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MaplePrimes Questions

Solve equations...

Asked by: yangtheary 290
solve
May 13 2015
1  7

solve 30a+75b+110c+85d+255e+160f+15g+12h+120i=800000 over the positive integers

how to export a plot from maple to excel...

Asked by: mostibra 20
plot export
May 13 2015
1  3

how to export a plot with its points  (x,y) from maple to excel

Calculating determinant of a matrix of Bessel Func...

Asked by: Sagar 15
linear-algebra determinant
May 13 2015
1  5

Hello Everyone

 

I am new to Maple and I have to find the determinant of the following matrix

 

Matrix comprising of Bessel Functions whose determinant is to be calculated

 

https://drive.google.com/file/d/0B_60Jre5scdoSTJ3WUVaMUlidzA/view?usp=sharing

Here k is a constant.

 

Can you please help me with it.

 

Thanks in advance.

general case of floats not handled...

Asked by: mcyf0913 5
May 13 2015
1  1

g:=Groebner:-Basis([a-2.0*b,b-2], plex);

Groebner:-Reduce(a, g, plex); 

Error, (in content/polynom) general case of floats not handled

How to solve this problem simply？

complicated wave equation ...

Asked by: mostibra 20
pde wave
May 12 2015
0  1

now the equation is

d2u/dt2-(2*d2u/x2)+d2u/dxdt=0    

initial condition: u(x,0)=1-(xsign(x)), abslute x<1,0 otherwise. Assume sign(x)=-1 for x<0, 1for x>0 

 Ut(x,0)=cos(pix), bslute x<1, 0 otherwise , he didnt give any B.Cs

so I would like to know the analytical and numerical sols, and plots for the wave at t=2,4

for Numerical:   delta x=0.1, delta t=0.025, range 0..4

How can Maple plot both analytic and numerical sol...

Asked by: emmantop 40
plot
May 12 2015
0  2

Please how can Maple plot both analytic and numerical solutions on the same axes for this problem Ana_Nume.mw

how to plot this traveling wave...

Asked by: mostibra 20
plot wave
May 12 2015
0  5

U(x,t)= 2/3f(x+t)+1/3f(x-2t)+(1/3pi)(sin(pi(x+t))+(1/3pi)(sin(pi(x-2t)),

f(x)=1-x,abslutex<1, zero otherwise

Plot sequence with null values...

Asked by: mantas84 30
plot sequence
May 12 2015
0  1

I am trying to plot sequence like:

arrayZ[1]:=NULL;
arrayZ[2]:=5;
arrayZ[3]:=NULL;
arrayZ[4]:=NULL;
arrayZ[5]:=8;

...

arrayZ[3000]:=1111;
data:=[seq([n,arrayZ[n]], n=1..3000)]:
t1:=plot(data, style=point, symbol = solidcircle, color= red):
plots[display]({t1});

but get incorrect first argument error. How to fix this?

PS. In original sequence instead of null I have constant value, but I don't want it in my plot.


How can error convergence be corrected?...

Asked by: emmantop 40
numeric bvp
May 12 2015
0  9

Good day,

How can this be corrected ''Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging'' see the worksheet here VT.mw

Towards a compiled Newton Raphson...

Asked by: Dr. Venkat Subramanian 431
May 11 2015
2  14

Acer, 

Thanks. This request from me comes from the need that Maple does not have a real DAE solver. (It converts ODEs to DAEs and then solves, which fails for nonlinear and most non-trivial DAEs).

Your question is valid. For situations which can be compiled (i.e, no Heaviside or functions that can't be compiled) at hardware floats, I would like to have a Newton Raphson solver. Some parameters (time values) change when you integrate DAEs, which means that there is a need to solve the same set of nonlinear equations again and again for minor changes in parameters.

While LinearSolve is fast, evaluating F and Jac for a large system of equations can kill the speed. I am attaching an example for Newton wherein F, Jac and a linear solver is compiled. But the Newton procedure is not. If we can compile the Newton procedure also, it will be much more faster.

Also, having a compiled code with parametric form will help in optimization. 

> 

restart:
> 

Digits:=15;

Digits := 15

 (1)
> 

N:=4;

N := 4

 (2)
> 

f:=array([seq(evalf(-2*x[i]+x[i]^2+0.99/i^2),i=1..N)]);

f := Vector[row](4, {(1) = -2.*x[1]+x[1]^2+.99, (2) = -2.*x[2]+x[2]^2+.247500000000000, (3) = -2.*x[3]+x[3]^2+.110000000000000, (4) = -2.*x[4]+x[4]^2+0.618750000000000e-1})

 (3)
> 

fsolve({f[1],f[2],f[3],f[4]},{x[1]=1.2,x[2]=1,x[3]=0,x[4]=0});

{x[1] = .900000000000000, x[2] = .132532421355126, x[3] = 1.94339811320566, x[4] = 0.314314686094742e-1}

 (4)
> 

 

> 

eqsA := [seq(F[i]=f[i],i=1..N)]:
> 

irform2 := StatSeq(seq(Assign(op(i)),i=eqsA)):
> 

prccons:= codegen[intrep2maple](Proc(Parameters(x::Array,F::Array),irform2)):
> 

f3:=Compiler:-Compile(prccons):

 

 
> 

x0:=Vector([seq(1/2,i=1..N)],datatype=float[8]);

x0 := Vector(4, {(1) = .500000000000000, (2) = .500000000000000, (3) = .500000000000000, (4) = .500000000000000})

 (5)
> 

f0:=Vector([seq(0,i=1..N)],datatype=float[8]);

f0 := Vector(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.})

 (6)
> 

eqsJ := [seq(seq(Jac[i,j]=evalf(diff(f[i],x[j])),j=1..N),i=1..N)];

eqsJ := [Jac[1, 1] = -2.+2.*x[1], Jac[1, 2] = 0., Jac[1, 3] = 0., Jac[1, 4] = 0., Jac[2, 1] = 0., Jac[2, 2] = -2.+2.*x[2], Jac[2, 3] = 0., Jac[2, 4] = 0., Jac[3, 1] = 0., Jac[3, 2] = 0., Jac[3, 3] = -2.+2.*x[3], Jac[3, 4] = 0., Jac[4, 1] = 0., Jac[4, 2] = 0., Jac[4, 3] = 0., Jac[4, 4] = -2.+2.*x[4]]

 (7)

 

> 

irformJ := StatSeq(seq(Assign(op(i)),i=eqsJ)):
> 

prcconsJ:= codegen[intrep2maple](Proc(Parameters(x::Array,Jac::Array),irformJ)):
> 

J3:=Compiler:-Compile(prcconsJ):

 

 
> 

j0:=Matrix(1..N,1..N,datatype=float[8]):

 Following linear sovler algorithm is basiclly from dsolve/numeric/SC

.

 

 
> 

s3:=proc(n::posint, A::Array( datatype = float[ 8 ] ) , ip::Array( datatype = integer[ 4 ] ),b::Array( datatype = float[ 8 ] ) )
local i::integer, j::integer, k::integer, m::integer, t::float;
      ip[n] := 1;
      for k to n-1 do
        m := k;
        for i from k+1 to n do
          if abs(A[m,k]) < abs(A[i,k]) then
            m := i
           end if
         end do;
        ip[k] := m;
        if m <> k then
          ip[n] := -ip[n]
         end if;
       t := A[m,k];
       A[m,k] := A[k,k];
       A[k,k] := t;
       if t = 0 then
         ip[n] := 0;
         #return ip
         end if;
       for i from k+1 to n do
         A[i,k] := -A[i,k]/t
         end do;
       for j from k+1 to n do
         t := A[m,j];
         A[m,j] := A[k,j];
         A[k,j] := t;
         if t <> 0 then
           for i from k+1 to n do
             A[i,j] := A[i,j]+A[i,k]*t
             end do
           end if
         end do
       end do;
     if A[n,n] = 0 then
       ip[n] := 0
       end if;
     #ip[n]
      if ip[n] = 0 then
        error "The matrix A is numerically singular"
       end if;
      if 1 < n then
        for k to n-1 do
          m := ip[k];
          t := b[m];
          b[m] := b[k];
          b[k] := t;
          for i from k+1 to n do
           b[i] := b[i]+A[i,k]*t
           end do
         end do;
       for k from n by -1 to 2 do
         b[k] := b[k]/A[k,k];
         t := -b[k];
        for i to k-1 do
           b[i] := b[i]+A[i,k]*t
           end do
         end do
       end if;
     b[1] := b[1]/A[1,1];
return;
end proc:
> 

s3c:=Compiler:-Compile(s3):

 

 
> 

x0:=Vector(N,[seq(0.5,i=1..N)],datatype=float[8]);

x0 := Vector(4, {(1) = .500000000000000, (2) = .500000000000000, (3) = .500000000000000, (4) = .500000000000000})

 (8)
> 

f0;

Vector(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.})

 (9)
> 

j0:=Matrix(1..N,1..N,datatype=float[8]);

j0 := Matrix(4, 4, {(1, 1) = 0., (1, 2) = 0., (1, 3) = 0., (1, 4) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0.})

 (10)

10

 (11)
> 

Newton:=proc(x0,f0,j0,N)
global f3,s3c;
local xnew,err,xold,ip,i::integer;
ip:=Vector(N,[seq(1,i=1..N)],datatype=integer[4]);
err:=10;
xold:=x0;
while err>1e-8 do
f3(xold,f0);
J3(xold,j0);
s3c(N,-j0,ip,f0);
xnew:=xold+f0;
err:=max(abs(f0))/N;
xold:=xnew;
end:
xnew;
end proc;
> 

 

Newton := proc (x0, f0, j0, N) local xnew, err, xold, ip, i::integer; global f3, s3c; ip := Vector(N, [seq(1, i = 1 .. N)], datatype = integer[4]); err := 10; xold := x0; while 0.1e-7 < err do f3(xold, f0); J3(xold, j0); s3c(N, -j0, ip, f0); xnew := xold+f0; err := max(abs(f0))/N; xold := xnew end do; xnew end proc

 (12)
> 

Compiler:-Compile(Newton);

Error, (in CodeGeneration:-IssueError) cannot analyze non-integer range boundary args[4]

  
> 

t11:=time():Newton(x0,f0,j0,N);time()-t11;

Vector(4, {(1) = .900000000000000, (2) = .132532421355126, (3) = 0.566018867943396e-1, (4) = 0.314314686094742e-1})

0.

 (13)


Download NewtonRaphsoncompileattempt.mws

Numerical sol 2nd order pde...

Asked by: mostibra 20
wave
May 11 2015
1  4

d2u/dt2-(2*d2u/x2)+d2u/dxdt=0    

initial condition: u(x,0)=1-x, abslute x<1   Ut(x,0)=cos(pix), bslute x<1 

B.C U(-4,t)=U(4,t)=0,   delta x=0.1, delta t=0.025, range 0..4                                      

memory leaking? maple consuming memory....

Asked by: mnpjf 20
plot memory inequal
May 11 2015
1  3

Hi all,

I have been trying to figure out why when I run my 'code' maple keeps building up memory. I am currently writing X number of inequalities and plotting the results. I begin the script with the  'restart' command to clear the memory of any previous runs. But this does nothing to the memory allocated. I check with my 'task manager' window.

I've been scouring the internet for similar issues and basically is this a software problem? how can this be avoided?

'restart' does clear the variables but doesn't seem to make the freed up memory accessible.

- pJ

Problem with dsolve/numeric/compile and Grid...

Asked by: mthkvv 180
compiler dsolve grid
May 11 2015
1  3

What is the correct mode of using dsolve/numeric/compile with Grid package?

I've tried a lot of different, but only one turned out to be working is by using Grid:-Seq(dsolve..., i=1).

For example:

...

dsol := Grid:-Seq(dsolve(dsys, numeric, parameters = [bb, qq, prf0, `p&theta;f0`], compile = true, optimize = true, output = listprocedure, maxfun = 0), i = 1):

dsol3 := proc (tt) try dsol[3](tt) catch "cannot evaluate the solution further": tt = 0. end try end proc:

st := time[real]():

A := Array([Grid:-Seq([seq(op(2, [dsol[1](parameters = [b[i, j], q[i, j], pr[i, j], `p&theta;`[i, j]]), rhs(dsol3(-10^6))]), j = 1 .. sz[2])], i = 1 .. sz[1])]);

time[real]()-st;

example.mw

But this mode not stable and causing to this error very often:

Error, (in dsolve/numeric/SC/preproc) unable to post-link (rc=31), please try again, and if that fails check that your Windows SDK installation is up to date, and compatible with your Windows compiler

How I can fix this problem?

Unable to understand the error in inverse FT...

Asked by: Sharaf 5
inverse transform
May 11 2015
1  6

Hallo:

I am trying to find the inverse fourier transform given a vector (of real) as input. I get the following error message:

Error, (in DiscreteTransforms:-InverseFourierTransform) entries of input data must all evaluate to complex floats, got '[.7644453211]'

I am unable to understand this message. I would much appreciate help to resolve this issue.

Thanks

Extending a Program(Function)...

Asked by: mahmood1800 260
matrix vector
May 10 2015
0  3

Hi all

Assume that we have following special matrix(Namely ATilde) for arbitrary vectore  z=[a0,a1,a2,a1*,a2*]:
atild.mws

and we want to use this as a general function for other arbitrary vector. is ther any way?

for example z1=[x,y,t,s,u]?

thanks for any help

best wishes

 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

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