Symbolic_functions.h File Reference

SymEngine-based symbolic algebra utilities for network analysis. More...

#include "../../Constants.h"

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Functions
DenseMatrix	createZeroMatrix (int size1, int size2)
	Creates a zero-filled SymEngine dense matrix.
void	fillWithZero (DenseMatrix &mat)
	Sets every entry of a SymEngine dense matrix to zero in place.
DenseMatrix	eigenToSymEngineDenseMatrix (const MatrixXcd &eigenMat)
	Converts an Eigen complex matrix to a SymEngine DenseMatrix.
complex< double >	substitute_symbol (const RCP< const Basic > &expr, const std::string &symbol_name, double value)
	Substitutes a named symbol with a real value in an expression.
complex< double >	substitute_symbol (const RCP< const Basic > &expr, RCP< const Basic > symbol_name, double value)
	Substitutes a symbolic variable with a real value in an expression.
complex< double >	substitute_symbol (const RCP< const Basic > &expr, const std::string &symbol_name, complex< double > value)
	Substitutes a named symbol with a complex value in an expression.
complex< double >	substitute_symbol (const RCP< const Basic > &expr, RCP< const Basic > symbol_name, complex< double > value)
	Substitutes a symbolic variable with a complex value in an expression.
MatrixXcd	substitute_symbol (DenseMatrix, const string &, double)
	Substitutes a named symbol with a real value in every matrix entry.
MatrixXcd	substitute_symbol (DenseMatrix, const string &, complex< double >)
	Substitutes a named symbol with a complex value in every matrix entry.
MatrixXcd	substitute_symbol (DenseMatrix, RCP< const Basic >, double)
	Substitutes a symbolic variable with a real value in every matrix entry.
MatrixXcd	substitute_symbol (DenseMatrix, RCP< const Basic >, complex< double >)
	Substitutes a symbolic variable with a complex value in every matrix entry.
RCP< const Basic >	substitute_symbols (const RCP< const Basic > &expr, const std::vector< RCP< const Basic > > &symbols, double value)
	Substitutes multiple symbols with the same real value in an expression.
double	eval_basic (const RCP< const Basic > &expr)
	Evaluates a symbolic expression to a real scalar.
MatrixXd	kron_reduction (MatrixXd, vector< int >)
	Kron-reduces a real matrix by eliminating specified nodes.
DenseMatrix	kron_reduction (DenseMatrix, vector< int >)
	Kron-reduces a symbolic dense matrix by eliminating specified nodes.
Eigen::SparseMatrix< double >	absoluteSparseMatrix (const Eigen::SparseMatrix< std::complex< double > > &matrix)
	Takes the element-wise absolute value of a complex sparse matrix.
RCP< const Basic >	inv (const RCP< const Basic > &val)
	Symbolic multiplicative inverse (1/x).
RCP< const Basic >	addSym (const RCP< const Basic > &a, const RCP< const Basic > &b)
	Symbolic addition a + b.
RCP< const Basic >	subSym (const RCP< const Basic > &a, const RCP< const Basic > &b)
	Symbolic subtraction a - b.

Variables
const RCP< const Basic >	PI
	Symbolic representation of π.
const double	mu_0
	Vacuum permeability (H/m).
const double	epsilon_0
	Vacuum permittivity (F/m).
const double	gamma_num
	Euler–Mascheroni constant.
RCP< const Basic >	j
	Imaginary unit j.
RCP< const Basic >	omega
	Angular frequency symbol ω.
RCP< const Basic >	s
	Complex frequency symbol s = jω.

Detailed Description

SymEngine-based symbolic algebra utilities for network analysis.

Provides symbolic constants, matrix creation/conversion, parameter substitution, Kron reduction, and basic symbolic arithmetic used when assembling MNA matrices and transfer functions.

Function Documentation

absoluteSparseMatrix()

Eigen::SparseMatrix< double > absoluteSparseMatrix ( const Eigen::SparseMatrix< std::complex< double > > &  matrix )

extern

Takes the element-wise absolute value of a complex sparse matrix.

Parameters

matrix

Input complex sparse matrix.

Returns

Real sparse matrix of magnitudes.

Referenced by PowerFlow::load_params_dc().

addSym()

RCP< const Basic > addSym ( const RCP< const Basic > &  a, const RCP< const Basic > &  b  )

extern

Symbolic addition a + b.

Parameters

a	First operand.
b	Second operand.

Returns

Simplified sum.

Referenced by Impedance::Impedance(), Impedance::Impedance(), MMC::writeMNAmatrix(), Resistor::writeMNAmatrix(), AC_source::writeMNAmatrix(), DC_source::writeMNAmatrix(), and Inductor::writeMNAmatrix().

createZeroMatrix()

DenseMatrix createZeroMatrix ( int  size1, int  size2  )

extern

Creates a zero-filled SymEngine dense matrix.

Parameters

size1	Number of rows.
size2	Number of columns.

Returns

Zero matrix of the requested dimensions.

References j.

Referenced by Cable::Cable(), Element::Element(), Generator::Generator(), Overhead_Line::Overhead_Line(), PVplant::PVplant(), TransformerDeltaDelta::TransformerDeltaDelta(), TransformerDeltaY::TransformerDeltaY(), TransformerDeltaY_real::TransformerDeltaY_real(), TransformerYDelta::TransformerYDelta(), WTtype3::WTtype3(), WTtype4::WTtype4(), StateSpaceModel::formState(), and kron_reduction().

eigenToSymEngineDenseMatrix()

DenseMatrix eigenToSymEngineDenseMatrix ( const MatrixXcd &  eigenMat )

extern

Converts an Eigen complex matrix to a SymEngine DenseMatrix.

Parameters

eigenMat

Input Eigen MatrixXcd.

Returns

Equivalent SymEngine dense matrix.

References j.

eval_basic()

double eval_basic ( const RCP< const Basic > &  expr )

extern

Evaluates a symbolic expression to a real scalar.

Parameters

expr	Symbolic expression (must be real-valued after substitution).

Returns

Numeric double result.

Referenced by extractCoefficient().

fillWithZero()

void fillWithZero ( DenseMatrix &  mat )

extern

Sets every entry of a SymEngine dense matrix to zero in place.

Parameters

mat	Matrix to zero.

References j.

inv()

RCP< const Basic > inv ( const RCP< const Basic > &  val )

extern

Symbolic multiplicative inverse (1/x).

Parameters

val	Symbolic value.

Returns

Symbolic inverse expression.

Referenced by Resistor::writeMNAmatrix().

kron_reduction() [1/2]

DenseMatrix kron_reduction ( DenseMatrix  matrix, vector< int >  no_eliminate  )

extern

Kron-reduces a symbolic dense matrix by eliminating specified nodes.

Parameters

matrix	Input symbolic matrix.
nodes	Indices of nodes to eliminate.

Returns

Symbolically reduced matrix.

References createZeroMatrix(), and j.

kron_reduction() [2/2]

MatrixXd kron_reduction ( MatrixXd  matrix, vector< int >  no_eliminate  )

extern

Kron-reduces a real matrix by eliminating specified nodes.

Parameters

matrix	Input admittance/impedance matrix.
nodes	Indices of nodes to eliminate.

Returns

Reduced matrix.

Referenced by Cable::Cable(), and Overhead_Line::Overhead_Line().

substitute_symbol() [1/8]

complex< double > substitute_symbol ( const RCP< const Basic > &  expr, const std::string &  symbol_name, complex< double >  value  )

extern

Substitutes a named symbol with a complex value in an expression.

Parameters

expr	Symbolic expression.
symbol_name	Name of the symbol to replace.
value	Complex substitution value.

Returns

Complex numeric result after substitution.

substitute_symbol() [2/8]

complex< double > substitute_symbol ( const RCP< const Basic > &  expr, const std::string &  symbol_name, double  value  )

extern

Substitutes a named symbol with a real value in an expression.

Parameters

expr	Symbolic expression.
symbol_name	Name of the symbol to replace.
value	Real substitution value.

Returns

Complex numeric result after substitution.

Referenced by AC_source::AC_source(), Cable::compute_y_parameters(), Overhead_Line::compute_y_parameters(), TransmissionLine::computePowerFlow(), Transformer_base::computePowerFlow(), and Impedance_base::computePowerFlow().

substitute_symbol() [3/8]

complex< double > substitute_symbol ( const RCP< const Basic > &  expr, RCP< const Basic >  symbol_name, complex< double >  value  )

extern

Substitutes a symbolic variable with a complex value in an expression.

Parameters

expr	Symbolic expression.
symbol_name	Symbol to replace.
value	Complex substitution value.

Returns

Complex numeric result after substitution.

substitute_symbol() [4/8]

complex< double > substitute_symbol ( const RCP< const Basic > &  expr, RCP< const Basic >  symbol_name, double  value  )

extern

Substitutes a symbolic variable with a real value in an expression.

Parameters

expr	Symbolic expression.
symbol_name	Symbol to replace.
value	Real substitution value.

Returns

Complex numeric result after substitution.

substitute_symbol() [5/8]

MatrixXcd substitute_symbol ( DenseMatrix  M, const string &  symbol_name, complex< double >  value  )

extern

Substitutes a named symbol with a complex value in every matrix entry.

Parameters

mat	Symbolic dense matrix.
symbol_name	Name of the symbol to replace.
value	Complex substitution value.

Returns

Numeric complex matrix after substitution.

References j.

substitute_symbol() [6/8]

MatrixXcd substitute_symbol ( DenseMatrix  M, const string &  symbol_name, double  value  )

extern

Substitutes a named symbol with a real value in every matrix entry.

Parameters

mat	Symbolic dense matrix.
symbol_name	Name of the symbol to replace.
value	Real substitution value.

Returns

Numeric complex matrix after substitution.

References j.

substitute_symbol() [7/8]

MatrixXcd substitute_symbol ( DenseMatrix  M, RCP< const Basic >  symbol, complex< double >  value  )

extern

Substitutes a symbolic variable with a complex value in every matrix entry.

Parameters

mat	Symbolic dense matrix.
symbol_name	Symbol to replace.
value	Complex substitution value.

Returns

Numeric complex matrix after substitution.

References j.

substitute_symbol() [8/8]

MatrixXcd substitute_symbol ( DenseMatrix  M, RCP< const Basic >  symbol, double  value  )

extern

Substitutes a symbolic variable with a real value in every matrix entry.

Parameters

mat	Symbolic dense matrix.
symbol_name	Symbol to replace.
value	Real substitution value.

Returns

Numeric complex matrix after substitution.

References j.

substitute_symbols()

RCP< const Basic > substitute_symbols ( const RCP< const Basic > &  expr, const std::vector< RCP< const Basic > > &  symbols, double  value  )

extern

Substitutes multiple symbols with the same real value in an expression.

Parameters

expr	Symbolic expression.
symbols	List of symbols to replace.
value	Common real substitution value.

Returns

Simplified symbolic expression after substitution.

subSym()

RCP< const Basic > subSym ( const RCP< const Basic > &  a, const RCP< const Basic > &  b  )

extern

Symbolic subtraction a - b.

Parameters

a	Minuend.
b	Subtrahend.

Returns

Simplified difference.

Referenced by Resistor::writeMNAmatrix().

Variable Documentation

epsilon_0

const double epsilon_0

extern

Vacuum permittivity (F/m).

Vacuum permittivity (F/m).

Referenced by Cable::Cable(), and Overhead_Line::Overhead_Line().

gamma_num

const double gamma_num

extern

Euler–Mascheroni constant.

Euler–Mascheroni constant.

Referenced by Cable::Cable().

j

RCP<const Basic> j

extern

Imaginary unit j.

Referenced by AC_source::AC_source(), AC_source::AC_source(), AC_source::AC_source(), Admittance::Admittance(), Cable::Cable(), DC_source::DC_source(), DC_source::DC_source(), DC_source::DC_source(), DC_source::DC_source(), Impedance::Impedance(), Impedance::Impedance(), Impedance::Impedance(), Impedance::Impedance(), Impedance::Impedance(), Load::Load(), Overhead_Line::Overhead_Line(), Resistor::Resistor(), Transformer_classic::Transformer_classic(), Transformer_real::Transformer_real(), TransformerDeltaDelta::TransformerDeltaDelta(), TransformerDeltaY::TransformerDeltaY(), TransformerDeltaY_real::TransformerDeltaY_real(), TransformerYDelta::TransformerYDelta(), WTtype3::WTtype3(), Element::apply_transformation(), bode_plot_implot(), StabilityEstimate::bodeplotTF(), StabilityEstimate::compute_equivalent_admittance_parameters_num(), Element::compute_y_parameters(), MMC::compute_y_parameters(), Cable::compute_y_parameters(), Overhead_Line::compute_y_parameters(), computeJacobians(), Converter::computeParticipationFactors(), MMC::computeStateDerivatives(), convertToPhasor(), createZeroMatrix(), eigen2sun(), eigenToSymEngineDenseMatrix(), fillWithZero(), ComponentBuilder::findNonEmptyNumericArray(), ComponentBuilder::findNonEmptyString(), ComponentBuilder::findNumber(), ComponentBuilder::findNumericOrReferenceArray(), ComponentBuilder::findScalar(), StateSpaceModel::form_cutset_nodes(), StateSpaceModel::formState(), get_block(), kron_reduction(), mat_add(), mat_mul(), mat_sub(), mat_transpose(), matrixToVector(), matrixToVector(), mul_scalar(), nyquist_plot_implot(), StabilityEstimate::nyquistplotTF(), plot_participation_factors_implot(), Element::plotYParameters(), Element::printElementValues(), Resistor::printElementValues(), PowerFlow::solve_opf(), substitute_symbol(), substitute_symbol(), substitute_symbol(), substitute_symbol(), SimulationBuilder::validateJSON(), vectorToMatrix(), vectorToMatrix(), viz_opf(), Element::writeFile(), StabilityEstimate::writeFileTF(), and Switch::writeMNAmatrix().

mu_0

const double mu_0

extern

Vacuum permeability (H/m).

Vacuum permeability (H/m).

Referenced by Cable::Cable(), and Overhead_Line::Overhead_Line().

omega

RCP<const Basic> omega

extern

Angular frequency symbol ω.

Referenced by AC_source::AC_source(), Load::Load(), MMC::MMC(), Transformer_classic::Transformer_classic(), Transformer_real::Transformer_real(), TransmissionLine::TransmissionLine(), Element::compute_y_parameters(), Cable::compute_y_parameters(), Overhead_Line::compute_y_parameters(), TransmissionLine::computePowerFlow(), Transformer_base::computePowerFlow(), Impedance_base::computePowerFlow(), Load::computePowerFlow(), example_DQsym_MMC_controlled(), example_DQsym_Simple_MMC(), example_MMC(), example_OPF_double_area(), example_OPF_PV(), example_OPF_single_area(), example_OPF_WT(), example_point2point_case(), and example_stability_check().

PI

const RCP<const Basic> PI

extern

Symbolic representation of π.

s

RCP<const Basic> s

extern

Complex frequency symbol s = jω.

Referenced by Cable::Cable(), Capacitor::Capacitor(), Generator::Generator(), Inductor::Inductor(), Overhead_Line::Overhead_Line(), PVplant::PVplant(), WTtype3::WTtype3(), WTtype4::WTtype4(), DQsym::buildMatricesForState(), Impedance_base::computePowerFlow(), dq_multiply(), and extractCoefficient().