cuAffineMatrixFunction< DataType > Class Template Reference

Base class for affine matrix functions of one parameter. More...

#include <cu_affine_matrix_function.h>

Inheritance diagram for cuAffineMatrixFunction< DataType >:

Collaboration diagram for cuAffineMatrixFunction< DataType >:

Public Member Functions
	cuAffineMatrixFunction ()
	Constructor.
virtual	~cuAffineMatrixFunction ()
	Virtual destructor.
void	set_parameters (DataType *t)
virtual void	set_symmetry (FlagType symmetric)=0
DataType	get_eigenvalue (const DataType *known_parameters, const DataType known_eigenvalue, const DataType *inquiry_parameters) const
	This function defines an analytic relationship between a given set of parameters and the corresponding eigenvalue of the operator. Namely, given a set of parameters and a known eigenvalue of the operator for that specific set of parameters, this function obtains the eigenvalue of the operator for an other given set of parameters.
Public Member Functions inherited from cuLinearOperator< DataType >
	cuLinearOperator ()
	Default constructor.
	cuLinearOperator (const int num_gpu_devices_)
	Constructor with setting num_rows and num_columns.
virtual	~cuLinearOperator ()
	Destructor.
cublasHandle_t	get_cublas_handle () const
	This function returns a reference to the cublasHandle_t object. The object will be created, if it is not created already.
void	set_parameters (DataType *parameters_)
	Sets the scalar parameter this->parameters. Parameter is initialized to NULL. However, before calling dot or transpose_dot functions, the parameters must be set.
virtual void	dot (const DataType *vector, DataType *product)=0
virtual void	transpose_dot (const DataType *vector, DataType *product)=0
Public Member Functions inherited from cLinearOperatorBase
	cLinearOperatorBase ()
	Default constructor.
	cLinearOperatorBase (const LongIndexType num_rows_, const LongIndexType num_columns_)
	Constructor with setting num_rows and num_columns.
virtual	~cLinearOperatorBase ()
	Destructor.
LongIndexType	get_num_rows () const
	Returns the number of rows of the matrix.
LongIndexType	get_num_columns () const
	Returns the number of columns of the matrix.
IndexType	get_num_parameters () const
	Returns the number of parameters of the linear operator.
FlagType	is_eigenvalue_relation_known () const
	Returns a flag that determines whether a relation between the parameters of the operator and its eigenvalue(s) is known.

Protected Member Functions
void	_add_scaled_vector (const DataType *input_vector, const LongIndexType vector_size, const DataType scale, DataType *output_vector) const
	Performs the operation \( \boldsymbol{c} = \boldsymbol{c} + \alpha \boldsymbol{b} \), where \( \boldsymbol{b} \) is an input vector scaled by \( \alpha \) and \( \boldsymbol{c} \) it the output vector.
Protected Member Functions inherited from cuLinearOperator< DataType >
int	query_gpu_devices () const
	Before any numerical computation, this method chechs if any gpu device is available on the machine, or notifies the user if nothing was found.
void	initialize_cublas_handle ()
	Creates a cublasHandle_t object, if not created already.
void	initialize_cusparse_handle ()
	Creates a cusparseHandle_t object, if not created already.

Protected Attributes
bool	B_is_identity
Protected Attributes inherited from cuLinearOperator< DataType >
int	num_gpu_devices
bool	copied_host_to_device
cublasHandle_t *	cublas_handle
cusparseHandle_t *	cusparse_handle
DataType *	parameters
Protected Attributes inherited from cLinearOperatorBase
const LongIndexType	num_rows
const LongIndexType	num_columns
FlagType	eigenvalue_relation_known
IndexType	num_parameters

Detailed Description

template<typename DataType>
class cuAffineMatrixFunction< DataType >

Base class for affine matrix functions of one parameter.

The cuAffineMatrixFunction holds a two two-dimensional dense matrices \( \mathbf{A} \) and \( \mathbf{B} \). The affine matrix function with the parameter \( t \) is defined by:

\[ t \mapsto \mathbf{A} + t \mathbf{B}. \]

This operoator can perofrom matrix-vector product and transposed matrix-vector product.

Note

The prefix c in this class's name (and its derivatves), stands for the cpp code, intrast to the cu prefix, which stands for the cuda code. Most derived classes have a cuda counterpart.

See also

cuMatrix, cuDenseAffineMatricFunction, cuCSRAffineMatrixFunction, cuCSCAffineMatrixFunction, cuLinearOperator, cAffineMatrixFunction

Definition at line 55 of file cu_affine_matrix_function.h.

Constructor & Destructor Documentation

cuAffineMatrixFunction()

template<typename DataType >

cuAffineMatrixFunction< DataType >::cuAffineMatrixFunction

(

)

Constructor.

Definition at line 34 of file cu_affine_matrix_function.cu.

                                                        :
    B_is_identity(false)
{
    // This class has one parameter that is t in A+tB
    this->num_parameters = 1;
}

References cLinearOperatorBase::num_parameters.

~cuAffineMatrixFunction()

template<typename DataType >

cuAffineMatrixFunction< DataType >::~cuAffineMatrixFunction ( )

virtual

Virtual destructor.

Definition at line 50 of file cu_affine_matrix_function.cu.

{
}

Member Function Documentation

_add_scaled_vector()

template<typename DataType >

void cuAffineMatrixFunction< DataType >::_add_scaled_vector ( const DataType *  input_vector, const LongIndexType  vector_size, const DataType  scale, DataType *  output_vector  ) const

protected

Performs the operation \( \boldsymbol{c} = \boldsymbol{c} + \alpha \boldsymbol{b} \), where \( \boldsymbol{b} \) is an input vector scaled by \( \alpha \) and \( \boldsymbol{c} \) it the output vector.

Parameters

[in]	input_vector	The input 1D vector of size vector_size.
[in]	vector_size	The size of both input_vector and output_vector
[in]	scale	The scalar scale at whch the input vector is multiplied by.
[in,out]	output_vector	The output 1D vector of size vector_size. This array will be written in-place.

Definition at line 140 of file cu_affine_matrix_function.cu.

{
    // Get device id
    int device_id = CudaAPI<DataType>::get_device();
 
    // Negative of scale (negate in double type as some types like
    // __nv_fp8_exmx does not yet support such operation yet)
    DataType neg_scale = cu_arithmetics::cast<double, DataType>(
            -cu_arithmetics::cast<DataType, double>(scale));
 
    // Subtracting two vectors with minus scale sign, which is adding.
    cuVectorOperations<DataType>::subtract_scaled_vector(
            this->cublas_handle[device_id], input_vector, vector_size,
            neg_scale, output_vector);
}

References cu_arithmetics::abs(), CudaAPI< ArrayType >::get_device(), and cuVectorOperations< DataType >::subtract_scaled_vector().

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get_eigenvalue()

template<typename DataType >

DataType cuAffineMatrixFunction< DataType >::get_eigenvalue ( const DataType *  known_parameters, const DataType  known_eigenvalue, const DataType *  inquiry_parameters  ) const

virtual

This function defines an analytic relationship between a given set of parameters and the corresponding eigenvalue of the operator. Namely, given a set of parameters and a known eigenvalue of the operator for that specific set of parameters, this function obtains the eigenvalue of the operator for an other given set of parameters.

A relation between eigenvalue(s) and the set of parameters can be made when the matrix \( \mathbf{B} \) is equal to the identity matrix \( \mathbf{I} \), and corresponding linear operator is as follows:

\[ \mathbf{A}(t) = \mathbf{A} + t \mathbf{I} \]

Then, the eigenvalues \( \lambda \) of the operator is

\[ \lambda(\mathbf{A}(t)) = \lambda(\mathbf{A}) + t. \]

Thus, by knowing the eigenvalue \( \lambda_{t_0} \) at the known parameter \( t_0 \), the eigenvalue \( \lambda_{t} \) at the inquiry parameter \( t \) can be obtained.

Parameters

[in]	known_parameters	A set of parameters of the operator where the corresponding eigenvalue of the parameter is known for.
[in]	known_eigenvalue	The known eigenvalue of the operator for the known parameters.
[in]	inquiry_parameters	A set of inquiry parameters of the operator where the corresponding eigenvalue of the operator is sought.

Returns

The eigenvalue of the operator corresponding the inquiry parameters.

Implements cuLinearOperator< DataType >.

Definition at line 97 of file cu_affine_matrix_function.cu.

{
    ASSERT((this->eigenvalue_relation_known == 1),
            "An eigenvalue relation is not known. This function should be "
            "called only when the matrix B is a scalar multiple of the "
            "identity matrix");
 
    // Shift the eigenvalue by the parameter
    DataType inquiry_eigenvalue = \
        cu_arithmetics::add<DataType>(
            cu_arithmetics::sub<DataType>(
                known_eigenvalue,
                known_parameters[0]),
            inquiry_parameters[0]
        );
 
    return inquiry_eigenvalue;
}

References cu_arithmetics::abs(), and ASSERT.

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set_parameters()

template<typename DataType >

void cuAffineMatrixFunction< DataType >::set_parameters

(

DataType *

t

)

set_symmetry()

template<typename DataType >

virtual void cuAffineMatrixFunction< DataType >::set_symmetry ( FlagType  symmetric )

pure virtual

Implements cLinearOperatorBase.

Implemented in cuCSCAffineMatrixFunction< DataType >, cuCSRAffineMatrixFunction< DataType >, and cuDenseAffineMatrixFunction< DataType >.

Member Data Documentation

B_is_identity

template<typename DataType >

bool cuAffineMatrixFunction< DataType >::B_is_identity

protected

Definition at line 83 of file cu_affine_matrix_function.h.

Referenced by cuCSCAffineMatrixFunction< DataType >::cuCSCAffineMatrixFunction(), cuCSCAffineMatrixFunction< DataType >::cuCSCAffineMatrixFunction(), cuCSRAffineMatrixFunction< DataType >::cuCSRAffineMatrixFunction(), cuCSRAffineMatrixFunction< DataType >::cuCSRAffineMatrixFunction(), cuDenseAffineMatrixFunction< DataType >::cuDenseAffineMatrixFunction(), and cuDenseAffineMatrixFunction< DataType >::cuDenseAffineMatrixFunction().

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The documentation for this class was generated from the following files:

• /home/runner/work/imate/imate/imate/_cu_linear_operator/cu_affine_matrix_function.h
• /home/runner/work/imate/imate/imate/_cu_linear_operator/cu_affine_matrix_function.cu