Math module, providing matrix operations. More...

Classes
class	Archive
	encapsulates I/O functions for Matrix More...

class	Matrix
	Standard matrix class. More...

class	MatrixBlock
	A generic view onto parts of a Matrix. More...

class	MatrixCWise
	coefficient wise access to Matrix More...

class	MatrixEigenSym
	Eigen decomposition of symmetric matrices. More...

class	MUMPS
	solver for sparse matrices using MUMPS. More...

class	SparseLU
	Base class of LU solvers. It already implements the standard LU decomposition. More...

class	SparseMatrix
	encapsulates sparse matrix classes and algorithms More...

class	SparseSolver
	The base class for sparse solvers. It provides a unified interface which can be used by generic algorithms. More...

class	SymSparseMatrix
	Symmetric sparse matrix class with selfadjoint storage. More...

struct	TMumpsInterface< float >
	a wrapper for the single precision MUMPS C API More...

struct	TMumpsInterface< number >
	a wrapper for the number precision MUMPS C API More...

Functions
void	CBDraw (Matrix x, Matrix y, string f, Matrix colors, int width=512, int height=384, string format="", string range="", string legends="", string title="")

	CBDraw2D (Matrixm, string fi, string frame_label, string legend_label, int width=512)
	Write the contents of the matrix as color plot to a CBDraw file. More...

void	CBDrawLines (Matrix m, string fi, int width=512, int height=384, bool drawLines=true)

void	Colorize (number xmin, number xmax, number val1, int posterize, bool bw, unsigned charr, unsigned char g, unsigned char b)
	encapsulates I/O functions for Matrix More...

void	ComplexDivide (Matrix mr1, Matrix mi1, Matrix mr2, Matrix mi2, Matrix ir, Matrix ii)
	Computes the real and imaginary parts of the componentwise quotient of two complex matrices defined by real and imaginary parts.

void	ComplexDivide (Matrix mr1, Matrix mi1, number mr2, number mi2, Matrix ir, Matrix ii)
	Computes the real and imaginary parts of the quotient of a complex matrix defined by real and imaginary parts with a complex number.

void	ComplexEigen (Matrix mr1, Matrix mi1, Matrix rval, Matrix ival, Matrix ir, Matrix ii)
	Computes the eigenvalues and the real and imaginary parts of the eigenvectors of a complex matrix.

void	ComplexFromPolar (Matrix mr1, Matrix mi1, Matrix ir, Matrix ii)
	Converts magnitude and phase angles into cartesian real and imaginary parts.

void	ComplexMultiply (Matrix mr1, Matrix mi1, Matrix mr2, Matrix mi2, Matrix ir, Matrix ii)
	Computes the real and imaginary parts of the componentwise product of two complex matrices defined by real and imaginary parts.

void	ComplexMultiply (Matrix mr1, Matrix mi1, number mr2, number mi2, Matrix ir, Matrix ii)
	Computes the real and imaginary parts of the product of a complex matrix defined by real and imaginary parts with a complex number.

void	ComplexProduct (Matrix mr1, Matrix mi1, Matrix mr2, Matrix mi2, Matrix ir, Matrix ii)
	encapsulates complex functions for Matrix More...

void	ComplexToPolar (Matrix mr1, Matrix mi1, Matrix ir, Matrix ii)
	Converts cartesian real and imaginary parts into magnitude and phase angles.

Matrix	Derivative (Matrix m)

Matrix	Derivative (Matrix m, number dx)

number	Det (MatrixBlock mat)
	encapsulates external functions for linalg objects More...

Matrix	Diagonal (MatrixBlock mat)

Matrix	Diagonal (sparse::SparseMatrix mat)

Matrix	Diagonal (sparse::SymSparseMatrix mat)

Matrix	Exp (Matrix a, number f=1.)

number	gamma (number z)
	Compute Gamma function. More...

number	Gamma (number x)
	Compute Gamma function. More...

number	gauss1_pdf (number x)
	Compute 1D standard normal density. More...

number	gauss2_pdf (number x, number y, number rho)
	Compute 2D standard normal density. More...

number	gaussn_pdf (Matrix x, Matrix *irho, number detl)
	Compute n-D standard normal density. More...

Matrix	Identity (number i)
	creates an identity matrix of dim i*i More...

Matrix	Identity (number i, number j)
	creates an identity matrix of dim i*j More...

	Image (Matrix m, string f, int posterize=0, bool bw=false)
	Write the contents of the matrix to a PNG file. More...

void	Image (Matrix m, string f, number min, number max, int posterize=0, bool bw=false)
	Write the contents of the matrix to a PNG file. More...

Matrix	Log (Matrix a, number f=1.)

Matrix	Log10 (Matrix a, number f=1.)

Matrix	MatrixInput (string f, int skip=0, string seps="")
	Reads a matrix from a text file or binary file. Binary files must have the extension '.bin'. More...

Matrix	operator+ (MatrixBlock a, Matrix b)
	encapsulates external functions for linalg objects

Matrix	operator+ (Matrix a, sparse::SparseMatrix b)

Matrix	operator+ (MatrixBlock a, sparse::SparseMatrix b)

Matrix	operator+ (sparse::SparseMatrix a, Matrix b)

Matrix	operator+ (sparse::SparseMatrix a, MatrixBlock b)

Matrix	operator+ (Matrix a, sparse::SymSparseMatrix b)

Matrix	operator+ (MatrixBlock a, sparse::SymSparseMatrix b)

Matrix	operator+ (sparse::SymSparseMatrix a, Matrix b)

Matrix	operator+ (sparse::SymSparseMatrix a, MatrixBlock b)

Matrix	operator- (MatrixBlock a, sparse::SparseMatrix b)

Matrix	operator- (sparse::SparseMatrix a, Matrix b)

Matrix	operator- (sparse::SparseMatrix a, MatrixBlock b)

Matrix	operator- (Matrix a, sparse::SymSparseMatrix b)

Matrix	operator- (MatrixBlock a, sparse::SymSparseMatrix b)

Matrix	operator- (sparse::SymSparseMatrix a, Matrix b)

Matrix	operator- (sparse::SymSparseMatrix a, MatrixBlock b)

	Output (Matrix m, string f)
	Write the contents of the matrix to a text file ore binary file. Binary files must have the extension '.bin'. More...

	Output (Matrix m, string file, string name, bool append=true)
	Write the contents of the matrix to a file containing tng code. More...

Matrix	Pow (Matrix a, number f=1.)

Archive	ReadArchive (string file)

Matrix	Sin (Matrix a, number f=1.)

Matrix	SortByCol (Matrix m, Matrix cols)
	Sort a matrix by multiple columns. More...

Matrix	SortByRow (Matrix m, number row, bool ascending=true)
	Sort a matrix by row. More...

number	Trace (MatrixBlock mat)
	returns the trace of the matrix More...

number	Trace (sparse::SparseMatrix mat)
	returns the trace of the matrix More...

number	Trace (sparse::SymSparseMatrix mat)
	returns the trace of the matrix More...

Matrix	ZeroMatrix (number i, number j)
	creates a zero matrix More...

Matrix	ZeroVector (number i)
	creates a zero column vector More...

Variables
int cbdrawlinecomparefunc *	a

Detailed Description

Math module, providing matrix operations.

Function Documentation

◆ CBDraw()

void CBDraw	(	Matrix	x,
		Matrix	y,
		string	f,
		Matrix	colors,
		int	width = `512`,
		int	height = `384`,
		string	format = `""`,
		string	range = `""`,
		string	legends = `""`,
		string	title = `""`
	)

Write the contents of the matrix to a CBDraw file. CBDraw files must have the extension '.cb'.

Parameters

x	contains the abscissa and must be one-dimensional (one row or one columns)
y	contains the ordinates.
format	defines the labelling of the axes according to CBDraw conventions

◆ CBDraw2D()

CBDraw2D	(	Matrixm	,
		string	fi,
		string	frame_label,
		string	legend_label,
		int	width = `512`
	)

Write the contents of the matrix as color plot to a CBDraw file.

Write the contents of the matrix to a CBDraw file. CBDraw files must have the extension '.cb'. The abscissa is generated from the indices

Parameters

m	contains the ordinates
f	contains the file name
width	defines the width of the picture
height	defines the height of the picture
format	defines the labelling of the axes according to CBDraw conventions

◆ CBDrawLines()

void CBDrawLines	(	Matrix	m,
		string	fi,
		int	width = `512`,
		int	height = `384`,
		bool	drawLines = `true`
	)

Write the contents of the matrix as lines to a CBDraw file. CBDraw files must have the extension '.cb'.

Parameters

m	contains the vertices of the lines
fi	contains the file name
width	defines the width of the picture
height	defines the height of the picture

◆ Colorize()

void Colorize	(	number	xmin,
		number	xmax,
		number	val1,
		int	posterize,
		bool	bw,
		unsigned	charr,
		unsigned char	g,
		unsigned char	b
	)

encapsulates I/O functions for Matrix

Computes the color values in RGB space for assuming blue for minimum and red for maximum.

◆ ComplexProduct()

void ComplexProduct	(	Matrix	mr1,
		Matrix	mi1,
		Matrix	mr2,
		Matrix	mi2,
		Matrix **	ir,
		Matrix **	ii
	)

encapsulates complex functions for Matrix

Computes the real and imaginary parts of the product of two complex matrices defined by real and imaginary parts.

◆ Det()

number Det ( MatrixBlock mat )

encapsulates external functions for linalg objects

Computes the determinant using LU

Parameters

mat	the matrix to be processed

Returns: the determinant of mat

◆ Diagonal()

Matrix Diagonal ( MatrixBlock mat )

encapsulates external functions for linalg objects

◆ Exp()

Matrix Exp	(	Matrix	a,
		number	f = `1.`
	)

Returns: a Matrix x with coefficientwise x=exp(a*f)

Parameters

a	the matrix a
f	the scalar factor f

◆ gamma()

number gamma ( number z )

Compute Gamma function.

Parameters

z argument

Returns: Gamma(z)

◆ Gamma()

number Gamma ( number x )

Compute Gamma function.

Parameters

x argument

Returns: Gamma(x)

◆ gauss1_pdf()

number gauss1_pdf ( number x )

Compute 1D standard normal density.

Parameters

x argument

Returns: PDF

◆ gauss2_pdf()

number gauss2_pdf	(	number	x,
		number	y,
		number	rho
	)

Compute 2D standard normal density.

Parameters

x	argument 1
y	argument 2
rho	correlation coefficient

Returns: PDF

◆ gaussn_pdf()

number gaussn_pdf	(	Matrix	x,
		Matrix *	irho,
		number	detl
	)

Compute n-D standard normal density.

Parameters

x	values
irho	inverse correlation matrix
detl	determinant of correlation matrix

Returns: PDF

◆ Identity() [1/2]

Matrix Identity ( number i )

creates an identity matrix of dim i*i

Parameters

i	the row and column number

Returns: a matrix object

◆ Identity() [2/2]

Matrix Identity	(	number	i,
		number	j
	)

creates an identity matrix of dim i*j

Parameters

i	the row number
j	the column number

Returns: a matrix object

◆ Image() [1/2]

Image	(	Matrix	m,
		string	f,
		int	posterize = `0`,
		bool	bw = `false`
	)

Write the contents of the matrix to a PNG file.

Parameters

m	contains the matrix
f	contains the file name
posterize	control the number of different colors actually used. if posterize==0, then colors vary smoothly.

◆ Image() [2/2]

void Image	(	Matrix	m,
		string	f,
		number	min,
		number	max,
		int	posterize = `0`,
		bool	bw = `false`
	)

Write the contents of the matrix to a PNG file.

Parameters

m	contains the matrix
f	contains the file name
posterize	control the number of different colors actually used. if posterize==0, then colors vary smoothly.
min	and
max	define the data range for colors.

◆ Log()

Matrix Log	(	Matrix	a,
		number	f = `1.`
	)

Returns: a Matrix x with coefficientwise x=log(a*f) (natural log)

Parameters

a	the matrix a
f	the scalar factor f

◆ Log10()

Matrix Log10	(	Matrix	a,
		number	f = `1.`
	)

Returns: a Matrix x with coefficientwise x=log10(a*f) (log base 10)

Parameters

a	the matrix a
f	the scalar factor f

◆ MatrixInput()

Matrix MatrixInput	(	string	f,
		int	skip = `0`,
		string	seps = `""`
	)

Reads a matrix from a text file or binary file. Binary files must have the extension '.bin'.

Parameters

f	contains the file name

Returns: Matrix containing data on file

Parameters

skip	contains the number of lines to be skipped at the beginning (for headers etc)

◆ operator-()

Matrix operator-	(	MatrixBlock	a,
		sparse::SparseMatrix	b
	)

encapsulates external functions for linalg objects

◆ Output() [1/2]

Output	(	Matrix	m,
		string	f
	)

Write the contents of the matrix to a text file ore binary file. Binary files must have the extension '.bin'.

Parameters

m	contains the matrix
f	contains the file name

◆ Output() [2/2]

Output	(	Matrix	m,
		string	file,
		string	name,
		bool	append = `true`
	)

Write the contents of the matrix to a file containing tng code.

Parameters

m	contains the matrix
file	contains the file name
name	contains the tng matrix object name

◆ Pow()

Matrix Pow	(	Matrix	a,
		number	f = `1.`
	)

Returns: a Matrix x with coefficientwise x=pow(a,f)

Parameters

a	the matrix a
f	the scalar factor f

◆ Sin()

Matrix Sin	(	Matrix	a,
		number	f = `1.`
	)

Returns: a Matrix x with coefficientwise x=sin(a*f)

Parameters

a	the matrix a
f	the scalar factor f

◆ SortByCol()

Matrix SortByCol	(	Matrix	m,
		Matrix	cols
	)

Sort a matrix by multiple columns.

Parameters

m	Matrix to be sorted
cols	defines the sort order for the individual columns. Is a vector of size numCols(); The first index is the first index, the last index the last index to sort for.

Returns: Sorted matrix Example: to_sort: 0 1 2 0 1 1 1 1 2 2 9 9 3 5 8 4 4 4 7 2 5 3 4 3 cols: 1 2 3 0 -> first sort for column #1, then for columns #2, columns #3 and #0 and less important here in this example sorted matrix: 1 1 1 1 0 1 2 0 2 2 9 9 5 3 4 3 4 4 7 2 3 5 8 4

◆ SortByRow()

Matrix SortByRow	(	Matrix	m,
		number	row,
		bool	ascending = `true`
	)

Sort a matrix by row.

Parameters

m	Matrix to be sorted
row	row defining sort order
ascending	if true then it will be sorted in ascending order, else descending

Returns: Sorted matrix

◆ Trace() [1/3]

number Trace ( MatrixBlock mat )

returns the trace of the matrix

encapsulates external functions for linalg objects

Parameters

mat	the matrix to be analyzed

Returns: the trace (a scalar)

◆ Trace() [2/3]

number Trace ( sparse::SparseMatrix mat )

returns the trace of the matrix

Parameters

mat	the matrix to be analyzed

Returns: the trace (a scalar)

◆ Trace() [3/3]

number Trace ( sparse::SymSparseMatrix mat )

returns the trace of the matrix

Parameters

mat	the matrix to be analyzed

Returns: the trace (a scalar)

◆ ZeroMatrix()

Matrix ZeroMatrix	(	number	i,
		number	j
	)

creates a zero matrix

Parameters

i	the row number
j	the column number

Returns: a matrix object

◆ ZeroVector()

Matrix ZeroVector ( number i )

creates a zero column vector

Parameters

i	the vector dimension

Returns: a matrix object

Variable Documentation

◆ a

int cbdrawlinecomparefunc * a

Compare depth of two objects for writing to CBDraw file

Parameters

a	first object
b	second object

Returns: integer containing result of comparison

tmath

Classes

Functions

Variables

Detailed Description

Function Documentation

◆ CBDraw()

◆ CBDraw2D()

◆ CBDrawLines()

◆ Colorize()

◆ ComplexProduct()

◆ Det()

◆ Diagonal()

◆ Exp()

◆ gamma()

◆ Gamma()

◆ gauss1_pdf()

◆ gauss2_pdf()

◆ gaussn_pdf()

◆ Identity() [1/2]

◆ Identity() [2/2]

◆ Image() [1/2]

◆ Image() [2/2]

◆ Log()

◆ Log10()

◆ MatrixInput()

◆ operator-()

◆ Output() [1/2]

◆ Output() [2/2]

◆ Pow()

◆ Sin()

◆ SortByCol()

◆ SortByRow()

◆ Trace() [1/3]

◆ Trace() [2/3]

◆ Trace() [3/3]

◆ ZeroMatrix()

◆ ZeroVector()

Variable Documentation

◆ a

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