I'm a little tired, but that reads a little odd to me.

The result of evalf(C) will contain symbols, since every entry in C is just an indexed name like corr[i,j]. So, I imagine that you wish to instantiate all those corr[i,j] at numeric values. Only then will the Cholesky factorization be fast, and the result be writable to float[8] datatype Matrix CD. So that's where the action of the GUI "component" must go, to give values to the corr[i,j]. They could be set either before C is created, or after, but they must be set prior to CD being calculated.

Now let's consider the number of variables. Your symmetric Matrix C has n*n/2 distinct indexed names in it, no? That's 500000 variables when n=1000 as you have it. It looks like they will all appear in Matrix B, since it's likely that no element of A is exactly zero. That doesn't match what you wrote about having 1000 variables. But no matter, because there is the more important issue to address: do you really want to have 1000 sliders to control?. And you mentioned 1000 images. But each slider need not get its own image (and the GUI would likely not support 1000 plot components well, if at all).

Maybe I've misunderstood. How many sliders do you want? How many plots? What should the sliders control? If the sliders control the values of the corr[i,j] variables then how, exactly (if it is not a 1-1 thing)?

As an aside, I was looking at Statistics:-CorrelationMatrix. Even for purely datatype=float[8] it doesn't treat Matrices efficiently. It breaks them up into Vectors, it seems. I got timings like this below, which are not great.

> for k from 1 to 10 do
> M := LinearAlgebra:-RandomMatrix(k*100,outputoptions=[datatype=float[8]]):
> print( time( Statistics:-CorrelationMatrix(M) ) );
> end do:
                                     0.391
 
                                     1.636
 
                                     4.310
 
                                     8.671
 
                                    15.534
 
                                    25.184
 
                                    38.933
 
                                    56.622
 
                                    76.200
 
                                    100.595

I would like to see if it can be improved, in a manner similar to this, for Matrix input (and no weights). I imagine that you would not want to have to wait 100 seconds for the CorrelationMatrix result, each time that B had some change in its values.

If only one or two columns of B changed, then the correlation Matrix could be updated more selectively and quickly. But I don't see how one can map simple changes to C into such simple changes in B, since there is a Cholesky factorization between them.

acer

And someone has incorporated those into Sage.  ;)

acer

And someone has incorporated those into Sage.  ;)

acer

For large numbers, better still might be to first split the number into an even number of equal-length "pieces" where each piece is an immediate integer. For example, one could compare the 1st and the 4th, and the 2nd and 3rd, if there were four pieces. That might reduce slowdown due to creation and memory management of big (gmp) integers.

Such slowdown for big integers makes `f` slow. Consider,

> f:=proc(n)
>     local a, k, len, m;
>     a:=n;
>     for len from length(a)-2 by -2 to 0 do
>         a:=iquo(a,10,'k');
>         a:=irem(a,10^len,'m');
>         if not k=m then return false fi
>         od;
>     true
> end:

> N := (10^10000+1)^2:
> f(N);
memory used=291.4MB, alloc=10.9MB, time=11.12
memory used=299.0MB, alloc=10.9MB, time=11.23
memory used=306.7MB, alloc=10.9MB, time=11.33
memory used=314.3MB, alloc=10.9MB, time=11.43
memory used=321.9MB, alloc=10.9MB, time=11.53
memory used=329.6MB, alloc=10.9MB, time=11.62
memory used=337.2MB, alloc=10.9MB, time=11.71
memory used=344.8MB, alloc=10.9MB, time=11.79
                                     true

> N := (10^100000+1)^2:
> f(N);
memory used=7.6MB, alloc=6.8MB, time=0.21
memory used=15.3MB, alloc=10.7MB, time=0.51
memory used=23.0MB, alloc=10.7MB, time=0.81
memory used=30.6MB, alloc=10.7MB, time=1.11
memory used=38.3MB, alloc=10.7MB, time=1.42
memory used=45.9MB, alloc=10.7MB, time=1.72
memory used=53.6MB, alloc=10.7MB, time=2.02
memory used=61.3MB, alloc=10.8MB, time=2.32
memory used=69.0MB, alloc=10.8MB, time=2.62
memory used=76.7MB, alloc=10.8MB, time=2.92
memory used=84.4MB, alloc=10.8MB, time=3.22
memory used=92.0MB, alloc=10.8MB, time=3.53
memory used=99.7MB, alloc=10.8MB, time=3.82
memory used=107.4MB, alloc=10.8MB, time=4.12
memory used=115.0MB, alloc=10.8MB, time=4.42
memory used=122.7MB, alloc=10.8MB, time=4.72
memory used=130.4MB, alloc=10.8MB, time=5.02
memory used=138.0MB, alloc=10.8MB, time=5.32
memory used=145.6MB, alloc=10.8MB, time=5.62
memory used=153.3MB, alloc=10.8MB, time=5.92
memory used=160.9MB, alloc=10.8MB, time=6.22
memory used=168.6MB, alloc=10.8MB, time=6.51
memory used=176.3MB, alloc=10.8MB, time=6.81
memory used=183.9MB, alloc=10.8MB, time=7.11
memory used=191.6MB, alloc=10.8MB, time=7.41
memory used=199.3MB, alloc=10.8MB, time=7.71
memory used=207.0MB, alloc=10.8MB, time=8.01
memory used=214.6MB, alloc=10.8MB, time=8.31
memory used=222.3MB, alloc=10.8MB, time=8.61
memory used=230.0MB, alloc=10.9MB, time=8.91
memory used=237.7MB, alloc=10.9MB, time=9.21
memory used=245.4MB, alloc=10.9MB, time=9.51
memory used=253.1MB, alloc=10.9MB, time=9.81
memory used=260.7MB, alloc=10.9MB, time=10.11
memory used=268.4MB, alloc=10.9MB, time=10.41
memory used=276.1MB, alloc=10.9MB, time=10.71
memory used=283.8MB, alloc=10.9MB, time=11.01
Interrupted

> g := proc(n)
>     local s;
>     s := ""||n;
>     evalb(s = StringTools:-Reverse(s));
> end:

> N := (10^100000+1)^2:
> g(N);
                                     true

> time( g(N) );
                                     0.055

> F(N); # Using `F` posted above.
                                     true
 
> time( F(N) );
                                     0.071

acer

For large numbers, better still might be to first split the number into an even number of equal-length "pieces" where each piece is an immediate integer. For example, one could compare the 1st and the 4th, and the 2nd and 3rd, if there were four pieces. That might reduce slowdown due to creation and memory management of big (gmp) integers.

Such slowdown for big integers makes `f` slow. Consider,

> f:=proc(n)
>     local a, k, len, m;
>     a:=n;
>     for len from length(a)-2 by -2 to 0 do
>         a:=iquo(a,10,'k');
>         a:=irem(a,10^len,'m');
>         if not k=m then return false fi
>         od;
>     true
> end:

> N := (10^10000+1)^2:
> f(N);
memory used=291.4MB, alloc=10.9MB, time=11.12
memory used=299.0MB, alloc=10.9MB, time=11.23
memory used=306.7MB, alloc=10.9MB, time=11.33
memory used=314.3MB, alloc=10.9MB, time=11.43
memory used=321.9MB, alloc=10.9MB, time=11.53
memory used=329.6MB, alloc=10.9MB, time=11.62
memory used=337.2MB, alloc=10.9MB, time=11.71
memory used=344.8MB, alloc=10.9MB, time=11.79
                                     true

> N := (10^100000+1)^2:
> f(N);
memory used=7.6MB, alloc=6.8MB, time=0.21
memory used=15.3MB, alloc=10.7MB, time=0.51
memory used=23.0MB, alloc=10.7MB, time=0.81
memory used=30.6MB, alloc=10.7MB, time=1.11
memory used=38.3MB, alloc=10.7MB, time=1.42
memory used=45.9MB, alloc=10.7MB, time=1.72
memory used=53.6MB, alloc=10.7MB, time=2.02
memory used=61.3MB, alloc=10.8MB, time=2.32
memory used=69.0MB, alloc=10.8MB, time=2.62
memory used=76.7MB, alloc=10.8MB, time=2.92
memory used=84.4MB, alloc=10.8MB, time=3.22
memory used=92.0MB, alloc=10.8MB, time=3.53
memory used=99.7MB, alloc=10.8MB, time=3.82
memory used=107.4MB, alloc=10.8MB, time=4.12
memory used=115.0MB, alloc=10.8MB, time=4.42
memory used=122.7MB, alloc=10.8MB, time=4.72
memory used=130.4MB, alloc=10.8MB, time=5.02
memory used=138.0MB, alloc=10.8MB, time=5.32
memory used=145.6MB, alloc=10.8MB, time=5.62
memory used=153.3MB, alloc=10.8MB, time=5.92
memory used=160.9MB, alloc=10.8MB, time=6.22
memory used=168.6MB, alloc=10.8MB, time=6.51
memory used=176.3MB, alloc=10.8MB, time=6.81
memory used=183.9MB, alloc=10.8MB, time=7.11
memory used=191.6MB, alloc=10.8MB, time=7.41
memory used=199.3MB, alloc=10.8MB, time=7.71
memory used=207.0MB, alloc=10.8MB, time=8.01
memory used=214.6MB, alloc=10.8MB, time=8.31
memory used=222.3MB, alloc=10.8MB, time=8.61
memory used=230.0MB, alloc=10.9MB, time=8.91
memory used=237.7MB, alloc=10.9MB, time=9.21
memory used=245.4MB, alloc=10.9MB, time=9.51
memory used=253.1MB, alloc=10.9MB, time=9.81
memory used=260.7MB, alloc=10.9MB, time=10.11
memory used=268.4MB, alloc=10.9MB, time=10.41
memory used=276.1MB, alloc=10.9MB, time=10.71
memory used=283.8MB, alloc=10.9MB, time=11.01
Interrupted

> g := proc(n)
>     local s;
>     s := ""||n;
>     evalb(s = StringTools:-Reverse(s));
> end:

> N := (10^100000+1)^2:
> g(N);
                                     true

> time( g(N) );
                                     0.055

> F(N); # Using `F` posted above.
                                     true
 
> time( F(N) );
                                     0.071

acer

Perhaps you could upload a short but representative example of your input to this site. (Use the green up-arrow in the bottom row of the editing toolbar, visible when one adds a comment.)

acer

Have a look at the help-pages for the Worksheet and XMLTools packages.

acer

The evalhf (fast, hardware floating-point) interpreter understands how to run procedures with calls to the `Array` constructor. It understands Matrix and rtable objects, but it doesn't understand  `Matrix` or `rtable` constructors calls.

> p := proc(x)
>   Array([[x^2, x], [1, x]]);
> end proc:

> evalhf( p(0.1) );
                [0.0100000000000000002    0.100000000000000006]
                [                                             ]
                [         1.              0.100000000000000006]
 
> rtable_options(%);
datatype = float[8], subtype = Array, storage = rectangular, order = Fortran_order

You can also use the eval command to escape back to regular Maple from within evalhf and so create Matrices (or other rtables, or other objects).

> p := proc(x)
>   Matrix([[x^2, x], [1, x]],datatype=float[8]);
> end proc:

> evalhf( p(0.1) );
Error, unable to evaluate expression to hardware floats: [[.1000000000e-1,
.100000000000000006], [1, .100000000000000006]]

> p := proc(x)
>   eval( Matrix([[x^2, x], [1, x]],datatype=float[8]) );
> end proc:

> evalhf( p(0.1) );
                [0.0100000000000000002    0.100000000000000006]
                [                                             ]
                [         1.              0.100000000000000006]
 
> rtable_options(%);
datatype = float[8], subtype = Matrix, storage = rectangular, order = Fortran_order

The performance penalty for the eval escape doesn't appear to be so bad.

acer

The evalhf (fast, hardware floating-point) interpreter understands how to run procedures with calls to the `Array` constructor. It understands Matrix and rtable objects, but it doesn't understand  `Matrix` or `rtable` constructors calls.

> p := proc(x)
>   Array([[x^2, x], [1, x]]);
> end proc:

> evalhf( p(0.1) );
                [0.0100000000000000002    0.100000000000000006]
                [                                             ]
                [         1.              0.100000000000000006]
 
> rtable_options(%);
datatype = float[8], subtype = Array, storage = rectangular, order = Fortran_order

You can also use the eval command to escape back to regular Maple from within evalhf and so create Matrices (or other rtables, or other objects).

> p := proc(x)
>   Matrix([[x^2, x], [1, x]],datatype=float[8]);
> end proc:

> evalhf( p(0.1) );
Error, unable to evaluate expression to hardware floats: [[.1000000000e-1,
.100000000000000006], [1, .100000000000000006]]

> p := proc(x)
>   eval( Matrix([[x^2, x], [1, x]],datatype=float[8]) );
> end proc:

> evalhf( p(0.1) );
                [0.0100000000000000002    0.100000000000000006]
                [                                             ]
                [         1.              0.100000000000000006]
 
> rtable_options(%);
datatype = float[8], subtype = Matrix, storage = rectangular, order = Fortran_order

The performance penalty for the eval escape doesn't appear to be so bad.

acer

I believe that you are right on track.

You might alternatively have the givens be entered in a TextArea. And the Equations appear in Math containers. There are all sorts of possible combinations as to layout. You could hide some of the flow control code, or make it visible (your choice). You could put some of the components inside worksheet tables (and keep the borders invisible, your choice).

acer

I believe that you are right on track.

You might alternatively have the givens be entered in a TextArea. And the Equations appear in Math containers. There are all sorts of possible combinations as to layout. You could hide some of the flow control code, or make it visible (your choice). You could put some of the components inside worksheet tables (and keep the borders invisible, your choice).

acer

It is usually not necessary to convert an expression to a procedure (or the other way around) in order to use the Optimization package to find a minimum numerically. That package accepts both expression form and procedure form for both objective and constraints of optimization problems.

Also, if you are simply trying to evaluate an expression at various values of the parameter then you might well not have to use unapply in order first to convert the expression to a procedure. The two-parameter form of the eval command can evaluate expressions at values of the variables. That should be efficient, while repeatedly using unapply for the same task would generally be less efficient.

There are some instances when unapply is unavoidably the easiest thing, but from what you've written so far I don't see that as the case. I could be wrong. Your comment below about a recursion limit while presumably using unapply within loop looks like suspicious usage. Seeing the full code might help.

acer

It is usually not necessary to convert an expression to a procedure (or the other way around) in order to use the Optimization package to find a minimum numerically. That package accepts both expression form and procedure form for both objective and constraints of optimization problems.

Also, if you are simply trying to evaluate an expression at various values of the parameter then you might well not have to use unapply in order first to convert the expression to a procedure. The two-parameter form of the eval command can evaluate expressions at values of the variables. That should be efficient, while repeatedly using unapply for the same task would generally be less efficient.

There are some instances when unapply is unavoidably the easiest thing, but from what you've written so far I don't see that as the case. I could be wrong. Your comment below about a recursion limit while presumably using unapply within loop looks like suspicious usage. Seeing the full code might help.

acer

Maybe there's a problem displaying the output. I haven't looked hard at it. This "3rd party" package seems to have problems. Maybe you could contact the author.

acer

Maybe there's a problem displaying the output. I haven't looked hard at it. This "3rd party" package seems to have problems. Maybe you could contact the author.

acer