## Problems with getting consistent execution timings...

I have been using CodeTools::Usage with Maple 17 to compare timings of a couple of matrix inversion routines against each other and against the Maple library routines LinearAlgebra::MatrixInverse and LinearAlgebra::Determinant.

The small section of code that I use to collect the cpu times for each method is:

----------------------------------------

udata := Usage(invTest(x,y,z,delta,mu), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
dat[1]:=udata[1]; dat[2]:=udata[2];

----------------------------------------
nRepeats has been set to 25.

In order to get the timings as accurate as possible, I only open a couple of terminal windows on my laptop so as to run the tests with as low a loaded machine as I can get. (I'm running Ubuntu 14.04 on an 8 core Intel (R) Core i7-3840QM, 2.8GHz CPU with 16Gb of memory.)

A test run consists of a sequence of test matrices each of which is run for an increasing sequence of matrix orders. I either time an implementation on its own or I time both an implementation and the Maple library routines. In the later case for each test matrix and order of matrix, I use Usage to first time the Maple routines and then the times for one of the implementations:

----------------------------------------

if compMaple then
udata := Usage(MatrixInverse(A), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
mdat[1]:=udata[1]; mdat[2]:=udata[2];

udata := Usage(Determinant(A), output=[cputime, bytesused],
iterations=nRepeats, quiet);
mdat[1]:=mdat[1]+udata[1];
mdat[2]:=mdat[2]+udata[2];
else
mdat[1..2] := 0:
end if:

udata := Usage(invTest(x,y,z,delta,mu), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
dat[1]:=udata[1]; dat[2]:=udata[2];

----------------------------------------

I have noticed the following:

a) If I time both Maple and an implementation, and the same implementation on its own I can get timings that vary up to a factor of 2 or more,

b) Changes in timings for the same test run and as close to the same environment as I can get (i.e., just the two user terminal windows open) can generate timing differences of up to 50%.

c) Sometimes chaotic' timings are generated, for example,

n = 150, t = 3 (secs)
n = 200, t = 24 (secs)
n = 250, t = 18 (secs)

which cannot be reflecting the times required to perform the calculations. This type of behaviour always seems to occur when the reported memory bytecount is increasing from ~0.25* 10^9 to over 10^9.

Is there anything I can be doing here to get more consistent timings?

I want to use the timings from these tests in a journal article so it would be good to have the same test run under very similar conditions to return timings within a few percent difference of one another. I certainly get this sort of tolerances (<10%) if I use the Fortran cpu_time intrinsic to time Fortran code.

## importing very large matrix from textfile ...

Hi !

I am importing a matrix from a text file. I am using the command,

ImportMatrix("Filelocation/Filename.txt", 'source' = 'delimited', 'delimiter' = " ");

I see the following error:

Error, (in ImportMatrix) cannot interpret file

I think it is because of the huge size.(700 MB, and 28 GB respectively)

How to import such a matrix in maple?

thanks,

## Solution of nonlinear system of ODEs...

Hello dear!

Hope you all are fine. I am trying to sloution the system of nonlinear system of ODEs (see attached file) but my solutions not converging please see and fix the problem. I am waiting your quick response.

Graph.mw

## applyrule with inequalities...

applyrule((x::anything < y::anything) = 0, a < b);
applyrule('x::anything < y::anything' = 0, a < b);
applyrule(<(x::anything, y::anything) = 0, a < b);
applyrule('<(x::anything, y::anything)' = 0, a < b);
a < b
a < b
a < b
0


All quotes matter, no doubt, but why is < different from the infix "<" and why does it need uneval?

## how to translate maple code to python code?...

https://gist.github.com/hoyeunglee/b0c6b61fafd1bee988fcafef3cfe6025

test1 = o(a(x,y),z)

test1.args[0]

python sympy can not get function name o and a

## how to verify f = grobner basis times syz...

restart;
with(Groebner):

DoExist := proc(tau, n)
if rtable_num_elems(tau) >= n then
return tau[n];
else
return 0;
end if;
end proc;

IsZero := proc(a, b)
if a=0 then
return 0;
else
return a/b;
end if
end proc;

g1 := x^2-w*y;
g2 := x*y - w*z;
g3 := y^2 - x*z;
gro := Basis([g1,g2,g3],plex(x,y,z,w));

X1 := *(LeadingTerm(g1, tdeg(x, y, z, w)));
X2 := *(LeadingTerm(g2, tdeg(x, y, z, w)));
X3 := *(LeadingTerm(g3, tdeg(x, y, z, w)));
X12 := lcm(X1,X2);
X13 := lcm(X1,X3);
X23 := lcm(X2,X3);
S12 := SPolynomial(g1, g2, lexdeg([x, y, z, w]));
S23 := SPolynomial(g2, g3, lexdeg([x, y, z, w]));
S13 := SPolynomial(g1, g3, lexdeg([x, y, z, w]));
e1 := Vector([1,0,0]);
e2 := Vector([0,1,0]);
e3 := Vector([0,0,1]);
eq1:= S12 = h121*g1 + h122*g2 + h123*g3;
eq1 := S12 - expand(h121*g1 + h122*g2 + h123*g3):
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h121, h122, h123)), tdeg(x, y, z, w, h121, h122, h123), 'Q');
h121 := 0;
h122 := 0;
h123 := 0;
s12 := IsZero(X12,X1)*e1-IsZero(X12,X2)*e2-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

eq1 := S13-expand(h131*g1+h132*g2+h133*g3):
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h131, h132, h133)), tdeg(x, y, z, w, h131, h132, h133), 'Q');
h131 := 0;
h132 := 0;
h133 := 0;
s13 := IsZero(X13,X1)*e1-IsZero(X13,X3)*e3-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

eq1:= S23 - expand(h231*g1 + h232*g2 + h233*g3);
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h231, h232, h233)), tdeg(x, y, z, w, h231, h232, h233), 'Q');
h231 := 0;
h232 := 0;
h233 := 0;
s23 := IsZero(X23,X2)*e2-IsZero(X23,X3)*e3-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

with(LinearAlgebra):
#F = Syz*GrobnerBasis
F := simplify(MatrixMatrixMultiply(Matrix([[s12[1],s13[1],s23[1]],[s12[2],s13[2],s23[2]],[s12[3],s13[3],s23[3]]]), Matrix([[gro[1]],[gro[2]],[gro[3]]])));
F[1][1] - g1 = 0;
F[2][1] - g2 = 0;
F[3][1] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[s12[1],0,s23[1]],[s12[2],0,s23[2]],[s12[3],0,s23[3]]]), Matrix([[gro[1]],[gro[2]],[gro[3]]])));
F[1][1] - g1 = 0;
F[2][1] - g2 = 0;
F[3][1] - g3 = 0;

#F = GrobnerBasis*Syz
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],s13[1],s23[1]],[s12[2],s13[2],s23[2]],[s12[3],s13[3],s23[3]]])));
F[1][1] - g1 = 0;
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],0,s23[1]],[s12[2],0,s23[2]],[s12[3],0,s23[3]]])));
F[1][1] - g1 = 0;
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;

#F = GrobnerBasis*Syz
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],s12[1],s12[1]],[s13[2],s13[2],s13[2]],[s23[3],s23[3],s23[3]]])));
F[1][1] - g1 = 0;
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],0,s12[1]],[s13[2],0,s13[2]],[s23[3],0,s23[3]]])));
F[1][1] - g1 = 0;
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;`

syz result is s12, s23

but after verify, F is not equal to GrobnerBasis*Syz

Is is possible to tell the latex output what to do if it finds a symbol?

Suppose I have the following expression:

O3^2 + k_O3NO

The normal latex output just takes it as it is and also translates k_O3NO to k_O3NO with the underscore.

I however want it to read (latex notation in math mode)

\left[ \text{O}_3 \right]^2 + k_{\text{O}_3\text{NO}}

So is that possible without changing everything manually?

edit: Just as a remark, the output at the moment for this expression reads

{{\it O3}}^{2}+{\it k\_O3NO}

and is kinda awful if compiled in latex...

Is it also possible for maple to latex realizing where a line-break is necessary?

## Crank Nicolson...

GREETINGS

How to derive a maple code for this attachment.

## How to do coding for Jacobian Matrix?...

Anybody know how to put this in coding for Jacobian Matrix?

## How to solve equation system?...

Hi,

i want to solve equation system u0(x,t),u1(x,t),v1(x,t),v0(x,t)v2(x,t) dependent on f(x,t).

I attached file.

worksheet.mwworksheet.mw

## Newbie that can't even maximize a quadratic needs ...

So I needed a CAS, and I spent a couple of months trying to get a basic understanding of SymPy and various applications starting with "M". We have Maple version 2016.

My "prototype problem" can be solved by hand, and is a system of quadratic Bellman equations, for i=1,2.  I'll return to it below, as I am obviously too clumsy to get even the second-to-simplest max/min working.  Oh, and I can't even insert Maple Math here in the forum, it does not like maximize or minimize.

Let's start easy. I enter
maximize((b-x)x,x)
which works as I expect. Then already at
maximize((abs(b)-x)x,x>=0)
I am stuck. Please, sweet Maple, you know that the answer is the same as before, don't you? (In the meantime I have tried to feed it maximize((b-x)x,x=0..1)... )

I was hoping my "proper" problem should be doable. What I really need is a sequence of quadratic optimization problems, where I have a vector x maximizing b'x-x'Ax subject to linear constraints, so it should not be too hard.  The "prototype problem" I needed for starters, is a system where for i=1,2 I have

v_i(0,y)=0 and inductively v_i(t+1,y)=max{x_i*(b_i-x_1-x_2)+ r_i v_i(t,y-x)}

where b_i and r_i are constants, x=(x_1,x_2), y=(y_1,y_2), and everything is nonnegative - including, the choice variables x_i must be between 0 and min{y_i, b_i-x_1-x_2}. And I want to plot both functions and the x with time as a slider, but ... I don't think I'll ever get that far?

Sorry for whining. (I know why I dropped out of computer science.)

## Linear solve command with multiple core (Maple 18,...

Daer maple useres,

I am solving around 170 linear algebraic equations (symbolic) using linearalgebra " solve" command. I see the cpu usage is only 15%; as I the cpu is  i-7, octacore ,15% means around 1 core is in use. With time (12 hours)  cpu usage goes down to 0% showing free memory approx 0.

Why  is it happening? Is it due to high memory usage in storing large symobic expressions? Is there a way to engage all the cores( 100% Cpu)?

Thanks and regards.

## What's the best way to search inserted table and r...

Using Insert->Table... and inserting information in the cells.

So I've created Table1 but I can't seem to call any row/column cell information using that name.  How do we do that?  Also, what is the best way to search for information in those cells and return information in adjacent cells?

## ImprovementsInPdsolve.mw...

Hello,

I have tryed, to run the file ImprovementsInPdsolve.mw with the Mapleversion 2017.3 but in the first example pde[1] I got this error:

Error, (in assuming) when calling 'dsolve'. Received: 'cannot determine if this expression is true or false: not 0 <= -(1/2)*Pi'

pde[2],  pde[3] and others are o.k. but pde[4] to pde[6] not. Can You give me a hint what's wrong?

With kindly regards

Wolfgang Gellien