Regina Calculation Engine
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Represents a matrix of arbitrary precision integers. More...
#include <maths/nmatrixint.h>
Public Member Functions | |
NMatrixInt (unsigned long rows, unsigned long cols) | |
Creates a new matrix of the given size. More... | |
NMatrixInt (const NMatrixInt &cloneMe) | |
Creates a new matrix that is a clone of the given matrix. More... | |
void | divRowExact (unsigned long row, const NLargeInteger &divBy) |
Divides all elements of the given row by the given integer. More... | |
void | divColExact (unsigned long col, const NLargeInteger &divBy) |
Divides all elements of the given column by the given integer. More... | |
NLargeInteger | gcdRow (unsigned long row) |
Computes the greatest common divisor of all elements of the given row. More... | |
NLargeInteger | 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... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format 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, NLargeIntegercopies) |
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, NLargeIntegercopies) |
Adds the given number of copies of the given source column to the given destination column. More... | |
void | multRow (unsigned long row, NLargeIntegerfactor) |
Multiplies the given row by the given factor. More... | |
void | multCol (unsigned long column, NLargeIntegerfactor) |
Multiplies the given column by the given factor. More... | |
std::auto_ptr< NMatrixRing < NLargeInteger > > | operator* (const NMatrixRing< NLargeInteger > &other) const |
Multiplies this by the given matrix, and returns the result. More... | |
std::auto_ptr< MatrixClass > | multiplyAs (const NMatrixRing< NLargeInteger > &other) const |
Multiplies this by the given matrix, and returns a new matrix of subclass MatrixClass. More... | |
NLargeInteger | det () const |
Evaluates the determinant of the matrix. More... | |
void | initialise (const NLargeInteger &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... | |
NLargeInteger & | entry (unsigned long row, unsigned long column) |
Returns the entry at the given row and column. More... | |
const NLargeInteger & | entry (unsigned long row, unsigned long column) const |
Returns the entry at the given row and column. More... | |
bool | operator== (const NMatrix< NLargeInteger > &other) const |
Determines whether this and the given matrix are identical. More... | |
bool | operator!= (const NMatrix< NLargeInteger > &other) const |
Determines whether this and the given matrix are different. More... | |
virtual 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... | |
Input and Output | |
std::string | str () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toString () const |
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More... | |
std::string | detail () const |
Returns the output from writeTextLong() as a string. More... | |
std::string | toStringLong () const |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More... | |
Static Public Attributes | |
static NLargeInteger | zero |
Zero in the underlying ring. More... | |
static NLargeInteger | one |
One (the multiplicative identity) in the underlying ring. More... | |
Protected Attributes | |
unsigned long | nRows |
The number of rows in the matrix. More... | |
unsigned long | nCols |
The number of columns in the matrix. More... | |
NLargeInteger ** | data |
The actual entries in the matrix. More... | |
Represents a matrix of arbitrary precision integers.
Calculations will be exact no matter how large the integers become.
Note that many important functions (such as entry()) are inherited from the superclasses NMatrix and NMatrixRing, and are not documented again here. Many other algorithms that work on the NMatrixInt class are available in the maths/matrixops.h file.
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inlineinherited |
Adds the given source column to the given destination column.
source | the columns to add. |
dest | the column that will be added to. |
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inlineinherited |
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.
source | the columns to add. |
dest | the column that will be added to. |
copies | the number of copies of source to add to dest. |
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inlineinherited |
Adds the given source row to the given destination row.
source | the row to add. |
dest | the row that will be added to. |
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inlineinherited |
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.
source | the row to add. |
dest | the row that will be added to. |
copies | the number of copies of source to add to dest. |
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inlineinherited |
Returns the number of columns in this matrix.
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inlineinherited |
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.
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inherited |
Returns the output from writeTextLong() as a string.
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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), and is much faster than ordinary division.
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 |
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), and is much faster than ordinary division.
row | the index of the row whose elements should be divided by divBy. |
divBy | the integer to divide each row element by. |
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inlineinherited |
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. |
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inlineinherited |
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. |
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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.
col | the index of the column whose gcd should be computed. |
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inline |
Computes the greatest common divisor of all elements of the given row.
The value returned is guaranteed to be non-negative.
row | the index of the row whose gcd should be computed. |
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inlineinherited |
Sets every entry in the matrix to the given value.
value | the value to assign to each entry. |
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inherited |
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. |
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inlineinherited |
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).
true
if and only if this is a square identity matrix.
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inlineinherited |
Determines whether this is the zero matrix.
true
if and only if all entries in the matrix are zero.
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inlineinherited |
Turns this matrix into an identity matrix.
This matrix need not be square; after this routine it will have entry(r,c)
equal to one
if r == c
and zero
otherwise.
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inlineinherited |
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.
column | the column to work with. |
factor | the factor by which to multiply the given column. |
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inlineinherited |
Multiplies this by the given matrix, and returns a new matrix of subclass MatrixClass.
This matrix is not changed.
other | the matrix by which to multiply this matrix. |
this * other
.
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inlineinherited |
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.
row | the row to work with. |
factor | the factor by which to multiply the given row. |
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inlineinherited |
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.
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inlineinherited |
Multiplies this by the given matrix, and returns the result.
This matrix is not changed.
other | the matrix by which to multiply this matrix. |
this * other
.
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inlineinherited |
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.
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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.
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.
row | the index of the row to reduce. |
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inlineinherited |
Returns the number of rows in this matrix.
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inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
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inlineinherited |
Swaps the elements of the two given columns in the matrix.
first | the first column to swap. |
second | the second column to swap. |
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inlineinherited |
Swaps the elements of the two given rows in the matrix.
first | the first row to swap. |
second | the second row to swap. |
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inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
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inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
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inlinevirtualinherited |
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. |
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protectedinherited |
The actual entries in the matrix.
data[r][c]
is the element in row r, column c.
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protectedinherited |
The number of columns in the matrix.
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protectedinherited |
The number of rows in the matrix.
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staticinherited |
One (the multiplicative identity) in the underlying ring.
This would be const
if it weren't for the fact that some compilers don't like this. It should never be modified!
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staticinherited |
Zero in the underlying ring.
This would be const
if it weren't for the fact that some compilers don't like this. It should never be modified!