Mercurial > hg > octave-lyh
diff doc/interpreter/sparse.txi @ 10828:322f43e0e170
Grammarcheck .txi documentation files.
author | Rik <octave@nomad.inbox5.com> |
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date | Wed, 28 Jul 2010 12:45:04 -0700 |
parents | 3140cb7a05a1 |
children | a4f482e66b65 |
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--- a/doc/interpreter/sparse.txi +++ b/doc/interpreter/sparse.txi @@ -177,14 +177,17 @@ @item Returned from a function There are many functions that directly return sparse matrices. These include @dfn{speye}, @dfn{sprand}, @dfn{diag}, etc. + @item Constructed from matrices or vectors The function @dfn{sparse} allows a sparse matrix to be constructed from three vectors representing the row, column and data. Alternatively, the function @dfn{spconvert} uses a three column matrix format to allow easy importation of data from elsewhere. + @item Created and then filled The function @dfn{sparse} or @dfn{spalloc} can be used to create an empty matrix that is then filled by the user + @item From a user binary program The user can directly create the sparse matrix within an oct-file. @end table @@ -206,7 +209,7 @@ Other functions of interest that directly create sparse matrices, are @dfn{diag} or its generalization @dfn{spdiags}, that can take the definition of the diagonals of the matrix and create the sparse matrix -that corresponds to this. For example +that corresponds to this. For example, @example s = diag (sparse(randn(1,n)), -1); @@ -236,7 +239,7 @@ The recommended way for the user to create a sparse matrix, is to create two vectors containing the row and column index of the data and a third -vector of the same size containing the data to be stored. For example +vector of the same size containing the data to be stored. For example, @example @group @@ -261,7 +264,7 @@ the third and four columns, the real and imaginary parts of the sparse matrix. The matrix can contain zero elements and the elements can be sorted in any order. Adding zero elements is a convenient way to define -the size of the sparse matrix. For example +the size of the sparse matrix. For example: @example @group @@ -346,7 +349,7 @@ matrix type when the div (/) or ldiv (\) operator is first used with the matrix and then caches the type. However the @dfn{matrix_type} function can be used to determine the type of the sparse matrix prior -to use of the div or ldiv operators. For example +to use of the div or ldiv operators. For example, @example @group @@ -357,9 +360,9 @@ @end group @end example -show that Octave correctly determines the matrix type for lower +shows that Octave correctly determines the matrix type for lower triangular matrices. @dfn{matrix_type} can also be used to force -the type of a matrix to be a particular type. For example +the type of a matrix to be a particular type. For example: @example @group @@ -395,7 +398,7 @@ command can be used to graphically display the interconnections between nodes. -As a trivial example of the use of @dfn{gplot}, consider the example +As a trivial example of the use of @dfn{gplot} consider the example, @example @group @@ -520,7 +523,7 @@ as a full matrix. For this reason operators and functions that have a high probability of returning a full matrix will always return one. For example adding a scalar constant to a sparse matrix will almost always -make it a full matrix, and so the example +make it a full matrix, and so the example, @example @group @@ -610,7 +613,7 @@ A particular problem of sparse matrices comes about due to the fact that as the zeros are not stored, the sign-bit of these zeros is equally not -stored. In certain cases the sign-bit of zero is important. For example +stored. In certain cases the sign-bit of zero is important. For example: @example @group @@ -713,8 +716,8 @@ In the case of an asymmetric matrix, the appropriate sparsity preserving permutation is @dfn{colamd} and the factorization using -this reordering can be visualized using the command @code{q = -colamd(A); [l, u, p] = lu(A(:,q)); spy(l+u)}. +this reordering can be visualized using the command +@code{q = colamd(A); [l, u, p] = lu(A(:,q)); spy(l+u)}. Finally, Octave implicitly reorders the matrix when using the div (/) and ldiv (\) operators, and so no the user does not need to explicitly @@ -762,18 +765,18 @@ continue, else goto 3b. @enumerate -@item If the matrix is hermitian, with a positive real diagonal, attempt +@item If the matrix is Hermitian, with a positive real diagonal, attempt Cholesky factorization using @sc{lapack} xPTSV. -@item If the above failed or the matrix is not hermitian with a positive +@item If the above failed or the matrix is not Hermitian with a positive real diagonal use Gaussian elimination with pivoting using @sc{lapack} xGTSV, and goto 8. @end enumerate -@item If the matrix is hermitian with a positive real diagonal, attempt +@item If the matrix is Hermitian with a positive real diagonal, attempt Cholesky factorization using @sc{lapack} xPBTRF. -@item if the above failed or the matrix is not hermitian with a positive +@item if the above failed or the matrix is not Hermitian with a positive real diagonal use Gaussian elimination with pivoting using @sc{lapack} xGBTRF, and goto 8. @end enumerate @@ -785,16 +788,16 @@ or lower triangular matrix with row permutations, perform a sparse forward or backward substitution, and goto 8 -@item If the matrix is square, hermitian with a real positive diagonal, attempt -sparse Cholesky factorization using CHOLMOD. +@item If the matrix is square, Hermitian with a real positive diagonal, attempt +sparse Cholesky factorization using @sc{cholmod}. @item If the sparse Cholesky factorization failed or the matrix is not -hermitian with a real positive diagonal, and the matrix is square, factorize +Hermitian with a real positive diagonal, and the matrix is square, factorize using @sc{umfpack}. @item If the matrix is not square, or any of the previous solvers flags a singular or near singular matrix, find a minimum norm solution using -CXSPARSE@footnote{The CHOLMOD, UMFPACK and CXSPARSE packages were +@sc{cxsparse}@footnote{The @sc{cholmod}, @sc{umfpack} and @sc{cxsparse} packages were written by Tim Davis and are available at http://www.cise.ufl.edu/research/sparse/}. @end enumerate