Re: [R] SVD with positivity constraints
If A is not square, which dimension is larger? There will most likely be either no solution or an infinity of solutions. If the latter, I think you are using the Moore-Penrose inverse (depends exactly how you use the SVD), that is the shortest solution, but the SVD will give you the whole space of solutions and you could compute if that intersects the positive orthant. On Tue, 27 Jul 2004, Molins, Jordi wrote: I have a matrix equation, Ax=b, that I need to solve for x. x should be a vector of positive numbers (between 0 and 1). A is not a square matrix in general. This lead me to using the SVD. However, using the SVD gives me positive and negative numbers, as well. I have some constraints included in the A matrix itself (i.e., that the sum of some xi should be equal to 1) but I do not know how to include the constraint that each xi should be non-negative. Is there in R (or somewhere else) an SVD that includes this kind of constraint? or some other optimizer that can cope with solving non-square matrix equations, including the positivity constraint? optim(method=L-BFGS-B) can cope with [0, 1] constraints. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
RE: [R] SVD with positivity constraints
Thank you to Prof Brian Ripley and to Ken Knoblauch for your replies.
I should explain a little bit more about the problem at hand: in principle,
the matrix can have more rows than columns or the other way around. However,
I always could include in an artificial way more equations, such that there
are more equations than unknowns. So, in practical terms, the first question
from Prof Brian Ripley is: more equations than unkowns.
I have
Additionally, I have seen in several places that is suggested to use La.svd
instead of the standard svd.
-Original Message-
From: Prof Brian Ripley [mailto:[EMAIL PROTECTED]
Sent: 27 July 2004 10:13
To: Molins, Jordi
Cc: '[EMAIL PROTECTED]'
Subject: Re: [R] SVD with positivity constraints
If A is not square, which dimension is larger? There will most likely be
either no solution or an infinity of solutions. If the latter, I think
you are using the Moore-Penrose inverse (depends exactly how you use the
SVD), that is the shortest solution, but the SVD will give you the whole
space of solutions and you could compute if that intersects the positive
orthant.
On Tue, 27 Jul 2004, Molins, Jordi wrote:
I have a matrix equation, Ax=b, that I need to solve for x. x should be a
vector of positive numbers (between 0 and 1). A is not a square matrix in
general. This lead me to using the SVD. However, using the SVD gives me
positive and negative numbers, as well. I have some constraints included
in
the A matrix itself (i.e., that the sum of some xi should be equal to 1)
but
I do not know how to include the constraint that each xi should be
non-negative.
Is there in R (or somewhere else) an SVD that includes this kind of
constraint? or some other optimizer that can cope with solving non-square
matrix equations, including the positivity constraint?
optim(method=L-BFGS-B) can cope with [0, 1] constraints.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UKFax: +44 1865 272595
The information contained herein is confidential and is inte...{{dropped}}
__
[EMAIL PROTECTED] mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
RE: [R] SVD with positivity constraints
Thank you to Prof Brian Ripley and to Ken Knoblauch for your fast replies.
I should explain a little bit more about the problem at hand: in principle,
the matrix can have more rows than columns or the other way around. However,
I always could include in an artificial way more equations, such that there
are more equations than unknowns. So, in practical terms, the answer to the
first question from Prof Brian Ripley is: more equations than unkowns.
I have checked in the Modern Applied Statistics with S 4th edition, and in
page 62 it is shown the use of svd. It is written that svd gives, as result,
u, v and d. If there is a space of solutions (as opposed to a unique
solution) how is the solution given? how can I retrieve the whole space of
solutions?
Additionally, I have seen in several places that is suggested to use La.svd
instead of the standard svd. Would the La.svd generate also the whole space
of solutions? I have looked the documentation
(http://cran.r-project.org/doc/packages/RScaLAPACK.pdf) but it is not
explicitly written how to retrieve non-unique solutions.
An additional question: in the Numerical Recipes for C++ it is written that
the small numbers in the diagonal of d should be set manually to 0. Is
this done (maybe as an option) in svd or in La.svd? could this resetting
have a material effect in the solutions found?
thank you
J
-Original Message-
From: Prof Brian Ripley [mailto:[EMAIL PROTECTED]
Sent: 27 July 2004 10:13
To: Molins, Jordi
Cc: '[EMAIL PROTECTED]'
Subject: Re: [R] SVD with positivity constraints
If A is not square, which dimension is larger? There will most likely be
either no solution or an infinity of solutions. If the latter, I think
you are using the Moore-Penrose inverse (depends exactly how you use the
SVD), that is the shortest solution, but the SVD will give you the whole
space of solutions and you could compute if that intersects the positive
orthant.
On Tue, 27 Jul 2004, Molins, Jordi wrote:
I have a matrix equation, Ax=b, that I need to solve for x. x should be a
vector of positive numbers (between 0 and 1). A is not a square matrix in
general. This lead me to using the SVD. However, using the SVD gives me
positive and negative numbers, as well. I have some constraints included
in
the A matrix itself (i.e., that the sum of some xi should be equal to 1)
but
I do not know how to include the constraint that each xi should be
non-negative.
Is there in R (or somewhere else) an SVD that includes this kind of
constraint? or some other optimizer that can cope with solving non-square
matrix equations, including the positivity constraint?
optim(method=L-BFGS-B) can cope with [0, 1] constraints.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UKFax: +44 1865 272595
The information contained herein is confidential and is inte...{{dropped}}
__
[EMAIL PROTECTED] mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
RE: [R] SVD with positivity constraints
Hello,
what I wrote below is nonsense: if the matrix has more equations than
unknowns, it makes no sense considering the general space of solutions.
Sorry for that.
Another consideration: could somebody give me an opinion about the following
procedure?
the simplex algorithm maximizes
z=a00x0 + a01x1+...+a0(N-1)x(N-1)
subject to x0=0, ... x(N-1)=0
and under M=m1+m2+m3 constraints: m1 equations for = inequalities(with x on
the left), m2 equations for = inequalities, and m3 equations for equalities
(=).
Consider a00=a01=...=a0(N-1)=0 (degenerate in some sense), and let me choose
also m1=m2=0, and then m3 being the number of equations I have.
Using the simplex method for linear programing would give me my solution,
or would this method give me a degenerate solution?
thank you, and please bear with me my desesperation ;-
Jordi
-Original Message-
From: Molins, Jordi
Sent: 27 July 2004 11:33
To: '[EMAIL PROTECTED]'
Cc: 'Prof Brian Ripley'; 'Ken Knoblauch'
Subject: RE: [R] SVD with positivity constraints
Thank you to Prof Brian Ripley and to Ken Knoblauch for your fast replies.
I should explain a little bit more about the problem at hand: in principle,
the matrix can have more rows than columns or the other way around. However,
I always could include in an artificial way more equations, such that there
are more equations than unknowns. So, in practical terms, the answer to the
first question from Prof Brian Ripley is: more equations than unkowns.
I have checked in the Modern Applied Statistics with S 4th edition, and in
page 62 it is shown the use of svd. It is written that svd gives, as result,
u, v and d. If there is a space of solutions (as opposed to a unique
solution) how is the solution given? how can I retrieve the whole space of
solutions?
Additionally, I have seen in several places that is suggested to use La.svd
instead of the standard svd. Would the La.svd generate also the whole space
of solutions? I have looked the documentation
(http://cran.r-project.org/doc/packages/RScaLAPACK.pdf) but it is not
explicitly written how to retrieve non-unique solutions.
An additional question: in the Numerical Recipes for C++ it is written that
the small numbers in the diagonal of d should be set manually to 0. Is
this done (maybe as an option) in svd or in La.svd? could this resetting
have a material effect in the solutions found?
thank you
J
-Original Message-
From: Prof Brian Ripley [mailto:[EMAIL PROTECTED]
Sent: 27 July 2004 10:13
To: Molins, Jordi
Cc: '[EMAIL PROTECTED]'
Subject: Re: [R] SVD with positivity constraints
If A is not square, which dimension is larger? There will most likely be
either no solution or an infinity of solutions. If the latter, I think
you are using the Moore-Penrose inverse (depends exactly how you use the
SVD), that is the shortest solution, but the SVD will give you the whole
space of solutions and you could compute if that intersects the positive
orthant.
On Tue, 27 Jul 2004, Molins, Jordi wrote:
I have a matrix equation, Ax=b, that I need to solve for x. x should be a
vector of positive numbers (between 0 and 1). A is not a square matrix in
general. This lead me to using the SVD. However, using the SVD gives me
positive and negative numbers, as well. I have some constraints included
in
the A matrix itself (i.e., that the sum of some xi should be equal to 1)
but
I do not know how to include the constraint that each xi should be
non-negative.
Is there in R (or somewhere else) an SVD that includes this kind of
constraint? or some other optimizer that can cope with solving non-square
matrix equations, including the positivity constraint?
optim(method=L-BFGS-B) can cope with [0, 1] constraints.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UKFax: +44 1865 272595
The information contained herein is confidential and is inte...{{dropped}}
__
[EMAIL PROTECTED] mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
