src

matrix.h File Reference

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Namespaces

namespace mimo

Complex Matrix operations

int real_size (const CMatrix &, int complex_size)

const Complex & c_assign (CMatrix &A, int i, int j, const Complex &c)

Complex c_access (const CMatrix &A, int i, int j)

std::ostream & c_print (std::ostream &s, const CMatrix &G)

int c_size (const CMatrix &A, int dim)

CMatrix c_eye (int i)

CMatrix c_zeros (int i, int j)

CMatrix c_ones (int i, int j)

const Complex & c_add_s (CMatrix &A, int i, int j, const Complex &c)

simth::Complex c_det (const CMatrix &A)

Real-valued Matrix operations

Matrix eye (int i)

Matrix zeros (int i, int j)

Matrix ones (int i, int j)

double det (const Matrix &A)

Complex Vector operations

const Complex & c_assign (CVector &A, int i, const Complex &c)

Complex c_access (const CVector &A, int i)

std::ostream & c_print (std::ostream &s, const CVector &G)

int c_size (const CVector &A)

const Complex & c_add_s (CVector &a, int i, const Complex &c)

CVector c_ones (int i)

CVector c_zeros (int i)

Vector zeros (int i)

Blas routines

All of these are originally defined inside the Blas++ headers. But there, they are (of course) only defined for real-valued vectors. Here we add versions that can deal with our complex vectors and matrices and also Complex numbers.

void Blas_Add_Mult (CVector &dy, const Complex &c, const CVector &dx)

void Blas_Mult (CVector &dy, const Complex &c, const CVector &dx)

void Blas_Scale (const Complex &c, CVector &dx)

Complex Blas_Dot_Prod (const CVector &dx, const CVector &dy)

void Blas_R1_Update (CMatrix &A, const CVector &dx, const CVector &dy, const Complex &alpha)

double Blas_NormF (const CMatrix &A)

double Blas_NormF (const Matrix &A)

double Blas_Cond (const CMatrix &a, double threshold=0.0)

unsigned Blas_Rank (const CMatrix &a, double threshold=0.0)

double Blas_NormF_squared (const CMatrix &A)

void Mat_Add_Norm (Matrix &A, const CMatrix &B)

Defines

#define LA_COMPLEX_SUPPORT

Typedefs

typedef LaComplex Complex

We need a special complex type here. It has the necessary conversion operators to everything else.

typedef LaGenMatDouble Matrix

Matrix of real double values.

typedef LaVectorDouble Vector

Vector of real double values.

typedef LaGenMatComplex CMatrix

Matrix of complex double values.

typedef LaVectorComplex CVector

Vector of complex double values.

Detailed Description

Matrix class and related functions.

The matrix and vector types appear for complex and real (double) values.

Historical note: Until 2004-01-14, we used a 'pseudo-complex matrix' which in fact was a real-valued matrix of double the size. This was the reason why we invented the c_access and c_assign functions.

Define Documentation

#define LA_COMPLEX_SUPPORT

Typedef Documentation

typedef LaComplex mimo::Complex

We need a special complex type here. It has the necessary conversion operators to everything else.

typedef LaGenMatDouble mimo::Matrix

Matrix of real double values.

typedef LaVectorDouble mimo::Vector

Vector of real double values.

typedef LaGenMatComplex mimo::CMatrix

Matrix of complex double values.
This is a matrix of complex (double) values. The row and column indices for accessing elements start from zero, different from what you would write in mathematical notation. This means you have

$A_{n\times m} = \left(\begin{array}{ccc} a_{11} & & a_{1m} \\ & \ddots & \\ a_{n1} & & a_{nm} \end{array}\right)$

but for accessing the element $a_{11}$ you have to write A(0,0).
More (but sometimes outdated) documentation can be found in the Lapackpp header files.
Historical note: Until 2004-01-14, we used a 'pseudo-complex matrix' which in fact was a real-valued matrix of double the size. This was the reason why we invented the c_access and c_assign functions.

typedef LaVectorComplex mimo::CVector

Vector of complex double values.
This is a vector of complex (double) values. The element indices start from zero, different from what you would write in mathematical notation. This means you have

$w_{n} = \left(\begin{array}{c} w_1 \\ \vdots \\ w_n \end{array}\right)$

but for accessing the element $w_1$ you have to write w(0).
More (but sometimes outdated) documentation can be found in the Lapackpp header files.
Historical note: Until 2004-01-14, we used a 'pseudo-complex vector' which in fact was a real-valued vector of double the size. This was the reason why we invented the c_access and c_assign functions.

Function Documentation

int real_size ( const CMatrix & ,

int complex_size

) [inline]

DEPRECATED. Returns the actual storage size for any given complex_size of the complex Matrix type. This function has no effect any longer -- it simply returns its argument.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

complex_size A size (i.e. any one of the matrix dimensions) that is used for the complex data type.

Returns:
The actual (i.e. any one of the matrix dimensions) size of the underlying real matrix.

const Complex& c_assign ( CMatrix & A,

int i,

int j,

const Complex & c

) [inline]

Assigns a complex value to an element of the given complex matrix A.
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

Parameters:

A The complex matrix where the element should be manipulated.

i Row index, starting at zero

j Column index, starting at zero

c The complex number that should be written into the complex matrix.

Returns:
A reference to the complex number that was just written into the matrix.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

Complex c_access ( const CMatrix & A,

int i,

int j

) [inline]

Returns a complex element of the complex matrix A.
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

A The complex matrix from which the element should be returned.

i Row index, starting at zero

j Column index, starting at zero

Returns:
The complex value at the given position in the matrix.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

std::ostream& c_print ( std::ostream & s,

const CMatrix & G

)

DEPRECATED. Print the complex matrices.

int c_size ( const CMatrix & A,

int dim

) [inline]

DEPRECATED. Returns the complex size of the complex matrix.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

A The matrix of which the size should be returned.

dim The dimension whose size should be returned. In mathematical notation dim=0 are the rows and dim=1 are the columns.

Returns:
The size of the specified dimension. The indices for row and column run from zero to size-1.

CMatrix c_eye ( int i )

Returns a newly created identity matrix, with complex size i x i.

CMatrix c_zeros ( int i,

int j

)

Returns a newly created matrix of zeros, with complex size i x j.

CMatrix c_ones ( int i,

int j

)

Returns a newly created matrix of ones, with complex size i x j.

const Complex& c_add_s ( CMatrix & A,

int i,

int j,

const Complex & c

) [inline]

Add a complex scalar to a matrix component.
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

A The complex matrix where the element should be manipulated.

i Row index, starting at zero

j Column index, starting at zero

c The complex number that should be added to the specified element of the complex matrix.

Returns:
A reference to the complex number that was just added to the matrix element.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

simth::Complex c_det ( const CMatrix & A )

Returns the complex determinant of the complex square matrix A. This algorithm calculated the LU factorization and multiplies its diagonal.

Matrix eye ( int i )

Returns a newly created identity matrix (square), with size i x i

Matrix zeros ( int i,

int j

)

Returns a newly created matrix of zeros, with size i x j.

Matrix ones ( int i,

int j

)

Returns a newly created matrix of ones, with size i x j.

double det ( const Matrix & A )

Returns the determinant of the square matrix A. This algorithm calculated the LU factorization and multiplies its diagonal.

const Complex& c_assign ( CVector & A,

int i,

const Complex & c

) [inline]

Assigns a complex value to an element of the given complex vector A
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

A The complex vector where the element should be manipulated.

i Position index, starting at zero

c The complex number that should be written into the complex vector.

Returns:
A reference to the complex number that was just written into the vector.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

Complex c_access ( const CVector & A,

int i

) [inline]

Returns a complex element of the complex vector A.
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

A The complex vector from which the element should be returned.

i Position index, starting at zero

Returns:
The complex value at the given position in the vector.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

std::ostream& c_print ( std::ostream & s,

const CVector & G

)

DEPRECATED. Print the complex vector.

int c_size ( const CVector & A ) [inline]

DEPRECATED. Returns the complex size of the complex vector.

const Complex& c_add_s ( CVector & a,

int i,

const Complex & c

) [inline]

Add a complex scalar to a vector component.
Even though this function is not strictly necessary nowadays, it might still be useful in order to have the correct type conversions taking place.
Historical note: This function used to be necessary until 2004-01-14, when 'pseudo-complex matrices' were used instead of native complex matrices. After that date, this project uses natively complex matrices and this function now is no longer necessary.

Parameters:

a The complex vector where the element should be manipulated.

i Position index, starting at zero

c The complex number that should be added to the specified element of the complex vector.

Returns:
A reference to the complex number that was just added into the vector.

Note:
If DEBUG is defined, i.e. you configured this package with --enable-debug, then every access is range-checked and any out of range access will result in a failed assertion in this file. However, if DEBUG is switched off, then any out of range access will probably result in very strange Lapack/Blas segmentation faults.

CVector c_ones ( int i )

Returns a newly created vector of ones, with complex size i x j.

CVector c_zeros ( int i )

Returns a newly created vector of zeros, with complex size i x j.

Vector zeros ( int i )

Returns a newly created vector of zeros, with size i x j.

void Blas_Add_Mult ( CVector & dy,

const Complex & c,

const CVector & dx

) [inline]

Combined vector scaling and addition: dy = dy + c * dx

void Blas_Mult ( CVector & dy,

const Complex & c,

const CVector & dx

) [inline]

Combined vector scaling: dy = c * dx

void Blas_Scale ( const Complex & c,

CVector & dx

) [inline]

Vector scaling: dx = c * dx

Complex Blas_Dot_Prod ( const CVector & dx,

const CVector & dy

) [inline]

Returns the dot product of two vectors x and y, which is x'*y. Note: For complex vectors this is no longer commutative, but rather complex conjugate commutative.

void Blas_R1_Update ( CMatrix & A,

const CVector & dx,

const CVector & dy,

const Complex & alpha

) [inline]

Perform the rank 1 operation A := alpha*dx*dy' + A Note: the vector dy' is the _conjugate_ transposed of dy.

double Blas_NormF ( const CMatrix & A )

Returns the Frobenius-Norm of matrix A (also called the Schur- or Euclidean norm): $||A||_F=\sqrt{\sum_{i,j}|a_{ij}|^2}$ , i.e. the square root of the sum of the absolute squares of its elements.

See also:
Eric W. Weisstein. "Matrix Norm." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixNorm.html

double Blas_NormF ( const Matrix & A )

Returns the Frobenius-Norm of matrix A (also called the Schur- or Euclidean norm): $||A||_F=\sqrt{\sum_{i,j}|a_{ij}|^2}$ , i.e. the square root of the sum of the absolute squares of its elements.

See also:
Eric W. Weisstein. "Matrix Norm." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixNorm.html

double Blas_Cond ( const CMatrix & a,

double threshold = 0.0

)

Calculates the condition number of a matrix. This is calculated by calculating the singular values first, which means this operation is probably rather expensive.
Since we are at numerics here, the threshold for considering a value equal to zero can be given as a second argument. Potential values are DBL_EPSILON, 10*DBL_EPSILON, DBL_MIN from <float.h>

See also:
http://mathworld.wolfram.com/ConditionNumber.html

unsigned Blas_Rank ( const CMatrix & a,

double threshold = 0.0

)

Calculates the rank of a matrix, which is the number of nonzero singular values. This is calculated by calculating the singular values first, which means this operation is probably rather expensive.
The returned value is the number of singular values that are truly greater than the threshold value.
Since we are at numerics here, the threshold for considering a value equal to zero can be given as a second argument. Potential values are DBL_EPSILON, 10*DBL_EPSILON, DBL_MIN from <float.h>

See also:
http://mathworld.wolfram.com/MatrixRank.html

double Blas_NormF_squared ( const CMatrix & A )

DEPRECATED. Returns the squared (!) Frobenius-Norm of matrix A: sum |h_ij|^2 over all i,j. This function is deprecated. Please try to use Blas_Norm2 instead, which will give you the square root of this value.

void Mat_Add_Norm ( Matrix & A,

const CMatrix & B

)

Calculate the std::norm of each element of B and add it to the respective element of the matrix A. B is a *complex* matrix, whereas A is a real-valued (nonnegative) matrix.

Generated on Tue Aug 9 14:43:10 2005 for mimolib by

1.4.1


Namespaces
namespace	mimo
Complex Matrix operations
int	real_size (const CMatrix &, int complex_size)
const Complex &	c_assign (CMatrix &A, int i, int j, const Complex &c)
Complex	c_access (const CMatrix &A, int i, int j)
std::ostream &	c_print (std::ostream &s, const CMatrix &G)
int	c_size (const CMatrix &A, int dim)
CMatrix	c_eye (int i)
CMatrix	c_zeros (int i, int j)
CMatrix	c_ones (int i, int j)
const Complex &	c_add_s (CMatrix &A, int i, int j, const Complex &c)
simth::Complex	c_det (const CMatrix &A)
Real-valued Matrix operations
Matrix	eye (int i)
Matrix	zeros (int i, int j)
Matrix	ones (int i, int j)
double	det (const Matrix &A)
Complex Vector operations
const Complex &	c_assign (CVector &A, int i, const Complex &c)
Complex	c_access (const CVector &A, int i)
std::ostream &	c_print (std::ostream &s, const CVector &G)
int	c_size (const CVector &A)
const Complex &	c_add_s (CVector &a, int i, const Complex &c)
CVector	c_ones (int i)
CVector	c_zeros (int i)
Vector	zeros (int i)
Blas routines
All of these are originally defined inside the Blas++ headers. But there, they are (of course) only defined for real-valued vectors. Here we add versions that can deal with our complex vectors and matrices and also Complex numbers.
void	Blas_Add_Mult (CVector &dy, const Complex &c, const CVector &dx)
void	Blas_Mult (CVector &dy, const Complex &c, const CVector &dx)
void	Blas_Scale (const Complex &c, CVector &dx)
Complex	Blas_Dot_Prod (const CVector &dx, const CVector &dy)
void	Blas_R1_Update (CMatrix &A, const CVector &dx, const CVector &dy, const Complex &alpha)
double	Blas_NormF (const CMatrix &A)
double	Blas_NormF (const Matrix &A)
double	Blas_Cond (const CMatrix &a, double threshold=0.0)
unsigned	Blas_Rank (const CMatrix &a, double threshold=0.0)
double	Blas_NormF_squared (const CMatrix &A)
void	Mat_Add_Norm (Matrix &A, const CMatrix &B)
Defines
#define	LA_COMPLEX_SUPPORT
Typedefs
typedef LaComplex	Complex
	We need a special complex type here. It has the necessary conversion operators to everything else.
typedef LaGenMatDouble	Matrix
	Matrix of real double values.
typedef LaVectorDouble	Vector
	Vector of real double values.
typedef LaGenMatComplex	CMatrix
	Matrix of complex double values.
typedef LaVectorComplex	CVector
	Vector of complex double values.