Developer Reference for Intel® oneAPI Math Kernel Library for C
mkl_sparse_?_sorv
Computes forward, backward sweeps or a symmetric successive over-relaxation preconditioner operation.
Syntax
sparse_status_t mkl_sparse_s_sorv( const sparse_sor_type_t type,
const struct matrix_descr descrA,
const sparse_matrix_t A,
float omega,
float alpha,
float* x,
float* b );sparse_status_t mkl_sparse_d_sorv( const sparse_sor_type_t type,
const struct matrix_descr descrA,
const sparse_matrix_t A,
double omega,
double alpha,
double* x,
double* b );Include Files
mkl_spblas.h
Description
The mkl_sparse_?_sorv routine performs one of the following operations:
SPARSE_SOR_FORWARD:
\[(\omega\cdot L + D)\cdot x^{1} = (D - \omega\cdot D - \omega\cdot U)\cdot x^{0} + \omega\cdot b\]
SPARSE_SOR_BACKWARD:
\[(\omega\cdot U + D)\cdot x^{1} = (D - \omega\cdot D - \omega\cdot L)\cdot x^{0} + \omega\cdot b\]
SPARSE_SOR_SYMMETRIC: Performs application of a
\[\frac{\omega}{2-\omega}\left(\frac{1}{\omega}D + L\right)D^{-1}\left(\frac{1}{\omega}D+L\right)^{T}\]
preconditioner.
where \(A = L + D + U\) and \(x^{0}\) is an input vector \(x\) scaled by input parameter \(\alpha\) and \(x^{1}\) is an output stored in vector \(x\).
CSR format of the input matrix
SPARSE_SOR_FORWARD operation
General matrix ( descr.type is SPARSE_MATRIX_TYPE_GENERAL ) or
Symmetric matrix with full portrait and unit diagonal ( descr.type is SPARSE_MATRIX_TYPE_SYMMETRIC , descr.mode is SPARSE_FILL_MODE_FULL , and descr.diag is SPARSE_DIAG_UNIT )
Product and Performance Information Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex . Notice revision #20201201
Input Parameters
type
Specifies the operation performed by the SORV preconditioner:
SPARSE_SOR_FORWARD |
Performs forward sweep as defined by: \((\omega\cdot L + D)\cdot x^{1} = (D - \omega\cdot D - \omega\cdot U)\cdot x^{0} + \omega\cdot b\) |
SPARSE_SOR_BACKWARD |
Performs backward sweep as defined by: \((\omega\cdot U + D)\cdot x^{1} = (D - \omega\cdot D - \omega\cdot L)\cdot x^{0} + \omega\cdot b\) |
SPARSE_SOR_SYMMETRIC |
Preconditioner matrix could be expressed as: \(\frac{\omega}{2-\omega}\left(\frac{1}{\omega}D + L\right)D^{-1}\left(\frac{1}{\omega}D+L\right)^{T}\) |
descr
Descriptor specifying sparse matrix properties.
sparse_matrix_type_t type |
Specifies the type of a sparse matrix:
|
sparse_fill_mode_t mode |
Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:
|
sparse_diag_type_t diag |
Specifies diagonal type for non-general matrices:
|
A
Handle containing internal data.
omega
Relaxation factor.
alpha
Parameter that could be used to normalize or set to zero the vector x that holds the initial guess.
x
Initial guess on input.
b
Right-hand side.
Output Parameters
x
Solution vector on output.
Return Values
The function returns a value indicating whether the operation was successful, and if not, why:
SPARSE_STATUS_SUCCESS |
The operation was successful or an additional optimization is currently not available. |
SPARSE_STATUS_NOT_INITIALIZED |
The routine encountered an empty handle or matrix array. |
SPARSE_STATUS_ALLOC_FAILED |
Internal memory allocation failed. |
SPARSE_STATUS_INVALID_VALUE |
The input parameters contain an invalid value. |
SPARSE_STATUS_EXECUTION_FAILED |
Execution failed. |
SPARSE_STATUS_INTERNAL_ERROR |
An error in algorithm implementation occurred. |
SPARSE_STATUS_NOT_SUPPORTED |
The requested operation is not supported. |