Venkat Subramanian

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11 years, 33 days

MaplePrimes Activity


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Hi All,

https://www.maplesoft.com/support/helpJP/Maple/view.aspx?path=NAG%2ff11dec

This link shows that there are 3 options rgmres, cgs and bicgstab. When I use iterative solver, it uses the cgs option.

LinearAlgebra:-LinearSolve(
      A, b, method= SparseIterative)

LinearSolve:   "copying right hand side to enable external call"
LinearSolve:   "using method"   SparseIterative
LinearSolve:   "using method  "   SparseIterative
LinearSolve:   "calling external function"
LinearSolve:   "using CGS method"
LinearSolve:   "preconditioning with incomplete LU factorization"
LinearSolve:   "level of fill = "   0
LinearSolve:   "using complete pivoting strategy"
LinearSolve:   "dimension of workspaces for preconditioner = "   44
LinearSolve:   "using infinity norm in stopping criteria"
LinearSolve:   "setting maximum iterations to "   200
LinearSolve:   "setting tolerance to "   .10e-7
LinearSolve:   "NAG"   hw_f11zaf
LinearSolve:   "NAG"   hw_f11daf
LinearSolve:   "NAG"   hw_f11dcf
LinearSolve:   "number of iterations"   1
LinearSolve:   "residual computed last as"   3.33066907387547e-016
 

 

How can I force Maple to use BiCGSTAB?

thanks

I understand how Browse() works. Sometimes Maple crashes or fails for some programs. Is it possible to add print("here" ) into the the mla files in the library to identify why and where Maple fails?

 

Thanks

 

I would like to return local variable y (line 4 in showstat) in the attached dummy procedure (s1) without manually adding any comment inside the procedure s1. This procedure is a simple one and easy to copy paste/or change. When we have a long procedure, it is difficult to do so. I will always know the name of the local variable I want (say, y) and/or line number in showstat

Thanks

PS, I want to get y:=array(1..,2[(1)=x,2=zz])
 

restart;

s1:=proc(n,x)
local y,xx,i,j,zz::array(1..n,1..n);
for i from 1 to n do for j from 1 to n do zz[i,j]:=x[i]*(1+x[j]^2);od:
od:
y:=array(1..2,[(1)=x, (2)=zz]):
for j from 1 to n do xx[i]:=zz[i,i]/(add(zz[i,j],j=1..n));od:
0;
end proc;

s1 := proc (n, x) local y, xx, i, j, zz::(array(1 .. n, 1 .. n)); for i to n do for j to n do zz[i, j] := x[i]*(1+x[j]^2) end do end do; y := array(1 .. 2, [1 = x, 2 = zz]); for j to n do xx[i] := zz[i, i]/add(zz[i, j], j = 1 .. n) end do; 0 end proc

(1)

showstat(s1);

 

s1 := proc(n, x)

local y, xx, i, j, zz::array(1 .. n,1 .. n);

   1   for i to n do

   2     for j to n do

   3       zz[i,j] := x[i]*(1+x[j]^2)

         end do

       end do;

   4   y := array(1 .. 2,[1 = x, 2 = zz]);

   5   for j to n do

   6     xx[i] := zz[i,i]/add(zz[i,j],j = 1 .. n)

       end do;

   7   0

end proc

 

 

x0:=Vector(2,[1,1]);

x0 := Vector(2, {(1) = 1, (2) = 1})

(2)

s1(2,x0);

0

(3)

 


 

Download showstatexample.mws


To summarize,

dsolve numeric parametric form gives wrong answers when fdiff is used to calculate the Hessian. Doing dsolve twice gives the correct answer. Hope I am not making syntax or programming errors.

Also, fdiff is not compatible with vector form.

restart;

Digits:=15;

Digits := 15

(1)

sys:=diff(y1(t),t)=-(u+u^2/2)*y1(t),diff(y2(t),t)=u*y1(t);

sys := diff(y1(t), t) = -(u+(1/2)*(u^2))*y1(t), diff(y2(t), t) = u*y1(t)

(2)

 The system is solved with initial conditions 1,0 and value of u being equal to u1 for t<=0.5, and u2 for t>0.5. The objective is y2 at t =1. There are errors when Hessian is calculated using parametric dsolve and fdiff

sol1 := dsolve({sys, y1(0) = alpha, y2(0) = beta}, type = numeric, 'parameters' = [alpha, beta, u],maxfun=0,range=0..0.5):

obj1:=proc(u1,u2)
local z1,s1,s2,z2;
global sol1;
sol1('parameters'=[1,0,u1]);
z1 := sol1(.5);
s1:=subs(z1,y1(t));
s2:=subs(z1,y2(t));
sol1('parameters'=[s1,s2,u2]):
z2:=sol1(0.5);
-subs(z2,y2(t));
end proc;

obj1 := proc (u1, u2) local z1, s1, s2, z2; global sol1; sol1('parameters' = [1, 0, u1]); z1 := sol1(.5); s1 := subs(z1, y1(t)); s2 := subs(z1, y2(t)); sol1('parameters' = [s1, s2, u2]); z2 := sol1(.5); -subs(z2, y2(t)) end proc

(3)

u0:=[0.8,1.8];

u0 := [.8, 1.8]

(4)

obj1(op(u0));

-.552540796143903

(5)

Hess1:=Matrix(2,2):for i from 1 to 2 do for j from 1 to 2 do Hess1[i,j]:=fdiff(obj1,[i,j],u0,workprec=1.0);od;od;Hess1;

Matrix(2, 2, {(1, 1) = 115.470000000000, (1, 2) = -1.11000000000000, (2, 1) = -1.11000000000000, (2, 2) = 2.22000000000000})

(6)

 Hessian is wrong. It should be noted that when dsolve is called twice inside the objective function there is no error in Hessian calculation with fdiff. The parametric dsolve is efficient, how to get correct answers with that? Another question is how to use fdiff with vector form instead u1,u2 etc to make it generic for any number of variables?

obj2:=proc(u1,u2)
local z1,s1,s2,z2,sol2;
sol2:=dsolve({op(subs(u=u1,[sys])), y1(0) = 1, y2(0) = 0}, type = numeric,maxfun=0,range=0..0.5);
z1 := sol2(.5);
s1:=subs(z1,y1(t));
s2:=subs(z1,y2(t));
sol2:=dsolve({op(subs(u=u2,[sys])), y1(0) = s1, y2(0) = s2}, type = numeric,maxfun=0,range=0..0.5):
z2:=sol2(0.5);
-subs(z2,y2(t));
end proc;

obj2 := proc (u1, u2) local z1, s1, s2, z2, sol2; sol2 := dsolve({op(subs(u = u1, [sys])), y1(0) = 1, y2(0) = 0}, type = numeric, maxfun = 0, range = 0 .. .5); z1 := sol2(.5); s1 := subs(z1, y1(t)); s2 := subs(z1, y2(t)); sol2 := dsolve({op(subs(u = u2, [sys])), y1(0) = s1, y2(0) = s2}, type = numeric, maxfun = 0, range = 0 .. .5); z2 := sol2(.5); -subs(z2, y2(t)) end proc

(7)

obj2(op(u0));

-.552540796143903

(8)

Hess2:=Matrix(2,2):for i from 1 to 2 do for j from 1 to 2 do Hess2[i,j]:=fdiff(obj2,[i,j],u0,workprec=1.0);od;od;Hess2;

Matrix(2, 2, {(1, 1) = .234295697631809, (1, 2) = 0.101868715004724e-1, (2, 1) = 0.101868715004724e-1, (2, 2) = 0.853480932660994e-1})

(9)

 Doing dsolve twice gives correct answer compared to one parametric dsolve even though objective returns the same number (even gradient returns the expected answers).


 

Download Bugindsolveorfdiff.mws

I have been in touch with Maplesoft trying to get this version for windows (they are not able to create a download for this). I have codes that used to run in Maple 6 but not in Maple 7 or later. (Maple V should work as well).

If you any of have this version, please let me know if I can try it out for a limited time (I have always had licenses from Maple V Release 3 or 4).

I am not able to post those codes for obvious confidentiality reasons.

 

Thanks

 

(I tried my code in Maple 7, but no use). 

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