Download Autoexecute.mw

I found that Maple has the following:
1. U, S, V: = MTM [svd] (A)
2. LinearAlgebra "LeastSquares (A, b, method = SVD)
3. u, s, v: = LinearAlgebra "SingularValues (evalf (A), output = ['U', 'S', 'Vt']);
4. S, U, V: = LinearAlgebra "SmithForm (A, output = ['S', 'U', 'V'])
Any substantial difference between them?
What is the most recommended?
How we make maple drive yourself this:
> U.dS.Vt;
Error, (in LinearAlgebra "MatrixMatrixMultiply) first matrix column dimension (3) <> second matrix row dimension (6)
dS: = LinearAlgebra "DiagonalMatrix (S)
[18.7790195322481088 0 0 0 0 0]
[0 7.79837340298600078 0 0 0 0]
[0 0 5.70384060743677868 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
I've solved this way:
U.dS:
U.dS
% [1 ..,.. 3]. Vt
Noting that
U. S. Vt = A

Gracias

I had read that we could avoid X = (ATA)-1AT x B, performing the SVD

X = V x S-1 x AT x B, but does not seem as simple as reading appreciated.

I get the following error:

 u, s, v := SingularValues(evalf(A), output = [U, S, Vt]);

Error, cannot split rhs for multiple assignment

u, s, v := SingularValues(evalf(A), output = [U, S, Vt], 'thin');

Error, cannot split rhs for multiple assignment

Thanks colleagues for your ride, all as desired.
Gracias

Hi colleagues, I need the correct sequence of steps
to achieve to enable the components.
I've done what you have proposed and I get the following error;
 
When I open the worksheet shows the following dialogue:
 

After this, if I click on some of the dials, I get the following message:
 
 

Only when I run the worksheet is that the components are activated,
but then resumed the variables (beta1) and have not received from the component values:
 

Gracias

Thanks, I really could not find how to 
activate the Auto executable.
Gracias

Switch sol in the last statement by Sol and everything will be fine.

plots[odeplot](Sol, [[t, E(t)], [t, S(t)], [t, ES(t)], [t, P(t)]], 
t = 0 .. 30, colour = [red, blue, green, black],
 legend = [enzyme, substrate, complex, product])

Hi colleagues, I have made indications targeted by you:

libname:="E:\\MapleWorksheets\\Maple Libs\\Trigonometry", libname

The result is the following:

DegreePlot(1);
 display([

   pieslice([0, 0], 1, 0 .. 0.01745329252, color = COLOR(RGB, 1, 0.85, 0)),

   pieslice([0, 0], 1, 0.01745329252 .. 2 Pi,

   color = COLOR(RGB, 0.8, 0.45, 0.05)),

   textplot([1.199817234, 0.02094288773, "1"])], scaling = constrained)

No commands are executed in the package. In this case:
 DegreePlot,
AnglePlot((2*Pi)/12),
AngleSpectrum(Pi/2);

Gracias

In the zip file is a maple.lib and maple.ind. This will mean:

"Execute the Code Resource section first..."


I ran the command  libname: = currentdir (), libname; 
no results
Any suggestions.
Gracias

Robert Israel's reply is very elegant.
But I've noticed that whenever the two realizations, one obtains the same sample to the value of X, so the graph does not vary from run to run. Variable X is not a randomly generated?

restart;
with(Statistics);

X := RandomVariable(Normal(0, 1)):

f1 := proc (x) options operator, arrow; PDF(X, x) end proc:

A := Sample(X, 500):

Q := FrequencyPlot(A, thickness = 3, color = red):

Tvalues := op([1, 1], Q):

x1 := Quantile(X, 0.5e-1): CDF(X, x1): f(x1):

x2 := Quantile(X, .95): CDF(X, x2): f(x2):

g1 := [op(Select(proc (t) options operator, arrow; is(t[1] < x1) end proc, Tvalues)), [x1, f(x1)]]:

g2 := [[x2, f(x2)], op(Select(proc (t) options operator, arrow; is(x2 < t[1]) end proc, Tvalues))]:

plots:-display([plot(g1, colour = gray, filled = true), plot(g2, colour = gray, filled = true)], Q);

I get the following error:
Any ideas?

make_equations(400, 2000);

Error, (in LinearAlgebra:-VectorMatrixMultiply) invalid input: LinearAlgebra:-VectorMatrixMultiply expects its 1st argument, v, to be of type Vector[row] but received Vector(10, {(1) = 418., (2) = 426., (3) = 377., (4) = 427., (5) = 407., (6) = 374., (7) = 388., (8) = 402., (9) = 435., (10) = 437.})
 

Gracias

Hermes

Hello colleagues,
Opening the maple worksheet I receive the following message:
"There were problems during the loading process.
 Your worksheet may be incomplete."

It is a worksheet where I have done several calculations that
 interests me not to lose.

When I save the file with another name, recovers only the initial
 part of the calculations. 
And the file is smaller than the original. What makes me think 
that in the old file, is missing information.
I performed the steps that are oriented in the Maple Help,
 without success.
To top it had disabled the autosave option,Unable to perform file
recovery.
I've been reading the comments in:

www.mapleprimes.com/forum/incompleteworksheetlostfile

www.mapleprimes.com/forum/incompleteworksheet


Without make nothing of it.
Any suggestions, or do I need to retype the whole document.

Gracias

How we can change the background plot, as shown in this picture?

Gracias

Thanks Doug;
In your last suggestion I maked the following change,
to add in the ranks, without taking the line item that is on the diagonal.

for i to LinearAlgebra:-RowDimension(B) do
 convert(subsop(i = NULL, convert(B[i, 1 .. -1], list)), `+`) 
end do;

To achieve:

res := Matrix(LinearAlgebra:-RowDimension(A), 2);
%;
for i to LinearAlgebra:-RowDimension(A) do
 res[i, 1] := evalb(abs(A[i, i]) >= abs(convert(subsop(i = NULL, convert(A[i, 1 .. -1], list)), `+`)));
 res[i, 2] := evalb(abs(A[i, i]) > abs(convert(subsop(i = NULL, convert(A[i, 1 .. -1], list)), `+`))) end do;

res;

                               [false  false]
                               [            ]
                               [true   true ]
                               [            ]
                               [false  false]
Student[NumericalAnalysis][IsMatrixShape](A, 'strictlydiagonallydominant');

                                    false
Student[NumericalAnalysis][IsMatrixShape](A, 'diagonallydominant');

                                    false

Thank you all for your comments and ideas;