CAROM::Matrix Class Reference

#include <Matrix.h>

Public Member Functions
	Matrix ()
	Matrix (int num_rows, int num_cols, bool distributed, bool randomized=false)
	Matrix (double *mat, int num_rows, int num_cols, bool distributed, bool copy_data=true)
	Matrix (const Matrix &other)
	Copy constructor. More...
	~Matrix ()
	Destructor.
Matrix &	operator= (const Matrix &rhs)
	Assignment operator. More...
Matrix &	operator= (const double a)
	Assignment operator. More...
Matrix &	operator+= (const Matrix &rhs)
	Addition operator. More...
Matrix &	operator-= (const Matrix &rhs)
	Subtraction operator. More...
void	setSize (int num_rows, int num_cols)
	Sets the number of rows and columns of the matrix and reallocates storage if needed. All values are initialized to zero. More...
bool	distributed () const
	Returns true if the Matrix is distributed. More...
bool	balanced () const
	Returns true if rows of matrix are load-balanced.
int	numRows () const
	Returns the number of rows of the Matrix on this processor. More...
int	numDistributedRows () const
	Returns the number of rows of the Matrix across all processors. More...
int	numColumns () const
	Returns the number of columns in the Matrix. This method will return the same value from each processor. More...
Matrix *	getFirstNColumns (int n) const
	Get the first N columns of a matrix. More...
void	getFirstNColumns (int n, Matrix *&result) const
	Get the first N columns of a matrix. More...
void	getFirstNColumns (int n, Matrix &result) const
	Get the first N columns of a matrix. More...
Matrix *	mult (const Matrix &other) const
	Multiplies this Matrix with other and returns the product, reference version. More...
Matrix *	mult (const Matrix *other) const
	Multiplies this Matrix with other and returns the product, pointer version. More...
void	mult (const Matrix &other, Matrix *&result) const
	Multiplies this Matrix with other and fills result with the answer. More...
void	mult (const Matrix &other, Matrix &result) const
	Multiplies this Matrix with other and fills result with the answer. More...
Vector *	mult (const Vector &other) const
	Multiplies this Matrix with other and returns the product, reference version. More...
Vector *	mult (const Vector *other) const
	Multiplies this Matrix with other and returns the product, pointer version. More...
void	mult (const Vector &other, Vector *&result) const
	Multiplies this Matrix with other and fills result with the answer. More...
void	mult (const Vector &other, Vector &result) const
	Multiplies this Matrix with other and fills result with the answer. More...
void	pointwise_mult (int this_row, const Vector &other, Vector &result) const
	Multiplies a specified row of this Matrix with other pointwise. More...
void	pointwise_mult (int this_row, Vector &other) const
	Multiplies a specified row of this Matrix with other pointwise. This modifies other. More...
Matrix *	elementwise_mult (const Matrix &other) const
	Multiplies two matrices element-wise. More...
Matrix *	elementwise_mult (const Matrix *other) const
	Multiplies two matrices element-wise and returns the product, pointer version. More...
void	elementwise_mult (const Matrix &other, Matrix *&result) const
	Multiplies two matrices element-wise and fills result with the answer. More...
void	elementwise_mult (const Matrix &other, Matrix &result) const
	Multiplies two matrices element-wise and fills result with the answer. More...
Matrix *	elementwise_square () const
	Square every element in the matrix. More...
void	elementwise_square (Matrix *&result) const
	Square every element in the matrix. More...
void	elementwise_square (Matrix &result) const
	Square every element in the matrix. More...
void	multPlus (Vector &a, const Vector &b, double c) const
	Computes a += this*b*c. More...
Matrix *	transposeMult (const Matrix &other) const
	Multiplies the transpose of this Matrix with other and returns the product, reference version. More...
Matrix *	transposeMult (const Matrix *other) const
	Multiplies the transpose of this Matrix with other and returns the product, pointer version. More...
void	transposeMult (const Matrix &other, Matrix *&result) const
	Multiplies the transpose of this Matrix with other and fills result with the answer. More...
void	transposeMult (const Matrix &other, Matrix &result) const
	Multiplies the transpose of this Matrix with other and fills result with the answer. More...
Vector *	transposeMult (const Vector &other) const
	Multiplies the transpose of this Matrix with other and returns the product, reference version. More...
Vector *	transposeMult (const Vector *other) const
	Multiplies the transpose of this Matrix with other and returns the product, pointer version. More...
void	transposeMult (const Vector &other, Vector *&result) const
	Multiplies the transpose of this Matrix with other and fills result with the answer. More...
void	transposeMult (const Vector &other, Vector &result) const
	Multiplies the transpose of this Matrix with other and fills result with the answer. More...
Matrix *	inverse () const
	Computes and returns the inverse of this. More...
void	inverse (Matrix *&result) const
	Computes and returns the inverse of this. More...
void	inverse (Matrix &result) const
	Computes and returns the inverse of this. More...
void	inverse ()
	Computes the inverse of this and stores result in this. More...
Vector *	getColumn (int column) const
	Returns a column of the matrix (not owned by Matrix). More...
void	getColumn (int column, Vector *&result) const
	Returns a column of the matrix (not owned by Matrix). More...
void	getColumn (int column, Vector &result) const
	Returns a column of the matrix (not owned by Matrix). More...
void	transpose ()
	Replaces this Matrix with its transpose (in place), in the serial square case only. More...
void	transposePseudoinverse ()
	Computes the transposePseudoinverse of this. More...
Matrix *	qr_factorize () const
	Computes and returns the Q of the QR factorization of this. More...
void	qrcp_pivots_transpose (int *row_pivot, int *row_pivot_owner, int pivots_requested) const
	Compute the leading numColumns() column pivots from a QR decomposition with column pivots (QRCP) of the transpose of this. More...
void	orthogonalize (bool double_pass=false, double zero_tol=1.0e-15)
	Orthonormalizes the matrix. More...
void	orthogonalize_last (int ncols=-1, bool double_pass=false, double zero_tol=1.0e-15)
	Orthonormalizes the matrix's last column, assuming the previous columns are already orthonormal. More...
void	rescale_rows_max ()
	Rescale every matrix row by its maximum absolute value.
void	rescale_cols_max ()
	Rescale every matrix column by its maximum absolute value.
const double &	item (int row, int col) const
	Const Matrix member access. Matrix data is stored in row-major format. More...
double &	item (int row, int col)
	Non-const Matrix member access. Matrix data is stored in row-major format. More...
const double &	operator() (int row, int col) const
	Const Matrix member access. More...
double &	operator() (int row, int col)
	Non-const Matrix member access. More...
void	print (const char *prefix) const
	print Matrix into (a) ascii file(s). More...
void	write (const std::string &base_file_name) const
	write Matrix into (a) HDF file(s). More...
void	read (const std::string &base_file_name)
	read Matrix into (a) HDF file(s). More...
void	local_read (const std::string &base_file_name, int rank)
	read a single rank of a distributed Matrix into (a) HDF file(s). More...
double *	getData () const
	Get the matrix data as a pointer.
void	distribute (const int &local_num_rows)
	Distribute this matrix rows among MPI processes, based on the specified local number of rows. This becomes distributed after this function is executed. More...
void	gather ()
	Gather all the distributed rows among MPI processes. This becomes not distributed after this function is executed. More...

Detailed Description

Class Matrix is a simple matrix class in which the rows may be distributed across multiple processes. This class supports only the basic operations that are needed by the SVD library.

Definition at line 30 of file Matrix.h.

Constructor & Destructor Documentation

Matrix() [1/4]

CAROM::Matrix::Matrix

(

)

Empty Constructor

Definition at line 63 of file Matrix.cpp.

Matrix() [2/4]

CAROM::Matrix::Matrix	(	int	num_rows,
		int	num_cols,
		bool	distributed,
		bool	randomized = false
	)

Constructor creating a Matrix with uninitialized values.

Precondition

num_rows > 0

num_cols > 0

Parameters

[in]	num_rows	When undistributed, the total number of rows of the Matrix. When distributed, the part of the total number of rows of the Matrix on this processor.
[in]	num_cols	The total number of columns of the Matrix.
[in]	distributed	If true the rows of the Matrix are spread over all processors.
[in]	randomized	If true the matrix will be a standard normally distributed random matrix.

Definition at line 70 of file Matrix.cpp.

Matrix() [3/4]

CAROM::Matrix::Matrix	(	double *	mat,
		int	num_rows,
		int	num_cols,
		bool	distributed,
		bool	copy_data = true
	)

Constructor creating a Matrix with uninitialized values.

Precondition

mat != 0

num_rows > 0

num_cols > 0

Parameters

[in]	mat	The initial values of the Matrix.
[in]	num_rows	When undistributed, the total number of rows of the Matrix. When distributed, the part of the total number of rows of the Matrix on this processor.
[in]	num_cols	The total number of columns of the Matrix.
[in]	distributed	If true the rows of the Matrix are spread over all processors.
[in]	copy_data	If true the matrix allocates its own storage and copies the contents of mat into its own storage. Otherwise it uses mat as its storage.

Definition at line 104 of file Matrix.cpp.

Matrix() [4/4]

CAROM::Matrix::Matrix

(

const Matrix &

other

)

Copy constructor.

Parameters

[in]

other

The Matrix to copy.

Definition at line 143 of file Matrix.cpp.

Member Function Documentation

distribute()

void CAROM::Matrix::distribute

(

const int &

local_num_rows

)

Distribute this matrix rows among MPI processes, based on the specified local number of rows. This becomes distributed after this function is executed.

Precondition

!distributed()

d_owns_data

Parameters

[in]

local_num_rows

number of rows for local MPI rank.

Definition at line 1046 of file Matrix.cpp.

distributed()

bool CAROM::Matrix::distributed ( ) const

inline

Returns true if the Matrix is distributed.

Returns

True if the Matrix is distributed.

Definition at line 177 of file Matrix.h.

elementwise_mult() [1/4]

Matrix* CAROM::Matrix::elementwise_mult ( const Matrix &  other ) const

inline

Multiplies two matrices element-wise.

Precondition

result.distributed() == distributed()

distributed() == other.distributed()

numRows() == other.numRows()

numColumns() == other.numColumns()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 507 of file Matrix.h.

elementwise_mult() [2/4]

void CAROM::Matrix::elementwise_mult	(	const Matrix &	other,
		Matrix &	result
	)		const

Multiplies two matrices element-wise and fills result with the answer.

Precondition

result == 0 || result->distributed() == distributed()

distributed() == other.distributed()

numRows() == other.numRows()

numColumns() == other.numColumns()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 479 of file Matrix.cpp.

elementwise_mult() [3/4]

void CAROM::Matrix::elementwise_mult	(	const Matrix &	other,
		Matrix *&	result
	)		const

Multiplies two matrices element-wise and fills result with the answer.

Precondition

result == 0 || result->distributed() == distributed()

distributed() == other.distributed()

numRows() == other.numRows()

numColumns() == other.numColumns()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 451 of file Matrix.cpp.

elementwise_mult() [4/4]

Matrix* CAROM::Matrix::elementwise_mult ( const Matrix *  other ) const

inline

Multiplies two matrices element-wise and returns the product, pointer version.

Precondition

other != 0

distributed() == other.distributed()

numRows() == other.numRows()

numColumns() == other.numColumns()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 529 of file Matrix.h.

elementwise_square() [1/3]

Matrix* CAROM::Matrix::elementwise_square ( ) const

inline

Square every element in the matrix.

Returns

The product Matrix.

Definition at line 576 of file Matrix.h.

elementwise_square() [2/3]

void CAROM::Matrix::elementwise_square

(

Matrix &

result

)

const

Square every element in the matrix.

Precondition

result == 0 || result->distributed() == distributed()

Parameters

[out]

result

The product Matrix.

Definition at line 523 of file Matrix.cpp.

elementwise_square() [3/3]

void CAROM::Matrix::elementwise_square

(

Matrix *&

result

)

const

Square every element in the matrix.

Precondition

result == 0 || result->distributed() == distributed()

Parameters

[out]

result

The product Matrix.

Definition at line 501 of file Matrix.cpp.

gather()

void CAROM::Matrix::gather

(

)

Gather all the distributed rows among MPI processes. This becomes not distributed after this function is executed.

Precondition

distributed()

d_owns_data

Definition at line 1073 of file Matrix.cpp.

getColumn() [1/3]

Vector* CAROM::Matrix::getColumn ( int  column ) const

inline

Returns a column of the matrix (not owned by Matrix).

Returns

A column of the matrix (not owned by Matrix).

Definition at line 870 of file Matrix.h.

getColumn() [2/3]

void CAROM::Matrix::getColumn	(	int	column,
		Vector &	result
	)		const

Returns a column of the matrix (not owned by Matrix).

Returns

A column of the matrix (not owned by Matrix).

Definition at line 713 of file Matrix.cpp.

getColumn() [3/3]

void CAROM::Matrix::getColumn	(	int	column,
		Vector *&	result
	)		const

Returns a column of the matrix (not owned by Matrix).

Returns

A column of the matrix (not owned by Matrix).

Definition at line 698 of file Matrix.cpp.

getFirstNColumns() [1/3]

Matrix * CAROM::Matrix::getFirstNColumns

(

int

n

)

const

Get the first N columns of a matrix.

Precondition

0 < n < numColumns()

Parameters

[in]

n

The number of columns to return.

Returns

The truncated Matrix.

Definition at line 256 of file Matrix.cpp.

getFirstNColumns() [2/3]

void CAROM::Matrix::getFirstNColumns	(	int	n,
		Matrix &	result
	)		const

Get the first N columns of a matrix.

Precondition

result.distributed() == distributed()

0 < n < numColumns()

Parameters

[in]	n	The number of columns to return.
[out]	result	The truncated Matrix.

Definition at line 294 of file Matrix.cpp.

getFirstNColumns() [3/3]

void CAROM::Matrix::getFirstNColumns	(	int	n,
		Matrix *&	result
	)		const

Get the first N columns of a matrix.

Precondition

result.distributed() == distributed()

0 < n < numColumns()

Parameters

[in]	n	The number of columns to return.
[out]	result	The truncated Matrix.

Definition at line 266 of file Matrix.cpp.

inverse() [1/4]

void CAROM::Matrix::inverse

(

)

Computes the inverse of this and stores result in this.

Precondition

!distributed()

numRows() == numColumns()

Definition at line 840 of file Matrix.cpp.

inverse() [2/4]

Matrix* CAROM::Matrix::inverse ( ) const

inline

Computes and returns the inverse of this.

Precondition

!distributed()

numRows() == numColumns()

Returns

The inverse of this.

Definition at line 814 of file Matrix.h.

inverse() [3/4]

void CAROM::Matrix::inverse

(

Matrix &

result

)

const

Computes and returns the inverse of this.

Result will be sized accordingly.

Precondition

!result.distributed() && result.numRows() == numRows() && result.numColumns() == numColumns()

!distributed()

numRows() == numColumns()

Parameters

[out]

result

The inverse of this.

Definition at line 778 of file Matrix.cpp.

inverse() [4/4]

void CAROM::Matrix::inverse

(

Matrix *&

result

)

const

Computes and returns the inverse of this.

If result has not been allocated it will be, otherwise it will be sized accordingly.

Precondition

result == 0 || (!result->distributed() && result->numRows() == numRows() && result->numColumns() == numColumns())

!distributed()

numRows() == numColumns()

Parameters

[out]

result

The inverse of this.

Definition at line 723 of file Matrix.cpp.

item() [1/2]

double& CAROM::Matrix::item ( int  row, int  col  )

inline

Non-const Matrix member access. Matrix data is stored in row-major format.

Allows constructs of the form mat[i, j] = val;

Precondition

(0 <= row) && (row < numRows())

(0 <= col) && (col < numColumns())

Parameters

[in]	row	The row of the Matrix value on this processor requested.
[in]	col	The column of the Matrix value requested.

Definition at line 1030 of file Matrix.h.

item() [2/2]

const double& CAROM::Matrix::item ( int  row, int  col  ) const

inline

Const Matrix member access. Matrix data is stored in row-major format.

Precondition

(0 <= row) && (row < numRows())

(0 <= col) && (col < numColumns())

Parameters

[in]	row	The row of the Matrix value on this processor requested.
[in]	col	The column of the Matrix value requested.

Definition at line 1007 of file Matrix.h.

local_read()

void CAROM::Matrix::local_read	(	const std::string &	base_file_name,
		int	rank
	)

read a single rank of a distributed Matrix into (a) HDF file(s).

Parameters

[in]	base_file_name	The base part of the file name.
[in]	rank	The rank to read from.

Definition at line 1009 of file Matrix.cpp.

mult() [1/8]

Matrix* CAROM::Matrix::mult ( const Matrix &  other ) const

inline

Multiplies this Matrix with other and returns the product, reference version.

Supports multiplication of two undistributed matrices returning an undistributed Matrix, and multiplication of a distributed Matrix with an undistributed Matrix returning a distributed Matrix.

Precondition

!other.distributed()

numColumns() == other.numRows()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 283 of file Matrix.h.

mult() [2/8]

void CAROM::Matrix::mult	(	const Matrix &	other,
		Matrix &	result
	)		const

Multiplies this Matrix with other and fills result with the answer.

Supports multiplication of two undistributed matrices resulting in an undistributed Matrix, and multiplication of a distributed Matrix with an undistributed Matrix resulting in a distributed Matrix. Result will be sized accordingly.

Precondition

result.distributed() == distributed()

!other.distributed()

numColumns() == other.numRows()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 344 of file Matrix.cpp.

mult() [3/8]

void CAROM::Matrix::mult	(	const Matrix &	other,
		Matrix *&	result
	)		const

Multiplies this Matrix with other and fills result with the answer.

Supports multiplication of two undistributed matrices resulting in an undistributed Matrix, and multiplication of a distributed Matrix with an undistributed Matrix resulting in a distributed Matrix. If result has not been allocated it will be, otherwise it will be sized accordingly.

Precondition

result == 0 || result->distributed() == distributed()

!other.distributed()

numColumns() == other.numRows()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 314 of file Matrix.cpp.

mult() [4/8]

Matrix* CAROM::Matrix::mult ( const Matrix *  other ) const

inline

Multiplies this Matrix with other and returns the product, pointer version.

Supports multiplication of two undistributed matrices returning an undistributed Matrix, and multiplication of a distributed Matrix with an undistributed Matrix returning a distributed Matrix.

Precondition

other != 0

!other->distributed()

numColumns() == other->numRows()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 308 of file Matrix.h.

mult() [5/8]

Vector* CAROM::Matrix::mult ( const Vector &  other ) const

inline

Multiplies this Matrix with other and returns the product, reference version.

Supports multiplication of an undistributed Matrix and Vector returning an undistributed Vector, and multiplication of a distributed Matrix and an undistributed Vector returning a distributed Vector.

Precondition

!other.distributed()

numColumns() == other.dim()

Parameters

[in]

other

The Vector to multiply with this.

Returns

The product Vector.

Definition at line 374 of file Matrix.h.

mult() [6/8]

void CAROM::Matrix::mult	(	const Vector &	other,
		Vector &	result
	)		const

Multiplies this Matrix with other and fills result with the answer.

Supports multiplication of an undistributed Matrix and Vector resulting in an undistributed Vector, and multiplication of a distributed Matrix and an undistributed Vector resulting in a distributed Vector. Result will be sized accordingly.

Precondition

result.distributed() == distributed()

!other.distributed()

numColumns() == other.dim()

Parameters

[in]	other	The Vector to multiply with this.
[out]	result	The product Vector.

Definition at line 396 of file Matrix.cpp.

mult() [7/8]

void CAROM::Matrix::mult	(	const Vector &	other,
		Vector *&	result
	)		const

Multiplies this Matrix with other and fills result with the answer.

Supports multiplication of an undistributed Matrix and Vector resulting in an undistributed Vector, and multiplication of a distributed Matrix and an undistributed Vector resulting in a distributed Vector. If result has not been allocated it will be, otherwise it will be sized accordingly.

Precondition

result == 0 || result->distributed() == distributed()

!other.distributed()

numColumns() == other.dim()

Parameters

[in]	other	The Vector to multiply with this.
[out]	result	The product Vector.

Definition at line 368 of file Matrix.cpp.

mult() [8/8]

Vector* CAROM::Matrix::mult ( const Vector *  other ) const

inline

Multiplies this Matrix with other and returns the product, pointer version.

Supports multiplication of an undistributed Matrix and Vector returning an undistributed Vector, and multiplication of a distributed Matrix and an undistributed Vector returning a distributed Vector.

Precondition

other != 0

!other->distributed()

numColumns() == other->dim()

Parameters

[in]

other

The Vector to multiply with this.

Returns

The product Vector.

Definition at line 399 of file Matrix.h.

multPlus()

void CAROM::Matrix::multPlus	(	Vector &	a,
		const Vector &	b,
		double	c
	)		const

Computes a += this*b*c.

Supports accumulation of the multiplication of an undistributed Matrix and Vector into an undistributed Vector, and accumulation of the multiplication of a distributed Matrix and an undistributed Vector into a distributed Vector.

Precondition

a.distributed() == distributed()

!b->distributed()

numColumns() == b.dim()

numRows() = a.dim()

Parameters

[in,out]	a	The Vector to accumulate this*b into.
[in]	b	The Vector multiplied by this.
[in]	c	Scalar multiplication factor.

Definition at line 539 of file Matrix.cpp.

numColumns()

int CAROM::Matrix::numColumns ( ) const

inline

Returns the number of columns in the Matrix. This method will return the same value from each processor.

Returns

The number of columns of the Matrix.

Definition at line 220 of file Matrix.h.

numDistributedRows()

int CAROM::Matrix::numDistributedRows ( ) const

inline

Returns the number of rows of the Matrix across all processors.

Returns

The number of rows of the Matrix across all processors.

Definition at line 205 of file Matrix.h.

numRows()

int CAROM::Matrix::numRows ( ) const

inline

Returns the number of rows of the Matrix on this processor.

Returns

The number of rows of the Matrix on this processor.

Definition at line 194 of file Matrix.h.

operator()() [1/2]

double& CAROM::Matrix::operator() ( int  row, int  col  )

inline

Non-const Matrix member access.

Allows constructs of the form mat[i, j] = val;

Precondition

(0 <= row) && (row < numRows())

(0 <= col) && (col < numColumns())

Parameters

[in]	row	The row of the Matrix value on this processor requested.
[in]	col	The column of the Matrix value requested.

Definition at line 1066 of file Matrix.h.

operator()() [2/2]

const double& CAROM::Matrix::operator() ( int  row, int  col  ) const

inline

Const Matrix member access.

Precondition

(0 <= row) && (row < numRows())

(0 <= col) && (col < numColumns())

Parameters

[in]	row	The row of the Matrix value on this processor requested.
[in]	col	The column of the Matrix value requested.

Definition at line 1049 of file Matrix.h.

operator+=()

Matrix & CAROM::Matrix::operator+=

(

const Matrix &

rhs

)

Addition operator.

Parameters

[in]

rhs

The Matrix to add to this.

Returns

This after rhs has been added to it.

Definition at line 183 of file Matrix.cpp.

operator-=()

Matrix & CAROM::Matrix::operator-=

(

const Matrix &

rhs

)

Subtraction operator.

Parameters

[in]

rhs

The Matrix to subtract to this.

Returns

This after rhs has been subtracted to it.

Definition at line 193 of file Matrix.cpp.

operator=() [1/2]

Matrix & CAROM::Matrix::operator=

(

const double

a

)

Assignment operator.

Parameters

[in]

a

constant value

Returns

This after filling all the data with a constant value

Definition at line 246 of file Matrix.cpp.

operator=() [2/2]

Matrix & CAROM::Matrix::operator=

(

const Matrix &

rhs

)

Assignment operator.

Parameters

[in]

rhs

The Matrix to assign to this.

Returns

This after rhs has been assigned to it.

Definition at line 172 of file Matrix.cpp.

orthogonalize()

void CAROM::Matrix::orthogonalize	(	bool	double_pass = false,
		double	zero_tol = 1.0e-15
	)

Orthonormalizes the matrix.

The method uses the modified Gram-Schmidt algorithm.

If double_pass == true, then each column is orthogonalized twice to limit loss of orthogonality due to numerical errors. By default, double_pass == false.

If the norm of a matrix column is below the value of zero_tol then it is considered to be zero, and we do not divide by it. Therefore, that column is considered to be zero and is not normalized. By default, zero_tol == 1.0e-15.

Definition at line 1803 of file Matrix.cpp.

orthogonalize_last()

void CAROM::Matrix::orthogonalize_last	(	int	ncols = -1,
		bool	double_pass = false,
		double	zero_tol = 1.0e-15
	)

Orthonormalizes the matrix's last column, assuming the previous columns are already orthonormal.

By default, ncols == -1, and the function considers the whole matrix. If ncols != -1 and ncols < d_num_cols, then a subset of the matrix is considered. This allows one to reorthonormalize the matrix every time a new column is added, assuming the previous columns have remained unchanged.

If double_pass == true, then the column is orthogonalized twice to limit loss of orthogonality due to numerical errors. By default, double_pass == false.

If the norm of a matrix column is below the value of zero_tol then it is considered to be zero, and we do not divide by it. Therefore, that column is considered to be zero and is not normalized. By default, zero_tol == 1.0e-15.

Definition at line 1853 of file Matrix.cpp.

pointwise_mult() [1/2]

void CAROM::Matrix::pointwise_mult	(	int	this_row,
		const Vector &	other,
		Vector &	result
	)		const

Multiplies a specified row of this Matrix with other pointwise.

Only supports multiplication of an undistributed Matrix and Vector resulting in an undistributed Vector. Result will be sized accordingly.

Precondition

!result.distributed()

!distributed()

!other.distributed()

numColumns() == other.dim()

Parameters

[in]	this_row	The row of the matrix to multiple with other.
[in]	other	The Vector to multiply with this_row of the matrix.
[out]	result	The product Vector.

Definition at line 418 of file Matrix.cpp.

pointwise_mult() [2/2]

void CAROM::Matrix::pointwise_mult	(	int	this_row,
		Vector &	other
	)		const

Multiplies a specified row of this Matrix with other pointwise. This modifies other.

Only supports multiplication of an undistributed Matrix and Vector resulting in an undistributed Vector. Result will be sized accordingly.

Precondition

!result.distributed()

!distributed()

!other.distributed()

numColumns() == other.dim()

Parameters

[in]	this_row	The row of the matrix to multiple with other.
[in]	other	The Vector to multiply with this_row of the matrix.
[out]	other	The product Vector.

Definition at line 436 of file Matrix.cpp.

print()

void CAROM::Matrix::print

(

const char *

prefix

)

const

print Matrix into (a) ascii file(s).

Parameters

[in]

prefix

The name of the prefix of the file name.

Definition at line 918 of file Matrix.cpp.

qr_factorize()

Matrix * CAROM::Matrix::qr_factorize

(

)

const

Computes and returns the Q of the QR factorization of this.

Returns

The Q of the QR factorization of this.

Definition at line 1125 of file Matrix.cpp.

qrcp_pivots_transpose()

void CAROM::Matrix::qrcp_pivots_transpose	(	int *	row_pivot,
		int *	row_pivot_owner,
		int	pivots_requested
	)		const

Compute the leading numColumns() column pivots from a QR decomposition with column pivots (QRCP) of the transpose of this.

Precondition

!distributed()

Parameters

[out]	row_pivot	Array of leading column pivots from QRCP of transpose of this Matrix, has length pivots_requested
[out]	row_pivot_owner	Array of process rank that owns each pivot on the communicator owned by this Matrix.
[in]	pivots_requested	The number of pivots requested, must be less than or equal to the number of rows of this Matrix.

Definition at line 1198 of file Matrix.cpp.

read()

void CAROM::Matrix::read

(

const std::string &

base_file_name

)

read Matrix into (a) HDF file(s).

Parameters

[in]

base_file_name

The base part of the file name.

Definition at line 969 of file Matrix.cpp.

setSize()

void CAROM::Matrix::setSize ( int  num_rows, int  num_cols  )

inline

Sets the number of rows and columns of the matrix and reallocates storage if needed. All values are initialized to zero.

Parameters

[in]	num_rows	New number of rows
[in]	num_cols	New number of cols

Definition at line 147 of file Matrix.h.

transpose()

void CAROM::Matrix::transpose

(

)

Replaces this Matrix with its transpose (in place), in the serial square case only.

Precondition

!distributed()

numRows() == numColumns()

Definition at line 824 of file Matrix.cpp.

transposeMult() [1/8]

Matrix* CAROM::Matrix::transposeMult ( const Matrix &  other ) const

inline

Multiplies the transpose of this Matrix with other and returns the product, reference version.

Supports multiplication of two undistributed matrices returning an undistributed Matrix or two distributed matrices returning an undistributed Matrix.

Precondition

distributed() == other.distributed()

numRows() == other.numRows()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 642 of file Matrix.h.

transposeMult() [2/8]

void CAROM::Matrix::transposeMult	(	const Matrix &	other,
		Matrix &	result
	)		const

Multiplies the transpose of this Matrix with other and fills result with the answer.

Supports multiplication of two undistributed matrices or two distributed matrices resulting in an undistributed Matrix. Result will be sized accordingly.

Precondition

!result.distributed()

distributed() == other.distributed()

numRows() == other.numRows()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 598 of file Matrix.cpp.

transposeMult() [3/8]

void CAROM::Matrix::transposeMult	(	const Matrix &	other,
		Matrix *&	result
	)		const

Multiplies the transpose of this Matrix with other and fills result with the answer.

Supports multiplication of two undistributed matrices or two distributed matrices resulting in an undistributed Matrix. If result has not been allocated it will be, otherwise it will be sized accordingly.

Precondition

result == 0 || !result->distributed()

distributed() == other.distributed()

numRows() == other.numRows()

Parameters

[in]	other	The Matrix to multiply with this.
[out]	result	The product Matrix.

Definition at line 559 of file Matrix.cpp.

transposeMult() [4/8]

Matrix* CAROM::Matrix::transposeMult ( const Matrix *  other ) const

inline

Multiplies the transpose of this Matrix with other and returns the product, pointer version.

Supports multiplication of two undistributed matrices returning an undistributed Matrix or two distributed matrices returning an undistributed Matrix.

Precondition

other != 0

distributed() == other->distributed()

numRows() == other->numRows()

Parameters

[in]

other

The Matrix to multiply with this.

Returns

The product Matrix.

Definition at line 667 of file Matrix.h.

transposeMult() [5/8]

Vector* CAROM::Matrix::transposeMult ( const Vector &  other ) const

inline

Multiplies the transpose of this Matrix with other and returns the product, reference version.

Supports multiplication of an undistributed Matrix and an undistributed Vector or a distributed Matrix and a distributed Vector returning an undistributed Vector.

Precondition

distributed() == other.distributed()

numRows() == other.dim();

Parameters

[in]

other

The Vector to multiply with this.

Returns

The product Vector.

Definition at line 731 of file Matrix.h.

transposeMult() [6/8]

void CAROM::Matrix::transposeMult	(	const Vector &	other,
		Vector &	result
	)		const

Multiplies the transpose of this Matrix with other and fills result with the answer.

Supports multiplication of an undistributed Matrix and an undistributed Vector or a distributed Matrix and a distributed Vector resulting in an undistributed Vector. Result will be sized accordingly.

Precondition

!result.distributed()

distributed() == other.distributed()

numRows() == other.dim();

Parameters

[in]	other	The Vector to multiply with this.
[out]	result	The product Vector.

Definition at line 667 of file Matrix.cpp.

transposeMult() [7/8]

void CAROM::Matrix::transposeMult	(	const Vector &	other,
		Vector *&	result
	)		const

Multiplies the transpose of this Matrix with other and fills result with the answer.

Supports multiplication of an undistributed Matrix and an undistributed Vector or a distributed Matrix and a distributed Vector resulting in an undistributed Vector. If result has not been allocated it will be, otherwise it will be sized accordingly.

Precondition

result == 0 || !result->distributed()

distributed() == other.distributed()

numRows() == other.dim();

Parameters

[in]	other	The Vector to multiply with this.
[out]	result	The product Vector.

Definition at line 631 of file Matrix.cpp.

transposeMult() [8/8]

Vector* CAROM::Matrix::transposeMult ( const Vector *  other ) const

inline

Multiplies the transpose of this Matrix with other and returns the product, pointer version.

Supports multiplication of an undistributed Matrix and an undistributed Vector or a distributed Matrix and a distributed Vector returning an undistributed Vector.

Precondition

other != 0

distributed() == other->distributed()

numRows() == other->dim();

Parameters

[in]

other

The Vector to multiply with this.

Returns

The product Vector.

Definition at line 756 of file Matrix.h.

transposePseudoinverse()

void CAROM::Matrix::transposePseudoinverse

(

)

Computes the transposePseudoinverse of this.

Precondition

!distributed()

numRows() >= numColumns()

Assumes this is full column rank; may fail if this is not full column rank.

Definition at line 882 of file Matrix.cpp.

write()

void CAROM::Matrix::write

(

const std::string &

base_file_name

)

const

write Matrix into (a) HDF file(s).

Parameters

[in]

base_file_name

The base part of the file name.

Definition at line 937 of file Matrix.cpp.

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

• lib/linalg/Matrix.h
• lib/linalg/Matrix.cpp