203.11.131.82 at 03:46, 1 December 2014

2014-12-01T03:46:09Z

← Older revision		Revision as of 05:46, 1 December 2014
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	~~{{Unreferenced\|date=December 2009}}~~		Hi there. Allow me start by introducing the writer, her name is Myrtle Cleary. What I love doing is playing baseball but I haven't made a dime with it. For a whilst I've been in South Dakota and my mothers and fathers live nearby. Bookkeeping is my occupation.<br><br>Look at my site - [http://cnx.dk/index.php?m=member_profile&p=profile&id=993 over the counter std test]

	~~A '''packed storage matrix''', also known as '''packed matrix'''~~, is ~~a term used in [[Mathematical programming\|programming]] for representing an <math>m\times n</math> [[Matrix (mathematics)\|matrix]]~~. It is a ~~more compact way than an m-by-n rectangular array by exploiting~~ a ~~special structure of the matrix.~~

	~~Typical examples of matrices that can take advantage of packed storage include:~~
	* [[Symmetric matrix\|symmetric]] or [[hermitian matrix]]
	* [[Triangular matrix]]
	* [[Banded matrix]].

	~~==Code examples (Fortran)==~~
	~~Both of the following storage schemes are used extensively~~ in ~~BLAS~~ and ~~LAPACK~~.

	~~An example of packed storage for hermitian matrix:~~
	~~<pre>~~
	~~complex:: A(n,n) ! a hermitian matrix~~
	~~complex:: AP(n*(n+1)/2) ! packed storage for A~~
	~~! the lower triangle of A~~ is ~~stored column-by-column in AP~~.
	~~! unpacking the matrix AP to A~~
	~~do j=1,n~~
	~~k = j*(j-1)/2~~
	~~A(1:j,j) = AP(1+k:j+k)~~
	~~A(j,1:j-1) = conjg(AP(1+k:j-1+k))~~
	~~end do~~
	<~~/pre~~>

	~~An example of packed storage for banded matrix:~~

	<~~pre~~>
	~~real:: A(m,n) ! a banded matrix with kl subdiagonals and ku superdiagonals~~
	~~real:: AP(~~-kl:~~ku,n) ! packed storage for A~~
	~~! the band of A is stored column-by-column in AP~~. ~~Some elements of AP are unused~~.
	~~! unpacking the matrix AP to A~~
	~~do j~~=~~1,n~~
	~~forall(i~~=~~max(1,j-kl):min(m,j+ku)) A(i,j)~~ = ~~AP(i-j,j)~~
	~~end do~~
	~~print *,AP(0,:) !~~ the ~~diagonal~~
	~~</pre>~~

	~~{{DEFAULTSORT:Packed Storage Matrix}}~~
	~~[[Category:Arrays]]~~
	~~[[Category:Matrices]~~]

en>Zfeinst: describe formula in terms of moments

2012-08-03T15:48:06Z

describe formula in terms of moments

New page

{{Unreferenced|date=December 2009}}

A '''packed storage matrix''', also known as '''packed matrix''', is a term used in [[Mathematical programming|programming]] for representing an <math>m\times n</math> [[Matrix (mathematics)|matrix]]. It is a more compact way than an m-by-n rectangular array by exploiting a special structure of the matrix.

Typical examples of matrices that can take advantage of packed storage include:
* [[Symmetric matrix|symmetric]] or [[hermitian matrix]]
* [[Triangular matrix]]
* [[Banded matrix]].

==Code examples (Fortran)==
Both of the following storage schemes are used extensively in BLAS and LAPACK.

An example of packed storage for hermitian matrix:
<pre>
complex:: A(n,n) ! a hermitian matrix
complex:: AP(n*(n+1)/2) ! packed storage for A
! the lower triangle of A is stored column-by-column in AP.
! unpacking the matrix AP to A
do j=1,n
k = j*(j-1)/2
A(1:j,j) = AP(1+k:j+k)
A(j,1:j-1) = conjg(AP(1+k:j-1+k))
end do
</pre>

An example of packed storage for banded matrix:

<pre>
real:: A(m,n) ! a banded matrix with kl subdiagonals and ku superdiagonals
real:: AP(-kl:ku,n) ! packed storage for A
! the band of A is stored column-by-column in AP. Some elements of AP are unused.
! unpacking the matrix AP to A
do j=1,n
forall(i=max(1,j-kl):min(m,j+ku)) A(i,j) = AP(i-j,j)
end do
print *,AP(0,:) ! the diagonal
</pre>

{{DEFAULTSORT:Packed Storage Matrix}}
[[Category:Arrays]]
[[Category:Matrices]]

Upside potential ratio - Revision history

203.11.131.82 at 03:46, 1 December 2014

en>Zfeinst: describe formula in terms of moments