sparse_mat_info¶

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Sparse Matrix Information¶

Syntax¶

CppAD::mixed::sparse_mat_info mat_info

mat_info . resize ( size )

Purpose¶

This structure holds information about a sparse matrix.

row¶

The field mat_info . row has prototype

CppAD::vector<size_t> mat_info . row

It has size zero when it is constructed. After initialization it should contain the row indices corresponding to possibly non-zero elements of the matrix.

K¶

We use K = mat_info . row.size () below.

col¶

The field mat_info . col has prototype

CppAD::vector<size_t> mat_info . col

It has size zero when it is constructed. After initialization it should have the same size as row and contain the column indices corresponding to possibly non-zero elements of the matrix.

val¶

The field mat_info . val has prototype

CppAD::vector<double> mat_info . val

It has size zero when it is constructed. After initialization it should either have size zero, or the same size as row .

resize¶

The resize argument has prototype

size_t size

All of the vectors, row , col , and val , are modified to have the specified size.

Notation¶

Sparsity Pattern¶

We say that mat_info is a sparsity pattern if, for k = 0 , … , K -1 , the element with index

( mat_info . row [ k ], mat_info . col [ k ])

is possibly non-zero and the size or elements of mat_info . val are not specified.

Sparse Matrix¶

We say that mat_info is a sparse matrix if, for k = 0 , … , K -1 , the element with index

( mat_info . row [ k ], mat_info . col [ k ])

is possibly non-zero and has value mat_info . val [ k ] .

Empty Matrix¶

If K is zero ( mat_info . row.size () is zero), we say that mat_info is the empty matrix.

Column Major Order¶

If for k = 0 , … , K -1 ,

        mat_info . col [ k ] <= mat_info . col [ k +1]
        if ( mat_info . col [ k ] == mat_info . col [ k +1] )
                mat_info . row [ k ] < mat_info . row [ k +1]

we say that mat_info is in column major order.

Row Major Order¶

If for k = 0 , … , K -1 ,

        mat_info . row [ k ] <= mat_info . row [ k +1]
        if ( mat_info . row [ k ] == mat_info . row [ k +1] )
                mat_info . col [ k ] < mat_info . col [ k +1]

we say that mat_info is in row major order.

Lower Triangular¶

If for k = 0 , … , K -1 ,

mat_info . row [ k ] >= mat_info . col [ k ]

we say that mat_info is lower triangular.