A class for storing and performing operations on general 2-dimensional matrices. More...
#include <matrix.h>
Public Types | |
| enum | Type { DENSE, SPARSE } |
Public Member Functions | |
| double | absMax () const |
| The largest absolute value of any element in this matrix. | |
| int | cols () const |
| The number of columns of this matrix. | |
| void | copyMatrix (const Matrix &m) |
| Copies the entire matrix m to this matrix; sizes must be identical. | |
| virtual void | copySubBlock (int startRow, int startCol, int rows, int cols, const Matrix &m, int startMRow, int startMCol) |
| Copies a block of the matrix m into a block of this matrix. | |
| void | copySubMatrix (int startRow, int startCol, const Matrix &m) |
| Copies the entire matrix m into a sub-block of this matrix. | |
| virtual const double & | elem (int m, int n) const |
| Not inlined as it is overloaded in SparseMatrix. | |
| virtual double & | elem (int m, int n) |
| Not inlined as it is overloaded in SparseMatrix. | |
| double | elementSum () const |
| The sum of all the elements in the matrix. | |
| void | eye () |
| Sets this matrix to identity. Not really used, use the static EYE instead. | |
| double | fnorm () const |
| Computes the Frobenius norm of the matrix: sqrt(sum_of_all_squared_elems). | |
| Matrix | getColumn (int c) const |
| virtual void | getData (std::vector< double > *data) const |
| Returns a copy of the data as a column major vector of doubles. | |
| virtual std::auto_ptr< double > | getDataCopy () const |
| Returns an auto_ptr to a copy of the data. | |
| virtual double * | getDataPointer () |
| Returns the actual data pointer for this matrix. | |
| virtual double | getDefault () const |
| Returns the default value for the elements of this matrix. | |
| Matrix | getRow (int r) const |
| Matrix | getSubMatrix (int startRow, int startCol, int rows, int cols) const |
| virtual Type | getType () const |
| Matrix (const double *M, int m, int n, bool colMajor) | |
| A matrix of the given size, with contents initialized from an array in memory. | |
| Matrix (const Matrix &M) | |
| Copy constructor. | |
| Matrix (int m, int n) | |
| A matrix of the given size with unspecified contents. | |
| void | multiply (double s) |
| Multiples the matrix by the scalar s. | |
| virtual bool | nextSequentialElement (int &i, int &j, double &val) const |
| Returns the next non-zero element, in sequential access. | |
| virtual int | numElements () const |
| Returns the number of elements set. | |
| void | print (FILE *fp=stderr) const |
| int | rank () const |
| Computes the rank of the matrix using SVD. | |
| virtual void | resize (int m, int n) |
| Resizes the matrix. All current data is lost. | |
| int | rows () const |
| The number of rows of this matrix. | |
| virtual void | sequentialReset () const |
| Resets the sequential access to the matrix. | |
| virtual void | setAllElements (double val) |
| void | swapCols (int c1, int c2) |
| void | swapRows (int r1, int r2) |
| virtual void | transpose () |
| Transposes this matrix in place. | |
| Matrix | transposed () const |
| Returns the transpose of this matrix; the original is unaffected. | |
| virtual | ~Matrix () |
Static Public Member Functions | |
| template<class MatrixType > | |
| static MatrixType | BLOCKCOLUMN (std::list< Matrix * > *blocks) |
| Builds a block column matrix from the column matrices in the list. | |
| template<class MatrixType > | |
| static MatrixType | BLOCKCOLUMN (const Matrix &M1, const Matrix &M2) |
| Builds a block column matrix from the two given matrices. | |
| template<class MatrixType > | |
| static MatrixType | BLOCKDIAG (std::list< Matrix * > *blocks) |
| Builds a block diagonal matrix from the matrices in the list. | |
| template<class MatrixType > | |
| static MatrixType | BLOCKDIAG (const Matrix &M1, const Matrix &M2) |
| Builds a block diagonal matrix from the two given matrices. | |
| template<class MatrixType > | |
| static MatrixType | BLOCKROW (std::list< Matrix * > *blocks) |
| Builds a block row matrix from the row matrices in the list. | |
| template<class MatrixType > | |
| static MatrixType | BLOCKROW (const Matrix &M1, const Matrix &M2) |
| Builds a block row matrix from the two given matrices. | |
| static Matrix | EYE (int m, int n) |
| An identity matrix of the given size. | |
| static Matrix | MAX_VECTOR (int rows) |
| Returns a vector filled with the max value that can be expressed as a double. | |
| static Matrix | MIN_VECTOR (int rows) |
| Returns a vector filled with the min value that can be expressed as a double. | |
| static Matrix | NEGEYE (int m, int n) |
| A negated identity matrix of the given size. | |
| static Matrix | PERMUTATION (int n, int *jpvt) |
| A permutation matrix initialized from a permutation vector in memory. | |
| static Matrix | ROTATION (const mat3 &rot) |
| A 3x3 rotation matrix that can be used to left-multiply a 3x1 vector. | |
| static Matrix | ROTATION2D (double theta) |
| A 2D 2x2 rotation matrix that can be used to left-multiply a 2x1 vector. | |
| static Matrix | TRANSFORM (const transf &t) |
| A 4x4 transform matrix that can be used to left-multiply a 4x1 homogeneous vector. | |
| template<class MatrixType > | |
| static MatrixType | ZEROES (int m, int n) |
| A mtrix of the given size filled with zeroes. | |
Static Public Attributes | |
| static const double | EPS = 1.0e-7 |
| Used for zero comparisons in all computations. | |
Protected Attributes | |
| int | mCols |
| int | mRows |
| The size of this matrix, set at construction time. | |
Private Member Functions | |
| void | initialize (int m, int n) |
| All the work that is common between all constructors. | |
| void | setFromColMajor (const double *M) |
| Copies the actual data from a column-major array in memory. | |
| void | setFromRowMajor (const double *M) |
| Copies the actual data from a row-major array in memory. | |
Private Attributes | |
| double * | mData |
| The actual data, in column-major format. | |
| int | mSequentialI |
| Used to keep track of sequential access. | |
| int | mSequentialJ |
| Used to keep track of sequential access. | |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const Matrix &m) |
A class for storing and performing operations on general 2-dimensional matrices.
The Matrix is a general 2-dimensional matrix, along with a (growing) number of operations that can be performed on it. The data itself is stored as a column-major array of doubles. The important design decisions are:
A Matrix only holds doubles for now. At some point I hope to template the class to hold anything you might want.
Many of the computations are done using LAPACK. This should be really fast, but also has problems. One of them is that it prevents using const correctly for all the operations and arguments that should be const.
A Matrix's size is determined when it is constructed, and can never be changed afterwards. This is somewhat inflexible, but allows us to catch size mismatches at run time. In debug mode, all operations first assert(...) the correct matrix sizes.
All Matrix copies are deep copies. This avoids lots of problem with consistency, but can also eat up memory and slow down operations. Be particularly careful when using the copy constructor, or any functions that return instances of the Matrix class: all are done using deep copies.
No operators have been implemented. Most operations that involve two or more matrices are external to this class, and rather than returning the result, they take in the result as an argument. This makes it somewhat easier to catch errors, but also makes chaining of operations annoying.
Also provides what I call "sequential access" so that a sparse matrix (which inherits from this class) can give you its non-zero elements in linear time in the number of elements. This is somewhat hackish, for now. The way sequential access works, for both dense and sparse matrix, is using two functions: sequentialReset() and nextSequentialElement(...). See documentation of those functions for details.
Definition at line 74 of file matrix.h.
| enum Matrix::Type |
| Matrix::Matrix | ( | int | m, | |
| int | n | |||
| ) |
A matrix of the given size with unspecified contents.
Definition at line 75 of file matrix.cpp.
| Matrix::Matrix | ( | const Matrix & | M | ) |
Copy constructor.
Definition at line 79 of file matrix.cpp.
| Matrix::Matrix | ( | const double * | M, | |
| int | m, | |||
| int | n, | |||
| bool | colMajor | |||
| ) |
A matrix of the given size, with contents initialized from an array in memory.
Definition at line 87 of file matrix.cpp.
| Matrix::~Matrix | ( | ) | [virtual] |
Definition at line 97 of file matrix.cpp.
| double Matrix::absMax | ( | ) | const |
The largest absolute value of any element in this matrix.
Definition at line 379 of file matrix.cpp.
| MatrixType Matrix::BLOCKCOLUMN | ( | std::list< Matrix * > * | blocks | ) | [inline, static] |
| MatrixType Matrix::BLOCKDIAG | ( | std::list< Matrix * > * | blocks | ) | [inline, static] |
| MatrixType Matrix::BLOCKROW | ( | std::list< Matrix * > * | blocks | ) | [inline, static] |
| int Matrix::cols | ( | ) | const [inline] |
| void Matrix::copyMatrix | ( | const Matrix & | m | ) | [inline] |
| void Matrix::copySubBlock | ( | int | startRow, | |
| int | startCol, | |||
| int | rows, | |||
| int | cols, | |||
| const Matrix & | m, | |||
| int | startMRow, | |||
| int | startMCol | |||
| ) | [virtual] |
Copies a block of the matrix m into a block of this matrix.
Reimplemented in SparseMatrix.
Definition at line 495 of file matrix.cpp.
| void Matrix::copySubMatrix | ( | int | startRow, | |
| int | startCol, | |||
| const Matrix & | m | |||
| ) | [inline] |
| const double & Matrix::elem | ( | int | m, | |
| int | n | |||
| ) | const [virtual] |
Not inlined as it is overloaded in SparseMatrix.
Reimplemented in SparseMatrix.
Definition at line 137 of file matrix.cpp.
| double & Matrix::elem | ( | int | m, | |
| int | n | |||
| ) | [virtual] |
Not inlined as it is overloaded in SparseMatrix.
Reimplemented in SparseMatrix.
Definition at line 129 of file matrix.cpp.
| double Matrix::elementSum | ( | ) | const |
The sum of all the elements in the matrix.
Definition at line 393 of file matrix.cpp.
| Matrix Matrix::EYE | ( | int | m, | |
| int | n | |||
| ) | [static] |
An identity matrix of the given size.
Reimplemented in SparseMatrix.
Definition at line 203 of file matrix.cpp.
| void Matrix::eye | ( | ) |
Sets this matrix to identity. Not really used, use the static EYE instead.
Definition at line 636 of file matrix.cpp.
| double Matrix::fnorm | ( | ) | const |
Computes the Frobenius norm of the matrix: sqrt(sum_of_all_squared_elems).
Definition at line 367 of file matrix.cpp.
| Matrix Matrix::getColumn | ( | int | c | ) | const |
Definition at line 455 of file matrix.cpp.
| void Matrix::getData | ( | std::vector< double > * | data | ) | const [virtual] |
Returns a copy of the data as a column major vector of doubles.
Reimplemented in SparseMatrix.
Definition at line 331 of file matrix.cpp.
| std::auto_ptr< double > Matrix::getDataCopy | ( | ) | const [virtual] |
Returns an auto_ptr to a copy of the data.
Reimplemented in SparseMatrix.
Definition at line 323 of file matrix.cpp.
| double * Matrix::getDataPointer | ( | ) | [virtual] |
Returns the actual data pointer for this matrix.
Reimplemented in SparseMatrix.
Definition at line 337 of file matrix.cpp.
| virtual double Matrix::getDefault | ( | ) | const [inline, virtual] |
Returns the default value for the elements of this matrix.
Really only makes sense for sparse matrices.
Reimplemented in SparseMatrix.
| Matrix Matrix::getRow | ( | int | r | ) | const |
Definition at line 466 of file matrix.cpp.
| Matrix Matrix::getSubMatrix | ( | int | startRow, | |
| int | startCol, | |||
| int | rows, | |||
| int | cols | |||
| ) | const |
Definition at line 477 of file matrix.cpp.
| virtual Type Matrix::getType | ( | ) | const [inline, virtual] |
Reimplemented in SparseMatrix.
| void Matrix::initialize | ( | int | m, | |
| int | n | |||
| ) | [private] |
All the work that is common between all constructors.
Definition at line 55 of file matrix.cpp.
| Matrix Matrix::MAX_VECTOR | ( | int | rows | ) | [static] |
Returns a vector filled with the max value that can be expressed as a double.
Definition at line 276 of file matrix.cpp.
| Matrix Matrix::MIN_VECTOR | ( | int | rows | ) | [static] |
Returns a vector filled with the min value that can be expressed as a double.
Definition at line 284 of file matrix.cpp.
| void Matrix::multiply | ( | double | s | ) |
Multiples the matrix by the scalar s.
Definition at line 650 of file matrix.cpp.
| Matrix Matrix::NEGEYE | ( | int | m, | |
| int | n | |||
| ) | [static] |
A negated identity matrix of the given size.
Reimplemented in SparseMatrix.
Definition at line 227 of file matrix.cpp.
| bool Matrix::nextSequentialElement | ( | int & | i, | |
| int & | j, | |||
| double & | val | |||
| ) | const [virtual] |
Returns the next non-zero element, in sequential access.
Reimplemented in SparseMatrix.
Definition at line 413 of file matrix.cpp.
| virtual int Matrix::numElements | ( | ) | const [inline, virtual] |
Returns the number of elements set.
Reimplemented in SparseMatrix.
| Matrix Matrix::PERMUTATION | ( | int | n, | |
| int * | jpvt | |||
| ) | [static] |
A permutation matrix initialized from a permutation vector in memory.
Definition at line 251 of file matrix.cpp.
| void Matrix::print | ( | FILE * | fp = stderr |
) | const |
Definition at line 597 of file matrix.cpp.
| int Matrix::rank | ( | ) | const |
Computes the rank of the matrix using SVD.
Definition at line 343 of file matrix.cpp.
| void Matrix::resize | ( | int | m, | |
| int | n | |||
| ) | [virtual] |
Resizes the matrix. All current data is lost.
Reimplemented in SparseMatrix.
Definition at line 104 of file matrix.cpp.
A 3x3 rotation matrix that can be used to left-multiply a 3x1 vector.
Definition at line 264 of file matrix.cpp.
| Matrix Matrix::ROTATION2D | ( | double | theta | ) | [static] |
A 2D 2x2 rotation matrix that can be used to left-multiply a 2x1 vector.
| cos(theta) -sin(theta) | | sin(theta) cos(theta) |
Definition at line 296 of file matrix.cpp.
| int Matrix::rows | ( | ) | const [inline] |
| void Matrix::sequentialReset | ( | ) | const [virtual] |
Resets the sequential access to the matrix.
Reimplemented in SparseMatrix.
Definition at line 406 of file matrix.cpp.
| void Matrix::setAllElements | ( | double | val | ) | [virtual] |
Reimplemented in SparseMatrix.
Definition at line 486 of file matrix.cpp.
| void Matrix::setFromColMajor | ( | const double * | M | ) | [private] |
Copies the actual data from a column-major array in memory.
Definition at line 305 of file matrix.cpp.
| void Matrix::setFromRowMajor | ( | const double * | M | ) | [private] |
Copies the actual data from a row-major array in memory.
Definition at line 312 of file matrix.cpp.
| void Matrix::swapCols | ( | int | c1, | |
| int | c2 | |||
| ) |
Definition at line 604 of file matrix.cpp.
| void Matrix::swapRows | ( | int | r1, | |
| int | r2 | |||
| ) |
Definition at line 612 of file matrix.cpp.
A 4x4 transform matrix that can be used to left-multiply a 4x1 homogeneous vector.
| void Matrix::transpose | ( | ) | [virtual] |
Transposes this matrix in place.
Reimplemented in SparseMatrix.
Definition at line 620 of file matrix.cpp.
| Matrix Matrix::transposed | ( | ) | const |
Returns the transpose of this matrix; the original is unaffected.
Definition at line 659 of file matrix.cpp.
| MatrixType Matrix::ZEROES | ( | int | m, | |
| int | n | |||
| ) | [inline, static] |
| std::ostream& operator<< | ( | std::ostream & | os, | |
| const Matrix & | m | |||
| ) | [friend] |
Definition at line 586 of file matrix.cpp.
const double Matrix::EPS = 1.0e-7 [static] |
int Matrix::mCols [protected] |
double* Matrix::mData [private] |
int Matrix::mRows [protected] |
int Matrix::mSequentialI [mutable, private] |
int Matrix::mSequentialJ [mutable, private] |
