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| | 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] |
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| 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.
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| Typical examples of matrices that can take advantage of packed storage include:
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| * [[Symmetric matrix|symmetric]] or [[hermitian matrix]]
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| * [[Triangular matrix]]
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| * [[Banded matrix]].
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| ==Code examples (Fortran)==
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| Both of the following storage schemes are used extensively in BLAS and LAPACK.
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| An example of packed storage for hermitian matrix:
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| <pre>
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| complex:: A(n,n) ! a hermitian matrix
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| complex:: AP(n*(n+1)/2) ! packed storage for A
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| ! the lower triangle of A is stored column-by-column in AP.
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| ! unpacking the matrix AP to A
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| do j=1,n
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| k = j*(j-1)/2
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| A(1:j,j) = AP(1+k:j+k)
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| A(j,1:j-1) = conjg(AP(1+k:j-1+k))
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| end do
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| </pre> | |
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| An example of packed storage for banded matrix:
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| <pre> | |
| real:: A(m,n) ! a banded matrix with kl subdiagonals and ku superdiagonals
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| real:: AP(-kl:ku,n) ! packed storage for A
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| ! the band of A is stored column-by-column in AP. Some elements of AP are unused.
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| ! unpacking the matrix AP to A
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| do j=1,n
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| forall(i=max(1,j-kl):min(m,j+ku)) A(i,j) = AP(i-j,j)
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| end do
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| print *,AP(0,:) ! the diagonal
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| </pre>
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| {{DEFAULTSORT:Packed Storage Matrix}}
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| [[Category:Arrays]]
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| [[Category:Matrices]]
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