Regina Calculation Engine
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Represents a matrix of elements of the given type T. More...
#include <maths/matrix.h>
Public Types | |
typedef T | Coefficient |
The type of each entry in the matrix. More... | |
Public Member Functions | |
Matrix (unsigned long rows, unsigned long cols) | |
Creates a new matrix of the given size. More... | |
Matrix (const Matrix &src) | |
Creates a new matrix that is a clone of the given matrix. More... | |
Matrix (Matrix &&src) noexcept | |
Moves the given matrix into this new matrix. More... | |
~Matrix () | |
Destroys this matrix. More... | |
Matrix & | operator= (const Matrix &src) |
Copies the given matrix into this matrix. More... | |
Matrix & | operator= (Matrix &&src) noexcept |
Moves the given matrix into this matrix. More... | |
void | initialise (const T &value) |
Sets every entry in the matrix to the given value. More... | |
void | initialise (List allValues) |
A Python-only routine that fills the matrix with the given set of elements. More... | |
unsigned long | rows () const |
Returns the number of rows in this matrix. More... | |
unsigned long | columns () const |
Returns the number of columns in this matrix. More... | |
T & | entry (unsigned long row, unsigned long column) |
Returns the entry at the given row and column. More... | |
const T & | entry (unsigned long row, unsigned long column) const |
Returns the entry at the given row and column. More... | |
bool | operator== (const Matrix &other) const |
Determines whether this and the given matrix are identical. More... | |
bool | operator!= (const Matrix &other) const |
Determines whether this and the given matrix are different. More... | |
void | writeMatrix (std::ostream &out) const |
Writes a complete representation of the matrix to the given output stream. More... | |
void | swapRows (unsigned long first, unsigned long second) |
Swaps the elements of the two given rows in the matrix. More... | |
void | swapColumns (unsigned long first, unsigned long second) |
Swaps the elements of the two given columns in the matrix. More... | |
void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const |
Writes a detailed text representation of this object to the given output stream. More... | |
REGINA_ENABLE_FOR_RING_STATIC (Matrix) identity(unsigned long size) | |
Returns an identity matrix of the given size. More... | |
void | makeIdentity () |
Turns this matrix into an identity matrix. More... | |
bool | isIdentity () const |
Determines whether this matrix is a square identity matrix. More... | |
bool | isZero () const |
Determines whether this is the zero matrix. More... | |
void | addRow (unsigned long source, unsigned long dest) |
Adds the given source row to the given destination row. More... | |
void | addRow (unsigned long source, unsigned long dest, T copies) |
Adds the given number of copies of the given source row to the given destination row. More... | |
void | addCol (unsigned long source, unsigned long dest) |
Adds the given source column to the given destination column. More... | |
void | addCol (unsigned long source, unsigned long dest, T copies) |
Adds the given number of copies of the given source column to the given destination column. More... | |
void | multRow (unsigned long row, T factor) |
Multiplies the given row by the given factor. More... | |
void | multCol (unsigned long column, T factor) |
Multiplies the given column by the given factor. More... | |
Matrix | operator* (const Matrix &other) const |
Multiplies this by the given matrix, and returns the result. More... | |
Matrix | multiplyAs (const Matrix &other) const |
Deprecated alias for the multiplication operator. More... | |
T | det () const |
Evaluates the determinant of the matrix. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (void) divRowExact(unsigned long row | |
Divides all elements of the given row by the given integer. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (void) divColExact(unsigned long col | |
Divides all elements of the given column by the given integer. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (T) gcdRow(unsigned long row) | |
Computes the greatest common divisor of all elements of the given row. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (T) gcdCol(unsigned long col) | |
Computes the greatest common divisor of all elements of the given column. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (void) reduceRow(unsigned long row) | |
Reduces the given row by dividing all its elements by their greatest common divisor. More... | |
REGINA_ENABLE_FOR_REGINA_INTEGER (void) reduceCol(unsigned long col) | |
Reduces the given column by dividing all its elements by their greatest common divisor. More... | |
Public Attributes | |
const T & | divBy |
Represents a matrix of elements of the given type T.
As of Regina 5.3, the old subclasses of Matrix have now been merged into a single Matrix class. The additional member functions that the old subclasses MatrixRing and MatrixIntDomain used to provide are now part of Matrix, and are enabled or disabled according to the Matrix template parameters.
It is generally safe to just use the type Matrix<T>, since the ring
argument has a sensible default. At present, ring
defaults to true
(thereby enabling member functions designed for matrices over rings) when T is one of the following types:
true
and T is not bool); orOther types may be added to this list in future versions of Regina.
There are several requirements for the underlying type T. For all matrix types:
<<
.If ring is true
, then in addition to this:
+
, -
and *
, and unary operators +=
, -=
and *=
.In particular, all of Regina's integer and rational types (Integer, LargeInteger, NativeInteger<...> and Rational) satisfy all of these requirements, and will set ring to true
by default.
The header maths/matrixops.h contains several other algorithms that work with the specific class Matrix<Integer>.
This class is designed to avoid deep copies wherever possible. In particular, it supports C++11 move constructors and move assignment. Functions that take or return objects by value are designed to be just as efficient as working with references or pointers, and long chains of operators such as a = b * c * d
do not make unwanted deep copies.
T | the type of each individual matrix element. |
ring | true if we should enable member functions that only work when T represents an element of a ring. This has a sensible default; see above in the class documentation for details. |
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inline |
Computes the greatest common divisor of all elements of the given column.
The value returned is guaranteed to be non-negative.
This routine is only available when T is one of Regina's own integer classes (Integer, LargeInteger, or NativeIntgeger).
col | the index of the column whose gcd should be computed. |
regina::Matrix< T, ring >::REGINA_ENABLE_FOR_REGINA_INTEGER | ( | void | ) |
Divides all elements of the given column by the given integer.
This can only be used when the given integer divides into all column elements exactly (with no remainder). For the Integer class, this may be much faster than ordinary division.
This routine is only available when T is one of Regina's own integer classes (Integer, LargeInteger, or NativeIntgeger).
col | the index of the column whose elements should be divided by divBy. |
divBy | the integer to divide each column element by. |
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inline |
Reduces the given column by dividing all its elements by their greatest common divisor.
It is guaranteed that, if the column is changed at all, it will be divided by a positive integer.
This routine is only available when T is one of Regina's own integer classes (Integer, LargeInteger, or NativeIntgeger).
col | the index of the column to reduce. |
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inline |
Reduces the given row by dividing all its elements by their greatest common divisor.
It is guaranteed that, if the row is changed at all, it will be divided by a positive integer.
This routine is only available when T is one of Regina's own integer classes (Integer, LargeInteger, or NativeIntgeger).
row | the index of the row to reduce. |