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physicsonly
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 Posted: Wed Jul 30, 2008 7:49 pm Post subject: Histogram |
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Dear All,
I am a new student in the field of Numerics. I have a problem. I do
exact diagonalization using Matpack or Lapack. Now I need to plot the
density of states of the system or in other words I need to create a
Histogram of the Eigenvalues. Now I want to know what is the effective
way of doing this keeping in mind that I have typical no of data
128*128 of 100 systems(128*128*100). So when I will do the
binning(what will be the proper way of binning) I need do the average
over samples also.
Is there any way to calculate eigenvalues(not all are interesting)
which is near zeros only of a sparse matrix?
Any help will be helpful?
Looking frwd for replies.
Thanking you
Soumya Bera |
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Peter Spellucci
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| Posted: Thu Jul 31, 2008 10:15 am Post subject: Re: Histogram |
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In article <b9535eaf-31d8-4109-8b3e-67c11a93d2e2@m73g2000hsh.googlegroups.com>,
physicsonly <onlyforsoumya@gmail.com> writes:
[quote]Dear All,
I am a new student in the field of Numerics. I have a problem. I do
exact diagonalization using Matpack or Lapack. Now I need to plot the
density of states of the system or in other words I need to create a
Histogram of the Eigenvalues. Now I want to know what is the effective
way of doing this keeping in mind that I have typical no of data
128*128 of 100 systems(128*128*100). So when I will do the
binning(what will be the proper way of binning) I need do the average
over samples also.
[/quote]
histograms are typically equidistant over the relevant span of values.
what if you first collect all computed eigenvalues in one set, prepare
a histogram of these and then prepare the single histograms using the same
interval decomposition? thiswouldbe allow you to look at same parametric
development of the eigenvalues. this however assumes that you have indeed
all the eigenvalues.
an eigenvalue of dimension 128 is "small" for today computers/software, so there
is no reason to bother about complexity here
[quote]
Is there any way to calculate eigenvalues(not all are interesting)
which is near zeros only of a sparse matrix?
Any help will be helpful?
[/quote]
yes of course: you can use arpack/lanczos or ritzit codes in combination with
inverse iteration to do this.
there is ready to use software in several versions.
but as long as your matrices are not very large
this does not pay for: not only are these methods less reliable,
the effort which may be necessary to compute the desired eigenvalues
with sufficient precision also depends on the distribution of all eigenvalues
and the quality of your initial subspace representation which you must
supply and hence is hardly predictable.
hth
peter |
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