Detailed Description

A compressed Sparse Row (CSR) sparse matrix is defined by four component vectors labeled w, v, and u.

Return the multiplication of the sparse matrix (specified by by values and indexing) by the specified dense vector.

They are defined as:

w: the non-zero values in the sparse matrix.
v: column index for each value in w, as a result this is the same length as w.
u: index of where each row starts in w, length is equal to the number of rows plus one. Last entry is one-past-the-end in w, following the Eigen spec. Indexing is either zero-based or one-based depending on the value of stan::error_index::value. Following the definition of the format in Eigen, we allow for unused garbage values in w/v which are never read. All indexing internal to a given function is zero-based.

With only m/n/w/v/u in hand, it is possible to check all dimensions are sane except the column dimension since it is implicit. The error-checking strategy is to check all dimensions except the column dimension before any work is done inside a function. The column index is checked as it is constructed and used for each entry. If the column index is not needed it is not checked. As a result indexing mistakes might produce non-sensical operations but out-of-bounds indexing will be caught.

Except for possible garbage values in w/v/u, memory usage is calculated from the number of non-zero entries (NNZE) and the number of rows (NR): 2*NNZE + 2*NR + 1.

The sparse matrix X of dimension m by n is represented by the vector w (of values), the integer array v (containing one-based column index of each value), the integer array u (containing one-based indexes of where each row starts in w).

Template Parameters

T1	type of the sparse matrix
T2	type of the dense vector

Parameters

m	Number of rows in matrix.
n	Number of columns in matrix.
w	Vector of non-zero values in matrix.
v	Column index of each non-zero value, same length as w.
u	Index of where each row starts in w, length equal to the number of rows plus one.
b	Eigen vector which the matrix is multiplied by.

Returns: Dense vector for the product.

Exceptions

std::domain_error	if m and n are not positive or are nan.
std::domain_error	if the implied sparse matrix and b are not multiplicable.
std::invalid_argument	if m/n/w/v/u are not internally consistent, as defined by the indexing scheme. Extractors are defined in Stan which guarantee a consistent set of m/n/w/v/u for a given sparse matrix.
std::out_of_range	if any of the indexes are out of range.

Functions
template<typename T >
const std::tuple< Eigen::Matrix< T, Eigen::Dynamic, 1 >, std::vector< int >, std::vector< int > >	stan::math::csr_extract (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
	Extract the non-zero values, column indexes for non-zero values, and the NZE index for each entry from a sparse matrix.

template<typename T , require_eigen_dense_base_t< T > * = nullptr>
const std::tuple< Eigen::Matrix< scalar_type_t< T >, Eigen::Dynamic, 1 >, std::vector< int >, std::vector< int > >	stan::math::csr_extract (const T &A)

template<typename T >
const std::vector< int >	stan::math::csr_extract_u (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
	Extract the NZE index for each entry from a sparse matrix.

template<typename T , require_eigen_dense_base_t< T > * = nullptr>
const std::vector< int >	stan::math::csr_extract_u (const T &A)
	Extract the NZE index for each entry from a sparse matrix.

template<typename T >
const std::vector< int >	stan::math::csr_extract_v (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
	Extract the column indexes for non-zero value from a sparse matrix.

template<typename T , require_eigen_dense_base_t< T > * = nullptr>
const std::vector< int >	stan::math::csr_extract_v (const T &A)
	Extract the column indexes for non-zero values from a dense matrix by converting to sparse and calling the sparse matrix extractor.

template<typename T >
const Eigen::Matrix< T, Eigen::Dynamic, 1 >	stan::math::csr_extract_w (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)

template<typename T , require_eigen_dense_base_t< T > * = nullptr>
const Eigen::Matrix< scalar_type_t< T >, Eigen::Dynamic, 1 >	stan::math::csr_extract_w (const T &A)

template<typename T >
Eigen::Matrix< value_type_t< T >, Eigen::Dynamic, Eigen::Dynamic >	stan::math::csr_to_dense_matrix (int m, int n, const T &w, const std::vector< int > &v, const std::vector< int > &u)
	Construct a dense Eigen matrix from the CSR format components.

int	stan::math::csr_u_to_z (const std::vector< int > &u, int i)
	Return the z vector computed from the specified u vector at the index for the z vector.

Detailed Description

Functions