
      fj:=fibonacci(j):
    #
    # Generate the arc section
    #
      a[j]:= arc
             ( [ g(j-1)[1]+cos((j+1)*Pi/2)*fj,
                 g(j-1)[2]+sin((j+1)*Pi/2)*fj
               ],             
               fj,
               (j-1)*Pi/2..j*Pi/2
             );
    #
    # and the corresponding rectangle
    #
      r[j]:= rectangle
             ( g(j),
               h(j),
               color=Color( [ seq( rand()/10^12, k=1..3 ) ] )
             );
  od:

#
# Animate both the arc and the rectangles of the spiral
#
  display
  ( [ seq
      ( display
        ( [ seq( [a[j],r[j]][], j=1..i) ] ),
        i=1..N
      )
    ],
    scaling=constrained,
    axes=none,
    insequence=true,
    size=[1200,1200]
  );

 

 

Download fibSpiral.mw

 

The attached shows two ways of achieving the same thing whilst alllowing for both numeric and non-numeric arguments

  h:= x->`if`( type(x, numeric),
               piecewise( x<=0,
                          sin(3*x),
                          sin(x/3)
                        ),
              'h(x)'
             ):
  h(1);h(x);
  plot( h(x), x=-10..10);

sin(1/3)

 

h(x)

 

 

  H:= proc(x)
           if   type(x, numeric)
           then  return piecewise( x<=0,
                                   sin(3*x),
                                   sin(x/3)
                                 ):
           else  return 'procname(x)'
           fi;
      end proc:
  H(1); H(x);
  plot( H(x), x=-10..10);

sin(1/3)

 

H(x)

 

 

 

 


 

Download pwise.mw

Although the CUDA help page states (my emphasis)

The CUDA package allows Maple to use the graphics processing unit (GPU) of your NVIDIA(R) Compute Unified Device Architecture (CUDA)-enabled hardware to accelerate certain LinearAlgebra routines.

However if you check the page referenced as

the Routines Accelerated by the CUDA Package help page.

You will find that it contains precisely one entry, namely MatrixMatrixMultiply(). I take this to mean that any time one uses a high-level command for the LinearAlgebra() package which contains a matrix multiplication operation, then that operatio will be "CUDA-accelerated".

When I try this on my own machine running the multiplication example on the CUDA help page, then everything *seems* to work, although the CUDA-acceleration is not significant. In fact I obtained tNoCUDA := 1.813 and tCUDA := 1.880. On the assumption that I needed a "bigger" problem with "bigger" matrices so that the cost of setup/retrieval etc did not dominate the actual multiplication, I doubled the matrix size to 8000 - and tried the help page example again and promptly got a (temporary) black screen followed by a pop-up stating display driver error!!!

Now I'm prepared to admit my (Nvidia) graphics card is pretty old (2047MB NVIDIA GeForce GTX680), although the drivers are up to date.

Maybe in order to obtain significant benefits from GPU processing I need a newer card, with more cores and significantly more vram? I have been promising myself a whole new computer for quite some time now, but just haven't got around to building one

 

 

other than the "large" file takes a while - see the attached

So you are probably going to have to expalin what you mean by "consistency"

Download csvReadStuff.mw

when I explained how to do this manually by pointing to the reference

https://www.mapleprimes.com/questions/229832-Phyysics-Updates-Installation

I'm going to try to make things really easy You have a directory called "C:\Users\jm\maple\toolbox. In order to update to the latest/greatest Physics udates, this directory needs a (valid) folder structure which looks like

2020
           PhysicsUpdates
                                       lib
                                             override_maple.txt
                                            
Physics Updates_1592550562672.maple                                      
                                       version.txt

Attached to this message is a zip file which 'starts' with the folder called '2020'. All you have to do is to unzip it to your directory "C:\Users\jm\maple\toolbox, in order to produce the following directory structure

C
    Users
               jm
                    maple
                               toolbox
                                            2020

                                                     PhysicsUpdates
                                                                                  lib
                                                                                        override_maple.txt
                                                                                       
Physics Updates_1592550562672.maple                                      
                                                                                  version.txt

 

If you manage to achieve this then everything should just "work".

Should the Maple update process be able to achieve this? Obviously yes. However it seems that it is very good at sticking up assorted html subwindows, progress bars and all sorts of other irrelevant crap. Jusr very bad at the basic task of putting the right effin files in the right effin place :-(

Attachment

physUpDate.zip

Good luck!

there is no way to (directly) access Sage from Maple. (obviously one could probably do it with system calls, but this generally gets very untidy, very quickly)

A better approach may be just to write the necessary code within Maple.

I don't know anything about "Topological indices in Graph theory" - but the definition of the Wiener index, given here

https://en.wikipedia.org/wiki/Wiener_index

seems pretty trivial to implement, using commands from Maple's Graph Theory package. (Not sure about other topological indices - I didn't check)

The attached (correctly!!) computes the Wiener index for the two examples given in the above Wikipedia article

  restart;

  with(GraphTheory):
  with(SpecialGraphs):
  G1:= Graph( {{1,2},{2,3},{3,4}});
  G2:= StarGraph(3);

GRAPHLN(undirected, unweighted, [1, 2, 3, 4], Array(1..4, {(1) = {2}, (2) = {1, 3}, (3) = {2, 4}, (4) = {3}}), `GRAPHLN/table/1`, 0)

 

GRAPHLN(undirected, unweighted, [0, 1, 2, 3], Array(1..4, {(1) = {2, 3, 4}, (2) = {1}, (3) = {1}, (4) = {1}}), `GRAPHLN/table/6`, 0)

(1)

  DrawGraph(G1);
  DrawGraph(G2);

 

 

  wienerIndex:=proc( g::Graph)
                     uses GraphTheory;
                     local v:=NumberOfVertices(g),
                           dists:=AllPairsDistance(g):
                     return add
                            ( add
                              ( dists[i,j],
                                j=i+1..v
                              ),
                              i=1..v
                            ):
         end proc:
  wienerIndex(G1);
  wienerIndex(G2);

10

 

9

(2)

 


Download wiener.mw

because it isn't obvious from your worksheet

I made a couple of animations in the attachment - maybe one of these is what you intend?


 

NULL

plots:-setoptions3d(scaling = constrained, axes = none, shading = zhue, view = [-1 .. 1, -1 .. 1, -1 .. 1])

with(plots)

with(plottools)

with(geom3d)

p := display(draw(tetrahedron(f, point(o, 0, 0, 0))), title = "Tetrahedron \n 4 Vertices, 6 Edges, 4 Faces")

 

p1 := display(draw(cube(f, point(o, 0, 0, 0))), title = "Cube (or hexahedron) \n 8 Vertices, 12 Edges, 6 Faces")

 

p2 := display(draw(octahedron(f, point(o, 0, 0, 0))), title = "Octahedron \n 6 Vertices, 12 Edges, 8 Faces")

 

p3 := display(draw(dodecahedron(f, point(o, 0, 0, 0), .6)), title = "Dodecahedron \n 20 Vertices, 30 Edges, 12 Faces")

 

p4 := display(draw(icosahedron(f, point(o, 0, 0, 0))), title = "Icosahedron \n 12 Vertices, 30 Edges, 20 Faces")

 

display([p, p1,p2,p3,p4], insequence=true);

 

display( [seq( plottools:-rotate(p, 0, 0, j), j=0..evalf(2*Pi), evalf(Pi/16))], insequence=true);

 

NULL


 

Download anim.mw

the use of the SolveTools() package can be useful. It appears to be in this case!

See the attached

restart:
expr:=-1/2*ln(u)-1/4*ln(u^2+2)-ln(x)-C[1]:
SolveTools:-Combine(expr);
solve(%, u);

-C[1]-(1/4)*ln(u^2*x^4*(u^2+2))

 

(-x^2+(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, -(-x^2+(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, (-x^2-(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x, -(-x^2-(x^4+exp(-4*C[1]))^(1/2))^(1/2)/x

(1)

 

Download STcom.mw

is just to test both solution for _B1 in {0,1} and a range of integers for _Z1 as in


 

restart;
s:=solve(sin(x^2)=1/2,allsolutions);

(1/6)*(24*Pi*_B1+72*Pi*_Z1+6*Pi)^(1/2), -(1/6)*(24*Pi*_B1+72*Pi*_Z1+6*Pi)^(1/2)

(1)

#
# Convert the above solutions to applicable
# functions
#
  tf:=unapply~(sin~(simplify~([s]^~2)), _B1,_Z1);
#
# Evaluate both of these functions for _B1 in {0,1}
# and _Z1 any value from -10..10
#
  seq
  ( seq
    ( tf(i,j)[],
      i=0..1
    ),
    j=-10..10
  );

[proc (_B1, _Z1) options operator, arrow; sin((1/6)*Pi*(4*_B1+12*_Z1+1)) end proc, proc (_B1, _Z1) options operator, arrow; sin((1/6)*Pi*(4*_B1+12*_Z1+1)) end proc]

 

1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2

(2)

 


 

Download testSol.mw

Well - if I fix the syntax errors, and then remove all references to parameters which are never used anywhere in your ODE system, but you want optimal values for (neat trick if you can do it!?), then allow for the fact that the Optimiser might attempt to use parameter values for whihc the dsolve() operation cannot find a meaningful solution etc, etc, etc, I can eventually come up with the attached - whihc does produce an "optimal" solution. However looking at the size of the residual error, I have doubts about how useful/relevant it is???

Anyhow for what it is worth (not much I suspect) see the attached

restart; with(plots); with(Optimization); with(Statistics)

A := 0.346e-1; mu := 0.491e-1
Parameterizing (with respect to l, m, n, rho, k, q, r, u, v, sigma, iota, nu, phi, upsilon, w, x, delta, g) the numerical solution of the model deq
      #Calculating the sum of the square of the errors between the model predictions and experimental data
     #Minimizing the sum of the square of the errors to find the best fit values of " l, m, n ,rho, k, q, r, u , v , sigma, iota, nu, phi,upsilon, w, x, delta, g."

0.346e-1

 

0.491e-1

(1)

times := [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

(2)

C__f := [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8, 12, 12, 22, 30, 40, 44, 51, 65, 70, 97, 111, 131, 135, 174, 184, 210, 214, 232, 238, 254, 276, 285, 305, 318, 323, 343, 373, 407, 442, 493, 542, 627, 665, 782, 873, 981, 1095, 1182, 1273, 1337, 1532, 1728, 1932, 2170, 2388, 2558, 2802, 2950, 3145, 3526, 3912, 4151, 4399, 4641, 4787, 4971, 5162, 5445, 5621, 5959, 6175, 6401, 6677, 7016, 7261, 7526, 7839, 8068, 8344, 8733, 8915, 9302, 9855, 10162, 10819, 11166, 11516, 11844, 12233, 12486, 12801, 13464, 13873, 14554, 15181, 15682, 16085, 16658, 17148, 17735]

DE1 := diff(B(T), T) = A-l*B(T)*C(T)/(1+sigma*C(T))-nu*m*B(T)*P(T)/(1+iota*P(T))-mu*B(T)-n*B(T)*E(T)/(E(T)+g); DE2 := diff(C(T), T) = l*B(T)*C(T)/(1+sigma*C(T))-q*C(T)-r*C(T)-phi; DE3 := diff(P(T), T) = nu*m*B(T)*P(T)/(1+iota*P(T))-u*P(T)-v*P(T)-upsilon; DE4 := diff(E(T), T) = phi*C(T)+upsilon*P(T)-delta*E(T); DE5 := diff(F(T), T) = q*C(T)+u*P(T)-mu*F(T); ics := B(0) = 19000, C(0) = 160000, P(0) = 17000, E(0) = 10000, F(0) = 15500

res := dsolve({DE1, DE2, DE3, DE4, DE5, ics}, parameters = [l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g], 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 := [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]; _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 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 5, (2) = 5, (3) = 0, (4) = 0, (5) = 14, (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) = 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, (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..19, {(1) = 19000., (2) = 160000., (3) = 10000., (4) = 15500., (5) = 17000., (6) = Float(undefined), (7) = Float(undefined), (8) = Float(undefined), (9) = Float(undefined), (10) = Float(undefined), (11) = Float(undefined), (12) = Float(undefined), (13) = Float(undefined), (14) = Float(undefined), (15) = Float(undefined), (16) = Float(undefined), (17) = Float(undefined), (18) = Float(undefined), (19) = Float(undefined)})), ( 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..5, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 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}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8]), Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..19, {(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}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 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] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..19, {(1) = 0., (2) = 19000., (3) = 160000., (4) = 10000., (5) = 15500., (6) = 17000., (7) = undefined, (8) = undefined, (9) = undefined, (10) = undefined, (11) = undefined, (12) = undefined, (13) = undefined, (14) = undefined, (15) = undefined, (16) = undefined, (17) = undefined, (18) = undefined, (19) = undefined}); _vmap := array( 1 .. 5, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5)  ] ); _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, B(T), C(T), E(T), F(T), P(T)], (4) = [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]}); _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

(3)

sse:=proc( l, m, n , q, r, u , v , sigma, iota, nu, phi,upsilon, delta, g);
     local testRes:

    res(parameters=[ l, m, n ,q, r, u , v , sigma, iota, nu, phi,upsilon, delta, g]);

    try   testRes:=add( (C__f[i]-rhs(res(times[1])[3]))^2, i=1..numelems(times))
    catch "cannot evaluate the solution":
          testRes:=10^12;
    end try;
    return testRes;
  end proc:

optPars:=Minimize( 'sse'( l, m, n, q, r, u, v, sigma, iota, nu, phi,upsilon, delta, g),
                   initialpoint={ l=0.05, m=0.02, n=0.017, q=0.004,
                                  r=0.098710, u=0.0100, v=0.08543,
                                  sigma=0.0349, iota=0.0032, nu=0.0014,
                                  phi=0.931, upsilon=0.0019, delta=0.01,
                                  g= 0.3
                                },
                   assume=nonnegative,
                   optimalitytolerance=0.00001
                 );

[78067722.2126978040, [delta = HFloat(0.0), g = HFloat(0.3000006496784401), iota = HFloat(0.0), l = HFloat(0.05574983967997584), m = HFloat(0.027015695985550744), n = HFloat(0.029159283217039977), nu = HFloat(3.9010512253698812), phi = HFloat(0.9316734694230215), q = HFloat(4.244163520259199e-4), r = HFloat(0.8781371378666069), sigma = HFloat(0.11661527098829708), u = HFloat(5.712096063240794e-7), upsilon = HFloat(1.1044840588712213e-4), v = HFloat(0.0854299992060102)]]

(4)

 

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