File numerics/src/tools/SparseBlockMatrix.h

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File numerics/src/tools/SparseBlockMatrix.h#

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Structure definition and functions related to SparseBlockStructuredMatrix

Defines

NUMERICS_SBM_FREE_BLOCK#
NUMERICS_SBM_FREE_SBM#

Functions

SparseBlockStructuredMatrix *SBM_new(void)#

Creation of an empty Sparse Block Matrix.

Returns:

a pointer on allocated and initialized space

void SBM_null(SparseBlockStructuredMatrix *sbm)#

set Sparse Block Matrix.

fields to NULL

Parameters:

sbm – a matrix

void SBM_gemv(unsigned int sizeX, unsigned int sizeY, double alpha, const SparseBlockStructuredMatrix *const A, const double *x, double beta, double *y)#

SparseMatrix - vector product y = alpha*A*x + beta*y.

Parameters:

  • sizeX – [in] dim of the vectors x

  • sizeY – [in] dim of the vectors y

  • alpha – [in] coefficient

  • A – [in] the matrix to be multiplied

  • x – [in] the vector to be multiplied

  • beta – [in] coefficient

  • y – [inout] the resulting vector

void SBM_gemv_3x3(unsigned int sizeX, unsigned int sizeY, const SparseBlockStructuredMatrix *const A, double *const x, double *y)#

SparseMatrix - vector product y = A*x + y for block of size 3x3.

Parameters:

  • sizeX – [in] dim of the vectors x

  • sizeY – [in] dim of the vectors y

  • A – [in] the matrix to be multiplied

  • x – [in] the vector to be multiplied

  • y – [inout] the resulting vector

void SBM_gemm_without_allocation(double alpha, const SparseBlockStructuredMatrix *const A, const SparseBlockStructuredMatrix *const B, double beta, SparseBlockStructuredMatrix *C)#

SparseBlockStructuredMatrix - SparseBlockStructuredMatrix product C = alpha*A*B + beta*C The routine has to be used with precaution.

The allocation of C is not done since we want to add beta*C. We assume that the structure and the allocation of the matrix C are right. Especially:

  • the blocks C(i,j) must exists

  • the sizes of blocks must be consistent

  • no extra block must be present in C

Parameters:

  • alpha – [in] coefficient

  • A – [in] the matrix to be multiplied

  • B – [in] the matrix to be multiplied

  • beta – [in] coefficient

  • C – [inout] the resulting matrix

SparseBlockStructuredMatrix *SBM_multiply(const SparseBlockStructuredMatrix *const A, const SparseBlockStructuredMatrix *const B)#

SparseBlockStructuredMatrix - SparseBlockStructuredMatrix multiplication C = A *B Correct allocation is performed.

Parameters:

  • A – [in] the matrix to be multiplied

  • B – [in] the matrix to be multiplied

Returns:

C the resulting matrix

SparseBlockStructuredMatrix *SBM_zero_matrix_for_multiply(const SparseBlockStructuredMatrix *const A, const SparseBlockStructuredMatrix *const B)#

Perform the allocation of a zero matrix that is compatible qith multiplication.

SparseBlockStructuredMatrix *SBM_add(SparseBlockStructuredMatrix *A, SparseBlockStructuredMatrix *B, double alpha, double beta)#

SparseBlockStructuredMatrix - SparseBlockStructuredMatrix addition C = alpha*A + beta*B.

Parameters:

  • A – [in] the matrix to be added

  • B – [in] the matrix to be added

  • alpha – [in] coefficient

  • beta – [in] coefficient

Returns:

C the resulting matrix

void SBM_add_without_allocation(SparseBlockStructuredMatrix *A, SparseBlockStructuredMatrix *B, double alpha, double beta, SparseBlockStructuredMatrix *C, double gamma)#

SparseBlockStructuredMatrix - SparseBlockStructuredMatrix addition C = alpha*A + beta*B + gamma*C without allocation.

We assume that C has the correct structure

Parameters:

  • A – [in] the matrix to be added

  • B – [in] the matrix to be added

  • alpha – [in] coefficient

  • beta – [in] coefficient

  • gamma – [in] coefficient

  • C – [inout] the resulting matrix

void SBM_scal(double alpha, SparseBlockStructuredMatrix *A)#

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

Parameters:

  • alpha – the coefficient

  • A – the matrix

void SBM_row_prod(unsigned int sizeX, unsigned int sizeY, unsigned int currentRowNumber, const SparseBlockStructuredMatrix *const A, const double *const x, double *y, int init)#

Row of a SparseMatrix - vector product y = rowA*x or y += rowA*x, rowA being a row of blocks of A.

Parameters:

  • sizeX – [in] dim of the vector x

  • sizeY – [in] dim of the vector y

  • currentRowNumber – [in] number of the required row of blocks

  • A – [in] the matrix to be multiplied

  • x – [in] the vector to be multiplied

  • y – [inout] the resulting vector

  • init – [in] = 0 for y += Ax, =1 for y = Ax

void SBM_row_prod_no_diag(unsigned int sizeX, unsigned int sizeY, unsigned int currentRowNumber, const SparseBlockStructuredMatrix *const A, const double *const x, double *y, int init)#

Row of a SparseMatrix - vector product y = rowA*x or y += rowA*x, rowA being a row of blocks of A.

Parameters:

  • sizeX – [in] dim of the vector x

  • sizeY – [in] dim of the vector y

  • currentRowNumber – [in] number of the required row of blocks

  • A – [in] the matrix to be multiplied

  • x – [in] the vector to be multiplied

  • y – [inout] the resulting vector

  • init – [in] = 0 for y += Ax, =1 for y = Ax

void SBM_row_prod_no_diag_3x3(unsigned int sizeX, unsigned int sizeY, unsigned int currentRowNumber, const SparseBlockStructuredMatrix *const A, double *const x, double *y)#

Row of a SparseMatrix - vector product y = rowA*x or y += rowA*x, rowA being a row of blocks of A of size 3x3.

Parameters:

  • sizeX – [in] dim of the vector x

  • sizeY – [in] dim of the vector y

  • currentRowNumber – [in] number of the required row of blocks

  • A – [in] the matrix to be multiplied

  • x – [in] the vector to be multiplied

  • y – [inout] the resulting vector

void SBM_row_prod_no_diag_2x2(unsigned int sizeX, unsigned int sizeY, unsigned int currentRowNumber, const SparseBlockStructuredMatrix *const A, double *const x, double *y)#
void SBM_row_prod_no_diag_1x1(unsigned int sizeX, unsigned int sizeY, unsigned int currentRowNumber, const SparseBlockStructuredMatrix *const A, double *const x, double *y)#
void SBM_extract_component_3x3(const SparseBlockStructuredMatrix *const A, SparseBlockStructuredMatrix *B, unsigned int *row_components, unsigned int row_components_size, unsigned int *col_components, unsigned int col_components_size)#
void SBM_clear(SparseBlockStructuredMatrix *blmat)#

Destructor for SparseBlockStructuredMatrix objects.

Parameters:

blmat – SparseBlockStructuredMatrix the matrix to be destroyed.

void SBMfree(SparseBlockStructuredMatrix *A, unsigned int level)#

To free a SBM matrix (for example allocated by NM_new_from_file).

Parameters:

  • A – [in] the SparseBlockStructuredMatrix that mus be de-allocated.

  • level – [in] use NUMERICS_SBM_FREE_BLOCK | NUMERICS_SBM_FREE_SBM

void SBM_print(const SparseBlockStructuredMatrix *const m)#

Screen display of the matrix content.

Parameters:

m – the matrix to be displayed

void SBM_write_in_file(const SparseBlockStructuredMatrix *const m, FILE *file)#

print in file of the matrix content

Parameters:

  • m – the matrix to be displayed

  • file – the corresponding file

void SBM_read_in_file(SparseBlockStructuredMatrix *const M, FILE *file)#

read in file of the matrix content without performing memory allocation

Parameters:

  • M – the matrix to be displayed

  • file – the corresponding name of the file

SparseBlockStructuredMatrix *SBM_new_from_file(FILE *file)#

Create from file a SparseBlockStructuredMatrix with memory allocation.

Parameters:

file – the corresponding name of the file

Returns:

the matrix to be displayed

void SBM_write_in_fileForScilab(const SparseBlockStructuredMatrix *const M, FILE *file)#

print in file of the matrix content in Scilab format for each block

Parameters:

  • M – the matrix to be displayed

  • file – the corresponding file

void SBM_write_in_filename(const SparseBlockStructuredMatrix *const M, const char *filename)#

print in file of the matrix content

Parameters:

  • M – the matrix to be displayed

  • filename – the corresponding file

void SBM_read_in_filename(SparseBlockStructuredMatrix *const M, const char *filename)#

read in file of the matrix content

Parameters:

  • M – the matrix to be displayed

  • filename – the corresponding name of the file

void SBM_clear_pred(SparseBlockStructuredMatrixPred *blmatpred)#

Destructor for SparseBlockStructuredMatrixPred objects.

Parameters:

blmatpred – SparseBlockStructuredMatrix, the matrix to be destroyed.

unsigned int *SBM_diagonal_block_indices(SparseBlockStructuredMatrix *const M)#

Compute the indices of blocks of the diagonal block.

Parameters:

M – the SparseBlockStructuredMatrix matrix

Returns:

the indices for all the rows

unsigned int SBM_diagonal_block_index(SparseBlockStructuredMatrix *const M, unsigned int row)#

Find index of the diagonal block in a row.

Parameters:
Returns:

pos the position of the block

int SBM_entry(SparseBlockStructuredMatrix *M, unsigned int row, unsigned int col, double val)#

insert an entry into a SparseBlockStructuredMatrix.

This method is expensive in terms of memory management. For a lot of entries, use an alternative

Parameters:
double SBM_get_value(const SparseBlockStructuredMatrix *const M, unsigned int row, unsigned int col)#

get the element of row i and column j of the matrix M

Parameters:
Returns:

the value

int SBM_copy(const SparseBlockStructuredMatrix *const A, SparseBlockStructuredMatrix *B, unsigned int copyBlock)#

Copy of a SBM A into B.

Parameters:
Returns:

0 if ok

int SBM_transpose(const SparseBlockStructuredMatrix *const A, SparseBlockStructuredMatrix *B)#

Transpose by copy of a SBM A into B.

Parameters:
Returns:

0 if ok

int SBM_inverse_diagonal_block_matrix_in_place(const SparseBlockStructuredMatrix *M, int *ipiv)#

Inverse (in place) a square diagonal block matrix.

Parameters:
Returns:

0 ik ok

void SBM_to_dense(const SparseBlockStructuredMatrix *const A, double *denseMat)#

Copy a SBM into a Dense Matrix.

Parameters:
int SBM_to_sparse(const SparseBlockStructuredMatrix *const A, CSparseMatrix *outSparseMat)#

Copy a SBM into a Sparse (CSR) Matrix.

Parameters:
Returns:

0 if ok

int SBM_to_sparse_init_memory(const SparseBlockStructuredMatrix *const A, CSparseMatrix *sparseMat)#

initMemory of a Sparse (CSR) Matrix form a SBM matrix

Parameters:
Returns:

0 if ok

void SBM_row_to_dense(const SparseBlockStructuredMatrix *const A, int row, double *denseMat, int rowPos, int rowNb)#

Copy a block row of the SBM into a Dense Matrix.

Parameters:

  • A – [in] the SparseBlockStructuredMatrix matrix to be inversed.

  • row – [in] the block row index copied.

  • denseMat – [in] pointer on the filled dense Matrix.

  • rowPos – [in] line pos in the dense matrix.

  • rowNb – [in] total number of line of the dense matrix. The number of line copied is contained in M.

void SBM_row_permutation(unsigned int *rowIndex, SparseBlockStructuredMatrix *A, SparseBlockStructuredMatrix *C)#
Parameters:

  • rowIndex – [in] permutation: the row numC of C is the row rowIndex[numC] of A.

  • A – [in] The source SBM.

  • C – [out] The target SBM. It assumes the structure SBM has been allocated. The memory allocation for its menber is done inside. NB : The blocks are not copied.

void SBM_column_permutation(unsigned int *colIndex, SparseBlockStructuredMatrix *A, SparseBlockStructuredMatrix *C)#
Parameters:

  • colIndex – [in] permutation: the col numC of C is the col colIndex[numC] of A.

  • A – [in] The source SBM.

  • C – [out] The target SBM. It assumes the structure SBM has been allocated. The memory allocation for its menber is done inside. NB : The blocks are not copied.

void SBCM_null(SparseBlockCoordinateMatrix *MC)#
SparseBlockCoordinateMatrix *SBCM_new(void)#
SparseBlockCoordinateMatrix *SBCM_new_3x3(unsigned int m, unsigned int n, unsigned int nbblocks, unsigned int *row, unsigned int *column, double *block)#

allocate a SparseBlockCoordinateMatrix from a list of 3x3 blocks

Parameters:

  • m – [in] the number of rows

  • n – [in] the number of colums

  • nbblocks – [in] the number of blocks

  • row – [in] a pointer to row of each block

  • column – [in] a pointer to column of each block

  • block – [in] a pointer to each block

Returns:

a pointer to a SparseBlockCoordinateMatrix structure

void SBCM_free_3x3(SparseBlockCoordinateMatrix *MC)#

free allocated memory in newSparseBlockCoordinateMatrix functions

Parameters:

MC – [in] matrix pointer

SparseBlockStructuredMatrix *SBCM_to_SBM(SparseBlockCoordinateMatrix *MC)#

copy a SparseBlockCoordinateMatrix to a SparseBlockStructuredMatrix

Parameters:

MC – [in] the SparseBlockCoordinateMatrix matrix

Returns:

a pointer to a SparseBlockCoordinateMatrix structure

void SBM_free_from_SBCM(SparseBlockStructuredMatrix *M)#

free a SparseBlockStructuredMatrix created with SBCM_to_SBM

Parameters:

M – [inout] a SparseBlockStructuredMatrix to free

int SBM_from_csparse(int blocksize, const CSparseMatrix *const sparseMat, SparseBlockStructuredMatrix *outSBM)#

Copy a Sparse Matrix into a SBM, with fixed blocksize.

Parameters:

  • blocksize – [in] the blocksize

  • sparseMat – [in] pointer on the Sparse Matrix

  • outSBM – [inout] pointer on an empty SparseBlockStructuredMatrix

Returns:

0 in ok

struct SparseBlockStructuredMatrix#
#include <SparseBlockMatrix.h>

Structure to store sparse block matrices with square diagonal blocks.

Related functions: SBM_gemv(), SBM_row_prod(), SBM_clear(), SBM_print, SBM_diagonal_block_index()

Note: the sparse format is the same as the one used by Boost C++ library to store compressed sparse row matrices. The same member names have been adopted in order to simplify usage from Siconos Kernel : filled1, filled2, index1_data, index2_data. Reference : http://ublas.sourceforge.net/refdoc/classboost_1_1numeric_1_1ublas_1_1compressed__matrix.html

If we consider the matrix M and the right-hand-side q defined as

\[\begin{split} M=\left[\begin{array}{cccc|cc|cc} 1 & 2 & 0 & 4 & 3 &-1 & 0 & 0 \\ 2 & 1 & 0 & 0 & 4 & 1 & 0 & 0 \\ 0 & 0 & 1 &-1 & 0 & 0 & 0 & 0 \\ 5 & 0 &-1 & 6 & 0 & 6 & 0 & 0 \\ \hline 0 & 0 & 0 & 0 & 1 & 0 & 0 & 5 \\ 0 & 0 & 0 & 0 & 0 & 2 & 0 & 2 \\ \hline 0 & 0 & 2 & 1 & 0 & 0 & 2 & 2 \\ 0 & 0 & 2 & 2 & 0 & 0 & -1 & 2 \\ \end{array}\right] \quad, q=\left[\begin{array}{c}-1 \\ -1 \\ 0 \\ -1 \\ \hline 1 \\ 0 \\ \hline -1 \\ 2 \end{array}\right]. \end{split}\]

then

  • the number of non null blocks is 6 (nbblocks=6)

  • the number of rows of blocks is 3 (blocknumber0 =3) and the number of columns of blocks is 3 (blocknumber1 =3)

  • the vector blocksize0 is equal to {4,6,8} and the vector blocksize1 is equal to {4,6,8}

  • the integer filled1 is equal to 4

  • the integer filled2 is equal to 6

  • the vector index1_data is equal to {0,2,4,6}

  • the vector index2_data is equal to {0,1,1,2,0,2}

  • the block contains all non null block matrices stored in Fortran order (column by column) as block[0] = {1,2,0,5,2,1,0,0,0,0,1,-1,4,0,-1,6} block[1] = {3,4,0,0,-1,1,0,6} … block[5] = {2,-1,2,2}

Param nbblocks:

the total number of non null blocks

Param **block:

: *block contains the double values of one block in Fortran storage (column by column) **block is the list of non null blocks

Param blocknumber0:

the first dimension of the block matrix (number of block rows)

Param blocknumber1:

the second dimension of the block matrix (number of block columns)

Param *blocksize0:

the list of sums of the number of rows of the first column of blocks of M: blocksize0[i] = blocksize0[i-1] + ni, ni being the number of rows of the block at row i

Param *blocksize1:

the list of sums of the number of columns of the first row of blocks of M: blocksize1[i] = blocksize1[i-1] + ni, ni being the number of columns of the block at column i

Param filled1:

index of the last non empty line + 1

Param filled2:

number of non null blocks

Param index1_data:

index1_data is of size equal to number of non empty lines + 1. A block with number blockNumber inside a row numbered rowNumber verify index1_data[rowNumber]<= blockNumber <index1_data[rowNumber+1]`

Param index2_data:

index2_data is of size filled2 index2_data[blockNumber] -> columnNumber.

Public Members

unsigned int nbblocks#
double **block#
unsigned int blocknumber0#
unsigned int blocknumber1#
unsigned int *blocksize0#
unsigned int *blocksize1#
size_t filled1#
size_t filled2#
size_t *index1_data#
size_t *index2_data#
unsigned int *diagonal_blocks#
NumericsDataVersion version#

version of storage

struct SparseBlockCoordinateMatrix#

Public Members

unsigned int nbblocks#

number of blocks

unsigned int blocknumber0#

number of rows

unsigned int blocknumber1#

number of columns

double **block#

block pointers

unsigned int *blocksize0#

cumulative number of rows in blocks

unsigned int *blocksize1#

cumulative number of columns in blocks

unsigned int *row#

row indices

unsigned int *column#

column indices

struct SparseBlockStructuredMatrixPred#

Public Members

int nbbldiag#
int **indic#
int **indicop#
double **submatlcp#
double **submatlcpop#
int **ipiv#
int *sizesublcp#
int *sizesublcpop#
double **subq#
double **bufz#
double **newz#
double **workspace#
struct SBM_index_by_column#

Public Members

size_t filled3#
size_t filled4#
size_t *index3_data#
size_t *index4_data#
size_t *blockMap#
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