#include <complex.h>
#include <string.h>
#include "electrode.h"
#include "blas.h"
#include "lapack.h"

Functions
int	fill_incidence_imm (_Complex double wg, const Electrode electrodes, size_t num_electrodes, const double *nodes, size_t num_nodes)

int	fill_impedance_imm (_Complex double wg, const _Complex double zl, const _Complex double *zt, size_t num_electrodes, size_t num_nodes)

int	solve_immittance (_Complex double wg, _Complex double ie, size_t num_electrodes, size_t num_nodes)

int	fill_incidence_adm (_Complex double a, _Complex double b, const Electrode electrodes, size_t num_electrodes, const double nodes, size_t num_nodes)

int	fill_impedance_adm (_Complex double yn, _Complex double zl, _Complex double zt, _Complex double a, _Complex double *b, size_t num_electrodes, size_t num_nodes)

int	calculate_yla_ytb (_Complex double yla, _Complex double ytb, _Complex double zl, _Complex double zt, _Complex double a, _Complex double b, size_t num_electrodes, size_t num_nodes)

int	fill_impedance_adm2 (_Complex double yn, _Complex double yla, _Complex double ytb, _Complex double a, _Complex double *b, size_t num_electrodes, size_t num_nodes)

int	solve_admittance (_Complex double yn, _Complex double ic, size_t num_nodes)

Function Documentation

◆ calculate_yla_ytb()

int calculate_yla_ytb	(	_Complex double *	yla,
		_Complex double *	ytb,
		_Complex double *	zl,
		_Complex double *	zt,
		_Complex double *	a,
		_Complex double *	b,
		size_t	num_electrodes,
		size_t	num_nodes
	)

Calculates the modified longitudinal and transversal admittances \( Z_L^{-1} A \) and \( Z_T^{-1} B \). \( Z_L \) and \( Z_T \) are replaced by their inverses in the process. Useful when they are needed to calculate the currents \( I_L = Z_L^{-1} A U \) and \( I_T = Z_T^{-1} B U \).

Parameters

yla	modified longitudinal admittance \( Z_L^{-1} A \) of size \( m \times n \)
ytb	modified transversal admittance \( Z_T^{-1} B \) of size \( m \times n \)
a	longitudinal incidence matrix \( A \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
b	transversal incidence matrix \( B \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
zl	longitudinal impedance matrix \( Z_L \) as a flat array of size \( m^2 \)
zt	transversal impedance matrix \( Z_T \) as a flat array of size \( m^2 \)
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_impedance_adm2

◆ fill_impedance_adm()

int fill_impedance_adm	(	_Complex double *	yn,
		_Complex double *	zl,
		_Complex double *	zt,
		_Complex double *	a,
		_Complex double *	b,
		size_t	num_electrodes,
		size_t	num_nodes
	)

Calculates the nodal admittance matrix \( Y_N = A^T Z_L^{-1} A + B^T Z_T^{-1} B \). As it is symmetric, only its lower half is stored (set).

Parameters

yn	nodal admmitance matrix \( Y_N \) as flat array of size \( n^2 \)
a	longitudinal incidence matrix \( A \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
b	transversal incidence matrix \( B \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
zl	longitudinal impedance matrix \( Z_L \) as a flat array of size \( m^2 \)
zt	transversal impedance matrix \( Z_T \) as a flat array of size \( m^2 \)
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_impedance_adm2; solve_admittance

◆ fill_impedance_adm2()

int fill_impedance_adm2	(	_Complex double *	yn,
		_Complex double *	yla,
		_Complex double *	ytb,
		_Complex double *	a,
		_Complex double *	b,
		size_t	num_electrodes,
		size_t	num_nodes
	)

Calculates the nodal admittance matrix \( Y_N = A^T Z_L^{-1} A + B^T Z_T^{-1} B \), were \( Z_L^{-1} A \) and \( Z_T^{-1} B \) are already calculated. Those matrices are preserved. Useful when they must be calculated to find the currents \( I_L = Z_L^{-1} A U \) and \( I_T = Z_T^{-1} B U \).

Parameters

yn	nodal admmitance matrix \( Y_N \) as flat array of size \( n^2 \)
a	longitudinal incidence matrix \( A \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
b	transversal incidence matrix \( B \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
yla	modified longitudinal admittance \( Z_L^{-1} A \)
ytb	modified transversal admittance \( Z_T^{-1} B \)
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_impedance_adm; calculate_yla_ylb; solve_admittance

◆ fill_impedance_imm()

int fill_impedance_imm	(	_Complex double *	wg,
		const _Complex double *	zl,
		const _Complex double *	zt,
		size_t	num_electrodes,
		size_t	num_nodes
	)

Fills the Global Immittance matrix \( W_G = \begin{bmatrix} Y_E & A^T & B^T \\ A & -Z_L & 0 \\ B & 0 & -Z_T \end{bmatrix} \) with the impedance matrices \( Z_L,Z_T \). As it is symmetric, only its lower half is stored (set).

Parameters

wg	Global Immittance matrix as flat array of size \( (2m + n)^2 \)
zl	longitudinal impedance matrix \( Z_L \) as a flat array of size \( m^2 \)
zt	transversal impedance matrix \( Z_T \) as a flat array of size \( m^2 \)
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_incidence_imm; solve_immittance

◆ fill_incidence_adm()

int fill_incidence_adm	(	_Complex double *	a,
		_Complex double *	b,
		const Electrode *	electrodes,
		size_t	num_electrodes,
		const double *	nodes,
		size_t	num_nodes
	)

Fills the nodal incidence matrices \( A \) and \( B \) used in the calculation of the nodal admittance matrix \( Y_N = A^T Z_L^{-1} A + B^T Z_T^{-1} B \).
Note that \( B = |A|/2 \) and if it is desired to save memory, A and B can be set to be the same pointer and, in that case, it is guaranteed that the end result will be \( A \). In other words: when only \( A \) is desired, \( B \) can point to \( A, (B := A)\), saving memory space. Then call the function as: fill_incidence_adm(a, a, electrodes, m, nodes, n); so that \( a:=A \).

Parameters

a	longitudinal incidence matrix \( A \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
b	transversal incidence matrix \( B \) as flat array of size \( m \times n \) in COLUMN MAJOR ordering
electrodes	array of electrodes
num_electrodes	number of electrodes \( m \)
nodes	array of nodes
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_impedance_adm; fill_impedance_adm2

◆ fill_incidence_imm()

int fill_incidence_imm	(	_Complex double *	wg,
		const Electrode *	electrodes,
		size_t	num_electrodes,
		const double *	nodes,
		size_t	num_nodes
	)

Fills the Global Immittance matrix \( W_G = \begin{bmatrix} Y_E & A^T & B^T \\ A & -Z_L & 0 \\ B & 0 & -Z_T \end{bmatrix} \) with the incidence matrices \( A,B \). This function is separated from fill_impedance because \( A,B \) depend only on geometry, while \( Z_L,Z_T \) will vary with frequency. It is expected that \( W_G \) was zero-ed before calling this function (or allocated through calloc). As \( W_G \) is symmetric, only its lower half is stored (set).

Parameters

wg	Global Immittance matrix \( W_G \) as flat array of size \( (2m + n)^2 \)
electrodes	array of electrodes
num_electrodes	number of electrodes \( m \)
nodes	array of nodes
num_nodes	number of nodes \( n \)

Returns: 0 on success

See also: fill_impedance_imm; solve_immittance

◆ solve_admittance()

int solve_admittance	(	_Complex double *	yn,
		_Complex double *	ic,
		size_t	num_nodes
	)

Solves the system of equations of the Nodal Admitance formulation \( Y_N U = I_E \). It is recommended to use the raw LAPACK routines instead of this function. That way, the same system can be used to solve multiple right hand sides (injection vectors), the optimal workspace can be queried just once when solving for multiple frequencies. See the source code of this function to have an idea.

Parameters

yn	nodal admittance matrix \( Y_N = A^T Z_L^{-1} A + B^T Z_T^{-1} B \), assumed to be symmetric with lower half stored. The LU decomposition is done in-place.
ie	RHS vector of injected currents in each node. The solution replaces this array in-place.
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on sucess

See also: fill_incidence_adm; fill_impedance_adm; fill_impedance_adm2

◆ solve_immittance()

int solve_immittance	(	_Complex double *	wg,
		_Complex double *	ie,
		size_t	num_electrodes,
		size_t	num_nodes
	)

Solves the system of equations of the Global Immitance formulation.

Parameters

wg	global immittance matrix \( W_G \), assumed to be symmetric with lower half stored. The LU decomposition is done in-place.
ie	RHS vector \([I_E, 0, 0]^T\) where \( I_E \) are injected currents in each node and 0 are null vectors of size \( m \) each. The solution replaces this array in-place becoming \( [U, I_L, I_T] \). Where \( U \) is the nodal potentials and \( I_L \) and \( I_T \) the longitudinal and transversal currents, respectively. It is recommended to use the raw LAPACK routines instead of this function. That way, the same system can be used to solve multiple right hand sides (injection vectors), the optimal workspace can be queried just once when solving for multiple frequencies. See the source code of this function to have an idea.
num_electrodes	number of electrodes \( m \)
num_nodes	number of nodes \( n \)

Returns: 0 on sucess

See also: fill_incidence_imm; fill_impedance_imm

Functions

Function Documentation

◆ calculate_yla_ytb()

◆ fill_impedance_adm()

◆ fill_impedance_adm2()

◆ fill_impedance_imm()

◆ fill_incidence_adm()

◆ fill_incidence_imm()

◆ solve_admittance()

◆ solve_immittance()