#include <permscale.h>
Inherits ScalingPermutation< T >< T >, and Matrix< T >< T >.
Inheritance diagram for PermScaleMatrix< T >:
Public Member Functions | |
| PermScaleMatrix () | |
| Default constructor; constructs a null permutation. | |
| PermScaleMatrix (itype n) | |
Constructs the identity permutation on n elements. | |
| PermScaleMatrix (const Permutation &other) | |
| Constructs the PermScaleMatrix corresponding to a given permutation, with identity scaling. | |
| PermScaleMatrix (const ScalingPermutation< T > &other) | |
| Quasi-copy Constructor; constructs the PermScaleMatrix corresponding to a given scaling permutation. | |
| PermScaleMatrix (const PermScaleMatrix< T > &other) | |
Copy Constructor; constructs a PermScaleMatrix identical to other. | |
| PermScaleMatrix (const std::vector< itype > &vec) | |
| Constructs a permutation from a STL vector of indices. | |
| PermScaleMatrix (const std::vector< itype > &vec, const std::vector< T > &scal) | |
| Constructs a permutation from a STL vector of indices, and an STL vector of scaling coefficients. | |
| virtual | ~PermScaleMatrix () |
| The destructor doesn't do anything. | |
| virtual itype | Rows () const |
| Returns the number of rows = size of permutation. (Mandatory override of pure virtual from Matrix). | |
| virtual itype | Columns () const |
| Returns the number of columns = size of permutation. (Mandatory override of pure virtual from Matrix). | |
| virtual itype | Size () const |
| Returns the number of nonzero elements = size of permutation. (Mandatory override of pure virtual from Matrix). | |
| virtual T & | operator() (itype r, itype c) |
| Returns a dummy copy of the requested element. (Mandatory override of pure virtual from Matrix). | |
| virtual T | operator() (itype r, itype c) const |
| Returns a copy of the requested element. (Mandatory override of pure virtual from Matrix). | |
| bool | isSquare () const |
| Identifies the matrix as being square. (Mirrors a method in DenseMatrix). | |
| T | Trace () const |
| Returns the trace, or sum of the diagonal elements. (Mirrors a method in DenseMatrix). | |
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PermScaleMatrix< typename linalg_traits< T >::conjugate_type > & | Conjugate () |
| Conjugates the matrix in place, and returns a reference to it. (Mirrors a method in DenseMatrix). | |
| linalg_traits< T >::norm_type | Norm () |
Returns the square of the 2-norm = Tr( Adjoint(M).M). (Mirrors a method in DenseMatrix). | |
| linalg_traits< T >::abs_type | Abs () |
Returns the 2-norm = sqrt( Tr( Adjoint(M).M) ). (Mirrors a method in DenseMatrix). | |
| PermScaleMatrix< T > & | Normalize () |
| Normalizes the matrix, so that Norm() and Abs() will return 1. (Mirrors a method in DenseMatrix). | |
| PermScaleMatrix< T > & | operator *= (T scalar) |
| Multiplies the matrix by a scalar, and returns a reference. (Mirrors a method in DenseMatrix). | |
| PermScaleMatrix< T > & | operator/= (T scalar) |
| Divides the matrix by a scalar, and returns a reference. (Mirrors a method in DenseMatrix). | |
| T | Scale (itype i) const |
| void | SetScale (itype i, complex s) |
| ScalingPermutation & | reset () |
| ScalingPermutation & | reset (itype newsize) |
| ScalingPermutation & | swap (itype i, itype j) |
| ScalingPermutation & | operator *= (const ScalingPermutation &other) |
| ScalingPermutation & | operator *= (const Permutation &other) |
| ScalingPermutation | inverse () const |
| void | Print (std::ostream &out=std::cout) const |
| bool | operator== (const Permutation &other) const |
| bool | operator== (const ScalingPermutation &other) const |
| ScalingPermutation | operator * (const Permutation &two) const |
| ScalingPermutation | operator * (const ScalingPermutation &two) const |
| itype | operator[] (itype n) const |
| void | PrintCycles (std::ostream &out=std::cout) const |
| Permutation & | randomize () |
| virtual void | print (std::ostream &os=std::cout) const |
| Prettyprints the Matrix to a stream, but without justification. | |
Protected Member Functions | |
| bool | badrange (itype i) const |
| bool | valid () const |
Protected Attributes | |
| T * | scale |
| itype * | map |
C-style array containing the action of the permutation as: ![$ i \rightarrow \mathrm{map}[i] $](form_141.png) . | |
| itype | N |
PermScaleMatrix defines the class of square matrices where each row and each column have exactly one element. The action of a PermScaleMatrix on a vector is thus to permute the elements, and scale each one by some constant factor. These matrices are closed under multiplication, and therefore form a semigroup.
PermScaleMatrix objects can be constructed from:
N (creates the N-dimensional identity matrix)PermScaleMatrix objects have all the inherited functionality of a Permutation or ScalingPermutation. They also support a restricted subset of basic linear algebra (although since they inherit from Matrix, they can always be converted to a DenseMatrix). Things you can do with a PermScaleMatrix include:
Note that you cannot add or subtract two PermScaleMatrix objects -- the result iss not a PermScaleMatrix. To do so, convert first to DenseMatrix.
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Returns a dummy copy of the requested element. (Mandatory override of pure virtual from Matrix). If the requested element is not one of the nonzero ones, then we have to return a reference to a dummy. However, it's not clear what we should do if the requested element is nonzero. Currently we return a dummy copy of the element, so that it's not possible to change an element directly. This behavior is open to debate -- as it stands, we cannot change an element directly, although it could be done rather awkwardly through multiplication by another matrix. Implements Matrix< T >. |
1.4.4