Dense matrix class implementation. More...

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "logging.h"
#include "object.h"
#include "complex.h"
#include "vector.h"
#include "matrix.h"

Include dependency graph for matrix.cpp:

Go to the source code of this file.

Functions
matrix	operator+ (matrix a, matrix b)
	Matrix addition.

matrix	operator- (matrix a, matrix b)
	Matrix subtraction.

matrix	operator* (matrix a, nr_complex_t z)
	Matrix scaling complex version.

matrix	operator* (nr_complex_t z, matrix a)
	Matrix scaling complex version (different order)

matrix	operator* (matrix a, nr_double_t d)
	Matrix scaling complex version.

matrix	operator* (nr_double_t d, matrix a)
	Matrix scaling real version (different order)

matrix	operator/ (matrix a, nr_complex_t z)
	Matrix scaling division by complex version.

matrix	operator/ (matrix a, nr_double_t d)
	Matrix scaling division by real version.

matrix	operator* (matrix a, matrix b)

matrix	operator+ (matrix a, nr_complex_t z)
	Complex scalar addition.

matrix	operator+ (nr_complex_t z, matrix a)
	Complex scalar addition different order.

matrix	operator+ (matrix a, nr_double_t d)
	Real scalar addition.

matrix	operator+ (nr_double_t d, matrix a)
	Real scalar addition different order.

matrix	operator- (matrix a, nr_complex_t z)
	Complex scalar substraction.

matrix	operator- (nr_complex_t z, matrix a)
	Complex scalar substraction different order.

matrix	operator- (matrix a, nr_double_t d)
	Real scalar substraction.

matrix	operator- (nr_double_t d, matrix a)
	Real scalar substraction different order.

matrix	transpose (matrix a)
	Matrix transposition.

matrix	conj (matrix a)
	Conjugate complex matrix.

matrix	adjoint (matrix a)
	adjoint matrix

matrix	abs (matrix a)
	Computes magnitude of each matrix element.

matrix	dB (matrix a)
	Computes magnitude in dB of each matrix element.

matrix	arg (matrix a)
	Computes the argument of each matrix element.

matrix	real (matrix a)
	Real part matrix.

matrix	imag (matrix a)
	Imaginary part matrix.

matrix	eye (int rs, int cs)
	Create identity matrix with specified number of rows and columns.

matrix	eye (int s)
	Create a square identity matrix.

matrix	diagonal (vector diag)
	Create a diagonal matrix from a vector.

matrix	pow (matrix a, int n)

nr_complex_t	cofactor (matrix a, int u, int v)
	Computes the complex cofactor of the given determinant.

nr_complex_t	detLaplace (matrix a)
	Compute determinant of the given matrix using Laplace expansion.

nr_complex_t	detGauss (matrix a)
	Compute determinant Gaussian algorithm.

nr_complex_t	det (matrix a)
	Compute determinant of the given matrix.

matrix	inverseLaplace (matrix a)
	Compute inverse matrix using Laplace expansion.

matrix	inverseGaussJordan (matrix a)
	Compute inverse matrix using Gauss-Jordan elimination.

matrix	inverse (matrix a)
	Compute inverse matrix.

matrix	stos (matrix s, vector zref, vector z0)
	S params to S params.

matrix	stos (matrix s, nr_complex_t zref, nr_complex_t z0)
	S renormalization with all part identic.

matrix	stos (matrix s, nr_double_t zref, nr_double_t z0)
	S renormalization with all part identic and real.

matrix	stos (matrix s, vector zref, nr_complex_t z0)
	S renormalization (variation)

matrix	stos (matrix s, nr_complex_t zref, vector z0)
	S renormalization (variation)

matrix	stoz (matrix s, vector z0)
	Scattering parameters to impedance matrix.

matrix	stoz (matrix s, nr_complex_t z0)
	Scattering parameters to impedance matrix identic case.

matrix	ztos (matrix z, vector z0)
	Convert impedance matrix scattering parameters.

matrix	ztos (matrix z, nr_complex_t z0)
	Convert impedance matrix to scattering parameters identic case.

matrix	ztoy (matrix z)
	impedance matrix to admittance matrix.

matrix	stoy (matrix s, vector z0)
	Scattering parameters to admittance matrix.

matrix	stoy (matrix s, nr_complex_t z0)
	Convert scattering pto adminttance parameters identic case.

matrix	ytos (matrix y, vector z0)
	Admittance matrix to scattering parameters.

matrix	ytos (matrix y, nr_complex_t z0)
	Convert Admittance matrix to scattering parameters identic case.

matrix	stoa (matrix s, nr_complex_t z1, nr_complex_t z2)
	Converts chain matrix to scattering parameters.

matrix	atos (matrix a, nr_complex_t z1, nr_complex_t z2)
	Converts chain matrix to scattering parameters.

matrix	stoh (matrix s, nr_complex_t z1, nr_complex_t z2)
	Converts scattering parameters to hybrid matrix.

matrix	htos (matrix h, nr_complex_t z1, nr_complex_t z2)
	Converts hybrid matrix to scattering parameters.

matrix	stog (matrix s, nr_complex_t z1, nr_complex_t z2)

matrix	gtos (matrix g, nr_complex_t z1, nr_complex_t z2)

matrix	ytoz (matrix y)
	Convert admittance matrix to impedance matrix.

matrix	cytocs (matrix cy, matrix s)
	Admittance noise correlation matrix to S-parameter noise correlation matrix.

matrix	cstocy (matrix cs, matrix y)
	Converts S-parameter noise correlation matrix to admittance noise correlation matrix.

matrix	cztocs (matrix cz, matrix s)
	Converts impedance noise correlation matrix to S-parameter noise correlation matrix.

matrix	cstocz (matrix cs, matrix z)
	Converts S-parameter noise correlation matrix to impedance noise correlation matrix.

matrix	cztocy (matrix cz, matrix y)
	Converts impedance noise correlation matrix to admittance noise correlation matrix.

matrix	cytocz (matrix cy, matrix z)
	Converts admittance noise correlation matrix to impedance noise correlation matrix.

matrix	twoport (matrix m, char in, char out)
	Generic conversion matrix.

Detailed Description

Dense matrix class implementation.

References:

[1] Power Waves and the Scattering Matrix Kurokawa, K. Microwave Theory and Techniques, IEEE Transactions on, Vol.13, Iss.2, Mar 1965 Pages: 194- 202

[2] A Rigorous Technique for Measuring the Scattering Matrix of a Multiport Device with a 2-Port Network Analyzer John C. TIPPET, Ross A. SPECIALE Microwave Theory and Techniques, IEEE Transactions on, Vol.82, Iss.5, May 1982 Pages: 661- 666

[3] Comments on "A Rigorous Techique for Measuring the Scattering Matrix of a Multiport Device with a Two-Port Network Analyzer" Dropkin, H. Microwave Theory and Techniques, IEEE Transactions on, Vol. 83, Iss.1, Jan 1983 Pages: 79 - 81

[4] Arbitrary Impedance "Accurate Measurements In Almost Any Impedance Environment" in Scropion Application note Anritsu online(2007/07/30) http://www.eu.anritsu.com/files/11410-00284B.pdf

[5] Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances Frickey, D.A. Microwave Theory and Techniques, IEEE Transactions on Vol. 42, Iss. 2, Feb 1994 pages: 205 - 211 doi: 10.1109/22.275248

[6] Comments on "Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances" [and reply] Marks, R.B.; Williams, D.F.; Frickey, D.A. Microwave Theory and Techniques, IEEE Transactions on, Vol.43, Iss.4, Apr 1995 Pages: 914- 915 doi: 10.1109/22.375247

[7] Wave Techniques for Noise Modeling and Measurement S. W. Wedge and D. B. Rutledge, IEEE Transactions on Microwave Theory and Techniques, vol. 40, no. 11, Nov. 1992. pages 2004-2012, doi: 10.1109/22.168757 Author copy online (2007/07/31) http://authors.library.caltech.edu/6226/01/WEDieeetmtt92.pdf

Definition in file matrix.cpp.

Function Documentation

matrix abs ( matrix a )

Computes magnitude of each matrix element.

Parameters

[in] a matrix

Todo:

add abs in place

a is const

Definition at line 529 of file matrix.cpp.

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matrix adjoint ( matrix a )

adjoint matrix

The function returns the adjoint complex matrix. This is also called the adjugate or transpose conjugate.

Parameters

[in] a Matrix to transpose

Todo:

add adjoint in place

Do not lazy and avoid conj and transpose copy

a is const

Definition at line 520 of file matrix.cpp.

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matrix arg ( matrix a )

Computes the argument of each matrix element.

Parameters

[in] a matrix

Todo:

add arg in place

a is const

Definition at line 553 of file matrix.cpp.

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matrix atos	(	matrix	a,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Converts chain matrix to scattering parameters.

Converts chain matrix to scattering parameters Formulae are given by [5] and are remembered here:

$\begin{align*} S_{11}&=\frac{AZ_{02}+B-CZ_{01}^*Z_{02}-DZ_{01}^*}{\Delta} \\ S_{12}&=\frac{2(AD-BC) (\Re\text{e}\;Z_{01}\Re\text{e}\;Z_{02})^{1/2}} {\Delta}\\ S_{21}&=\frac{2(\Re\text{e}\;Z_{01}\Re\text{e}\;Z_{02})^{1/2}}{\Delta}\\ S_{22}&=\frac{-AZ_{02}^*+B-CZ_{01}^*Z_{02}+DZ_{01}}{\Delta} \end{align*}$

Where:

$\Delta =AZ_{02}+B+CZ_{01}Z_{02}-DZ_{01}$

Parameters

[in]	a	Chain matrix
[in]	z1	impedance at input 1
[in]	z2	impedance at input 2

Returns: Scattering matrix

Bug:: Do not use fabs

Todo:: a, z1, z2 const

Definition at line 1213 of file matrix.cpp.

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nr_complex_t cofactor	(	matrix	a,
		int	u,
		int	v
	)

Computes the complex cofactor of the given determinant.

The cofactor is the determinant obtained by deleting the row and column of a given element of a matrix or determinant. The cofactor is preceded by a + or - sign depending of the sign of $(-1)^(u+v)$

Bug:: This algortihm is recursive! Stack overfull!

Todo:

((u + v) & 1) is cryptic use (u + v)% 2

#ifdef 0

static?

Definition at line 648 of file matrix.cpp.

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matrix conj ( matrix a )

Conjugate complex matrix.

Parameters

[in] a Matrix to conjugate

Todo:

add conj in place

a is const

Definition at line 503 of file matrix.cpp.

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matrix cstocy	(	matrix	cs,
		matrix	y
	)

Converts S-parameter noise correlation matrix to admittance noise correlation matrix.

According to [7] fig 2:

$C_y=(I+Y)C_s(I+Y)^+$

Where $C_s$ is the scattering noise correlation matrix, $C_y$ the admittance noise correlation matrix, $I$ the identity matrix and $S$ the scattering matrix of device. $x^+$ is the adjoint of $x$

Warning: cs matrix and y matrix are assumed to be normalized

Parameters

[in]	cs	S parameter noise correlation
[in]	y	Admittance matrix of device

Returns: admittance noise correlation matrix

Todo:: cs, y const

Definition at line 1421 of file matrix.cpp.

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matrix cstocz	(	matrix	cs,
		matrix	z
	)

Converts S-parameter noise correlation matrix to impedance noise correlation matrix.

According to [7] fig 2:

$C_z=(I+Z)C_s(I+Z)^+$

Where $C_s$ is the scattering noise correlation matrix, $C_z$ the impedance noise correlation matrix, $I$ the identity matrix and $S$ the scattering matrix of device. $x^+$ is the adjoint of $x$

Warning: cs matrix and y matrix are assumed to be normalized

Parameters

[in]	cs	S parameter noise correlation
[in]	z	Impedance matrix of device

Returns: Impedance noise correlation matrix

Todo:: cs, z const

Definition at line 1474 of file matrix.cpp.

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matrix cytocs	(	matrix	cy,
		matrix	s
	)

Admittance noise correlation matrix to S-parameter noise correlation matrix.

Converts admittance noise correlation matrix to S-parameter noise correlation matrix. According to [7] fig 2:

$C_s=\frac{1}{4}(I+S)C_y(I+S)^+$

Where $C_s$ is the scattering noise correlation matrix, $C_y$ the admittance noise correlation matrix, $I$ the identity matrix and $S$ the scattering matrix of device. $x^+$ is the adjoint of $x$

Warning: cy matrix and s matrix are assumed to be normalized

Parameters

[in]	cy	Admittance noise correlation
[in]	s	S parameter matrix of device

Returns: S-parameter noise correlation matrix

Note: Assert compatiblity of matrix

Todo:: cy s const

Definition at line 1395 of file matrix.cpp.

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matrix cytocz	(	matrix	cy,
		matrix	z
	)

Converts admittance noise correlation matrix to impedance noise correlation matrix.

According to [7] fig 2:

$C_z=ZC_yZ^+$

Where $C_z$ is the impedance correlation matrix, $I$ the identity matrix and $C_y$ the admittance noise correlation matrix. $x^+$ is the adjoint of $x$

Warning: cy matrix and z matrix are assumed to be normalized

Parameters

[in]	cy	Admittance noise correlation
[in]	z	Impedance matrix of device

Returns: Impedance noise correlation matrix

Todo:: cs, z const

Definition at line 1522 of file matrix.cpp.

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matrix cztocs	(	matrix	cz,
		matrix	s
	)

Converts impedance noise correlation matrix to S-parameter noise correlation matrix.

According to [7] fig 2:

$C_s=\frac{1}{4}(I-S)C_z(I-S)$

Where $C_s$ is the scattering noise correlation matrix, $C_z$ the impedance noise correlation matrix, $I$ the identity matrix and $S$ the scattering matrix of device. $x^+$ is the adjoint of $x$

Warning: Cz matrix and s matrix are assumed to be normalized

Parameters

[in]	cz	Impedance noise correlation
[in]	s	S parameter matrix of device

Returns: S-parameter noise correlation matrix

Note: Assert compatiblity of matrix

Todo:: cz, s const

Definition at line 1448 of file matrix.cpp.

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matrix cztocy	(	matrix	cz,
		matrix	y
	)

Converts impedance noise correlation matrix to admittance noise correlation matrix.

According to [7] fig 2:

$C_y=YC_zY^+$

Where $C_z$ is the impedance correlation matrix, $I$ the identity matrix and $C_y$ the admittance noise correlation matrix. $x^+$ is the adjoint of $x$

Warning: cz matrix and y matrix are assumed to be normalized

Parameters

[in]	cz	impedance noise correlation
[in]	y	Admittance matrix of device

Returns: admittance noise correlation matrix

Todo:: cs, y const

Definition at line 1498 of file matrix.cpp.

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matrix dB ( matrix a )

Computes magnitude in dB of each matrix element.

Parameters

[in] a matrix

Definition at line 540 of file matrix.cpp.

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nr_complex_t det ( matrix a )

Compute determinant of the given matrix.

Parameters

[in] a matrix

Returns: Complex determinant

Todo:: a const?

Definition at line 753 of file matrix.cpp.

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nr_complex_t detGauss ( matrix a )

Compute determinant Gaussian algorithm.

Compute determinant of the given matrix using the Gaussian algorithm. This means to triangulate the matrix and multiply all the diagonal elements.

Parameters

[in] a matrix

Note: assert square matrix

Todo:

static ?

a const?

Definition at line 708 of file matrix.cpp.

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nr_complex_t detLaplace ( matrix a )

Compute determinant of the given matrix using Laplace expansion.

The Laplace expansion of the determinant of an n by n square matrix a expresses the determinant of a as a sum of n determinants of (n-1) by (n-1) sub-matrices of a. There are 2n such expressions, one for each row and column of a.

See Wikipedia http://en.wikipedia.org/wiki/Laplace_expansion

Parameters

[in] a matrix

Bug:: This algortihm is recursive! Stack overfull!

Note: assert square matrix

Todo:

#ifdef 0

static ?

Definition at line 677 of file matrix.cpp.

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matrix diagonal ( vector diag )

Create a diagonal matrix from a vector.

Parameters

[in] diag vector to write on the diagonal

Todo:: diag is const

Definition at line 615 of file matrix.cpp.

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matrix eye	(	int	rs,
		int	cs
	)

Create identity matrix with specified number of rows and columns.

Parameters

[in]	rs	row number
[in]	cs	column number

Todo:

Avoid res.get*

Use memset

rs, cs are const

Definition at line 594 of file matrix.cpp.

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matrix eye ( int s )

Create a square identity matrix.

Parameters

[in] s row or column number of square matrix

Todo:

Do not by lazy and implement it

s is const

Definition at line 607 of file matrix.cpp.

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matrix gtos	(	matrix	g,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Definition at line 1346 of file matrix.cpp.

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matrix htos	(	matrix	h,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Converts hybrid matrix to scattering parameters.

Formulae are given by [5] and are remembered here:

$\begin{align*} S_{11}&=\frac{(h_{11}-Z_{01}^*)(1+h_{22}Z_{02})-h_{12}h_{21}Z_{02}} {\Delta}\\ S_{12}&=\frac{-2h_{12}(\Re\text{e}\;Z_{01}\Re\text{e}\;Z_{02})^\frac{1}{2}} {\Delta}\\ S_{21}&=\frac{-2h_{21}(\Re\text{e}\;Z_{01}\Re\text{e}\;Z_{02})^\frac{1}{2}} {\Delta}\\ S_{22}&=\frac{(h_{11}+Z_{01})(1-h_{22}Z_{02}^*)-h_{12}h_{21}Z_{02}^*} {\Delta} \end{align*}$

Where $\Delta$ is:

$\Delta=(Z_{01}+h_{11})(1+h_{22}Z_{02})-h_{12}h_{21}Z_{02}$

Parameters

[in]	h	hybrid matrix
[in]	z1	impedance at input 1
[in]	z2	impedance at input 2

Returns: scattering matrix

Note: Assert 2 by 2 matrix

Todo:: Why not h,z1,z2 const

Definition at line 1298 of file matrix.cpp.

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matrix imag ( matrix a )

Imaginary part matrix.

Parameters

[in] a matrix

Todo:

add imag in place

a is const

Definition at line 579 of file matrix.cpp.

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matrix inverse ( matrix a )

Compute inverse matrix.

Parameters

[in] a matrix to invert

Todo:: a is const

Definition at line 838 of file matrix.cpp.

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matrix inverseGaussJordan ( matrix a )

Compute inverse matrix using Gauss-Jordan elimination.

Compute inverse matrix of the given matrix by Gauss-Jordan elimination.

Todo:

a const?

static?

Note: assert non singulat matix

Parameters

[in] a matrix to invert

Definition at line 789 of file matrix.cpp.

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matrix inverseLaplace ( matrix a )

Compute inverse matrix using Laplace expansion.

Compute inverse matrix of the given matrix using Laplace expansion.

Parameters

[in] a matrix to invert

Todo:

Static?

#ifdef 0

Bug:: recursive! Stack overflow

Todo:: a const?

Definition at line 770 of file matrix.cpp.

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matrix operator*	(	matrix	a,
		nr_complex_t	z
	)

Matrix scaling complex version.

Parameters

[in]	a	matrix to scale
[in]	z	scaling complex

Returns: Scaled matrix

Todo:: Why not a and z const

Definition at line 296 of file matrix.cpp.

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matrix operator*	(	nr_complex_t	z,
		matrix	a
	)

Matrix scaling complex version (different order)

Parameters

[in]	a	matrix to scale
[in]	z	scaling complex

Returns: Scaled matrix

Todo:

Why not a and z const

Why not inline

Definition at line 311 of file matrix.cpp.

matrix operator*	(	matrix	a,
		nr_double_t	d
	)

Matrix scaling complex version.

Parameters

[in]	a	matrix to scale
[in]	d	scaling real

Returns: Scaled matrix

Todo:: Why not d and a const

Definition at line 321 of file matrix.cpp.

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matrix operator*	(	nr_double_t	d,
		matrix	a
	)

Matrix scaling real version (different order)

Parameters

[in]	a	matrix to scale
[in]	d	scaling real

Returns: Scaled matrix

Todo:

Why not inline?

Why not d and a const

Definition at line 336 of file matrix.cpp.

matrix operator*	(	matrix	a,
		matrix	b
	)

Matrix multiplication.

Dumb and not optimized matrix multiplication

Parameters

a]	first matrix
b]	second matrix

Note: assert compatibility

Todo:: a and b are const

Definition at line 376 of file matrix.cpp.

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matrix operator+	(	matrix	a,
		matrix	b
	)

Matrix addition.

Parameters

a]	first matrix
b]	second matrix

Note: assert same size

Todo:: a and b are const

Definition at line 226 of file matrix.cpp.

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matrix operator+	(	matrix	a,
		nr_complex_t	z
	)

Complex scalar addition.

Parameters

[in]	a	matrix
[in]	z	complex to add

Todo:

Move near other +

a and z are const

Definition at line 397 of file matrix.cpp.

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matrix operator+	(	nr_complex_t	z,
		matrix	a
	)

Complex scalar addition different order.

Parameters

[in]	a	matrix
[in]	z	complex to add

Todo:

Move near other +

a and z are const

Why not inline

Definition at line 412 of file matrix.cpp.

matrix operator+	(	matrix	a,
		nr_double_t	d
	)

Real scalar addition.

Parameters

[in]	a	matrix
[in]	d	real to add

Todo:

Move near other +

a and d are const

Definition at line 422 of file matrix.cpp.

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matrix operator+	(	nr_double_t	d,
		matrix	a
	)

Real scalar addition different order.

Parameters

[in]	a	matrix
[in]	d	real to add

Todo:

Move near other +

a and d are const

Why not inline

Definition at line 437 of file matrix.cpp.

matrix operator-	(	matrix	a,
		matrix	b
	)

Matrix subtraction.

Parameters

a]	first matrix
b]	second matrix

Note: assert same size

Todo:: a and b are const

Definition at line 257 of file matrix.cpp.

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matrix operator-	(	matrix	a,
		nr_complex_t	z
	)

Complex scalar substraction.

Parameters

[in]	a	matrix
[in]	z	complex to add

Todo:

Move near other +

a and z are const

Why not inline

Definition at line 448 of file matrix.cpp.

matrix operator-	(	nr_complex_t	z,
		matrix	a
	)

Complex scalar substraction different order.

Parameters

[in]	a	matrix
[in]	z	complex to add

Todo:

Move near other +

a and z are const

Why not inline

Definition at line 459 of file matrix.cpp.

matrix operator-	(	matrix	a,
		nr_double_t	d
	)

Real scalar substraction.

Parameters

[in]	a	matrix
[in]	z	real to add

Todo:

Move near other +

a and z are const

Why not inline

Definition at line 470 of file matrix.cpp.

matrix operator-	(	nr_double_t	d,
		matrix	a
	)

Real scalar substraction different order.

Parameters

[in]	a	matrix
[in]	z	real to add

Todo:

Move near other +

a and z are const

Why not inline

Definition at line 481 of file matrix.cpp.

matrix operator/	(	matrix	a,
		nr_complex_t	z
	)

Matrix scaling division by complex version.

Parameters

[in]	a	matrix to scale
[in]	z	scaling complex

Returns: Scaled matrix

Todo:: Why not a and z const

Definition at line 346 of file matrix.cpp.

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matrix operator/	(	matrix	a,
		nr_double_t	d
	)

Matrix scaling division by real version.

Parameters

[in]	a	matrix to scale
[in]	d	scaling real

Returns: Scaled matrix

Todo:: Why not a and d const

Definition at line 360 of file matrix.cpp.

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matrix pow	(	matrix	a,
		int	n
	)

Definition at line 623 of file matrix.cpp.

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matrix real ( matrix a )

Real part matrix.

Parameters

[in] a matrix

Todo:

add real in place

a is const

Definition at line 566 of file matrix.cpp.

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matrix stoa	(	matrix	s,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Converts chain matrix to scattering parameters.

Converts scattering parameters to chain matrix. Formulae are given by [5] tab 1. and are remembered here:

$\begin{align*} A&=\frac{(Z_{01}^*+S_{11}Z_{01})(1-S_{22}) +S_{12}S_{21}Z_{01}}{\Delta} \\ B&=\frac{(Z_{01}^*+S_{11}Z_{01})(Z_{02}^*+S_{22}Z_{02}) -S_{12}S_{21}Z_{01}Z_{02}}{\Delta} \\ C&=\frac{(1-S_{11})(1-S_{22}) -S_{12}S_{21}}{\Delta} \\ D&=\frac{(1-S_{11})(Z_{02}^*+S_{22}Z_{02}) +S_{12}S_{21}Z_{02}}{\Delta} \end{align*}$

Where:

$\Delta = 2 S_{21}\sqrt{\Re\text{e}\;Z_{01}\Re\text{e}\;Z_{02}}$

Bug:: Do not need fabs

Parameters

[in]	s	Scattering matrix
[in]	z1	impedance at input 1
[in]	z2	impedance at input 2

Returns: Chain matrix

Note: Assert 2 by 2 matrix

Todo:: Why not s,z1,z2 const

Definition at line 1172 of file matrix.cpp.

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matrix stog	(	matrix	s,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Definition at line 1322 of file matrix.cpp.

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matrix stoh	(	matrix	s,
		nr_complex_t	z1 = `50.0`,
		nr_complex_t	z2 = `50.0`
	)

Converts scattering parameters to hybrid matrix.

Converts chain matrix to scattering parameters Formulae are given by [5] and are remembered here:

$\begin{align*} h_{11}&=\frac{(Z_{01}^*+S_{11}Z_{01}) (Z_{02}^*+S_{22}Z_{02}) -S_{12}S_{21}Z_{01}Z_{02}}{\Delta}\\ h_{12}&=\frac{2S_{12} (\Re\text{e}\;Z_{01} \Re\text{e}\;Z_{02})^\frac{1}{2}} {\Delta} \\ h_{21}&=\frac{-2S_{21} (\Re\text{e}\;Z_{01} \Re\text{e}\;Z_{02})^\frac{1}{2}} {\Delta} \\ h_{22}&=\frac{(1-S_{11})(1-S_{22})-S_{12}S_{21}}{\Delta} \end{align*}$

Where $\Delta$ is:

$\Delta=(1-S_{11})(Z_{02}^*+S_{22}Z_{02})+S_{12}S_{21}Z_{02}$

Bug:: {Programmed formulae are valid only for Z real}

Parameters

[in]	s	Scattering matrix
[in]	z1	impedance at input 1
[in]	z2	impedance at input 2

Returns: hybrid matrix

Note: Assert 2 by 2 matrix

Todo:: Why not s,z1,z2 const

Definition at line 1260 of file matrix.cpp.

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matrix stos	(	matrix	s,
		vector	zref,
		vector	z0
	)

S params to S params.

Convert scattering parameters with the reference impedance 'zref' to scattering parameters with the reference impedance 'z0'.

Detail are given in [1], under equation (32)

New scatering matrix $S'$ is:

$S'=A^{-1}(S-\Gamma^+)(I-\Gamma S)^{-1}A^+$

Where x^+ is the adjoint (or complex tranposate) of x, I the identity matrix and $A$ is diagonal the matrix such as: $\Gamma_i= r_i$ and $A$ the diagonal matrix such as:

$A_i = \frac{(1-r_i^*)\sqrt{|1-r_ir_i^*|}}{|1-r_i|}$

Where $x*$ is the complex conjugate of $x$ and $r_i$ is wave reflexion coefficient of $Z_i'$ with respect to $Z_i^*$ (where $Z_i'$ is the new impedance and $Z_i$ is the old impedance), ie:

$r_i = \frac{Z_i'-Z_i}{Z_i'-Z_i^*}$

Parameters

[in]	s	original S matrix
[in]	zref	original reference impedance
[in]	z0	new reference impedance

Bug:: This formula is valid only for real z!

Todo:

Correct documentation about standing waves [1-4]

Implement Speciale implementation [2-3] if applicable

Returns: Renormalized scattering matrix

Todo:: s, zref and z0 const

Definition at line 881 of file matrix.cpp.

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matrix stos	(	matrix	s,
		nr_complex_t	zref,
		nr_complex_t	z0 = `50.0`
	)

S renormalization with all part identic.

Parameters

[in]	s	original S matrix
[in]	zref	original reference impedance
[in]	z0	new reference impedance

Todo:: Why not inline

Returns: Renormalized scattering matrix

Todo:: s, zref and z0 const

Definition at line 901 of file matrix.cpp.

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matrix stos	(	matrix	s,
		nr_double_t	zref,
		nr_double_t	z0 = `50.0`
	)

S renormalization with all part identic and real.

Parameters

[in]	s	original S matrix
[in]	zref	original reference impedance
[in]	z0	new reference impedance

Todo:: Why not inline

Returns: Renormalized scattering matrix

Todo:: s, zref and z0 const

Definition at line 914 of file matrix.cpp.

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matrix stos	(	matrix	s,
		vector	zref,
		nr_complex_t	z0 = `50.0`
	)

S renormalization (variation)

Parameters

[in]	s	original S matrix
[in]	zref	original reference impedance
[in]	z0	new reference impedance

Todo:: Why not inline

Returns: Renormalized scattering matrix

Todo:: s, zref and z0 const

Definition at line 926 of file matrix.cpp.

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matrix stos	(	matrix	s,
		nr_complex_t	zref,
		vector	z0
	)

S renormalization (variation)

Parameters

[in]	s	original S matrix
[in]	zref	original reference impedance
[in]	z0	new reference impedance

Todo:

Why not inline

s, zref and z0 const

Returns: Renormalized scattering matrix

Definition at line 938 of file matrix.cpp.

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matrix stoy	(	matrix	s,
		vector	z0
	)

Scattering parameters to admittance matrix.

Convert scattering parameters to admittance matrix. According to [1] eq (19):

$Z=F^{-1} (I- S)^{-1} (SG + G^+) F$

Where $S$ is the scattering matrix, $x^+$ is the adjoint of x, I the identity matrix. The matrix F and G are diagonal matrix defined by:

$\begin{align*} F_i&=\frac{1}{2\sqrt{\Re\text{e}\; Z_i}} \\ G_i&=Z_i \end{align*}$

Using the well know formula $(AB)^{-1}=B^{1}A^{1}$ , we derivate:

$Y=F^{-1} (SG+G^+)^{-1} (I-S) F$

Parameters

[in]	s	Scattering matrix
[in]	z0	Normalisation impedance

Note: We could safely drop the in because we compute $FXF^{-1}$ and therefore will simplify.

Bug:: not correct if zref is complex

Todo:: s and z0 const

Returns: Admittance matrix

Definition at line 1073 of file matrix.cpp.

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matrix stoy	(	matrix	s,
		nr_complex_t	z0 = `50.0`
	)

Convert scattering pto adminttance parameters identic case.

Parameters

[in]	S	Scattering matrix
[in]	z0	Normalisation impedance

Returns: Admittance matrix

Todo:

Why not inline

s and z0 const

Definition at line 1092 of file matrix.cpp.

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matrix stoz	(	matrix	s,
		vector	z0
	)

Scattering parameters to impedance matrix.

Convert scattering parameters to impedance matrix. According to [1] eq (19):

$Z=F^{-1} (I- S)^{-1} (SG + G^+) F$

Where $S$ is the scattering matrix, $x^+$ is the adjoint of x, I the identity matrix. The matrix F and G are diagonal matrix defined by:

$\begin{align*} F_i&=\frac{1}{2\sqrt{\Re\text{e}\; Z_i}} \\ G_i&=Z_i \end{align*}$

Parameters

[in]	s	Scattering matrix
[in]	z0	Normalisation impedance

Note: We could safely drop the in because we compute $FXF^{-1}$ and therefore will simplify.

Bug:: not correct if zref is complex

Todo:: s, z0 const

Returns: Impedance matrix

Definition at line 964 of file matrix.cpp.

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matrix stoz	(	matrix	s,
		nr_complex_t	z0 = `50.0`
	)

Scattering parameters to impedance matrix identic case.

Parameters

[in]	s	Scattering matrix
[in]	z0	Normalisation impedance

Returns: Impedance matrix

Todo:

Why not inline?

s and z0 const?

Definition at line 983 of file matrix.cpp.

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matrix transpose ( matrix a )

Matrix transposition.

Parameters

[in] a Matrix to transpose

Todo:

add transpose in place

a is const

Definition at line 490 of file matrix.cpp.

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matrix twoport	(	matrix	m,
		char	in,
		char	out
	)

Generic conversion matrix.

This function converts 2x2 matrices from any of the matrix forms Y, Z, H, G and A to any other. Also converts S<->(A, T, H, Y and Z) matrices. Convertion assumed:

Y->Y, Y->Z, Y->H, Y->G, Y->A, Y->S, Z->Y, Z->Z, Z->H, Z->G, Z->A, Z->S, H->Y, H->Z, H->H, H->G, H->A, H->S, G->Y, G->Z, G->H, G->G, G->A, G->S, A->Y, A->Z, A->H, A->G, A->A, A->S, S->Y, S->Z, S->H, S->G, S->A, S->S, S->T,T->T,T->S