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cusp::precond::scaled_bridson_ainv< ValueType, MemorySpace > Class Template Reference

Detailed description

template<typename ValueType, typename MemorySpace>
class cusp::precond::scaled_bridson_ainv< ValueType, MemorySpace >

scaled_bridson_ainv : Approximate Inverse preconditoner (from Bridson's "outer product" formulation) The diagonal matrix is folded into the factorization to reduce operation count during preconditioner application. Not sure if this is a good idea or not, yet. This preconditioner allows for a novel dropping strategy, where rather than a fixed drop tolerance, you can specify now many non-zeroes are allowed per row. The non-zeroes will be chosen based on largest magnitude. This idea has been applied to IC factorization, but not AINV as far as I'm aware. See: Lin, C. and More, J. J. 1999. Incomplete Cholesky Factorizations with Limited Memory. SIAM J. Sci. Comput. 21, 1 (Aug. 1999), 24-45. This preconditioner will only work for SPD matrices.


Definition at line 52 of file ainv.h.

#include <ainv.h>

Inheritance diagram for cusp::precond::scaled_bridson_ainv< ValueType, MemorySpace >:
cusp::linear_operator<ValueType, MemorySpace >

Public Methods

template<typename MatrixTypeA >
 scaled_bridson_ainv (const MatrixTypeA &A, ValueType drop_tolerance=0.1, int nonzero_per_row=-1, bool lin_dropping=false, int lin_param=1)
template<typename VectorType1 , typename VectorType2 >
void operator() (const VectorType1 &x, VectorType2 &y)
- Public Methods inherited from cusp::linear_operator<ValueType, MemorySpace >
 linear_operator (void)
 linear_operator (intnum_rows, intnum_cols)
 linear_operator (intnum_rows, intnum_cols, intnum_entries)

Public Members

cusp::hyb_matrix< int,
ValueType, MemorySpace > 
cusp::hyb_matrix< int,
ValueType, MemorySpace > 

Protected Members

cusp::array1d< ValueType,
MemorySpace > 

Constructor & Destructor Documentation

template<typename ValueType, typename MemorySpace>
template<typename MatrixTypeA >
cusp::precond::scaled_bridson_ainv< ValueType, MemorySpace >::scaled_bridson_ainv ( const MatrixTypeA &  A,
ValueType  drop_tolerance = 0.1,
int  nonzero_per_row = -1,
bool  lin_dropping = false,
int  lin_param = 1 

construct a ainv preconditioner

Amatrix to precondition
Template Parameters
ValueTypedrop_tolerance Tolerance for dropping during factorization
nonzero_per_rowCount of non-zeroes allowed per row of the factored matrix. If negative or lin_dropping==true, this will be ignored.
lin_droppingWhen true, this will use the dropping strategy from Lin & More, where the per-row count will be based on A's structure.
lin_paramwhen lin_dropping set to true, this indicates how many additional non-zeros per row to include

Member Function Documentation

template<typename ValueType, typename MemorySpace>
template<typename VectorType1 , typename VectorType2 >
void cusp::precond::scaled_bridson_ainv< ValueType, MemorySpace >::operator() ( const VectorType1 &  x,
VectorType2 &  y 

apply the preconditioner to vector x and store the result in y

xinput vector
youput vector
Template Parameters