## How to compute inverse of a matrix for solving eig...

I have a eigenvalue problem like:

[FF1]* {w}=N^2 *[FF2] *{w}

[FF1] and [FF2] are a*b matrices (non square matrix) , {w} are vectors(eigenvectors) and the values of N are eigenvalues.

I want to obtain eigenvalues and eigenvectors by computing Moore-Penrose pseudo-inverse of [FF2] and do the procedures below :

[FF2]^-1 * [FF1] *{w} =N^2 *{w}            ,        (assume  [FF2]^-1   is Moore-Penrose pseudo-inverse of [FF2]   )

[FF2]^-1 * [FF1] = [FF3]  ,  ( [FF3] is a b*b matrix- squre matrix)

so  [FF3] *{w}=N^2 *{w}

then I can use LinearAlgebra[Eigenvectors](FF3) to get eigenvalues and eigenvectors.

I know that Moore-Penrose pseudo-inverse of [FF2] * [FF1] isn't equal to Identity matrix. [FF2]^-1 * [FF1] <> [ I ] . But assume it can be. ( I have a solution for this problem) .

My biggest problem is [FF2] and [FF1] are large-scale sparse matrix and it takes hours or several days that maple can compute Moore-Penrose pseudo-inverse of [FF2]  and also LinearAlgebra[Eigenvectors](FF3).

Main question : can I compute Moore-Penrose pseudo-inverse and LinearAlgebra[Eigenvectors]  by using Parallel Programming?  if the answer is yes , how? give me an example please.

if the answer is No , is there any way (any algorithm) to find the inverse of a large non-sqaure matrix or eigenvalues of a large matrix faster?

please introduce some books for parallel programming in maple or general.

Thanks.

1.mw

## Maple to Fortran...

From the attached code, you can see that I have a Matrix, A, that I am trying to output into Fortran code so that I can simply copy and paste this long matrix into fortran. The output does not look correct. Doesa anyone have an idea on how to put this matrix A into a form that can be easily copy and pasted into Fortran? You can see that I tried to do each line individually in the attatched code but I am really looking for a way to do the entire Matrix. Thanks for any help or suggestions.

## maxfun limit exceeded in dsolve...

I'm trying to solve an ODE system from an IVP problem, but the error occurs: "Error, (in ...) cannot evaluate the solution further left of ..., maxfun limit exceeded (see ?dsolve,maxfun for details)"

I've already tried modifying the maxfun value but this did not work. I would like some suggestion.

Thank you

ODE_System.mw

## How do I edit a package ...

Hello,

I created my own costum package and I want to edit this package: insert procedures or modules. Is there a way?

Thank you.

## Expressions in procedures acting unevaluated when ...

What's going on here? Am I missing something, or is it a bug? If it's a bug, then it's by far the deepest and most profound bug that I've ever found or seen in Maple (and I've seen thousands over the decades). And since that surprises me, my guess is that I'm missing something obvious.

```restart:
Op:= (R,F)-> F(['R()'\$2]):
Op(rand(1..9), [f,f]);
[f([7, 6]), f([2, 4])]
```

The expected output is [f([7,6]), f([7,6])]. The same thing happens if I replace with seq, or if I replace -> with proc.

## Finite element method...

pls help me cirrect this. i am trying to use finite element method to siolve a fluid equation. The code is give below

> pde := alpha^2*(diff(u(t, r), t))+2*(-1/2)^(1/n)*(diff(u(t, r), r))/r-(-1/2)^((1-n)/n)*(diff(u(t, r), `\$`(r, 2)))*(diff(u(t, r), r))^(1/n-1)/n+2*theta/r-4*(1+e)+4*B*cos(.2) = 0; /1\ |-| \n/ /-1\ / d \ 2 |--| |--- u(t, r)| 2 / d \ \2 / \ dr / alpha |--- u(t, r)| + ----------------------- \ dt / r /1 - n\ /1 \ |-----| |- - 1| \ n / \n / /-1\ / d / d \\ / d \ |--| |--- |--- u(t, r)|| |--- u(t, r)| \2 / \ dr \ dr // \ dr / 2 theta - ---------------------------------------------------- + ------- - 4 - 4 e n r + 3.920266311 B = 0 > tmax := 0.5e-1; > rmin := 0; > rmax := 10; > N := 6; > bc1 := diff(u(t, r = rmin), r) = 1/mu; > bc2 := u(t, r = rmax) = 0; > ic1 := u(0, r) = 0; > PDE*Boundary*condition*colllection; > bcs := {u(0, r) = rhs(ic1), D[1](diff(u(t, r = rmin), r)) = rhs(bc1), (D[1](u))(t, r = rmax) = rhs(bc2)}; / / d \ 1 \ { u(0, r) = 0, D[1]|--- u(t, r = 0)| = --, D[1](u)(t, r = 10) = 0 } \ \ dr / mu / > > Collocation*method; > Typesetting[delayDotProduct](Define*a*simple*function*with*known*solution.one, can, true)*choose*either*a*trigonometric*function, othorgonal*polynomia, (Typesetting[delayDotProduct](legendre*polynomia*etc.we, want, true)*will*choose*a*simple*polynomia*which*will)*make*our*work*easier; > basis := r^i; > uhat := sum(A[i](t)*basis, i = 0 .. N-1); > Alist := indets(uhat, function(identical(t))); > Here, we*will*determine*the^2*two*unknowns*(A1, A2)*using*boundary*conditions; > duhat := diff(uhat, r); > knownAs := solve({subs(r = rmin, duhat) = rhs(bc1), subs(A[1](t) = 0, r = rmax, duhat) = rhs(bc2)}, {A[1](t), A[2](t)}); > unknownAs := `minus`(Alist, {seq(lhs(knownAs[i]), i = 1 .. nops(knownAs))}); > `and`(uhat*after*substituting*A1, A2); > uhat := subs(knownAs, uhat); > uhat := collect(uhat, Alist); > Residual*function*is*obtai*ned*after*substituting*uhat*into*the*original*pde; > residual := eval(subs(u(t, r) = uhat, pde)); > residual := collect(residual, r); > `and`(Typesetting[delayDotProduct](Now*we*choose*points*where*exact*solution*must*be*matched.since, we, true)*have*point*A[1], A[2]), we*will*only*need*N-2*points; > odes := {seq(subs(r = i*rmax/N, residual), i = 1 .. nops(unknownAs))}; > Find*ICs*of*unknown*A(t)*s; > iceqs := {seq(subs(t = 0, r = i*rmax/N, uhat) = rhs(bc2), i = 1 .. nops(unknownAs))}; > ics := solve(iceqs, subs(t = 0, unknownAs)); > > sols := dsolve(`union`(odes, ics)); Warning, computation interrupted > Approximate*solution; > uhat := subs(sols, uhat); Error, invalid input: subs received sols, which is not valid for its 1st argument > uhat := collect(uhat, r); > Plot*solution; > plot3d(uhat, r = 0 .. rmax, t = 0 .. tmax, axes = boxed, lightmodel = light4, orientation = [-120, 40], shading = zhue, transparency = .3); Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct > >

## How do i make a subsection on mac, Maple 2018...

The question is all in the title really. I am struggling to make a subsection on my macbook, using 2018 Maple software. The cmd + shift + . will only make sections, regardless of where i place my cursor.

## Solving improper integrals using Maple?...

I am trying to solve improper integrals using Maple. I need to choose at least one from attached and I am leaning towards number 26 but I am having trouble. I am new to Maple and have no idea where to even begin. Please provide the correct steps needed to get to the right answer.

## "stack limit reached" when using Grid:-Map...

Hi there:

i use Grid:-Map() to run some code on many cores. When I set

Grid:-Setup(numnodes=23);

everything runs fine. When I set (note I have 28 logical cores present):

Grid:-Setup(numnodes=24);

I get the "stack limit reached" message (see attached image below). I've explored setting stack limits to 'unlimited' at the OS level (ubuntu 18.04), as well as setting

kernelopts(stacklimit=infinity)

However, these do not help, and I still end up with the same message.

Any ideas what could be the problem? Also, I am assuming that kernelopts settings get passed to other, spawned kernels, but even if not, I experimented with setting this directly inside the function that gets passed to Grid:-Map()

thanks

## solve eqution ...

a:=sin(theta3(t))*(diff(theta3(t), t))^2*cos(theta1(t))*l1*l3*m3+sin(theta3(t))*(diff(theta3(t), t))^2*cos(theta1(t))*l1*l3*mi+sin(theta3(t))*(diff(theta3(t), t))^2*cos(theta1(t))*l1*l3*m4+l1^2*m2*(diff(theta1(t), t, t))-sin(theta3(t))*(diff(theta3(t), t))^2*cos(theta1(t))*l1*lc3*m3+sin(theta4(t))*(diff(theta4(t), t))^2*cos(theta1(t))*l1*l4*mi+sin(theta4(t))*(diff(theta4(t), t))^2*cos(theta1(t))*l1*l4*m4-sin(theta4(t))*(diff(theta4(t), t))^2*cos(theta1(t))*l1*lc4*m4+sin(theta6(t))*(diff(theta6(t), t))^2*cos(theta1(t))*h2*l1*ml+sin(theta6(t))*(diff(theta6(t), t))^2*cos(theta1(t))*h2*l1*m3+l1^2*ml*(diff(theta1(t), t, t))+l1^2*mr*(diff(theta1(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*ml*(diff(theta2(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*mc*(diff(theta2(t), t, t))+sin(theta5(t))*sin(theta1(t))*h2*l1*mi*(diff(theta5(t), t, t))-cos(theta3(t))*cos(theta1(t))*l1*l3*m4*(diff(theta3(t), t, t))+cos(theta5(t))*cos(theta1(t))*h2*l1*mc*(diff(theta5(t), t, t))+sin(theta6(t))*(diff(theta6(t), t))^2*cos(theta1(t))*h2*l1*mi+sin(theta6(t))*(diff(theta6(t), t))^2*cos(theta1(t))*h2*l1*m4-sin(theta5(t))*(diff(theta5(t), t))^2*cos(theta1(t))*h2*l1*mi-sin(theta5(t))*(diff(theta5(t), t))^2*cos(theta1(t))*h2*l1*m4-sin(theta5(t))*(diff(theta5(t), t))^2*cos(theta1(t))*h2*l1*m3-sin(theta5(t))*(diff(theta5(t), t))^2*cos(theta1(t))*h2*l1*mr-sin(theta5(t))*(diff(theta5(t), t))^2*cos(theta1(t))*h2*l1*mc-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*m3-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*lc2*m2-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*mr+sin(theta2(t))*sin(theta1(t))*l1*l2*ml*(diff(theta2(t), t, t))+cos(theta5(t))*cos(theta1(t))*h2*l1*mi*(diff(theta5(t), t, t))+l1^2*m4*(diff(theta1(t), t, t))+sin(theta5(t))*sin(theta1(t))*h2*l1*m3*(diff(theta5(t), t, t))+cos(theta3(t))*cos(theta1(t))*l1*lc3*m3*(diff(theta3(t), t, t))-sin(theta3(t))*sin(theta1(t))*l1*l3*m4*(diff(theta3(t), t, t))-cos(theta6(t))*cos(theta1(t))*h2*l1*m4*(diff(theta6(t), t, t))-sin(theta4(t))*sin(theta1(t))*l1*l4*m4*(diff(theta4(t), t, t))-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*mi-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*mc-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*ml-sin(theta2(t))*(diff(theta2(t), t))^2*cos(theta1(t))*l1*l2*m4-sin(theta7(t))*(diff(theta7(t), t))^2*cos(theta1(t))*h3*l1*mc-cos(theta4(t))*cos(theta1(t))*l1*l4*mi*(diff(theta4(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*mr*(diff(theta2(t), t, t))-cos(theta6(t))*(diff(theta6(t), t))^2*sin(theta1(t))*h2*l1*mi-cos(theta6(t))*(diff(theta6(t), t))^2*sin(theta1(t))*h2*l1*m4+cos(theta5(t))*(diff(theta5(t), t))^2*sin(theta1(t))*h2*l1*m3+cos(theta5(t))*(diff(theta5(t), t))^2*sin(theta1(t))*h2*l1*mi+cos(theta5(t))*(diff(theta5(t), t))^2*sin(theta1(t))*h2*l1*mc+cos(theta5(t))*(diff(theta5(t), t))^2*sin(theta1(t))*h2*l1*mr+cos(q2(t))*sin(theta1(t))*l1*l2*mi*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*l2*m4*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*lc2*m2*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*l2*m3*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*l2*mc*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*l2*ml*(diff(theta2(t), t))*(diff(theta1(t), t))+cos(q2(t))*sin(theta1(t))*l1*l2*mr*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*mc*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*m4*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*mr*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*m3*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*mi*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*l2*ml*(diff(theta2(t), t))*(diff(theta1(t), t))-sin(q2(t))*cos(theta1(t))*l1*lc2*m2*(diff(theta2(t), t))*(diff(theta1(t), t))-cos(theta3(t))*(diff(theta3(t), t))^2*sin(theta1(t))*l1*l3*mi+cos(theta3(t))*(diff(theta3(t), t))^2*sin(theta1(t))*l1*lc3*m3-cos(theta4(t))*(diff(theta4(t), t))^2*sin(theta1(t))*l1*l4*m4-cos(theta4(t))*(diff(theta4(t), t))^2*sin(theta1(t))*l1*l4*mi+cos(theta4(t))*(diff(theta4(t), t))^2*sin(theta1(t))*l1*lc4*m4-cos(theta6(t))*(diff(theta6(t), t))^2*sin(theta1(t))*h2*l1*ml-cos(theta6(t))*(diff(theta6(t), t))^2*sin(theta1(t))*h2*l1*m3-cos(theta3(t))*(diff(theta3(t), t))^2*sin(theta1(t))*l1*l3*m4-cos(theta3(t))*(diff(theta3(t), t))^2*sin(theta1(t))*l1*l3*m3+l1^2*mc*(diff(theta1(t), t, t))-cos(theta4(t))*cos(theta1(t))*l1*l4*m4*(diff(theta4(t), t, t))+cos(theta5(t))*cos(theta1(t))*h2*l1*mr*(diff(theta5(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*lc2*m2*(diff(theta2(t), t, t))+cos(theta1(t))*g*l1*mr+cos(theta1(t))*g*l1*m3+cos(theta1(t))*g*l1*m2+cos(theta1(t))*g*l1*m4+cos(theta1(t))*g*l1*ml+cos(theta1(t))*g*l1*mc+m1*g*lc1*cos(theta1(t))+cos(theta1(t))*g*l1*mi+cos(theta5(t))*cos(theta1(t))*h2*l1*m3*(diff(theta5(t), t, t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*m4*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*mc+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*mc*(diff(theta2(t), t))+cos(theta7(t))*(diff(theta7(t), t))^2*sin(theta1(t))*h3*l1*mc+l1^2*m3*(diff(theta1(t), t, t))+l1^2*mi*(diff(theta1(t), t, t))+cos(theta5(t))*(diff(theta5(t), t))^2*sin(theta1(t))*h2*l1*m4-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*m3*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*ml+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*ml*(diff(theta2(t), t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*lc2*m2*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*mr+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*mr*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*m4+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*m4*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*mi+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*mi*(diff(theta2(t), t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*mr*(diff(theta2(t), t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*mi*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*l2*m3+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*l2*m3*(diff(theta2(t), t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*mc*(diff(theta2(t), t))-cos(theta2(t))*sin(theta1(t))*(diff(theta1(t), t))*l1*l2*ml*(diff(theta2(t), t))+cos(theta2(t))*(diff(theta2(t), t))^2*sin(theta1(t))*l1*lc2*m2+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*l1*lc2*m2*(diff(theta2(t), t))+sin(theta2(t))*sin(theta1(t))*l1*l2*m3*(diff(theta2(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*m3*(diff(theta2(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*mi*(diff(theta2(t), t, t))+cos(theta5(t))*cos(theta1(t))*h2*l1*m4*(diff(theta5(t), t, t))+sin(theta2(t))*sin(theta1(t))*l1*l2*mr*(diff(theta2(t), t, t))+m1*lc1^2*(diff(theta1(t), t, t))-sin(theta6(t))*sin(theta1(t))*h2*l1*m4*(diff(theta6(t), t, t))+sin(theta5(t))*sin(theta1(t))*h2*l1*mr*(diff(theta5(t), t, t))+sin(theta5(t))*sin(theta1(t))*h2*l1*mc*(diff(theta5(t), t, t))-cos(theta6(t))*cos(theta1(t))*h2*l1*mi*(diff(theta6(t), t, t))-sin(theta6(t))*sin(theta1(t))*h2*l1*mi*(diff(theta6(t), t, t))-cos(theta6(t))*cos(theta1(t))*h2*l1*m3*(diff(theta6(t), t, t))-sin(theta6(t))*sin(theta1(t))*h2*l1*m3*(diff(theta6(t), t, t))+sin(theta2(t))*sin(theta1(t))*l1*lc2*m2*(diff(theta2(t), t, t))+cos(theta2(t))*cos(theta1(t))*l1*l2*m4*(diff(theta2(t), t, t))+sin(theta2(t))*sin(theta1(t))*l1*l2*mc*(diff(theta2(t), t, t))+sin(theta3(t))*sin(theta1(t))*l1*lc3*m3*(diff(theta3(t), t, t))-cos(theta3(t))*cos(theta1(t))*l1*l3*mi*(diff(theta3(t), t, t))-sin(theta3(t))*sin(theta1(t))*l1*l3*mi*(diff(theta3(t), t, t))-cos(theta3(t))*cos(theta1(t))*l1*l3*m3*(diff(theta3(t), t, t))-sin(theta3(t))*sin(theta1(t))*l1*l3*m3*(diff(theta3(t), t, t))+cos(theta7(t))*cos(theta1(t))*h3*l1*mc*(diff(theta7(t), t, t))-cos(theta6(t))*cos(theta1(t))*h2*l1*ml*(diff(theta6(t), t, t))+sin(theta7(t))*sin(theta1(t))*h3*l1*mc*(diff(theta7(t), t, t))-sin(theta6(t))*sin(theta1(t))*h2*l1*ml*(diff(theta6(t), t, t))+sin(theta4(t))*sin(theta1(t))*l1*lc4*m4*(diff(theta4(t), t, t))+cos(theta4(t))*cos(theta1(t))*l1*lc4*m4*(diff(theta4(t), t, t))-sin(theta4(t))*sin(theta1(t))*l1*l4*mi*(diff(theta4(t), t, t))+sin(theta2(t))*sin(theta1(t))*l1*l2*m4*(diff(theta2(t), t, t))+sin(theta2(t))*sin(theta1(t))*l1*l2*mi*(diff(theta2(t), t, t))+sin(theta5(t))*sin(theta1(t))*h2*l1*m4*(diff(theta5(t), t, t))

## How to delete mapleprime account...

I am not interested in the mapleprime group, so I want to delete my account in this group.

## Why my questions are continuously deleted. ...

Recently, my questions are deleted. last month I ask 3 questions but that all questions are deleted without my knowledge. yesterday also i ask one question "how to plot3d graph" that also deleted. "https://www.mapleprimes.com/questions/225618-How-To-Plot-The-3d-Graph?sq=225618". In the mapleprime, I am following the ethics and rules.

## K & C syntax not + & -...

Hi

I am having problems with the syntax/symbols i maple. I down know what "setting" has changed but + and - and so on, has change to K and C. anyone know how to fix this?

Regards

Morten

## How do i define a piecewise function on maple with...

Define a piecewise function of  so that the the value of the function is  if  or if , it is equal to the vertical distance between the curves if . Numerically integrate the area under this curve on the non-zero interval and explain how the numerical answer is what you would anticipate the answer to be given that this curve is related to semi-circles.

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