CSparseMatrix.h¶

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Structure definition and functions related to sparse matrix storage in Numerics

Defines

CS_INT¶

css¶

csn¶

NSM_UNKNOWN_ERR(func, orig)¶

NSM_NROW_CSR(mat)¶

NSM_NCOL_CSR(mat)¶

Typedefs

typedef struct cs_dl_symbolic cs_dls¶

typedef struct cs_di_symbolic cs_dis¶

typedef struct cs_dl_numeric cs_dln¶

typedef struct cs_di_numeric cs_din¶

typedef struct cs_di_sparse CSparseMatrix¶

Functions

int CSparseMatrix_lu_factorization(CS_INT order, const CSparseMatrix *A, double tol, CSparseMatrix_factors *cs_lu_A)¶

compute a LU factorization of A and store it in a workspace

Parameters

order – control if ordering is used
A – the sparse matrix
tol – the tolerance
cs_lu_A – the parameter structure that eventually holds the factors

Returns

1 if the factorization was successful, 1 otherwise

int CSparseMatrix_chol_factorization(CS_INT order, const CSparseMatrix *A, CSparseMatrix_factors *cs_chol_A)¶

compute a Cholesky factorization of A and store it in a workspace

Parameters

order – control if ordering is used
A – the sparse matrix
cs_chol_A – the parameter structure that eventually holds the factors

Returns

1 if the factorization was successful, 1 otherwise

int CSparseMatrix_ldlt_factorization(CS_INT order, const CSparseMatrix *A, CSparseMatrix_factors *cs_ldlt_A)¶

compute a LDLT factorization of A and store it in a workspace

Parameters

order – control if ordering is used
A – the sparse matrix
cs_ldlt_A – the parameter structure that eventually holds the factors

Returns

1 if the factorization was successful, 1 otherwise

CS_INT CSparseMatrix_solve(CSparseMatrix_factors *cs_lu_A, double *x, double *b)¶

reuse a LU factorization (stored in the cs_lu_A) to solve a linear system Ax = b

Parameters

cs_lu_A – contains the LU factors of A, permutation information
x – workspace
b – [inout] on input RHS of the linear system; on output the solution

Returns

0 if failed, 1 otherwise

CS_INT CSparseMatrix_spsolve(CSparseMatrix_factors *cs_lu_A, CSparseMatrix *X, CSparseMatrix *B)¶

reuse a LU factorization (stored in the cs_lu_A) to solve a linear system Ax = B with a sparse r.h.s

Parameters

cs_lu_A – contains the LU factors of A, permutation information
X – a csc sparse matrix workspace
B – [inout] on input sparse RHS of the linear system; on output the solution

Returns

0 if failed, 1 otherwise

CS_INT CSparseMatrix_chol_solve(CSparseMatrix_factors *cs_chol_A, double *x, double *b)¶

reuse a Cholesky factorization (stored in the cs_chol_A) to solve a linear system Ax = b

Parameters

cs_chol_A – contains the Cholesky factors of A, permutation information
x – workspace
b – [inout] on input RHS of the linear system; on output the solution

Returns

0 if failed, 1 otherwise

CS_INT CSparseMatrix_chol_spsolve(CSparseMatrix_factors *cs_chol_A, CSparseMatrix *X, CSparseMatrix *B)¶

reuse a Cholesky factorization (stored in the cs_chol_A) to solve a linear system Ax = B with a sparse r.h.s

Parameters

cs_chol_A – contains the Cholesky factors of A, permutation information
X – a csc sparse matrix workspace
b – [inout] on input sparse RHS of the linear system; on output the solution

Returns

0 if failed, 1 otherwise

CS_INT CSparseMatrix_ldlt_solve(CSparseMatrix_factors *cs_ldlt_A, double *x, double *b)¶

reuse a LDLT factorization (stored in the cs_ldlt_A) to solve a linear system Ax = b

Parameters

cs_ldlt_A – contains the LDLT factors of A, permutation information
x – workspace
b – [inout] on input RHS of the linear system; on output the solution

Returns

0 if failed, 1 otherwise

void CSparseMatrix_free_lu_factors(CSparseMatrix_factors *cs_lu_A)¶

Free a workspace related to a LU factorization.

Parameters: cs_lu_A – the structure to free

int CSparseMatrix_aaxpby(const double alpha, const CSparseMatrix *A, const double *x, const double beta, double *y)¶

Matrix vector multiplication : y = alpha*A*x+beta*y.

Parameters

alpha – [in] matrix coefficient
A – [in] the sparse matrix
x – [in] pointer on a dense vector of size A->n
beta – [in] vector coefficient
y – [inout] pointer on a dense vector of size A->n

Returns

0 if A x or y is NULL else 1

CSparseMatrix *CSparseMatrix_alloc_for_copy(const CSparseMatrix *const m)¶

Allocate a CSparse matrix for future copy (as in NSM_copy)

Parameters: m – the matrix used as model
Returns: an newly allocated matrix

CS_INT CSparseMatrix_to_dense(const CSparseMatrix *const A, double *B)¶

int CSparseMatrix_print(const CSparseMatrix *A, int brief)¶

print a matrix to std output

Parameters

A – matrix to print
brief – if positive, print only a portion of the matrix

int CSparseMatrix_print_in_file(const CSparseMatrix *A, int brief, FILE *file)¶

print a matrix to a text file

Parameters

A – matrix to print
brief – if positive, print only a portion of the matrix
file – file descriptor

CSparseMatrix *CSparseMatrix_new_from_file(FILE *file)¶

CS_INT CSparseMatrix_zentry(CSparseMatrix *T, CS_INT i, CS_INT j, double x, double threshold)¶

Add an entry to a triplet matrix only if the absolute value is greater than threshold.

Parameters

T – the sparse matrix
i – row index
j – column index
x – the value

Returns

integer value : 1 if the absolute value is less than DBL_EPSILON, otherwise the return value of cs_entry.

CS_INT CSparseMatrix_block_dense_zentry(CSparseMatrix *T, CS_INT row_off, CS_INT col_off, double *x, CS_INT row_size, CS_INT col_size, double threshold)¶

CS_INT CSparseMatrix_symmetric_zentry(CSparseMatrix *T, CS_INT i, CS_INT j, double x, double threshold)¶

Add an entry to a symmetric triplet matrix only if the absolute value is greater than threshold.

Parameters

T – the sparse matrix
i – row index
j – column index
x – the value

Returns

integer value : 1 if the absolute value is less than DBL_EPSILON, otherwise the return value of cs_entry.

CS_INT CSparseMatrix_entry(CSparseMatrix *T, CS_INT i, CS_INT j, double x)¶

Add an entry to a triplet matrix.

Parameters

T – the sparse matrix
i – row index
j – column index
x – the value

CS_INT CSparseMatrix_symmetric_entry(CSparseMatrix *T, CS_INT i, CS_INT j, double x)¶

Add an entry to a symmetric triplet matrix.

Parameters

T – the sparse matrix
i – row index
j – column index
x – the value

int CSparseMatrix_check_triplet(CSparseMatrix *T)¶

Check if the given triplet matrix is properly constructed (col and row indices are correct)

Parameters: T – the sparse matrix to check
Returns: 0 if the matrix is fine, 1 otherwise

int CSparseMatrix_check_csc(CSparseMatrix *T)¶

Check if the given triplet matrix is properly constructed (col and row indices are correct)

Parameters: T – the sparse matrix to check
Returns: 0 if the matrix is fine, 1 otherwise

CSparseMatrix *CSparseMatrix_spfree_on_stack(CSparseMatrix *A)¶

Free space allocated for a SparseMatrix.

note : cs_spfree also free the cs_struct this fails when the struct is allocated on the stack.

Parameters: A – the sparse matrix
Returns: NULL on success

void CSparseMatrix_copy(const CSparseMatrix *const A, CSparseMatrix *B)¶

Copy a CSparseMatrix inside another CSparseMatrix.

Reallocations are performed if B cannot hold a copy of A

Parameters

A – [in] a CSparseMatrix
B – [inout] a CSparseMatrix

int CSparseMatrix_scal(const double alpha, const CSparseMatrix *A)¶

Multiply a matrix with a double alpha*A –> A.

Parameters

alpha – the coefficient
A – the matrix

double CSparseMatrix_get_value(const CSparseMatrix *A, CS_INT i, CS_INT j)¶

Return the element A(i,j)

Parameters

A – the sparse matrix
i – the row index
j – the column index

void CSparseMatrix_write_in_file_python(const CSparseMatrix *const m, FILE *file)¶

print a matrix to a text file in pyhton format

Parameters

m – matrix to print
file – file descriptor

int CSparseMatrix_max_by_columns(const CSparseMatrix *A, double *max)¶

Compute the max by columns of a sparse matrix.

Parameters

A – the sparse matrix
max – the vector of maximum by columns
j – the column index

int CSparseMatrix_max_abs_by_columns(const CSparseMatrix *A, double *max)¶

Compute the max in absolute value by columns of a sparse matrix.

Parameters

A – the sparse matrix
max – the vector of maximum by columns
j – the column index

struct CSparseMatrix_factors¶

#include <>

Information used and produced by CSparse for an LU factorization.

Public Members

CS_INT n¶: size of linear system

css *S¶: symbolic analysis

csn *N¶: numerics factorization