LAPACKFullMatrix< number > Class Template Reference
[Basic matrices]

Inheritance diagram for LAPACKFullMatrix< number >:
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List of all members.

Public Member Functions

 LAPACKFullMatrix (const unsigned int n=0)
 LAPACKFullMatrix (const unsigned int rows, const unsigned int cols)
 LAPACKFullMatrix (const LAPACKFullMatrix &)
LAPACKFullMatrix< number > & operator= (const LAPACKFullMatrix< number > &)
template<typename number2 >
LAPACKFullMatrix< number > & operator= (const FullMatrix< number2 > &)
LAPACKFullMatrix< number > & operator= (const double d)
template<class MATRIX >
void copy_from (const MATRIX &)
template<class MATRIX >
void fill (const MATRIX &src, const unsigned int dst_offset_i=0, const unsigned int dst_offset_j=0, const unsigned int src_offset_i=0, const unsigned int src_offset_j=0, const number factor=1., const bool transpose=false)
void vmult (Vector< number > &w, const Vector< number > &v, const bool adding=false) const
void vmult_add (Vector< number > &w, const Vector< number > &v) const
void Tvmult (Vector< number > &w, const Vector< number > &v, const bool adding=false) const
void Tvmult_add (Vector< number > &w, const Vector< number > &v) const
void compute_lu_factorization ()
void invert ()
void apply_lu_factorization (Vector< number > &v, const bool transposed) const
void compute_eigenvalues (const bool right_eigenvectors=false, const bool left_eigenvectors=false)
std::complex< number > eigenvalue (const unsigned int i) const
void print_formatted (std::ostream &out, const unsigned int presicion=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1., const double threshold=0.) const

Private Attributes

LAPACKSupport::State state
LAPACKSupport::Properties properties
std::vector< number > work
std::vector< intipiv
std::vector< number > inv_work
std::vector< number > wr
std::vector< number > wi
std::vector< number > vl
std::vector< number > vr

Detailed Description

template<typename number>
class LAPACKFullMatrix< number >

A variant of FullMatrix using LAPACK functions whereever possible. In order to do this, the matrix is stored in transposed order. The element access functions hide this fact by reverting the transposition.

Note:
In order to perform LAPACK functions, the class contains a lot of auxiliary data in the private section. The names of these data vectors are usually the names chosen for the arguments in the LAPACK documentation.
Author:
Guido Kanschat, 2005

Constructor & Destructor Documentation

template<typename number>
LAPACKFullMatrix< number >::LAPACKFullMatrix ( const unsigned int  n = 0  )  [explicit]

Constructor. Initialize the matrix as a square matrix with dimension n.

In order to avoid the implicit conversion of integers and other types to a matrix, this constructor is declared explicit.

By default, no memory is allocated.

template<typename number>
LAPACKFullMatrix< number >::LAPACKFullMatrix ( const unsigned int  rows,
const unsigned int  cols 
)

Constructor. Initialize the matrix as a rectangular matrix.

template<typename number>
LAPACKFullMatrix< number >::LAPACKFullMatrix ( const LAPACKFullMatrix< number > &   ) 

Copy constructor. This constructor does a deep copy of the matrix. Therefore, it poses a possible efficiency problem, if for example, function arguments are passed by value rather than by reference. Unfortunately, we can't mark this copy constructor explicit, since that prevents the use of this class in containers, such as std::vector. The responsibility to check performance of programs must therefore remain with the user of this class.


Member Function Documentation

template<typename number>
LAPACKFullMatrix<number>& LAPACKFullMatrix< number >::operator= ( const LAPACKFullMatrix< number > &   ) 

Assignment operator.

Reimplemented from Subscriptor.

template<typename number>
template<typename number2 >
LAPACKFullMatrix<number>& LAPACKFullMatrix< number >::operator= ( const FullMatrix< number2 > &   )  [inline]

Assignment operator for a regular FullMatrix.

template<typename number>
LAPACKFullMatrix<number>& LAPACKFullMatrix< number >::operator= ( const double  d  ) 

This operator assigns a scalar to a matrix. To avoid confusion with constructors, zero is the only value allowed for d

template<typename number >
template<class MATRIX >
void LAPACKFullMatrix< number >::copy_from ( const MATRIX &  M  )  [inline]

Assignment from different matrix classes. This assignment operator uses iterators of the class MATRIX. Therefore, sparse matrices are possible sources.

References TransposeTable< number >::el(), LAPACKSupport::matrix, TransposeTable< number >::reinit(), and LAPACKFullMatrix< number >::state.

template<typename number >
template<class MATRIX >
void LAPACKFullMatrix< number >::fill ( const MATRIX &  src,
const unsigned int  dst_offset_i = 0,
const unsigned int  dst_offset_j = 0,
const unsigned int  src_offset_i = 0,
const unsigned int  src_offset_j = 0,
const number  factor = 1.,
const bool  transpose = false 
) [inline]

Fill rectangular block.

A rectangular block of the matrix src is copied into this. The upper left corner of the block being copied is (src_offset_i,src_offset_j). The upper left corner of the copied block is (dst_offset_i,dst_offset_j). The size of the rectangular block being copied is the maximum size possible, determined either by the size of this or src.

The final two arguments allow to enter a multiple of the source or its transpose.

References LAPACKSupport::matrix, TransposeTable< number >::n_cols(), TransposeTable< number >::n_rows(), and LAPACKFullMatrix< number >::state.

template<typename number>
void LAPACKFullMatrix< number >::vmult ( Vector< number > &  w,
const Vector< number > &  v,
const bool  adding = false 
) const

Matrix-vector-multiplication.

The optional parameter adding determines, whether the result is stored in w or added to w.

if (adding) w += A*v

if (!adding) w = A*v

Source and destination must not be the same vector.

template<typename number>
void LAPACKFullMatrix< number >::vmult_add ( Vector< number > &  w,
const Vector< number > &  v 
) const

Adding Matrix-vector-multiplication. w += A*v

Source and destination must not be the same vector.

template<typename number>
void LAPACKFullMatrix< number >::Tvmult ( Vector< number > &  w,
const Vector< number > &  v,
const bool  adding = false 
) const

Transpose matrix-vector-multiplication.

The optional parameter adding determines, whether the result is stored in w or added to w.

if (adding) w += AT*v

if (!adding) w = AT*v

Source and destination must not be the same vector.

template<typename number>
void LAPACKFullMatrix< number >::Tvmult_add ( Vector< number > &  w,
const Vector< number > &  v 
) const

Adding transpose matrix-vector-multiplication. w += AT*v

Source and destination must not be the same vector.

template<typename number>
void LAPACKFullMatrix< number >::compute_lu_factorization (  ) 

Compute the LU factorization of the matrix using LAPACK function Xgetrf.

template<typename number>
void LAPACKFullMatrix< number >::invert (  ) 

Invert the matrix by first computing an LU factorization with the LAPACK function Xgetrf and then building the actual inverse using Xgetri.

template<typename number>
void LAPACKFullMatrix< number >::apply_lu_factorization ( Vector< number > &  v,
const bool  transposed 
) const

Solve the linear system with right hand side given by applying forward/backward substitution to the previously computed LU factorization. Uses LAPACK function Xgetrs.

template<typename number>
void LAPACKFullMatrix< number >::compute_eigenvalues ( const bool  right_eigenvectors = false,
const bool  left_eigenvectors = false 
)

Compute eigenvalues of the matrix. After this routine has been called, eigenvalues can be retrieved using the eigenvalue() function. The matrix itself will be LAPACKSupport::unusable after this operation.

The optional arguments allow to compute left and right eigenvectors as well.

Note that the function does not return the computed eigenvalues right away since that involves copying data around between the output arrays of the LAPACK functions and any return array. This is often unnecessary since one may not be interested in all eigenvalues at once, but for example only the extreme ones. In that case, it is cheaper to just have this function compute the eigenvalues and have a separate function that returns whatever eigenvalue is requested.

Note:
Calls the LAPACK function Xgeev.
template<typename number >
std::complex< number > LAPACKFullMatrix< number >::eigenvalue ( const unsigned int  i  )  const [inline]
template<typename number>
void LAPACKFullMatrix< number >::print_formatted ( std::ostream &  out,
const unsigned int  presicion = 3,
const bool  scientific = true,
const unsigned int  width = 0,
const char *  zero_string = " ",
const double  denominator = 1.,
const double  threshold = 0. 
) const

Print the matrix and allow formatting of entries.

The parameters allow for a flexible setting of the output format:

  • precision denotes the number of trailing digits.
  • scientific is used to determine the number format, where scientific = false means fixed point notation.
  • width denotes the with of each column. A zero entry for width makes the function compute a width, but it may be changed to a positive value, if output is crude.
  • zero_string specifies a string printed for zero entries.
  • denominator Multiply the whole matrix by this common denominator to get nicer numbers.
  • threshold: all entries with absolute value smaller than this are considered zero.

Member Data Documentation

template<typename number>
LAPACKSupport::State LAPACKFullMatrix< number >::state [private]

Since LAPACK operations notoriously change the meaning of the matrix entries, we record the current state after the last operation here.

Referenced by LAPACKFullMatrix< number >::copy_from(), LAPACKFullMatrix< number >::eigenvalue(), and LAPACKFullMatrix< number >::fill().

template<typename number>
LAPACKSupport::Properties LAPACKFullMatrix< number >::properties [private]

Additional properties of the matrix which may help to select more efficient LAPACK functions.

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::work [mutable, private]

The working array used for some LAPACK functions.

template<typename number>
std::vector<int> LAPACKFullMatrix< number >::ipiv [private]

The vector storing the permutations applied for pivoting in the LU-factorization.

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::inv_work [private]

Workspace for calculating the inverse matrix from an LU factorization.

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::wr [private]

Real parts of eigenvalues. Filled by compute_eigenvalues.

Referenced by LAPACKFullMatrix< number >::eigenvalue().

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::wi [private]

Imaginary parts of eigenvalues. Filled by compute_eigenvalues.

Referenced by LAPACKFullMatrix< number >::eigenvalue().

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::vl [private]

Space where left eigenvectors can be stored.

template<typename number>
std::vector<number> LAPACKFullMatrix< number >::vr [private]

Space where right eigenvectors can be stored.


The documentation for this class was generated from the following file:

deal.II documentation generated on Mon Nov 23 22:57:52 2009 by doxygen 1.6.1