Regina Calculation Engine
|
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... | |
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... | |
void | divRowExact (unsigned long row, const T &divBy) |
Divides all elements of the given row by the given integer. More... | |
void | divColExact (unsigned long col, const T &divBy) |
Divides all elements of the given column by the given integer. More... | |
T | gcdRow (unsigned long row) |
Computes the greatest common divisor of all elements of the given row. More... | |
T | gcdCol (unsigned long col) |
Computes the greatest common divisor of all elements of the given column. More... | |
void | reduceRow (unsigned long row) |
Reduces the given row by dividing all its elements by their greatest common divisor. More... | |
void | reduceCol (unsigned long col) |
Reduces the given column by dividing all its elements by their greatest common divisor. More... | |
std::string | str () const |
Returns a short text representation of this object. More... | |
std::string | utf8 () const |
Returns a short text representation of this object using unicode characters. More... | |
std::string | detail () const |
Returns a detailed text representation of this object. More... | |
Static Public Member Functions | |
static Matrix | identity (unsigned long size) |
Returns an identity matrix of the given size. More... | |
Static Public Attributes | |
static const T | zero |
The additive identity in the underlying ring. More... | |
static const T | one |
The multiplicative identity in the underlying ring. More... | |
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. |
typedef T regina::Matrix< T, ring >::Coefficient |
The type of each entry in the matrix.
|
inline |
Creates a new matrix of the given size.
All entries will be initialised using their default constructors.
In particular, this means that for Regina's own integer classes (Integer, LargeInteger and NativeInteger), all entries will be initialised to zero.
int
or long
), then the matrix elements will not be initialised to any particular value.rows | the number of rows in the new matrix. |
cols | the number of columns in the new matrix. |
|
inline |
Creates a new matrix that is a clone of the given matrix.
This constructor induces a deep copy of src.
src | the matrix to clone. |
|
inlinenoexcept |
Moves the given matrix into this new matrix.
This is a fast (constant time) operation.
The matrix that is passed (src) will no longer be usable.
src | the matrix to move. |
|
inline |
Destroys this matrix.
|
inline |
Adds the given source column to the given destination column.
This routine is only available when the template argument ring is true
.
source | the columns to add. |
dest | the column that will be added to. |
|
inline |
Adds the given number of copies of the given source column to the given destination column.
Note that copies is passed by value in case it is an element of the row to be changed.
This routine is only available when the template argument ring is true
.
source | the columns to add. |
dest | the column that will be added to. |
copies | the number of copies of source to add to dest. |
|
inline |
Adds the given source row to the given destination row.
This routine is only available when the template argument ring is true
.
source | the row to add. |
dest | the row that will be added to. |
|
inline |
Adds the given number of copies of the given source row to the given destination row.
Note that copies is passed by value in case it is an element of the row to be changed.
This routine is only available when the template argument ring is true
.
source | the row to add. |
dest | the row that will be added to. |
copies | the number of copies of source to add to dest. |
|
inline |
Returns the number of columns in this matrix.
|
inline |
Evaluates the determinant of the matrix.
This algorithm has quartic complexity, and uses the dynamic programming approach of Mahajan and Vinay. For further details, see Meena Mahajan and V. Vinay, "Determinant: Combinatorics, algorithms, and complexity", Chicago J. Theor. Comput. Sci., Vol. 1997, Article 5.
This routine is only available when the template argument ring is true
.
|
inherited |
Returns a detailed text representation of this object.
This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.
|
inline |
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. |
|
inline |
Divides all elements of the given row by the given integer.
This can only be used when the given integer divides into all row 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).
row | the index of the row whose elements should be divided by divBy. |
divBy | the integer to divide each row element by. |
|
inline |
Returns the entry at the given row and column.
Rows and columns are numbered beginning at zero.
matrix.entry(row, column) = value
still cannot be used in python to set a matrix element directly. For this, you can use the syntax matrix.set(row, column, value)
. This set() routine returns nothing, and is provided for python only (i.e., it is not part of the C++ calculation engine).row | the row of the desired entry. |
column | the column of the desired entry. |
|
inline |
Returns the entry at the given row and column.
Rows and columns are numbered beginning at zero.
row | the row of the desired entry. |
column | the column of the desired entry. |
|
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. |
|
inline |
Computes the greatest common divisor of all elements of the given row.
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).
row | the index of the row whose gcd should be computed. |
|
inlinestatic |
Returns an identity matrix of the given size.
The matrix returned will have size rows and size columns.
This routine is only available when the template argument ring is true
.
size | the number of rows and columns of the matrix to build. |
|
inline |
Sets every entry in the matrix to the given value.
value | the value to assign to each entry. |
void regina::Matrix< T, ring >::initialise | ( | List | allValues | ) |
A Python-only routine that fills the matrix with the given set of elements.
The argument allValues must be a Python list of length rows() * columns(). Its values will be inserted into the matrix row by row (i.e., the first row will be filled, then the second row, and so on).
allValues | the individual elements to place into the matrix. |
|
inline |
Determines whether this matrix is a square identity matrix.
If this matrix is square, isIdentity() will return true
if and only if the matrix has ones in the main diagonal and zeroes everywhere else.
If this matrix is not square, isIdentity() will always return false
(even if makeIdentity() was called earlier).
This routine is only available when the template argument ring is true
.
true
if and only if this is a square identity matrix.
|
inline |
Determines whether this is the zero matrix.
This routine is only available when the template argument ring is true
.
true
if and only if all entries in the matrix are zero.
|
inline |
Turns this matrix into an identity matrix.
This matrix need not be square; after this routine it will have entry(r,c)
equal to 1 if r == c
and 0 otherwise.
This routine is only available when the template argument ring is true
.
|
inline |
Multiplies the given column by the given factor.
Note that factor is passed by value in case it is an element of the row to be changed.
This routine is only available when the template argument ring is true
.
column | the column to work with. |
factor | the factor by which to multiply the given column. |
|
inline |
Deprecated alias for the multiplication operator.
Multiplies this by the given matrix, and returns a new matrix (of this same class) as a result. This matrix is not changed.
As of Regina 5.3, the template parameter MatrixClass has been removed, since Regina's old matrix class hierarchy has been replaced with a single Matrix class. It is harmless if you still pass a template parameter, but your parameter will be ignored.
This routine is only available when the template argument ring is true
.
\par Python
Not present.
other | the other matrix to multiply this matrix by. |
this * other
.
|
inline |
Multiplies the given row by the given factor.
Note that factor is passed by value in case it is an element of the row to be changed.
This routine is only available when the template argument ring is true
.
row | the row to work with. |
factor | the factor by which to multiply the given row. |
|
inline |
Determines whether this and the given matrix are different.
Two matrices are different if either (i) their dimensions differ, or (ii) the corresponding elements of each matrix differ in at least one location.
Note that this routine can happily deal with two matrices of different dimensions (in which case it will always return true
).
This routine returns true
if and only if the equality operator (==) returns false
.
other | the matrix to compare with this. |
true
if the matrices are different as described above, or false
otherwise.
|
inline |
Multiplies this by the given matrix, and returns the result.
This matrix is not changed.
This routine is only available when the template argument ring is true
.
other | the other matrix to multiply this matrix by. |
this * other
.
|
inline |
Copies the given matrix into this matrix.
It does not matter if this and the given matrix have different sizes; if they do then this matrix will be resized as a result.
This operator induces a deep copy of src.
src | the matrix to copy. |
|
inlinenoexcept |
Moves the given matrix into this matrix.
This is a fast (constant time) operation.
It does not matter if this and the given matrix have different sizes; if they do then this matrix will be resized as a result.
The matrix that is passed (src) will no longer be usable.
src | the matrix to move. |
|
inline |
Determines whether this and the given matrix are identical.
Two matrices are identical if and only if (i) their dimensions are the same, and (ii) the corresponding elements of each matrix are equal.
Note that this routine can happily deal with two matrices of different dimensions (in which case it will always return false
).
This routine returns true
if and only if the inequality operator (!=) returns false
.
other | the matrix to compare with this. |
true
if the matrices are equal as described above, or false
otherwise.
|
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. |
|
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. |
|
inline |
Returns the number of rows in this matrix.
|
inherited |
Returns a short text representation of this object.
This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
__str__()
.
|
inline |
Swaps the elements of the two given columns in the matrix.
first | the first column to swap. |
second | the second column to swap. |
|
inline |
Swaps the elements of the two given rows in the matrix.
first | the first row to swap. |
second | the second row to swap. |
|
inherited |
Returns a short text representation of this object using unicode characters.
Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.
|
inline |
Writes a complete representation of the matrix to the given output stream.
Each row will be written on a separate line with elements in each row separated by single spaces.
out | the output stream to which to write. |
|
inline |
Writes a detailed text representation of this object to the given output stream.
out | the output stream to which to write. |
|
inline |
Writes a short text representation of this object to the given output stream.
out | the output stream to which to write. |
|
staticinherited |
The multiplicative identity in the underlying ring.
|
staticinherited |
The additive identity in the underlying ring.