As Demmel and others have noted, SVD is both more reliable and more expensive than QR as a method of solving rank-deficient least squares problems.

SVD is the method that LinearAlgebra:-LeastSquares will choose when the Matrix has more columns than rows (n>m), unless instructed otherwise using the optional 'method' parameter.

LinearAlgebra:-SingularValues always computes a full U and Vt. But for least squares computations, such as when n>m, this is not necessary. Including the smaller singular values may just be (re-)introducing noise. See here for more detail.

Here's a 20x2000 example, using wrapperless external calling and the SVD routine dgesvd in the CLAPACK library. The effective speedup by using the Thin SVD for that 20x2000 least squares example is about a factor of 100 (ie, 2000/20), with a similar reduction in additional memory allocation.

I am having problems using implicitplot.  I run this code and it worked and today I tried it again and it gives me the following:

with(plots,implicitplot);

implicitplot(0=int(erf(  (T-e*t)/sqrt(2)  )*t^2*exp(-t/2),t=0..infinity),e=0..1,T=0..10);

Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {t}

The weird thing is that this worked before (took about 10min though) and now it isn't.  Any suggestions?

Thanks

May be that some other people want to use pattern-matching techniques in wrong ways or contexts. What I am interested in is much simpler and clear.

I frequently see references to data being loaded from maplesoft.112.2o7.net -- what is that?  It's annoying because the page seems to have been loaded, but the browser is still active doing stuff, so that interaction is slower.  If this is not doing something really useful, could it be turned off?

Using dsolve gives the incorrect solution unless you force it to use Laplace transforms. 

Notice that Y5 is the correct solution, not the Y coming from dsolve.

DE17:=diff(y(t),t$2)+y(t)=Dirac(t-Pi)+Dirac(t-2*Pi)+Dirac(t-3*Pi);
Y:=dsolve({DE17,y(0)=0,D(y)(0)=0},y(t));
plot(rhs(Y),t=0..6*Pi);
with(inttrans):
Y2:=laplace(DE17,t,s);
Y3:=solve(Y2,laplace(y(t),t,s));
Y4:=subs({y(0)=0,D(y)(0)=0},Y3);
Y5:=invlaplace(Y4,s,t);
plot(Y5,t=0..6*Pi);
 

 

Anybody run into this problem before?

I was playing with a problem from the Maple NG, one can state it as
  
  Int( arccos(x) / ( 1+x^4) , x=0 .. 1)

Maple 11.02 gives a result, which numerical can not be valid.

Using real (!) partial fractions (Maple uses decomposition over the
complex, no?) I got a similar problem with denominator = parabola
(and continuity over the integration interval):

  Int( arccos(x) / (x^2 - x * 2^(1/2) + 1), x = 0 .. 1)

Some more and time-consuming consuming experiments reduces troubles
to the following example, where symbolics are disproven by numerics:

You have options to open tabs in separate windows or move existing multiple tabs into separate windows. 

Can we add an option to combine tabs into one window? 

View 8340_helpweaklynonlinear.mw on MapleNet or Download 8340_helpweaklynonlinear.mw

A colleague recently showed me some strange behavior when trying to plot vertical lines. The following works to create the unit square:

plot( [x=0,x=1,0,1], x=0..1, y=0..1, color=black, axes=none ); # OK

But doubling the size in each direction does not produce a square:

plot( [x=0,x=2,0,2], x=0..2, y=0..2, color=black, axes=none ); # BAD

The vertical lines extend only up to y=1, not y=2 as requested. The next command shows that vertical lines at the boundary are treated differently.

How do I change the default font used in Maple 12?  I'm in WinXP.

As many of you have experienced, the maplet MathMLEditor, has some problem when it comes to interpret correctly the typing functions, even some functions with the help of the palette.

I was trying to input this function : sin(4*x)+cos(2*x) but after moving form the unknown tag _XML_ error, I end up with misinterpretations of this function, to things like  4*sin(x)+cos(2*x).

So, the comments in this blog tells that the better solution is to use a TextField to get the input function, but now I face this problem

f := Get('txtFunction');
 

Hi, I am just wondering who is currently using Maple in Finance. While I would keen to know any commercial or academic uses, I am especially interested in two areas: 1. Asset valuation and modelling 2. Portfolio analysis including risk, hedging, rebalancing or optimisation 3. High frequency (from 15min to readtime) processing of data (FX, Equity or IR) We recently completed a quite extensive benchmarking of Maple, Mathematica and Matlab using finance and portfolio related problems and would be interested know other experiences here.

I run Maple on a Wintel machine, specifically a Dell Dimension 9100 Mini-Tower: Pentium D Processor 820 with Dual Core Technology (2.80GHz, 800FSB) Microsoft Windows XP Media Center 2005.  I also recently acquired an OLPC.  I don't think that the OLPC will be much of a Maple platform in the near future but it does run Linux.

After fighting with the Maplet Table control, I decided to give it a try to the TextBox, using tabulator spaces, to have some degree of control over the column layout I need to present tablar results.

The problem I am facing now, is that the "\t" tabulator scape caractar on the textbox has a size to big, in some applications you can set the tab size, in number of caracters or something else, anyone know if this is possible in Maple or on  a Maplet?