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seq slower than proc ...

Asked by: Harry Garst 269
performance programming linear-algebra
May 22 2023
1  5

I learned about Dodgson calculation of the determinant only recently (https://en.m.wikipedia.org/wiki/Dodgson_condensation).
I am only interested in symbolic expressions of the determinant.
Furthermore, I compared several methods. Not surprisingly, the build in method is the fastest. But why is the seq method slower than the proc method for the Dodgson method? Is there anything I could do to program it more efficiently?
 

> 

restart; with(LinearAlgebra)
> 

with(combinat); with(GroupTheory)
> 

DetDef := proc (A) local i, n, sigma; description "Jeremy Johnson. Downloaded from https://www.cs.drexel.edu/~jjohnson/2016-17/winter/cs300/lectures/determinant.mw"; n := RowDimension(A); add(PermParity(Perm(sigma))*mul(A[i, sigma[i]], i = 1 .. n), `in`(sigma, permute([`$`(1 .. n)]))) end proc
> 

InnerMatrix := proc (M::Matrix) SubMatrix(M, 2 .. RowDimension(M)-1, 2 .. ColumnDimension(M)-1) end proc
> 

MatrixDet := proc (M::Matrix) local C, n, i, j; n := RowDimension(M)-1; C := Matrix(n, n); seq(seq(assign('C[i, j]', Determinant(M([i, i+1], [j, j+1]))), j = 1 .. n), i = 1 .. n); return C end proc
> 

Dodgson := proc(M::Matrix)
 MatrixDet(M);
InnerMatrix(M) ^~ (-1) *~ MatrixDet(MatrixDet(M));
do if 1 < RowDimension(%) then InnerMatrix(`%%`) ^~ (-1) *~ MatrixDet(%);
end if;
until RowDimension(%) = 1;
Trace(%):
end proc:
> 

Dodgsonseq := proc (E::Matrix) local w, dim, Z; dim := RowDimension(E); Z[dim] := E; Z[dim-1] := MatrixDet(E); Z[dim-2] := `~`[`*`](`~`[`^`](InnerMatrix(E), -1), MatrixDet(MatrixDet(E))); seq(assign('Z[w-1]', `~`[`*`](`~`[`^`](InnerMatrix(Z[w+1]), -1), MatrixDet(Z[w]))), w = dim-1 .. 1, -1); Trace(Z[1]) end proc
> 

LaPlace := proc (M::Matrix) local c; add((-1)^(c+1)*M[1, c]*Minor(M, 1, c), c = 1 .. ColumnDimension(M)) end proc
> 

dim := 7; A := Matrix(dim, dim, shape = symmetric, symbol = a)

7

 (1)
> 

start_time := time(); st := time[real](); Det1 := abs(A); CPUtime_used_Build_in_Determinant := time()-start_time; REALtime_used_Build_in_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det2 := DetDef(A); CPUtime_used_Jeremy_Johnson_Determinant := time()-start_time; REALtime_used_Jeremy_Johnson_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det3 := Dodgsonseq(A); CPUtime_usedDodgsonseq := time()-start_time; REALCPUtime_usedDodgsonseq := time[real]()-st; start_time := time(); st := time[real](); Det4 := Dodgson(A); CPUtime_usedDodgson := time()-start_time; REALtime_usedDodgson := time[real]()-st; start_time := time(); st := time[real](); Det5 := LaPlace(A); CPUtime_usedLaPlace := time()-start_time; REALtime_usedLaPlace := time[real]()-st; simplify(Det1-Det2); simplify(Det1-Det3); simplify(Det1-Det4); simplify(Det1-Det5)
``

0.32e-1

  

0.34e-1

  

0.93e-1

  

.108

  

47.094

  

41.295

  

40.766

  

38.158

  

0.31e-1

  

0.50e-1

  

0

  

0

  

0

  

0

 (2)

Download test_Determinants_symbolic.mw

Maple 2023 toolbox regarding...

Asked by: vs140580 495
upgrade toolbox chemistry
May 22 2023
0  2

I had purchached reseach licience Maple 2022 towards the end of 2022 only and Quantum Chemistry Toolbox I purchased in Feb 2022 only.

Now i find significant update in toolbox in just 3 months. Now guide me how should i address this issuse.

I had to take loan in india to buy the toolbox.

It is only 3 months.

Can you suggest me how solve the problem to get the update without spending again.

What is the way guide someone.

Have I calculated the limit correctly?...

Asked by: EugeneKalentev 85
calculus integral limit
May 22 2023
0  2

I calculate the limit

Let me know if there are any errors in my calculations?


 

> 

restart
> 

assume(a > 0)
> 

limit(int(sin(x)/x, x = n .. n+a), n = infinity)

0

 (1)
> 

int(sin(x)/x, x = n .. n+a)

-Si(n)+Si(n+a)

 (2)
> 

plot3d(-Si(n)+Si(n+a), a = -5 .. 5, n = -5 .. 5)

 
> 

limit(-Si(n)+Si(n+a), n = infinity)

0

 (3)
> 

limit(-Si(n), n = infinity)

-(1/2)*Pi

 (4)
> 

limit(Si(n+a), n = infinity)

(1/2)*Pi

 (5)
> 

NULL


Thank you in advance.

Download limit_int.mw

How do I calculate volume of a polyhedron knowing ...

Asked by: minhthien2016 385
May 21 2023
0  5

I have a polyhedron with A(1,1,0), B(-1,1,0), C(-1,-1,0), H(-1/2,0,1), K(1/2,-1/2,0). How can I calculate volume of polyhedron ABCHK?
 

How can a horizontal axis be curved in a plot?...

Asked by: kambiz1199 170
axis plotting incomplete-question
May 21 2023
1  11

How can a horizontal axis be curved in a plot? like this

plot(F*r*sin(theta) - m, theta = 0 .. Pi)

setting coordinates in the physics package....

Asked by: Jamie128 165
coordinates spherical-coordinates physics
May 20 2023
2  2

When I am setting up the coordinates in the physics package, I use the following command. And it sets it to (r,theta,phi,t).

Setup(dimension = 4, mathematicalnotation = true, coordinates = spherical)

Is there a way to change it to (t,r,theta,phi)?

It gets a bit more confusing when we are looking at rank 2 objects.

a small issue with the display of the ellipse and ...

Asked by: jalal 440
spacecurve conic plotting
May 20 2023
0  2

Hi, I am working on an activity about conic sections, but I have a small issue with the display of the ellipse and the circle. My outlines are not complete. Any ideas on how to identify my error? Thanks  SectionsConiquesTest.mw

How to find the eigen values of 3*3 matrix in mapl...

Asked by: Naseem35 25
linearalgebra eigenvalues
May 20 2023
0  1

Hi to every one. I have attached a maple for eigenvalues. Please see and tell be solution of problem.

Thanks for time.

Eigen_Values.mw

How do I transform a plot with plot3d...

Asked by: mylikes 25
transform plotting incomplete-question
May 19 2023
0  2

Hi, here is my question.

test:=v^3;

plot3d(test,u=0..1-v, v=0..1);

How can I  transform this plot in the right triangle into an equilateral triangle? 

So that the three edges of the plot are the same length.

I wanna, squish it, or shear?

any tools i can use? Or can I do it using some tricks to change the function?

 

 

how to solve do- looping question in Maple?...

Asked by: syahirah rahimi 15
May 19 2023
1  2

why the output wont appear eventhough I think the working is right?

hello can you help me to plot the following ...

Asked by: olian 5
May 19 2023
1  2

y'' + 1/x * u' + u = 6 - 9x + x^2 - x^3

with baundary condition :

u(0) = 0 , and u(1) = 0

How to download the "ONE Optimal system" package i...

Asked by: Mohd_Zub 10
May 19 2023
2  1

problem using solve...

Asked by: delvin 60
solve incomplete-question
May 18 2023
0  3

 I run the attached code, but after waiting for a few minutes, there is no response, does anyone know the reason?

 It only shows Evaluating!!!!

 sy01.mw

How to solve this PDE system ?...

Asked by: Prakash J 100
homework pde differential-equations
May 18 2023
0  3

eq1:=( d)/(dt)u+(d^(2))/(dy^(2))u + s*( d)/(dy)u + delta * theta = 0;

eq2:=( d)/(dt)theta + (d^(2))/(dy^(2))theta + s*Pr*( d)/(dy)theta +lambda* exp(theta/(1 +(epsilon*theta))) = 0; 

initial and boundary conditons   

t <=0; u = theta = 0, for 0 <= y  <= 1   

t> 0;  u =0, theta = 0   at  y = 0;  

t> 0;  u =1, theta = 0   at   y = 1  ;

where, s, epsilon, Pr, lambda, delta are arbitrary parameters

Eliminate irrelevant derivative terms...

Asked by: wxyhgk 5
differentiation
May 18 2023
1  2

Assuming I have an expression

you can know that the derivative with respect to y will vanish when y is a constant y0.

How can we use the mathematical software Maple to simplify this expression?

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