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fmatvec Namespace Reference

Namespace fmatvec. More...

Classes

class  Atom
 
class  Matrix< GeneralBand, Ref, Ref, AT >
 This is a matrix class for general band matrices. More...
 
class  Matrix< Diagonal, Ref, Ref, AT >
 This is a matrix class for diagonal matrices. More...
 
class  Matrix< General, Fixed< M >, Fixed< N >, AT >
 This is a matrix class for general matrices. More...
 
class  Matrix< Rotation, Fixed< M >, Fixed< M >, double >
 
class  RowVector< Fixed< N >, AT >
 This is a rowvector class of general shape in dense storage format. More...
 
class  SquareMatrix< Fixed< M >, AT >
 This is a matrix class of general quadratic matrices. More...
 
class  Matrix< Symmetric, Fixed< M >, Fixed< M >, AT >
 This is a matrix class for symmetric matrices. More...
 
class  Matrix< General, Fixed< M >, Var, AT >
 This is a matrix class for general matrices. More...
 
class  Vector< Fixed< M >, AT >
 This is a vector class of general shape in dense storage format. More...
 
class  ErrorType
 
struct  Size
 
struct  Size< double >
 Defines the size type of a double as int. More...
 
struct  Size< Vector< Shape, double > >
 Defines the size type of a (column) vector as int. More...
 
struct  Size< RowVector< Shape, double > >
 Defines the size type of a row vector as int. More...
 
struct  Size< Matrix< Type, RowShape, ColShape, double > >
 Defines the size type of a matrix as a fixed size vector of type int (two integers). More...
 
struct  StaticSize
 
struct  StaticSize< double >
 Defines the static size (dimension) of a double. More...
 
struct  StaticSize< Vector< Shape, AT > >
 Defines the static size (dimension) of a vector. More...
 
struct  StaticSize< RowVector< Shape, AT > >
 Defines the static size (dimension) of a row vector. More...
 
struct  StaticSize< Vector< Fixed< N >, AT > >
 Defines the static size (dimension) of a fixed vector. More...
 
struct  StaticSize< RowVector< Fixed< N >, AT > >
 Defines the static size (dimension) of a fixed rowvector. More...
 
struct  StaticSize< Matrix< Storage, Fixed< N >, Fixed< M >, AT > >
 Defines the static size (dimension) of a fixed matrix. More...
 
struct  StaticSize< Matrix< Storage, Fixed< N >, ColShape, AT > >
 Defines the static size (dimension) of a partial fixed matrix. More...
 
struct  StaticSize< Matrix< Storage, RowShape, Fixed< M >, AT > >
 Defines the static size (dimension) of a partial fixed matrix. More...
 
struct  Der
 
struct  Der< Dep, double >
 
struct  Der< double, Vector< IndepVecShape, double > >
 
struct  Der< Vector< DepVecShape, double >, Vector< IndepVecShape, double > >
 
struct  Der< Matrix< Rotation, DepMatShape, DepMatShape, double >, double >
 
struct  Der< Matrix< Rotation, DepMatShape, DepMatShape, double >, Vector< IndepVecShape, double > >
 
class  Function
 
class  Function< Ret(Arg)>
 A function object with 1 argument. More...
 
class  Function< Ret(Arg1, Arg2)>
 A function object with 2 arguments. More...
 
class  Matrix< General, Ref, Ref, AT >
 This is a matrix class for general matrices. More...
 
class  Index
 This is an index class for creating submatrices. More...
 
class  Noinit
 
class  Init
 
class  Eye
 
class  Matrix
 This is the basic matrix class for arbitrary matrices. More...
 
class  SquareMatrix
 
class  Vector
 
class  RowVector
 
class  Range
 This is an index class for creating submatrices. More...
 
class  Range< Var, Var >
 This is an index class for creating submatrices. More...
 
class  Range< Fixed< I1 >, Fixed< I2 > >
 This is an index class for creating submatrices. More...
 
class  RowVector< Ref, AT >
 This is a rowvector class of general shape in dense storage format. More...
 
class  Matrix< Sparse, Ref, Ref, AT >
 This is a matrix class for sparse quadratic matrices. More...
 
class  SquareMatrix< Ref, AT >
 This is a matrix class of general quadratic matrices. More...
 
class  Matrix< Symmetric, Ref, Ref, AT >
 This is a matrix class for symmetric matrices. More...
 
class  Ref
 
class  Var
 
class  Fixed
 
class  General
 Basic shape class for matrices. More...
 
class  GeneralBand
 Shape class for general band matrices. More...
 
class  Symmetric
 Shape class for symmetric matrices. More...
 
class  Rotation
 Shape class for rotation matrices. More...
 
class  Diagonal
 Shape class for diagonal matrices. More...
 
class  Sparse
 Shape class for sparse matrices. More...
 
class  Matrix< General, Var, Fixed< N >, AT >
 This is a matrix class for general matrices. More...
 
class  Matrix< General, Var, Var, AT >
 This is a matrix class for general matrices. More...
 
class  RowVector< Var, AT >
 This is a vector class of general shape in dense storage format. More...
 
class  SquareMatrix< Var, AT >
 This is a matrix class of general quadratic matrices. More...
 
class  Matrix< Symmetric, Var, Var, AT >
 This is a matrix class for symmetric matrices. More...
 
class  Vector< Var, AT >
 This is a vector class of general shape in dense storage format. More...
 
class  Vector< Ref, AT >
 This is a vector class of general shape in dense storage format. More...
 

Typedefs

typedef Matrix< General, Ref,
Ref, double > 
Mat
 General matrix. More...
 
typedef Vector< Ref, double > Vec
 Vector. More...
 
typedef RowVector< Ref, double > RowVec
 Row vector. More...
 
typedef SquareMatrix< Ref, double > SqrMat
 Square matrix. More...
 
typedef Matrix< Diagonal, Ref,
Ref, double > 
DiagMat
 Diagonal matrix. More...
 
typedef Matrix< Symmetric, Ref,
Ref, double > 
SymMat
 Symmetric matrix. More...
 
typedef Matrix< GeneralBand,
Ref, Ref, double > 
BandMat
 Band matrix. More...
 
typedef Matrix< Sparse, Ref,
Ref, double > 
SparseMat
 
typedef Vector< Ref, int > VecInt
 
typedef Vector< Var, int > VecVI
 
typedef Vector< Fixed
< 1 >, double > 
Vec1
 
typedef Vector< Fixed
< 2 >, double > 
Vec2
 
typedef Vector< Fixed< 2 >, int > Vec2I
 
typedef Vector< Fixed
< 3 >, double > 
Vec3
 
typedef Vector< Fixed
< 4 >, double > 
Vec4
 
typedef Vector< Fixed
< 11 >, double > 
Vec11
 
typedef Vector< Fixed
< 16 >, double > 
Vec16
 
typedef RowVector< Fixed
< 1 >, double > 
RowVec1
 
typedef RowVector< Fixed
< 2 >, double > 
RowVec2
 
typedef RowVector< Fixed
< 3 >, double > 
RowVec3
 
typedef RowVector< Fixed
< 4 >, double > 
RowVec4
 
typedef RowVector< Fixed
< 11 >, double > 
RowVec11
 
typedef RowVector< Fixed
< 16 >, double > 
RowVec16
 
typedef Matrix< General, Fixed
< 3 >, Fixed< 3 >, double > 
Mat3x3
 
typedef Matrix< General, Fixed
< 3 >, Fixed< 2 >, double > 
Mat3x2
 
typedef Matrix< General, Fixed
< 3 >, Fixed< 11 >, double > 
Mat3x11
 
typedef Matrix< General, Fixed
< 3 >, Fixed< 16 >, double > 
Mat3x16
 
typedef Matrix< General, Fixed
< 4 >, Fixed< 16 >, double > 
Mat4x16
 
typedef Matrix< General, Fixed
< 16 >, Fixed< 3 >, double > 
Mat16x3
 
typedef Matrix< General, Fixed
< 16 >, Fixed< 4 >, double > 
Mat16x4
 
typedef SquareMatrix< Fixed
< 1 >, double > 
SqrMat1
 
typedef SquareMatrix< Fixed
< 2 >, double > 
SqrMat2
 
typedef SquareMatrix< Fixed
< 3 >, double > 
SqrMat3
 
typedef SquareMatrix< Fixed
< 11 >, double > 
SqrMat11
 
typedef SquareMatrix< Fixed
< 16 >, double > 
SqrMat16
 
typedef Matrix< Symmetric,
Fixed< 3 >, Fixed< 3 >, double > 
SymMat3
 
typedef Matrix< Symmetric,
Fixed< 4 >, Fixed< 4 >, double > 
SymMat4
 
typedef Matrix< Symmetric, Var,
Var, double > 
SymMatV
 
typedef Matrix< General, Var,
Var, double > 
MatV
 
typedef Matrix< General, Var,
Var, int > 
MatVI
 
typedef SquareMatrix< Var, double > SqrMatV
 
typedef Vector< Var, double > VecV
 
typedef RowVector< Var, double > RowVecV
 
typedef RowVector< Var, int > RowVecVI
 
typedef Matrix< Rotation,
Fixed< 3 >, Fixed< 3 >, double > 
RotMat3
 
typedef Matrix< General, Fixed
< 2 >, Var, double > 
Mat2xV
 
typedef Matrix< General, Var,
Fixed< 2 >, int > 
MatVx2I
 
typedef Matrix< General, Fixed
< 3 >, Var, double > 
Mat3xV
 
typedef Matrix< General, Fixed
< 3 >, Var, int > 
Mat3xVI
 
typedef Matrix< General, Var,
Fixed< 2 >, double > 
MatVx2
 
typedef Matrix< General, Var,
Fixed< 3 >, double > 
MatVx3
 
typedef Matrix< General, Var,
Fixed< 3 >, int > 
MatVx3I
 
typedef Range< Var, VarIndex
 

Functions

bool operator== (const Index &I, const Index &J)
 Equality operator for indices. More...
 
template<class AT >
Vector< Ref, AT > operator+ (const Vector< Ref, AT > &x, const Vector< Ref, AT > &y)
 Vector-vector addition. More...
 
template<class Row1 , class Row2 , class Row3 , class AT >
void add (const Vector< Row1, AT > &a1, const Vector< Row2, AT > &a2, Vector< Row3, AT > &a3)
 
template<class Row1 , class Row2 , class AT >
void add (Vector< Row1, AT > &a1, const Vector< Row2, AT > &a2)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void sub (const Vector< Row1, AT > &a1, const Vector< Row2, AT > &a2, Vector< Row3, AT > &a3)
 
template<class Row1 , class Row2 , class AT >
void sub (Vector< Row1, AT > &a1, const Vector< Row2, AT > &a2)
 
template<class AT , class Row1 , class Row2 >
Vector< Var, AT > operator+ (const Vector< Row1, AT > &a, const Vector< Row2, AT > &b)
 
template<class AT , class Row >
Vector< Row, AT > operator+ (const Vector< Row, AT > &a, const Vector< Row, AT > &b)
 
template<class AT , int M, class Row >
Vector< Fixed< M >, AT > operator+ (const Vector< Fixed< M >, AT > &a, const Vector< Row, AT > &b)
 
template<class AT , int M>
Vector< Fixed< M >, AT > operator+ (const Vector< Fixed< M >, AT > &a, const Vector< Fixed< M >, AT > &b)
 
template<class AT , class Row1 , class Row2 >
Vector< Row1, AT > operator+= (const Vector< Row1, AT > &a_, const Vector< Row2, AT > &b)
 
template<class AT , class Row1 , class Row2 >
Vector< Var, AT > operator- (const Vector< Row1, AT > &a, const Vector< Row2, AT > &b)
 // Subtraction
 
template<class AT , class Row >
Vector< Row, AT > operator- (const Vector< Row, AT > &a, const Vector< Row, AT > &b)
 
template<class AT , int M, class Row2 >
Vector< Fixed< M >, AT > operator- (const Vector< Fixed< M >, AT > &a, const Vector< Row2, AT > &b)
 
template<class AT , int M>
Vector< Fixed< M >, AT > operator- (const Vector< Fixed< M >, AT > &a, const Vector< Fixed< M >, AT > &b)
 
template<class AT , class Row1 , class Row2 >
Vector< Row1, AT > operator-= (const Vector< Row1, AT > &a_, const Vector< Row2, AT > &b)
 
template<class Col1 , class Col2 , class Col3 , class AT >
void add (const RowVector< Col1, AT > &a1, const RowVector< Col2, AT > &a2, RowVector< Col3, AT > &a3)
 
template<class Col1 , class Col2 , class AT >
void add (RowVector< Col1, AT > &a1, const RowVector< Col2, AT > &a2)
 
template<class Col1 , class Col2 , class Col3 , class AT >
void sub (const RowVector< Col1, AT > &a1, const RowVector< Col2, AT > &a2, RowVector< Col3, AT > &a3)
 
template<class Col1 , class Col2 , class AT >
void sub (RowVector< Col1, AT > &a1, const RowVector< Col2, AT > &a2)
 
template<class AT , class Col1 , class Col2 >
RowVector< Var, AT > operator+ (const RowVector< Col1, AT > &a, const RowVector< Col2, AT > &b)
 
template<class AT , class Col >
RowVector< Col, AT > operator+ (const RowVector< Col, AT > &a, const RowVector< Col, AT > &b)
 
template<class AT , int N, class Col2 >
RowVector< Fixed< N >, AT > operator+ (const RowVector< Fixed< N >, AT > &a, const RowVector< Col2, AT > &b)
 
template<class AT , int N>
RowVector< Fixed< N >, AT > operator+ (const RowVector< Fixed< N >, AT > &a, const RowVector< Fixed< N >, AT > &b)
 
template<class AT , class Col1 , class Col2 >
RowVector< Col1, AT > operator+= (const RowVector< Col1, AT > &a_, const RowVector< Col2, AT > &b)
 
template<class AT , class Col1 , class Col2 >
RowVector< Var, AT > operator- (const RowVector< Col1, AT > &a, const RowVector< Col2, AT > &b)
 // Subtraction
 
template<class AT , class Col >
RowVector< Col, AT > operator- (const RowVector< Col, AT > &a, const RowVector< Col, AT > &b)
 
template<class AT , int N, class Col2 >
RowVector< Fixed< N >, AT > operator- (const RowVector< Fixed< N >, AT > &a, const RowVector< Col2, AT > &b)
 
template<class AT , int N>
RowVector< Fixed< N >, AT > operator- (const RowVector< Fixed< N >, AT > &a, const RowVector< Fixed< N >, AT > &b)
 
template<class AT , class Col1 , class Col2 >
RowVector< Col1, AT > operator-= (const RowVector< Col1, AT > &a_, const RowVector< Col2, AT > &b)
 
template<class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 , class Type3 , class Row3 , class Col3 , class AT >
void add (const Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2, Matrix< Type3, Row3, Col3, AT > &A3)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void add (const Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Symmetric, Row2, Row2, AT > &A2, Matrix< Symmetric, Row3, Row3, AT > &A3)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void add (const Matrix< Diagonal, Row1, Row1, AT > &A1, const Matrix< Diagonal, Row2, Row2, AT > &A2, Matrix< Diagonal, Row3, Row3, AT > &A3)
 
template<class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 , class AT >
void add (Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2)
 
template<class Row1 , class Row2 , class AT >
void add (Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Symmetric, Row2, Row2, AT > &A2)
 
template<class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 , class Type3 , class Row3 , class Col3 , class AT >
void sub (const Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2, Matrix< Type3, Row3, Col3, AT > &A3)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void sub (const Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Symmetric, Row2, Row2, AT > &A2, Matrix< Symmetric, Row3, Row3, AT > &A3)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void sub (const Matrix< Diagonal, Row1, Row1, AT > &A1, const Matrix< Diagonal, Row2, Row2, AT > &A2, Matrix< Diagonal, Row3, Row3, AT > &A3)
 
template<class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 , class AT >
void sub (Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2)
 
template<class Row1 , class Row2 , class AT >
void sub (Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Symmetric, Row2, Row2, AT > &A2)
 
template<class AT , class Type1 , class Type2 , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< General, Var, Var, AT > operator+ (const Matrix< Type1, Row1, Col1, AT > &A, const Matrix< Type2, Row2, Col2, AT > &B)
 
template<class AT , class Type1 , class Type2 , class Row , class Col >
Matrix< General, Row, Col, AT > operator+ (const Matrix< Type1, Row, Col, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Var, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Var, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Var, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Var, AT > &A, const Matrix< Type2, Fixed< M >, Var, AT > &B)
 
template<class AT , int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Var, Fixed< N >
, AT > 
operator+ (const Matrix< Type1, Var, Fixed< N >, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int N, class Type1 , class Type2 >
Matrix< General, Var, Fixed< N >
, AT > 
operator+ (const Matrix< Type1, Var, Fixed< N >, AT > &A, const Matrix< Type2, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Fixed< M >, Var, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type2, Row, Col, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type2, Fixed< M >, Var, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type2, Var, Fixed< N >, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , class Type , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< Type, Var, Var, AT > operator+ (const Matrix< Type, Row1, Col1, AT > &A, const Matrix< Type, Row2, Col2, AT > &B)
 
template<class AT , class Type , class Row , class Col >
Matrix< Type, Row, Col, AT > operator+ (const Matrix< Type, Row, Col, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, class Type , class Row , class Col >
Matrix< Type, Fixed< M >, Var, AT > operator+ (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, class Type >
Matrix< Type, Fixed< M >, Var, AT > operator+ (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Fixed< M >, Var, AT > &B)
 
template<class AT , int N, class Type , class Row , class Col >
Matrix< Type, Var, Fixed< N >, AT > operator+ (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int N, class Type >
Matrix< Type, Var, Fixed< N >, AT > operator+ (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type , class Row , class Col >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Var, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type , class Row , class Col >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Row, Col, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator+ (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
Matrix< Type1, Row1, Col1, AT > & operator+= (const Matrix< Type1, Row1, Col1, AT > &A_, const Matrix< Type2, Row2, Col2, AT > &B)
 
template<class AT , class Type1 , class Type2 , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< General, Var, Var, AT > operator- (const Matrix< Type1, Row1, Col1, AT > &A, const Matrix< Type2, Row2, Col2, AT > &B)
 
template<class AT , class Type1 , class Type2 , class Row , class Col >
Matrix< General, Row, Col, AT > operator- (const Matrix< Type1, Row, Col, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Var, AT > 
operator- (const Matrix< Type1, Fixed< M >, Var, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Var, AT > 
operator- (const Matrix< Type1, Fixed< M >, Var, AT > &A, const Matrix< Type2, Fixed< M >, Var, AT > &B)
 
template<class AT , int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Var, Fixed< N >
, AT > 
operator- (const Matrix< Type1, Var, Fixed< N >, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int N, class Type1 , class Type2 >
Matrix< General, Var, Fixed< N >
, AT > 
operator- (const Matrix< Type1, Var, Fixed< N >, AT > &A, const Matrix< Type2, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Row, Col, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Fixed< M >, Var, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type2, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 , class Row , class Col >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type2, Row, Col, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type2, Fixed< M >, Var, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type2, Var, Fixed< N >, AT > &A, const Matrix< Type1, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , class Type , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< Type, Var, Var, AT > operator- (const Matrix< Type, Row1, Col1, AT > &A, const Matrix< Type, Row2, Col2, AT > &B)
 
template<class AT , class Type , class Row , class Col >
Matrix< Type, Row, Col, AT > operator- (const Matrix< Type, Row, Col, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, class Type , class Row , class Col >
Matrix< Type, Fixed< M >, Var, AT > operator- (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, class Type >
Matrix< Type, Fixed< M >, Var, AT > operator- (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Fixed< M >, Var, AT > &B)
 
template<class AT , int N, class Type , class Row , class Col >
Matrix< Type, Var, Fixed< N >, AT > operator- (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int N, class Type >
Matrix< Type, Var, Fixed< N >, AT > operator- (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type , class Row , class Col >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Row, Col, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Var, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Var, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type , class Row , class Col >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Row, Col, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Fixed< M >, Var, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , int M, int N, class Type >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator- (const Matrix< Type, Var, Fixed< N >, AT > &A, const Matrix< Type, Fixed< M >, Fixed< N >, AT > &B)
 
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
Matrix< Type1, Row1, Col1, AT > & operator-= (const Matrix< Type1, Row1, Col1, AT > &A_, const Matrix< Type2, Row2, Col2, AT > &B)
 
template<class AT , class Row1 , class Row2 >
SquareMatrix< Var, AT > operator+ (const SquareMatrix< Row1, AT > &A1, const SquareMatrix< Row2, AT > &A2)
 
template<class AT , class Row >
SquareMatrix< Row, AT > operator+ (const SquareMatrix< Row, AT > &A1, const SquareMatrix< Row, AT > &A2)
 
template<class AT , class Row1 , class Row2 >
SquareMatrix< Var, AT > operator- (const SquareMatrix< Row1, AT > &A1, const SquareMatrix< Row2, AT > &A2)
 
template<class AT , class Row >
SquareMatrix< Row, AT > operator- (const SquareMatrix< Row, AT > &A1, const SquareMatrix< Row, AT > &A2)
 
template<class Type1 , class Row1 , class Col1 , class Row2 , class Row3 , class AT >
void mult (const Matrix< Type1, Row1, Col1, AT > &A, const Vector< Row2, AT > &x, Vector< Row3, AT > &y)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void mult (const Matrix< Symmetric, Row1, Row1, AT > &A, const Vector< Row2, AT > &x, Vector< Row3, AT > &y)
 
template<class AT , class Type1 , class Row1 , class Col1 , class Row2 >
Vector< Var, AT > operator* (const Matrix< Type1, Row1, Col1, AT > &A, const Vector< Row2, AT > &x)
 
template<class AT , class Type1 , class Row , class Col >
Vector< Row, AT > operator* (const Matrix< Type1, Row, Col, AT > &A, const Vector< Row, AT > &x)
 
template<class AT , int M, class Type1 , class Col1 , class Row2 >
Vector< Fixed< M >, AT > operator* (const Matrix< Type1, Fixed< M >, Col1, AT > &A, const Vector< Row2, AT > &x)
 
template<class AT , int M, class Type1 >
Vector< Fixed< M >, AT > operator* (const Matrix< Type1, Fixed< M >, Fixed< M >, AT > &A, const Vector< Fixed< M >, AT > &x)
 
template<class AT , int M, int N, class Type , class Row2 >
Vector< Fixed< M >, AT > operator* (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Vector< Row2, AT > &x)
 
template<class AT , int M, int N, class Type >
Vector< Fixed< M >, AT > operator* (const Matrix< Type, Fixed< M >, Fixed< N >, AT > &A, const Vector< Fixed< N >, AT > &x)
 
template<class Col1 , class Type2 , class Row2 , class Col2 , class Type3 , class Col3 , class AT >
void mult (const RowVector< Col1, AT > &x, const Matrix< Type2, Row2, Col2, AT > &A, RowVector< Col3, AT > &y)
 
template<class Col1 , class Row2 , class Col3 , class AT >
void mult (const RowVector< Col1, AT > &x, const Matrix< Symmetric, Row2, Row2, AT > &A, RowVector< Col3, AT > &y)
 
template<class AT , class Type2 , class Col2 , class Row1 , class Col1 >
RowVector< Var, AT > operator* (const RowVector< Col2, AT > &x, const Matrix< Type2, Row1, Col1, AT > &A)
 
template<class AT , class Type2 , class Row , class Col >
RowVector< Col, AT > operator* (const RowVector< Col, AT > &x, const Matrix< Type2, Row, Col, AT > &A)
 
template<class AT , int N, class Type2 , class Col1 , class Row2 >
RowVector< Fixed< N >, AT > operator* (const RowVector< Col1, AT > &x, const Matrix< Type2, Row2, Fixed< N >, AT > &A)
 
template<class AT , int N, class Type2 >
RowVector< Fixed< N >, AT > operator* (const RowVector< Fixed< N >, AT > &x, const Matrix< Type2, Fixed< N >, Fixed< N >, AT > &A)
 
template<class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 , class Type3 , class Row3 , class Col3 , class AT >
void mult (const Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2, Matrix< Type3, Row3, Col3, AT > &A3)
 
template<class Row1 , class Type2 , class Row2 , class Col2 , class Type3 , class Row3 , class Col3 , class AT >
void mult (const Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2, Matrix< Type3, Row3, Col3, AT > &A3)
 
template<class Row1 , class Row2 , class Row3 , class AT >
void mult (const Matrix< Diagonal, Row1, Row1, AT > &A1, const Matrix< Diagonal, Row2, Row2, AT > &A2, Matrix< Diagonal, Row3, Row3, AT > &A3)
 
template<class AT , class Type1 , class Type2 , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< General, Var, Var, AT > operator* (const Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2)
 
template<class AT , class Type1 , class Type2 , class Row , class Col >
Matrix< General, Row, Col, AT > operator* (const Matrix< Type1, Row, Col, AT > &A1, const Matrix< Type2, Row, Col, AT > &A2)
 
template<class AT , int M, class Type1 , class Type2 , class Col1 , class Row2 , class Col2 >
Matrix< General, Fixed< M >
, Var, AT > 
operator* (const Matrix< Type1, Fixed< M >, Col1, AT > &A1, const Matrix< Type2, Row2, Col2, AT > &A2)
 
template<class AT , int N, class Type1 , class Row1 , class Col1 , class Type2 , class Row2 >
Matrix< General, Var, Fixed< N >
, AT > 
operator* (const Matrix< Type1, Row1, Col1, AT > &A1, const Matrix< Type2, Row2, Fixed< N >, AT > &A2)
 
template<class AT , int M, int N, class Type1 , class Type2 , class Col1 , class Row2 >
Matrix< General, Fixed< M >
, Fixed< N >, AT > 
operator* (const Matrix< Type1, Fixed< M >, Col1, AT > &A1, const Matrix< Type2, Row2, Fixed< N >, AT > &A2)
 
template<class AT , int M, class Type1 , class Type2 >
Matrix< General, Fixed< M >
, Fixed< M >, AT > 
operator* (const Matrix< Type1, Fixed< M >, Fixed< M >, AT > &A1, const Matrix< Type2, Fixed< M >, Fixed< M >, AT > &A2)
 
template<class AT , class Type , class Row1 , class Col1 , class Row2 , class Col2 >
Matrix< Type, Var, Var, AT > operator* (const Matrix< Type, Row1, Col1, AT > &A1, const Matrix< Type, Row2, Col2, AT > &A2)
 
template<class AT , class Type , class Row , class Col >
Matrix< Type, Row, Col, AT > operator* (const Matrix< Type, Row, Col, AT > &A1, const Matrix< Type, Row, Col, AT > &A2)
 
template<class AT , int M, class Type , class Col1 , class Row2 , class Col2 >
Matrix< Type, Fixed< M >, Var, AT > operator* (const Matrix< Type, Fixed< M >, Col1, AT > &A1, const Matrix< Type, Row2, Col2, AT > &A2)
 
template<class AT , int N, class Type , class Row1 , class Col1 , class Row2 >
Matrix< Type, Var, Fixed< N >, AT > operator* (const Matrix< Type, Row1, Col1, AT > &A1, const Matrix< Type, Row2, Fixed< N >, AT > &A2)
 
template<class AT , int M, int N, class Type , class Col1 , class Row2 >
Matrix< Type, Fixed< M >
, Fixed< N >, AT > 
operator* (const Matrix< Type, Fixed< M >, Col1, AT > &A1, const Matrix< Type, Row2, Fixed< N >, AT > &A2)
 
template<class AT , int M, class Type >
Matrix< Type, Fixed< M >
, Fixed< M >, AT > 
operator* (const Matrix< Type, Fixed< M >, Fixed< M >, AT > &A1, const Matrix< Type, Fixed< M >, Fixed< M >, AT > &A2)
 
template<class AT , class Row1 , class Row2 >
SquareMatrix< Var, AT > operator* (const SquareMatrix< Row1, AT > &A1, const SquareMatrix< Row2, AT > &A2)
 
template<class AT , class Row >
SquareMatrix< Row, AT > operator* (const SquareMatrix< Row, AT > &A1, const SquareMatrix< Row, AT > &A2)
 
template<class AT , class Row1 , class Row2 >
Matrix< General, Var, Var, AT > operator* (const Matrix< Symmetric, Row1, Row1, AT > &A1, const Matrix< Symmetric, Row2, Row2, AT > &A2)
 
template<class AT , class Row >
Matrix< General, Row, Row, AT > operator* (const Matrix< Symmetric, Row, Row, AT > &A1, const Matrix< Symmetric, Row, Row, AT > &A2)
 
template<class Row , class AT >
Vector< Row, AT > operator* (const Vector< Row, AT > &x, const AT &alpha)
 Vector-scalar multiplication. More...
 
template<class Row , class AT >
Vector< Row, AT > operator* (const AT &alpha, const Vector< Row, AT > &x)
 Scalar-vector multiplication. More...
 
template<class Row , class AT >
Vector< Row, AT > operator*= (const Vector< Row, AT > &x_, const AT &alpha)
 
template<class Row , class AT >
Vector< Row, AT > operator/ (const Vector< Row, AT > &x, const AT &alpha)
 
template<class Row , class AT >
Vector< Row, AT > operator/= (const Vector< Row, AT > &x_, const AT &alpha)
 
template<class Col , class AT >
RowVector< Col, AT > operator* (const RowVector< Col, AT > &x, const AT &alpha)
 Rowvector-scalar multiplication. More...
 
template<class Col , class AT >
RowVector< Col, AT > operator* (const AT &alpha, const RowVector< Col, AT > &x)
 Scalar-rowvector multiplication. More...
 
template<class Col , class AT >
RowVector< Col, AT > operator*= (const RowVector< Col, AT > &x_, const AT &alpha)
 
template<class Col , class AT >
RowVector< Col, AT > operator/ (const RowVector< Col, AT > &x, const AT &a)
 
template<class Col , class AT >
RowVector< Col, AT > operator/= (const RowVector< Col, AT > &x_, const AT &a)
 
template<class Col , class Row , class AT >
AT operator* (const RowVector< Col, AT > &x, const Vector< Row, AT > &y)
 Scalar product. More...
 
template<class Row , class AT >
AT scalarProduct (const Vector< Row, AT > &x, const Vector< Row, AT > &y)
 Scalar product. More...
 
template<class Row , class AT >
Vector< Row, AT > crossProduct (const Vector< Row, AT > &x, const Vector< Row, AT > &y)
 Cross product. More...
 
template<class Row , class AT >
double tripleProduct (const Vector< Row, AT > &a, const Vector< Row, AT > &x, const Vector< Row, AT > &y)
 Triple product. More...
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator* (const Matrix< Type, Row, Col, AT > &A, const AT &alpha)
 Matrix-scalar multiplication. More...
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator* (const AT &alpha, const Matrix< Type, Row, Col, AT > &A)
 
template<class Row , class AT >
Matrix< Symmetric, Row, Row, AT > operator* (const AT &alpha, const Matrix< Symmetric, Row, Row, AT > &A)
 
template<class Row , class AT >
Matrix< Symmetric, Row, Row, AT > operator* (const Matrix< Symmetric, Row, Row, AT > &A, const AT &alpha)
 
template<class Row , class AT >
Matrix< Diagonal, Row, Row, AT > operator* (const AT &alpha, const Matrix< Diagonal, Row, Row, AT > &A)
 
template<class Row , class AT >
Matrix< Diagonal, Row, Row, AT > operator* (const Matrix< Diagonal, Row, Row, AT > &A, const AT &alpha)
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator/ (const Matrix< Type, Row, Col, AT > &A, const AT &alpha)
 
template<class Row , class AT >
Matrix< Symmetric, Row, Row, AT > operator/ (const Matrix< Symmetric, Row, Row, AT > &A, const AT &alpha)
 
template<class Row , class AT >
Matrix< Diagonal, Row, Row, AT > operator/ (const Matrix< Diagonal, Row, Row, AT > &A, const AT &alpha)
 
template<class Row , class AT >
SquareMatrix< Row, AT > operator* (const SquareMatrix< Row, AT > &A, const AT &alpha)
 
template<class Row , class AT >
SquareMatrix< Row, AT > operator* (const AT &alpha, const SquareMatrix< Row, AT > &A)
 
template<class Row , class AT >
SquareMatrix< Row, AT > operator/ (const SquareMatrix< Row, AT > &A, const AT &alpha)
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator*= (const Matrix< Type, Row, Col, AT > &A_, const AT &alpha)
 
template<class Row , class AT >
Matrix< Symmetric, Row, Row, AT > operator*= (const Matrix< Symmetric, Row, Row, AT > &A_, const AT &alpha)
 
template<class Row , class AT >
Matrix< Diagonal, Row, Row, AT > operator*= (const Matrix< Diagonal, Row, Row, AT > &A_, const AT &alpha)
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator/= (const Matrix< Type, Row, Col, AT > &A_, const AT &alpha)
 
template<class Row , class AT >
Matrix< Symmetric, Row, Row, AT > operator/= (const Matrix< Symmetric, Row, Row, AT > &A_, const AT &alpha)
 
template<class Row , class AT >
Matrix< Diagonal, Row, Row, AT > operator/= (const Matrix< Diagonal, Row, Row, AT > &A_, const AT &alpha)
 
template<class Row , class AT >
Vector< Row, AT > operator- (const Vector< Row, AT > &x)
 Negation. More...
 
template<class Col , class AT >
RowVector< Col, AT > operator- (const RowVector< Col, AT > &a)
 Negation. More...
 
template<class Row , class AT >
SquareMatrix< Row, AT > operator- (const SquareMatrix< Row, AT > &A)
 Negation. More...
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Row, Col, AT > operator- (const Matrix< Type, Row, Col, AT > &A)
 Negation. More...
 
template<class AT >
RowVector< Ref, AT > trans (const Vector< Ref, AT > &x)
 Transpose of a vector. More...
 
template<class AT >
Vector< Ref, AT > trans (const RowVector< Ref, AT > &x)
 Transpose of a rowvector. More...
 
template<class AT >
Matrix< General, Ref, Ref, AT > trans (const Matrix< General, Ref, Ref, AT > &A)
 Transpose of a matrix. More...
 
template<class AT >
SquareMatrix< Ref, AT > trans (const SquareMatrix< Ref, AT > &A)
 Transpose of a matrix. More...
 
template<class Type , class Row , class Col , class AT >
Matrix< Type, Col, Row, AT > trans (const Matrix< Type, Row, Col, AT > &A)
 
template<class Row , class AT >
SquareMatrix< Row, AT > trans (const SquareMatrix< Row, AT > &A)
 
template<class Row , class AT >
RowVector< Row, AT > trans (const Vector< Row, AT > &x)
 
template<class Row , class AT >
Vector< Row, AT > trans (const RowVector< Row, AT > &x)
 
template<class Row , class AT >
AT nrmInf (const Vector< Row, AT > &x)
 
template<class Row , class AT >
AT nrmInf (const RowVector< Row, AT > &x)
 
template<class Row , class AT >
AT nrm2 (const Vector< Row, AT > &x)
 
template<class Col , class AT >
AT nrm2 (const RowVector< Col, AT > &x)
 
template<class Row , class AT >
SquareMatrix< Row, AT > tilde (const Vector< Row, AT > &x)
 Tilde operator. More...
 
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
bool operator== (const Matrix< Type1, Row1, Col1, AT > &A, const Matrix< Type2, Row2, Col2, AT > &B)
 Matrix-matrix comparison. More...
 
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
bool operator!= (const Matrix< Type1, Row1, Col1, AT > &A, const Matrix< Type2, Row2, Col2, AT > &B)
 Matrix-matrix comparison. More...
 
template<class Row , class AT >
AT max (const Vector< Row, AT > &x)
 Maximum value. More...
 
template<class Row , class AT >
int maxIndex (const Vector< Row, AT > &x)
 Index of maximum value. More...
 
template<class Row , class AT >
AT min (const Vector< Row, AT > &x)
 Minimum value. More...
 
template<class Row , class AT >
int minIndex (const Vector< Row, AT > &x)
 Index of minimum value. More...
 
template<class AT >
Matrix< General, Ref, Ref, AT > bubbleSort (const Matrix< General, Ref, Ref, AT > &A_, int PivotCol)
 Bubble Sort Algorithm (stable sorting Algorithm ) More...
 
template<class AT >
void quicksortmedian_intern (Matrix< General, Ref, Ref, AT > &A, int PivotCol, RowVector< Ref, AT > &tmp, int l, int r)
 
template<class AT >
Matrix< General, Ref, Ref, AT > quickSortMedian (const Matrix< General, Ref, Ref, AT > &A_, int PivotCol)
 Modified QuickSort Algorithm (unstable sorting Algorithm ) More...
 
template<class AT >
int countElements (const SquareMatrix< Ref, AT > &A)
 Count nonzero elements. More...
 
template<class AT >
int countElementsLT (const Matrix< Symmetric, Ref, Ref, AT > &A)
 Count nonzero elements of the low triangular part of a symmetric matrix. More...
 
template<class AT >
int countElementsLT (const Matrix< Symmetric, Var, Var, AT > &A)
 Count nonzero elements of the low triangular part of a symmetric matrix. More...
 
template<class Row , class Col , class AT >
Matrix< Symmetric, Col, Col, AT > JTJ (const Matrix< General, Row, Col, AT > &A)
 
template<class Row , class Col , class AT >
Matrix< Symmetric, Col, Col, AT > JTMJ (const Matrix< Symmetric, Row, Row, AT > &B, const Matrix< General, Row, Col, AT > &A)
 
template<class Row , class Col , class AT >
Matrix< Symmetric, Row, Row, AT > JMJT (const Matrix< General, Row, Col, AT > &A, const Matrix< Symmetric, Col, Col, AT > &B)
 
Vector< Ref, std::complex
< double > > 
slvLU (const SquareMatrix< Ref, std::complex< double > > &A, const Vector< Ref, std::complex< double > > &b)
 System of linear equations. More...
 
Matrix< General, Ref, Ref, double > slvLU (const SquareMatrix< Ref, double > &A, const Matrix< General, Ref, Ref, double > &B)
 Systems of linear equations. More...
 
Matrix< General, Var, Var, double > slvLU (const SquareMatrix< Var, double > &A, const Matrix< General, Var, Var, double > &X, int info)
 
Matrix< General, Ref, Ref, double > slvLUFac (const SquareMatrix< Ref, double > &A, const Matrix< General, Ref, Ref, double > &B, const Vector< Ref, int > &ipiv)
 Systems of linear equations. More...
 
Matrix< General, Var, Var, double > slvLUFac (const SquareMatrix< Var, double > &A, const Matrix< General, Var, Var, double > &X, const Vector< Var, int > &ipiv)
 
Matrix< General, Ref, Ref, double > slvQR (const SquareMatrix< Ref, double > &A, const Matrix< General, Ref, Ref, double > &B)
 Systems of linear equations. More...
 
int Doolittle_LU_with_Pivoting_Solve (double *A, double B[], int pivot[], double x[], int n)
 solve linear system with LU decomposed matrix More...
 
Vector< Ref, double > slvLU (const SquareMatrix< Ref, double > &A, const Vector< Ref, double > &b)
 System of linear equations. More...
 
Vector< Ref, double > slvLU (const SquareMatrix< Ref, double > &A, const Vector< Ref, double > &x, int &info)
 System of linear equations. More...
 
Vector< Var, double > slvLU (const SquareMatrix< Var, double > &A, const Vector< Var, double > &x, int &info)
 
Vector< Ref, double > slvLUFac (const SquareMatrix< Ref, double > &A, const Vector< Ref, double > &b, const Vector< Ref, int > &ipiv)
 System of linear equations. More...
 
Vector< Var, double > slvLUFac (const SquareMatrix< Var, double > &A, const Vector< Var, double > &x, const Vector< Var, int > &ipiv)
 
Vector< Ref, double > slvQR (const SquareMatrix< Ref, double > &A, const Vector< Ref, double > &b)
 System of linear equations. More...
 
SquareMatrix< Ref, double > inv (const SquareMatrix< Ref, double > &A)
 Inverse. More...
 
Matrix< Symmetric, Ref, Ref,
double > 
inv (const Matrix< Symmetric, Ref, Ref, double > &A)
 Inverse. More...
 
Matrix< Diagonal, Ref, Ref,
double > 
inv (const Matrix< Diagonal, Ref, Ref, double > &A)
 Inverse. More...
 
Matrix< General, Ref, Ref, double > facLU (const Matrix< General, Ref, Ref, double > &A, Vector< Ref, int > &ipiv)
 LU decomposition. More...
 
SquareMatrix< Ref, double > facLU (const SquareMatrix< Ref, double > &A, Vector< Ref, int > &ipiv)
 LU decomposition. More...
 
SquareMatrix< Var, double > facLU (const SquareMatrix< Var, double > &A, Vector< Var, int > &ipiv)
 
int facLU (double *A, int pivot[], int n)
 LU decomposition. More...
 
Matrix< Symmetric, Ref, Ref,
double > 
facLL (const Matrix< Symmetric, Ref, Ref, double > &A)
 LL decomposition. More...
 
double nrm1 (const Vector< Ref, double > &x)
 1-norm More...
 
double nrmInf (const Vector< Ref, double > &x)
 Infinity-norm. More...
 
double nrm2 (const Vector< Ref, double > &x)
 2-norm More...
 
Vector< Ref, double > slvLL (const Matrix< Symmetric, Ref, Ref, double > &A, const Vector< Ref, double > &b)
 System of linear equations. More...
 
Matrix< General, Ref, Ref, double > slvLL (const Matrix< Symmetric, Ref, Ref, double > &A, const Matrix< General, Ref, Ref, double > &B)
 Systems of linear equations. More...
 
Vector< Ref, double > slvLLFac (const Matrix< Symmetric, Ref, Ref, double > &A, const Vector< Ref, double > &x)
 
Matrix< General, Ref, Ref, double > slvLLFac (const Matrix< Symmetric, Ref, Ref, double > &A, const Matrix< General, Ref, Ref, double > &X)
 
Vector< Ref, std::complex
< double > > 
eigval (const SquareMatrix< Ref, double > &A)
 Eigenvalues. More...
 
int eigvec (const SquareMatrix< Ref, double > &A, SquareMatrix< Ref, std::complex< double > > &eigenvectors, Vector< Ref, std::complex< double > > &eigenvalues)
 Eigenvectors and Eigenvalues. More...
 
int eigvec (const Matrix< Symmetric, Ref, Ref, double > &A, const Matrix< Symmetric, Ref, Ref, double > &B, SquareMatrix< Ref, double > &eigenvectors, Vector< Ref, double > &eigenvalues)
 Eigenvectors and Eigenvalues. More...
 
int svd (Matrix< General, Ref, Ref, double > &A, Matrix< General, Ref, Ref, double > &S, SquareMatrix< Ref, double > &U, SquareMatrix< Ref, double > &VT, int Rueckgabe)
 
Vector< Ref, double > eigval (const Matrix< Symmetric, Ref, Ref, double > &A)
 Eigenvalues. More...
 
Vector< Ref, double > eigvalSel (const Matrix< Symmetric, Ref, Ref, double > &A, int il, int iu, double abstol=0)
 Eigenvalues. More...
 
double rho (const SquareMatrix< Ref, double > &A)
 Spectral radius. More...
 
double rho (const Matrix< Symmetric, Ref, Ref, double > &A)
 Spectral radius. More...
 
double nrmInf (const Matrix< General, Ref, Ref, double > &A)
 Infinity-norm. More...
 
double nrmInf (const Matrix< Symmetric, Ref, Ref, double > &A)
 Infinity-norm. More...
 
double nrm1 (const Matrix< General, Ref, Ref, double > &A)
 1-norm More...
 
double nrmFro (const Matrix< General, Ref, Ref, double > &A)
 Frobenius-norm. More...
 
double nrm2 (const Matrix< General, Ref, Ref, double > &A)
 2-norm More...
 
Matrix< General, Ref, Ref, double > slvLS (const Matrix< General, Ref, Ref, double > &A, const Matrix< General, Ref, Ref, double > &B, double rcond)
 
Vector< Ref, double > slvLS (const Matrix< General, Ref, Ref, double > &A, const Vector< Ref, double > &b, double rcond)
 
Matrix< General, Var, Var, double > slvLU (const SquareMatrix< Var, double > &A, const Matrix< General, Var, Var, double > &B, int &info)
 
template<int size>
Vector< Fixed< size >, double > slvLU (const SquareMatrix< Fixed< size >, double > &A, const Vector< Fixed< size >, double > &b, int &info)
 Row interchanges. More...
 
template<class Type , class Row , class Col , class AT >
std::ostream & operator<< (std::ostream &os, const Matrix< Type, Row, Col, AT > &A)
 Matrix output. More...
 
template<class Type , class Row , class Col , class AT >
std::istream & operator>> (std::istream &is, Matrix< Type, Row, Col, AT > &A)
 Matrix input. More...
 
template<class Type , class Row , class Col , class AT >
void dump (const char *str, const Matrix< Type, Row, Col, AT > &A)
 Matrix dump. More...
 
bool operator== (const Range< Var, Var > &I, const Range< Var, Var > &J)
 Equality operator for indices. More...
 
int dgels (const CBLAS_TRANSPOSE ctr, const int m, const int n, const int nrhs, double *a, const int lda, double *b, const int ldb)
 
int dgelss (const int m, const int n, const int nrhs, double *a, const int lda, double *b, const int ldb, const double rcond)
 
int dgeev (const char jobvl, const char jobvr, const int n, double *a, const int lda, double *wr, double *wi, double *vl, const int ldvl, double *vr, const int ldvr)
 
int dsygv (const int itype, const char jobz, const char uplo, const int n, double *a, const int lda, double *b, const int ldb, double *w)
 
int dgesvd (const char jobu, const char jobvt, const int m, const int n, double *a, const int lda, double *s, double *u, const int ldu, double *vt, const int ldvt)
 
int dsyev (const char jobz, const char ul, const int n, double *a, const int lda, double *w)
 
int dsyevx (const char jobz, const char range, const enum CBLAS_UPLO cuplo, const int n, double *a, const int lda, const double vl, const double vu, const int il, const int iu, const double abstol, const int *m, double *w, double *z, const int ldz)
 
double dlange (const char norm, const int m, const int n, const double *a, const int lda)
 
double dlansy (const char norm, const char uplo, const int n, const double *a, const int lda)
 

Detailed Description

Namespace fmatvec.

Typedef Documentation

Band matrix.

BandMat is an abbreviation for band matrices of type double.

typedef Matrix<Diagonal, Ref, Ref, double> fmatvec::DiagMat

Diagonal matrix.

DiagMat is an abbreviation for diagonal matrices of type double.

typedef Matrix<General, Ref, Ref, double> fmatvec::Mat

General matrix.

Mat is an abbreviation for general matrices of type double.

typedef RowVector<Ref, double> fmatvec::RowVec

Row vector.

RowVec is an abbreviation for row vectors of type double.

typedef SquareMatrix<Ref, double> fmatvec::SqrMat

Square matrix.

SqrMat is an abbreviation for square matrices of type double.

typedef Matrix<Symmetric, Ref, Ref, double> fmatvec::SymMat

Symmetric matrix.

SymMat is an abbreviation for symmetric matrices of type double.

typedef Vector<Ref, double> fmatvec::Vec

Vector.

Vec is an abbreviation for vectors of type double.

Function Documentation

template<class AT >
Matrix<General, Ref, Ref, AT> fmatvec::bubbleSort ( const Matrix< General, Ref, Ref, AT > &  A_,
int  PivotCol 
)

Bubble Sort Algorithm (stable sorting Algorithm )

Values of rowvectors of Matrix A are sorted in ascending order

Parameters
A_Matrix to be sorted
PivotColColumn of A used as sorting index
template<class AT >
int fmatvec::countElements ( const SquareMatrix< Ref, AT > &  A)

Count nonzero elements.

This function counts the nonzero elements of a matrix. ALL diagonal elements are treated as NONZERO!!! (See the storage format for sparse matrix)

Returns
The number of nonzero or diagonal elemets.
template<class AT >
int fmatvec::countElementsLT ( const Matrix< Symmetric, Ref, Ref, AT > &  A)

Count nonzero elements of the low triangular part of a symmetric matrix.

This function counts the nonzero elements of the low triangular part of a symmetric matrix. ALL diagonal elements are treated as NONZERO!!! (See the storage format for sparse matrix)

Returns
The number of nonzero or diagonal elemets.
template<class AT >
int fmatvec::countElementsLT ( const Matrix< Symmetric, Var, Var, AT > &  A)

Count nonzero elements of the low triangular part of a symmetric matrix.

This function counts the nonzero elements of the low triangular part of a symmetric matrix. ALL diagonal elements are treated as NONZERO!!! (See the storage format for sparse matrix)

Returns
The number of nonzero or diagonal elemets.
template<class Row , class AT >
Vector<Row, AT> fmatvec::crossProduct ( const Vector< Row, AT > &  x,
const Vector< Row, AT > &  y 
)

Cross product.

This function computes the cross product of two vectors.

Returns
The cross product.
int fmatvec::Doolittle_LU_with_Pivoting_Solve ( double *  A,
double  B[],
int  pivot[],
double  x[],
int  n 
)

solve linear system with LU decomposed matrix

Parameters
*LUPointer to the first element of the matrix whose elements form the lower and upper triangular matrix factors of A
*BPointer to the column vector, (n x 1) matrix, B.
pivot[]The i-th element is the pivot row interchanged with row i
*xSolution to the equation Ax = B
nThe number of rows or columns of the matrix LU
Returns
success of routine (1 = Success, -1 Failure (matrix LU is singular)

This routine uses Doolittle's method to solve the linear equation Ax = B. This routine is called after the matrix A has been decomposed into a product of a unit lower triangular matrix L and an upper triangular matrix U with pivoting. The argument LU is a pointer to the matrix the subdiagonal part of which is L and the superdiagonal together with the diagonal part is U. (The diagonal part of L is 1 and is not stored.) The matrix A = LU. The solution proceeds by solving the linear equation Ly = B for y and subsequently solving the linear equation Ux = y for x.

REMARK: Copied and fitted on 28.01.2013 of http://www.mymathlib.com/c_source/matrices/linearsystems/doolittle_pivot.c

template<class Type , class Row , class Col , class AT >
void fmatvec::dump ( const char *  str,
const Matrix< Type, Row, Col, AT > &  A 
)

Matrix dump.

This function dumps a matrix to a file in ASCII-format.

Parameters
isThe filename.
AA matrix of any shape and type.
Vector< Ref, std::complex< double > > fmatvec::eigval ( const SquareMatrix< Ref, double > &  A)

Eigenvalues.

This function computes the complex eigenvalues of a square matrix.

Parameters
AA square matrix.
Returns
A vector containig the eigenvalues.
Vector< Ref, double > fmatvec::eigval ( const Matrix< Symmetric, Ref, Ref, double > &  A)

Eigenvalues.

This function computes the eigenvalues of a symmetric matrix.

Parameters
AA symmetric matrix.
Returns
A vector containig the eigenvalues.
Vector< Ref, double > fmatvec::eigvalSel ( const Matrix< Symmetric, Ref, Ref, double > &  A,
int  il,
int  iu,
double  abstol = 0 
)

Eigenvalues.

This function computes selected eigenvalues of a symmetric matrix. The eigenvalues can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters
AA symmetric matrix.
ilThe index of the smallest eigenvalue to be returned
iuThe index of the largest eigenvalue to be returned
abstolThe absolute error tolerance for the eigenvalues
Returns
A vector containig the eigenvalues.
int fmatvec::eigvec ( const SquareMatrix< Ref, double > &  A,
SquareMatrix< Ref, std::complex< double > > &  eigenvectors,
Vector< Ref, std::complex< double > > &  eigenvalues 
)

Eigenvectors and Eigenvalues.

This function computes the complex eigenvalues and eigenvectors of a square matrix.

Parameters
AA square matrix.
eigenvectorA square matrix in the dimension of A, containing the normalized eigenvectors.
eigenvaluesA vector in the size of A, containing the eigenvalues.
Returns
If 0, successful exit. If -i, the i-th argument had an illegal value. If i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed.
int fmatvec::eigvec ( const Matrix< Symmetric, Ref, Ref, double > &  A,
const Matrix< Symmetric, Ref, Ref, double > &  B,
SquareMatrix< Ref, double > &  eigenvectors,
Vector< Ref, double > &  eigenvalues 
)

Eigenvectors and Eigenvalues.

This function computes all the eigenvectors and the eigenvalues of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and B is also positive definite.

Parameters
AA symmetric matrix.
BA symmetric, positive definite matrix.
eigenvectorA square matrix in the dimension of A, containing the normalized Eigenvectors at the end of the function.
eigenvaluesA vector in the size of A, containing the Eigenvalues at the end of the function
Returns
void
Matrix< Symmetric, Ref, Ref, double > fmatvec::facLL ( const Matrix< Symmetric, Ref, Ref, double > &  A)

LL decomposition.

This function computes the Cholesky decomposition of a symmetric matrix according to

\[\boldsymbol{A}=\boldsymbol{L}\,\boldsymbol{L} \]

Parameters
AA symmetric matrix.
Returns
A symmetric matrix containig the result.
Matrix< General, Ref, Ref, double > fmatvec::facLU ( const Matrix< General, Ref, Ref, double > &  A,
Vector< Ref, int > &  ipiv 
)

LU decomposition.

This function computes the LU decomposition of a general matrix according to

\[\boldsymbol{A}=\boldsymbol{P}\,\boldsymbol{L}\,\boldsymbol{U} \]

Parameters
AA general matrix.
ipivA vector of integers containing the pivot indices.
Returns
A general matrix containig the result.
SquareMatrix< Ref, double > fmatvec::facLU ( const SquareMatrix< Ref, double > &  A,
Vector< Ref, int > &  ipiv 
)

LU decomposition.

This function computes the LU decomposition of a square matrix according to

\[\boldsymbol{A}=\boldsymbol{P}\,\boldsymbol{L}\,\boldsymbol{U} \]

Parameters
AA square matrix.
ipivA vector of integers containing the pivot indices.
Returns
A square matrix containig the result.
int fmatvec::facLU ( double *  A,
int  pivot[],
int  n 
)

LU decomposition.

This function computes the LU decomposition of a square matrix according to

\[\boldsymbol{A}=\boldsymbol{P}\,\boldsymbol{L}\,\boldsymbol{U} \]

Parameters
APointer to first element of a square matrix.
ipivA vector of integers containing the pivot indices.
infoInformation about success of routine
Returns
A square matrix containig the result.

Copied and fitted on 28.01.2013 of http://www.mymathlib.com/c_source/matrices/linearsystems/doolittle_pivot.c

SquareMatrix< Ref, double > fmatvec::inv ( const SquareMatrix< Ref, double > &  A)

Inverse.

This function computes the inverse of a general matrix according to

\[\boldsymbol{A}^{-1} \]

Parameters
AA square matrix.
Returns
A square matrix containig the result.
Matrix< Symmetric, Ref, Ref, double > fmatvec::inv ( const Matrix< Symmetric, Ref, Ref, double > &  A)

Inverse.

This function computes the inverse of a symmetric matrix according to

\[\boldsymbol{A}^{-1} \]

Parameters
AA symmetric matrix.
Returns
A symmetric matrix containig the result.
Matrix< Diagonal, Ref, Ref, double > fmatvec::inv ( const Matrix< Diagonal, Ref, Ref, double > &  A)

Inverse.

This function computes the inverse of a diagonal matrix according to

\[\boldsymbol{A}^{-1} \]

Parameters
AA diagonal matrix.
Returns
A diagonal matrix containig the result.
template<class Row , class AT >
AT fmatvec::max ( const Vector< Row, AT > &  x)

Maximum value.

This function computes the maximum value of a vector.

Returns
The maximum value.
template<class Row , class AT >
int fmatvec::maxIndex ( const Vector< Row, AT > &  x)

Index of maximum value.

This function computes the index of the maximum value of a vector

Returns
The index of the maximum value.
template<class Row , class AT >
AT fmatvec::min ( const Vector< Row, AT > &  x)

Minimum value.

This function computes the minimum value of a vector.

Returns
The minimum value.
template<class Row , class AT >
int fmatvec::minIndex ( const Vector< Row, AT > &  x)

Index of minimum value.

This function computes the index of the minimum value of a vector

Returns
The index of the minimum value.
double fmatvec::nrm1 ( const Vector< Ref, double > &  x)

1-norm

This function computes the sum of the absolute values of a vector.

Parameters
xA vector.
Returns
A scalar containig the result.
double fmatvec::nrm1 ( const Matrix< General, Ref, Ref, double > &  A)

1-norm

This function computes the largest column sum of the absolute values of a general matrix.

Parameters
AA general matrix.
Returns
A scalar containig the result.
double fmatvec::nrm2 ( const Vector< Ref, double > &  x)

2-norm

This function computes the the Euclidean norm of a vector.

Parameters
xA vector.
Returns
A scalar containig the result.
double fmatvec::nrm2 ( const Matrix< General, Ref, Ref, double > &  A)

2-norm

This function computes the largest singular value of a general matrix.

Parameters
AA general matrix.
Returns
A scalar containig the result.
double fmatvec::nrmFro ( const Matrix< General, Ref, Ref, double > &  A)

Frobenius-norm.

This function computes the Frobenius norm of a general matrix.

Parameters
AA general matrix.
Returns
A scalar containig the result.
double fmatvec::nrmInf ( const Vector< Ref, double > &  x)

Infinity-norm.

This function computes the the largest absolute value of a vector.

Parameters
xA vector.
Returns
A scalar containig the result.
double fmatvec::nrmInf ( const Matrix< General, Ref, Ref, double > &  A)

Infinity-norm.

This function computes the largest row sum of the absolute values of a general matrix.

Parameters
AA general matrix.
Returns
A scalar containing the result.
double fmatvec::nrmInf ( const Matrix< Symmetric, Ref, Ref, double > &  A)

Infinity-norm.

This function computes the largest row sum of the absolute values of a symmetric matrix.

Parameters
AA general matrix.
Returns
A scalar containing the result.
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
bool fmatvec::operator!= ( const Matrix< Type1, Row1, Col1, AT > &  A,
const Matrix< Type2, Row2, Col2, AT > &  B 
)

Matrix-matrix comparison.

This function compares two matrices.

Returns
True, if the matrices are different, false otherwise.
template<class Row , class AT >
Vector<Row, AT> fmatvec::operator* ( const Vector< Row, AT > &  x,
const AT &  alpha 
)

Vector-scalar multiplication.

This function computes the product of a vector and a scalar.

Returns
The product.
template<class Row , class AT >
Vector<Row, AT> fmatvec::operator* ( const AT &  alpha,
const Vector< Row, AT > &  x 
)

Scalar-vector multiplication.

See Also
operator*(const Vector<Ref,AT>&x,const AT&).
template<class Col , class AT >
RowVector<Col, AT> fmatvec::operator* ( const RowVector< Col, AT > &  x,
const AT &  alpha 
)

Rowvector-scalar multiplication.

This function computes the product of a rowvector and a scalar.

Returns
The product.
template<class Col , class AT >
RowVector<Col, AT> fmatvec::operator* ( const AT &  alpha,
const RowVector< Col, AT > &  x 
)

Scalar-rowvector multiplication.

See Also
operator*(const RowVector<Col>, AT>&, const AT&).
template<class Col , class Row , class AT >
AT fmatvec::operator* ( const RowVector< Col, AT > &  x,
const Vector< Row, AT > &  y 
)

Scalar product.

This function computes the product of a vector and a rowvector. The result is a scalar.

Returns
The product.
template<class Type , class Row , class Col , class AT >
Matrix<Type, Row, Col, AT> fmatvec::operator* ( const Matrix< Type, Row, Col, AT > &  A,
const AT &  alpha 
)

Matrix-scalar multiplication.

This function computes the product of a matrix and a scalar.

Parameters
AThe matrix.
alphaThe scalar.
Returns
The product.
template<class AT >
Vector<Ref, AT> fmatvec::operator+ ( const Vector< Ref, AT > &  x,
const Vector< Ref, AT > &  y 
)
inline

Vector-vector addition.

This function computes the sum of two vectors

Returns
The sum.
template<class Row , class AT >
Vector<Row, AT> fmatvec::operator- ( const Vector< Row, AT > &  x)

Negation.

This function computes the negation of a vector.

Returns
The negation.
template<class Col , class AT >
RowVector<Col, AT> fmatvec::operator- ( const RowVector< Col, AT > &  a)

Negation.

This function computes the negation of a rowvector.

Returns
The negation.
template<class Row , class AT >
SquareMatrix<Row, AT> fmatvec::operator- ( const SquareMatrix< Row, AT > &  A)

Negation.

This function computes the negation of a vector.

Returns
The negation.
template<class Type , class Row , class Col , class AT >
Matrix<Type, Row, Col, AT> fmatvec::operator- ( const Matrix< Type, Row, Col, AT > &  A)

Negation.

This function computes the negation of a vector.

Returns
The negation.
template<class Type , class Row , class Col , class AT >
std::ostream& fmatvec::operator<< ( std::ostream &  os,
const Matrix< Type, Row, Col, AT > &  A 
)

Matrix output.

This function writes a matrix into a stream.

Parameters
osAn output stream.
AA matrix of any shape and type.
Returns
A reference to the output stream.
bool fmatvec::operator== ( const Index &  I,
const Index &  J 
)

Equality operator for indices.

Checks for equality of two indices.

Returns
true if two index objects are equal, false otherwise.
bool fmatvec::operator== ( const Range< Var, Var > &  I,
const Range< Var, Var > &  J 
)
inline

Equality operator for indices.

Checks for equality of two indices.

Returns
true if two index objects are equal, false otherwise.
template<class AT , class Type1 , class Row1 , class Col1 , class Type2 , class Row2 , class Col2 >
bool fmatvec::operator== ( const Matrix< Type1, Row1, Col1, AT > &  A,
const Matrix< Type2, Row2, Col2, AT > &  B 
)

Matrix-matrix comparison.

This function compares two matrices

Returns
True, if the matrices are identical, false otherwise.
template<class Type , class Row , class Col , class AT >
std::istream& fmatvec::operator>> ( std::istream &  is,
Matrix< Type, Row, Col, AT > &  A 
)

Matrix input.

This function loads a matrix from a stream.

Parameters
isAn input stream.
AA matrix of any shape and type.
Returns
A reference to the input stream.
template<class AT >
Matrix<General, Ref, Ref, AT> fmatvec::quickSortMedian ( const Matrix< General, Ref, Ref, AT > &  A_,
int  PivotCol 
)

Modified QuickSort Algorithm (unstable sorting Algorithm )

Values of rowvectors of Matrix A are sorted in ascending order unstabel but very quick sorting Algorithm Pivot Elements as 'Median of three'

Parameters
A_Matrix to be sorted
PivotColColumn of A used as sorting index
template<class AT >
void fmatvec::quicksortmedian_intern ( Matrix< General, Ref, Ref, AT > &  A,
int  PivotCol,
RowVector< Ref, AT > &  tmp,
int  l,
int  r 
)

internal function of QuickSortMedian

double fmatvec::rho ( const SquareMatrix< Ref, double > &  A)

Spectral radius.

This function computes the spectral radius of a square matrix.

Parameters
AA square matrix.
Returns
A scalar containig the result.
double fmatvec::rho ( const Matrix< Symmetric, Ref, Ref, double > &  A)

Spectral radius.

This function computes the spectral radius of a symmetric matrix.

Parameters
AA symmetric matrix.
Returns
A scalar containig the result.
template<class Row , class AT >
AT fmatvec::scalarProduct ( const Vector< Row, AT > &  x,
const Vector< Row, AT > &  y 
)

Scalar product.

This function computes the scalar product of two vectors.

Returns
The scalar product.
Vector< Ref, double > fmatvec::slvLL ( const Matrix< Symmetric, Ref, Ref, double > &  A,
const Vector< Ref, double > &  b 
)

System of linear equations.

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a LL decompostion.

Parameters
AA symmetric matrix.
bA vector containing the right hand side.
Returns
A vector containig the solution.
Matrix< General, Ref, Ref, double > fmatvec::slvLL ( const Matrix< Symmetric, Ref, Ref, double > &  A,
const Matrix< General, Ref, Ref, double > &  B 
)

Systems of linear equations.

This function solves systems of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{X}=\boldsymbol{B} \]

by a LL decompostion.

Parameters
AA symmetric matrix.
BA general matrix containing the right hand sides.
Returns
A general matrix containig the solution.
Vector< Ref, std::complex< double > > fmatvec::slvLU ( const SquareMatrix< Ref, std::complex< double > > &  A,
const Vector< Ref, std::complex< double > > &  b 
)

System of linear equations.

This function solves a complex system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a LU decompostion.

Parameters
AA complex square matrix.
bA complex vector containing the right hand side.
Returns
A complex vector containig the solution.
Matrix< General, Ref, Ref, double > fmatvec::slvLU ( const SquareMatrix< Ref, double > &  A,
const Matrix< General, Ref, Ref, double > &  B 
)

Systems of linear equations.

This function solves systems of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{X}=\boldsymbol{B} \]

by a LU decompostion.

Parameters
AA square matrix.
BA general matrix containing the right hand sides.
Returns
A general matrix containig the solution.
Vector< Ref, double > fmatvec::slvLU ( const SquareMatrix< Ref, double > &  A,
const Vector< Ref, double > &  b 
)

System of linear equations.

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a LU decompostion.

Parameters
AA square matrix.
bA vector containing the right hand side.
Returns
A vector containig the solution.
Vector< Ref, double > fmatvec::slvLU ( const SquareMatrix< Ref, double > &  A,
const Vector< Ref, double > &  x,
int &  info 
)

System of linear equations.

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a LU decompostion.

Parameters
AA square matrix.
bA vector containing the right hand side.
infoInformation about the success of the routine (0 = success)
Returns
A vector containig the solution.
template<int size>
Vector<Fixed<size>, double> fmatvec::slvLU ( const SquareMatrix< Fixed< size >, double > &  A,
const Vector< Fixed< size >, double > &  b,
int &  info 
)

Row interchanges.

This function performs a series of row interchanges on a general matrix.

Parameters
AA general matrix.
ipivA vector of integers containing the pivot indices.
Returns
A Matrix containig the result.

System of linear equations

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a LU decompostion.

Parameters
AA square matrix.
bA vector containing the right hand side.
infoInformation about the success of the routine (0 = success)
Returns
A vector containig the solution.
Matrix< General, Ref, Ref, double > fmatvec::slvLUFac ( const SquareMatrix< Ref, double > &  A,
const Matrix< General, Ref, Ref, double > &  B,
const Vector< Ref, int > &  ipiv 
)

Systems of linear equations.

This function solves systems of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{X}=\boldsymbol{B} \]

. The matrix is already decomposed by a LU decompostion.

Parameters
AA square matrix decomposed by a LU decompostion.
BA general matrix containing the right hand sides.
ipivA vector of integers containing the pivot indices.
Returns
A general matrix containig the solution.
Vector< Ref, double > fmatvec::slvLUFac ( const SquareMatrix< Ref, double > &  A,
const Vector< Ref, double > &  b,
const Vector< Ref, int > &  ipiv 
)

System of linear equations.

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

. The matrix is already decomposed by a LU decompostion.

Parameters
AA square matrix decomposed by a LU decompostion.
bA vector containing the right hand side.
ipivA vector of integers containing the pivot indices.
Returns
A vector containig the solution.
Matrix< General, Ref, Ref, double > fmatvec::slvQR ( const SquareMatrix< Ref, double > &  A,
const Matrix< General, Ref, Ref, double > &  B 
)

Systems of linear equations.

This function solves systems of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{X}=\boldsymbol{B} \]

by a QR decompostion.

Parameters
AA square matrix.
BA general matrix containing the right hand sides.
Returns
A general matrix containig the solution.
Vector< Ref, double > fmatvec::slvQR ( const SquareMatrix< Ref, double > &  A,
const Vector< Ref, double > &  b 
)

System of linear equations.

This function solves a system of linear equations according to

\[\boldsymbol{A}\,\boldsymbol{x}=\boldsymbol{b} \]

by a QR decompostion.

Parameters
AA symmetric matrix.
bA vector containing the right hand side.
Returns
A vector containig the solution.
int fmatvec::svd ( Matrix< General, Ref, Ref, double > &  A,
Matrix< General, Ref, Ref, double > &  S,
SquareMatrix< Ref, double > &  U,
SquareMatrix< Ref, double > &  VT,
int  Rueckgabe 
)

This funtion computes the SVD

template<class Row , class AT >
SquareMatrix<Row, AT> fmatvec::tilde ( const Vector< Row, AT > &  x)

Tilde operator.

Example:

* tilde(x);
*

\[ x=\begin{pmatrix}x_1 \\ x_2 \\ x_3\end{pmatrix} \quad \Rightarrow \quad \tilde x = \begin{pmatrix} 0 & -x_3 & x_2 \\ x_3 & 0 & -x_1 \\ -x_2 & x_1 & 0\end{pmatrix} \]

template<class AT >
RowVector<Ref, AT> fmatvec::trans ( const Vector< Ref, AT > &  x)

Transpose of a vector.

This function computes the transpose of a vector. The result is a rowvector.

Returns
The transpose.
template<class AT >
Vector<Ref, AT> fmatvec::trans ( const RowVector< Ref, AT > &  x)

Transpose of a rowvector.

This function computes the transpose of a rowvector. The result is a vector.

Parameters
xA vector.
Returns
The transpose.
template<class AT >
Matrix<General, Ref, Ref, AT> fmatvec::trans ( const Matrix< General, Ref, Ref, AT > &  A)

Transpose of a matrix.

This function computes the transpose of a matrix.

\[ \boldsymbol{A} \rightarrow \boldsymbol{A}^T \]

The result is a matrix.

Parameters
AA general matrix.
Returns
The transpose.
template<class AT >
SquareMatrix<Ref, AT> fmatvec::trans ( const SquareMatrix< Ref, AT > &  A)

Transpose of a matrix.

This function computes the transpose of a square matrix.

\[ \boldsymbol{A} \rightarrow \boldsymbol{A}^T \]

The result is a square matrix.

Parameters
AA square matrix.
Returns
The transpose.
template<class Row , class AT >
double fmatvec::tripleProduct ( const Vector< Row, AT > &  a,
const Vector< Row, AT > &  x,
const Vector< Row, AT > &  y 
)

Triple product.

This function computes the triple product of three vectors.

Returns
The triple product.

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