# Procedures

ProcedureLocationProcedure TypeDescription

Adds a given element at a certain (row, column) position to the matrix datastructure. Elements that are zero are not added, sanity checks are done on the row and column indices.

Adds a new node to the linked list with a given column index and value.

Adds a given element to the node element, does type-checking of the polymorphic element given. Allowed types are complex, real, integer.

This routine builds the quadblock at one particular grid point in the Gaussian grid and for one particular Gaussian weight. For a 2x2 block at index $(i, j)$ in the top-left block we have $(2i, 2j)$ as index of the bottom-right corner of the 2x2 block. The other corners are then filled by subtracting one from an index.

interface to the different equilibrium submodules

append_nodemod_matrix_rowSubroutine

Subroutine to append a new node to an already existing list of nodes. A new node is created, appended, and the tail is updated.

apply_boundary_conditionsmod_boundary_managerSubroutine
apply_essential_boundaries_leftmod_boundary_managerInterface
apply_essential_boundaries_rightmod_boundary_managerInterface
apply_natural_boundaries_leftmod_boundary_managerInterface
apply_natural_boundaries_rightmod_boundary_managerInterface
are_setmod_unitsFunction
arnoldimod_solversInterface

interface to the different solution methods implemented in submodules

array_to_bandedmod_transform_matrixInterface
array_to_complex_bandedmod_transform_matrixSubroutine

Converts a given array to a banded datastructure.

array_to_complex_hermitian_bandedmod_transform_matrixSubroutine

Converts a given array to a Hermitian banded datastructure.

array_to_hermitian_bandedmod_transform_matrixInterface
array_to_matrixmod_transform_matrixInterface
assemblemod_eigenfunctionsSubroutine
assemblemod_derived_efsSubroutine
assemblemod_base_efsSubroutine
assemble_eigenfunctionmod_ef_assemblyFunction
assertmod_assertSubroutine

Utility function used by assert.fpp's assert macro.

banded_matrix_x_vectormod_banded_operationsFunction

Calculates the matrix-vector product of a general complex banded matrix and a complex vector. Uses the level 2 BLAS routine zgbmv.

banded_to_arraymod_transform_matrixInterface
banded_to_complex_arraymod_transform_matrixFunction

Converts a banded datastructure to a full complex array.

build_matricesmod_matrix_managerSubroutine

can_calculate_pp_quantitiesmod_derived_ef_namesFunction
can_get_B1mod_derived_ef_namesFunction
can_get_B2mod_derived_ef_namesFunction
can_get_B3mod_derived_ef_namesFunction
can_get_B_ppmod_derived_ef_namesFunction
can_get_curl_B_imod_derived_ef_namesFunction
can_get_curl_B_ppmod_derived_ef_namesFunction
can_get_curl_v_1mod_derived_ef_namesFunction
can_get_curl_v_2mod_derived_ef_namesFunction
can_get_curl_v_3mod_derived_ef_namesFunction
can_get_curl_v_ppmod_derived_ef_namesFunction
can_get_div_Bmod_derived_ef_namesFunction
can_get_div_vmod_derived_ef_namesFunction
can_get_entropymod_derived_ef_namesFunction
can_get_v_ppmod_derived_ef_namesFunction
cast_node_element_to_complexmod_matrix_elementsFunction
character_array_tostringmod_loggingFunction
check_eigenfunction_subset_paramsmod_inputSubroutine

Called when the eigenfunction subset selection is enabled, this checks if the global variables are properly set.

check_on_axis_valuesmod_inspectionsSubroutine

Checks if on-axis regularity conditions are satisfied in cylindrical geometry. We check if $B_\theta, B_z', v_\theta$ and $v_z'$ are smaller than 1e-3 on-axis. Nothing is checked if the geometry is Cartesian.

check_wavenumbersmod_inspectionsSubroutine

Sanity check on the wavenumbers. Checks if k2 is an integer in cylindrical geometry.

cleanuplegolasSubroutine

Deallocates all main variables, then calls the cleanup routines of all relevant subroutines to do the same thing.

complex_is_equalmod_check_valuesFunction

Equality check between complex values

complex_is_zeromod_check_valuesFunction

Checks if complex values are zero

complex_tostringmod_loggingFunction
constant_current_eqmod_equilibriumInterface

interface to the different equilibrium submodules

contains_NaN_complexmod_check_valuesFunction

Checks a given complex value/array/matrix for NaN.

contains_NaN_realmod_check_valuesFunction

Checks a given real value/array/matrix for NaN.

continuity_equil_conditionsmod_inspectionsSubroutine

Checks the continuity equation for the equilibrium state. This is given by

copymod_matrix_structureFunction

Dedicated function to copy a matrix structure into a new matrix structure. The datastructure contains pointers, such that simply setting matrix1 = matrix2 may result in pointer target losses (and wrong results).

coronal_flux_tube_eqmod_equilibriumInterface

interface to the different equilibrium submodules

couette_flow_eqmod_equilibriumInterface

interface to the different equilibrium submodules

cputicmod_timingSubroutine

Subroutine to start a CPU timer.

cputocmod_timingSubroutine

Subroutine to end a CPU timer.

create_and_set_derived_state_vectormod_derived_ef_namesFunction
create_atmosphere_curvesmod_solar_atmosphereSubroutine

Interpolates the atmospheric tables to the desired resolution. The temperature derivative is obtained numerically.

Creates an interpolated cooling curve based on the chosen table. Calls a second-order polynomial interpolation routine and takes care of normalisations.

create_datfilemod_outputSubroutine
create_first_nodemod_matrix_rowSubroutine

Subroutine to add the first node to the linked list. Allocates a new node and sets both the head and tail to this node.

create_matricesmod_matrix_creationSubroutine

Main subroutine to assemble the matrices A and B, which are already allocated when entering this subroutine but not yet initialised. The quadblock is calculated for every grid interval and used to assemble both matrices. On exit, both matrices are fully assembled and boundary conditions are imposed.

cubic_factorsmod_spline_functionsSubroutine

Calculates the cubic basis functions.

cubic_factors_derivmod_spline_functionsSubroutine

@brief Calculates the derivatives of the cubic basis functions.

cubic_factors_deriv2mod_spline_functionsSubroutine

@brief Calculates the second derivatives of the cubic basis functions.

deallocate_bfield_typemod_typesSubroutine

Deallocates all attributes contained in the magnetic field type.

deallocate_conduction_typemod_typesSubroutine

Deallocates all attributes contained in the thermal conduction type.

deallocate_cooling_typemod_typesSubroutine

Deallocates all attributes contained in the radiative cooling type.

deallocate_density_typemod_typesSubroutine

Deallocates all attributes contained in the density type.

deallocate_derived_ef_module_variablesmod_derived_efsSubroutine
deallocate_gravity_typemod_typesSubroutine

Deallocates all attributes contained in the gravity type.

deallocate_hall_typemod_typesSubroutine

Deallocates all attributes contained in the Hall type.

deallocate_resistivity_typemod_typesSubroutine

Deallocates all attributes contained in the resistivity type.

deallocate_temperature_typemod_typesSubroutine

Deallocates all attributes contained in the temperature type.

deallocate_typemod_typesInterface

interface to deallocate all the different types

deallocate_velocity_typemod_typesSubroutine

Deallocates all attributes contained in the velocity type.

debugmod_loggingSubroutine
default_b02_profilemod_solar_atmosphereFunction

Sets the default profile for B02, taken to be zero.

default_b03_profilemod_solar_atmosphereFunction

Sets the default profile for B03, taken to be a uniform field of 10 Gauss.

default_db02_profilemod_solar_atmosphereFunction

Sets the default profile for dB02, taken to be zero.

default_db03_profilemod_solar_atmosphereFunction

Sets the default profile for dB03, taken to be zero.

default_gravity_profilemod_solar_atmosphereFunction

Sets the default profile for the gravitational field, taken to be

deletemod_matrix_nodeSubroutine

Destructor, deallocates the node attributes.

deletemod_matrix_elementsSubroutine
deletemod_matrix_element_nodeSubroutine
deletemod_solver_settingsSubroutine
deletemod_io_settingsSubroutine
deletemod_settingsSubroutine
deletemod_grid_settingsSubroutine
deletemod_equilibrium_settingsSubroutine
deletemod_eigenfunctionsSubroutine
deletemod_derived_efsSubroutine
deletemod_base_efsSubroutine
delete_matrixmod_matrix_structureSubroutine

Deallocates the matrix datastructure, nullifies all corresponding pointers and deallocates the various nodes in the rows.

delete_node_from_rowmod_matrix_rowSubroutine

Deletes a given node from the current row.

delete_rowmod_matrix_rowSubroutine

Deletes a given linked list row by recursively iterating over all nodes. Nullifies the pointers and deallocates the elements.

derived_ef_funcmod_derived_efsInterface
derived_state_vector_is_setmod_settingsFunction
destroymod_banded_matrix_hermitianSubroutine

Destructor, deallocates the datastructure.

destroymod_banded_matrixSubroutine

Destructor, deallocates the datastructure.

destroymod_arpack_typeSubroutine

Destructor, deallocates variables.

dimensions_are_validmod_banded_matrixFunction

Checks if the given matrix dimensions are valid. For now, we only accept square matrices. Returns .true. if rows equals cols, .false. otherwise.

disablemod_hall_settingsSubroutine
disablemod_resistivity_settingsSubroutine
disablemod_flow_settingsSubroutine
disablemod_gravity_settingsSubroutine
disablemod_viscosity_settingsSubroutine
disablemod_cooling_settingsSubroutine
disablemod_conduction_settingsSubroutine
disable_prefixmod_loggingSubroutine
discrete_alfven_eqmod_equilibriumInterface

interface to the different equilibrium submodules

enablemod_hall_settingsSubroutine
enablemod_resistivity_settingsSubroutine
enablemod_flow_settingsSubroutine
enablemod_gravity_settingsSubroutine
enablemod_cooling_settingsSubroutine
enable_coolingmod_physics_settingsSubroutine
enable_electron_inertiamod_hall_settingsSubroutine
enable_flowmod_physics_settingsSubroutine
enable_gravitymod_physics_settingsSubroutine
enable_hallmod_physics_settingsSubroutine
enable_para_conductionmod_conduction_settingsSubroutine
enable_parallel_conductionmod_physics_settingsSubroutine
enable_perp_conductionmod_conduction_settingsSubroutine
enable_perpendicular_conductionmod_physics_settingsSubroutine
enable_prefixmod_loggingSubroutine
enable_resistivitymod_physics_settingsSubroutine
enable_viscositymod_physics_settingsSubroutine
enable_viscous_heatingmod_viscosity_settingsSubroutine
end_timermod_timingFunction
equilibrium_cleanmod_equilibriumSubroutine

Cleaning routine, deallocates the equilibrium types.

errormod_loggingSubroutine
find_index_in_character_arraymod_get_indicesFunction

Function to locate the index of a given character in a character array. Iterates over the elements and returns on the first hit, if no match was found zero is returned.

find_indices_in_character_arraymod_get_indicesFunction

Function to locate the indices of an array of characters in another character array. Returns the indices of the first hit, it no match was found zero is returned.

flow_driven_instabilities_eqmod_equilibriumInterface

interface to the different equilibrium submodules

general_array_to_matrixmod_transform_matrixFunction

Converts a given 2D array to the linked-list matrix datastructure.

get_A_elementsmod_matrix_creationSubroutine

Retrieves the A-matrix elements for a given quadblock corresponding to a particular point in the grid and a particular Gaussian weight. This routine is called n_gauss times for every grid interval.

get_arpack_modemod_solver_settingsFunction
get_array_elementmod_transform_matrixFunction

Retrieves the element at index (i, j) for an array of general type. Returns the element as a (casted) complex type.

get_B1mod_derived_efsFunction
get_B2mod_derived_efsFunction
get_B3mod_derived_efsFunction
get_B_elementsmod_matrix_creationSubroutine

Retrieves the B-matrix elements for a given quadblock corresponding to a particular point in the grid and a particular Gaussian weight. This routine is called n_gauss times for every grid interval.

get_B_paramod_derived_efsFunction
get_B_perpmod_derived_efsFunction
get_base_eigenfunctionmod_derived_efsFunction
get_basename_datfilemod_io_settingsFunction
get_basis_functionmod_ef_assemblyFunction
get_bmatmod_arpack_typeFunction

Getter for kind of B-matrix in eigenvalue problem.

get_boundary_typemod_equilibrium_settingsFunction
get_combined_value_from_eigenvectormod_ef_assemblyFunction
get_complex_elementmod_matrix_structureFunction

Returns the complex element associated with the linked-list node at position (row, column) in the matrix datastructure. Non-existing nodes correspond to zero values, so when a node at (row, column) is not foudn this function returns (complex) zero.

get_constantsmod_resistivitySubroutine

Retrieves resistivity constants. Returns all physical constants used to calculate the Spitzer resistivity.

get_cooling_curvemod_cooling_settingsFunction
get_curl_B_1mod_derived_efsFunction
get_curl_B_2mod_derived_efsFunction
get_curl_B_3mod_derived_efsFunction
get_curl_B_paramod_derived_efsFunction
get_curl_B_perpmod_derived_efsFunction
get_curl_v_1mod_derived_efsFunction
get_curl_v_2mod_derived_efsFunction
get_curl_v_3mod_derived_efsFunction
get_curl_v_paramod_derived_efsFunction
get_curl_v_perpmod_derived_efsFunction
get_datfile_pathmod_outputFunction
get_derived_state_vectormod_settingsFunction
get_deta_dTmod_resistivitySubroutine

Calculates the derivative of the resistivity. Returns the derivative of the full Spitzer resistivity with respect to the equilibrium temperature, if a fixed resistivity was set instead this routine returns zero.

get_diagonal_factorsmod_essential_boundariesFunction

Returns the value that is introduced on the main block diagonal after zeroing out the corresponding row and column. Depends on the matrix that is used.

get_diffF_operatormod_matrix_shortcutsFunction

Calculates the derivative of the operator, given as

get_dim_integralblockmod_dimsFunction
get_dim_matrixmod_dimsFunction
get_dim_subblockmod_dimsFunction
get_div_Bmod_derived_efsFunction
get_div_vmod_derived_efsFunction
get_ef_depsmod_ef_assemblyFunction
get_ef_epsmod_ef_assemblyFunction
get_ef_gridmod_eigenfunctionsFunction
get_ef_gridptsmod_grid_settingsFunction
get_eigenfunctionslegolasSubroutine

Initialises and calculates the eigenfunctions if requested.

get_electron_fractionmod_hall_settingsFunction
get_elementmod_banded_matrix_hermitianFunction

Retrieves the element at position (row, col) of the original matrix. See the LAPACK documentation, element $a_{ij}$ of the original matrix is stored at position $(kd + 1 + i - j, j)$ if uplo = "U" and at position $(1 + i - j, j)$ if uplo = "L" in the banded storage.

get_elementmod_banded_matrixFunction

Retrieves the element at position (row, col) of the original matrix. See the LAPACK documentation, element $a_{ij}$ of the original matrix is stored at position $(ku + 1 + i - j, j)$ (with $ku$ the number of superdiagonals).

get_elementmod_matrix_element_nodeFunction
get_elementsmod_matrix_elementsFunction
get_entropymod_derived_efsFunction
get_equilibrium_typemod_equilibrium_settingsFunction
get_etamod_resistivitySubroutine

Calculates the resistivity. Returns either the full Spitzer resistivity based on the equilibrium parameters, or a fixed resistivity value if specified in the global variables module. The unit resistivity is also set in this routine. If a fixed resistivity is used, eta is assumed to be normalised and the unit resistivity remains unity.

get_evpdimmod_arpack_typeFunction

Getter for dimension of eigenvalue problem.

get_F_operatormod_matrix_shortcutsFunction

Calculates the operator, given as

get_fixed_resistivitymod_resistivity_settingsFunction
get_fixed_tc_paramod_conduction_settingsFunction
get_fixed_tc_perpmod_conduction_settingsFunction
get_G_operatormod_matrix_shortcutsFunction

Calculates the operator, given as

get_gammamod_physics_settingsFunction
get_gamma_1mod_physics_settingsFunction
get_gauss_gridptsmod_grid_settingsFunction
get_geometrymod_grid_settingsFunction
get_grid_endmod_grid_settingsFunction
get_grid_startmod_grid_settingsFunction
get_gridptsmod_grid_settingsFunction
get_indexmod_get_indicesInterface

interface to retrieve the index of an element in an array.

get_interpolation_pointsmod_cooling_settingsFunction
get_Kp_operatormod_matrix_shortcutsFunction

Calculates the (modified) conduction prefactor, given as \boldsymbol{K_p^+} = \left(\boldsymbol{K_p} + \frac{\partial \kappa_\perp}{\partial(B^2)}\right) \boldsymbol{K_p^{++}} = \left( \frac{\partial \kappa_\perp}{\partial(B^2)} - \frac{B_{01}^2}{B_0^2}\boldsymbol{K_p^+} \right) 

get_labelmod_matrix_structureFunction

Returns the current label.

get_logging_levelmod_loggingFunction
get_LU_factorisation_bandedmod_linear_systemsSubroutine

Calculates the LU factorisation of a complex banded matrix $A$. Uses the LAPACK routine zgbtrf.

get_lworklmod_arpack_typeFunction

Getter for length of workl array, returns 3 * ncv**2 + 5 * ncv

get_maxitermod_arpack_typeFunction

Getter for maximum number of iterations.

get_mean_molecular_weightmod_unitsFunction
get_nb_diagonalsmod_matrix_structureSubroutine

Subroutine to get the number of super- and sub-diagonals in the matrix.

get_nb_elementsmod_matrix_elementsFunction
get_nb_eqsmod_settingsFunction
get_ncvmod_arpack_typeFunction

Getter for number of Arnoldi basis vectors that should be calculated.

get_nevmod_arpack_typeFunction

Getter for number of eigenvalues to calculate.

get_nodemod_matrix_rowFunction

Returns a pointer to the node corresponding to the given column. Returns a nullified pointer if no node containing the given column index was found.

get_nodemod_matrix_elementsFunction
get_node_elementmod_matrix_nodeFunction

Returns the node element.

get_numerical_derivativemod_interpolationSubroutine

Calculates the numerical derivative of a given array. A sixth-order accurate central difference stencil is used to calculate the derivative. Near the edges a sixth-order accurate forward and backward difference stencil is used for the left and right boundary, respectively. It is assumed that the x values are all equally spaced. If this is not the case, a polynomial interpolation on a uniform grid can be done and that one can be differentiated instead. The stencils are as follows:

get_output_foldermod_io_settingsFunction
get_parfilemod_inputSubroutine

Parses the command line arguments and retrieves the parfile passed.

get_physics_typemod_settingsFunction
get_positionmod_matrix_element_nodeFunction
get_positionsmod_matrix_elementsFunction
get_residualmod_outputFunction
get_rosner_coolingmod_cooling_curvesSubroutine

Uses the piecewise rosner cooling curve to calculate the radiative cooling values based on the equilibrium temperature.

get_solvermod_solver_settingsFunction
get_spline1mod_matrix_element_nodeFunction
get_spline2mod_matrix_element_nodeFunction
get_state_vectormod_settingsFunction
get_subblock_indexmod_get_indicesInterface
get_tolerancemod_arpack_typeFunction

Getter for tolerance (relative accuracy) to indicate eigenvalue convergence.

get_total_nb_elementsmod_matrix_structureFunction

Returns the total number of elements (nodes) across the various rows.

get_total_nb_elementsmod_banded_matrix_hermitianFunction

Returns the total number of elements inside the banded matrix

get_total_nb_elementsmod_banded_matrixFunction

Returns the total number of elements inside the banded matrix.

get_total_nb_nonzero_elementsmod_banded_matrixFunction

Returns the total number of nonzero elements inside the banded matrix.

get_total_timemod_timingFunction
get_unit_conductionmod_unitsFunction
get_unit_densitymod_unitsFunction
get_unit_gravitymod_unitsFunction
get_unit_lambdaTmod_unitsFunction
get_unit_lengthmod_unitsFunction
get_unit_magneticfieldmod_unitsFunction
get_unit_massmod_unitsFunction
get_unit_numberdensitymod_unitsFunction
get_unit_pressuremod_unitsFunction
get_unit_resistivitymod_unitsFunction
get_unit_temperaturemod_unitsFunction
get_unit_timemod_unitsFunction
get_unit_velocitymod_unitsFunction
get_v_paramod_derived_efsFunction
get_v_perpmod_derived_efsFunction
get_viscosity_termsmod_viscositySubroutine
get_viscosity_valuemod_viscosity_settingsFunction
get_whichmod_arpack_typeFunction

Getter for which eigenvalues to return.

get_wv_operatormod_matrix_shortcutsFunction

Calculates the wave vector operator , given as

gold_hoyle_eqmod_equilibriumInterface

interface to the different equilibrium submodules

gravito_acoustic_eqmod_equilibriumInterface

interface to the different equilibrium submodules

gravito_mhd_eqmod_equilibriumInterface

interface to the different equilibrium submodules

grid_cleanmod_gridSubroutine

Cleanup routine, deallocates the arrays at module scope.

harris_sheet_eqmod_equilibriumInterface

interface to the different equilibrium submodules

has_electron_inertiamod_hall_settingsFunction
has_fixed_resistivitymod_resistivity_settingsFunction
has_fixed_tc_paramod_conduction_settingsFunction
has_fixed_tc_perpmod_conduction_settingsFunction
has_parallel_conductionmod_conduction_settingsFunction
has_perpendicular_conductionmod_conduction_settingsFunction
has_viscous_heatingmod_viscosity_settingsFunction
hermitian_banded_to_arraymod_transform_matrixInterface
hermitian_banded_to_complex_arraymod_transform_matrixFunction

Converts a Hermitian banded datastructure to a full complex array.

in_cgsmod_unitsFunction
increment_nb_elementsmod_matrix_elementsSubroutine
induction_equil_conditionsmod_inspectionsSubroutine

Checks the induction equation for the equilibrium state. The two (nonzero) resulting expressions are and should both be fulfilled.

infomod_loggingSubroutine
init_equilibrium_paramsmod_equilibrium_paramsSubroutine

Initialises all variables defined at module scope to NaN, including the wave numbers. This ensures that these have to be explicitly set.

initialisationlegolasSubroutine

Subroutine responsible for all initialisations. Allocates and initialises main and global variables, then the equilibrium state and eigenfunctions are initialised and the equilibrium is set.

initialisemod_eigenfunctionsSubroutine
initialisemod_derived_efsSubroutine
initialisemod_base_efsSubroutine
initialisemod_loggingSubroutine
initialise_bfield_typemod_typesSubroutine

Allocates the magnetic field type and initialises all values to zero.

initialise_conduction_typemod_typesSubroutine

Allocates the thermal conduction type and initialises all values to zero.

initialise_cooling_typemod_typesSubroutine

Allocates the radiative cooling type and initialises all values to zero.

initialise_density_typemod_typesSubroutine

Allocates the density type and initialises all values to zero.

initialise_equilibriummod_equilibriumSubroutine

Initialises the equilibrium types by calling the corresponding subroutine, which allocates all necessary attributes.

initialise_exceptionsmod_exceptionsSubroutine

Private subroutine, sets the pointer to the default method to be used when raising exceptions.

initialise_globalsmod_global_variablesSubroutine

Initialises the global variables in this module. All variables in this module are first set to their default values. These are either regular values or NaN, the latter in case variables must be explicitly set in the parfile or equilibrium submodule.

initialise_gravity_typemod_typesSubroutine

Allocates the gravity type and initialises all values to zero.

initialise_gridmod_gridSubroutine

General grid initialisations. Initialises both the regular grid and the Gaussian grid. Does calls to the mesh accumulation routines if needed, and sets the scale factor and its derivative.

initialise_hall_typemod_typesSubroutine

Allocates the Hall type and initialises all values to zero.

Initialises the radiative cooling variables. This routine first selects and allocates the correct cooling tables, depending on the desired curve. These tables are used to interpolate the final cooling curve using \p ncool points.

initialise_resistivity_typemod_typesSubroutine

Allocates the resistivity type and initialises all values to zero.

initialise_temperature_typemod_typesSubroutine

Allocates the temperature type and initialises all values to zero.

initialise_typemod_typesInterface

interface to initialise all the different types

initialise_velocity_typemod_typesSubroutine

Allocates the velocity type and initialises all values to zero.

integer_tostringmod_loggingFunction
integrate_ode_rkmod_integrationSubroutine

Integrates a first order differential equation of the form using a fifth-order Runge-Kutta method. The argument nbpoints determines the stepsize through If the arrays $A(x), B(x)$ are not of size nbpoints, then these are interpolated to that resolution. The differential equation is then integrated, the solution will also be of size nbpoints and can be downsampled using the appropriate subroutine. If desired the optional argument dyvalues can be provided, which contains the (numerical) derivative of y.

interchange_modes_eqmod_equilibriumInterface

interface to the different equilibrium submodules

internal_kink_eqmod_equilibriumInterface

interface to the different equilibrium submodules

interpolate_array_on_ef_gridmod_derived_efsFunction
interpolate_tablemod_interpolationSubroutine

Interpolates a given set of tables (x, y(x)) into a smooth curve. Assumes that x_table is an array with a monotone increase in values. Interpolation is done using n_interp points, in general a second order polynomial approximation is used except near sharp jumps.

inverse_iterationmod_solversInterface

interface to the different solution methods implemented in submodules

is_compatible_withmod_banded_matrix_hermitianFunction

Checks if a Hermitian band matrix is compatible with another Hermitian band matrix. This implies that the following attributes should be equal: - number of rows/columns - number of sub/superdiagonals - storage of upper or lower triangular part - dimensions of the banded matrices themselves Returns .true. if all criteria are satisfied, .false. otherwise.

is_compatible_withmod_banded_matrixFunction

Checks if a banded matrix is compatibe with another banded matrix. This implies that the following attributes should be equal: - dimensions of the original matrices - number of superdiagonals and subdiagonals - dimensions of the banded matrices themselves Returns .true. if these three criteria are satisfied, .false. otherwise.

is_constantmod_check_valuesInterface

interface to check if an array is constant

is_enabledmod_hall_settingsFunction
is_enabledmod_resistivity_settingsFunction
is_enabledmod_flow_settingsFunction
is_enabledmod_gravity_settingsFunction
is_enabledmod_viscosity_settingsFunction
is_enabledmod_cooling_settingsFunction
is_enabledmod_conduction_settingsFunction
is_equalmod_check_valuesInterface

interface to check equality between values/arrays

is_in_state_vectormod_derived_ef_namesFunction
is_NaNmod_check_valuesInterface

interface to check for NaN values

is_negativemod_check_valuesInterface

interface to check for negative values

is_using_substitutionmod_hall_settingsFunction
is_valid_elementmod_matrix_structureFunction

Checks if a given element is valid in order to add it to the matrix. Returns .true. if the element is of type real or complex, .false. otherwise.

is_valid_indexmod_matrix_structureFunction

Checks if a given index is valid for the current matrix datastructure. Returns .true. if the index (either row or column) is larger than 0 and smaller than the dimension of the matrix. Returns .false. otherwise.

is_valid_positionmod_matrix_elementsFunction
is_within_bandmod_banded_matrix_hermitianFunction

Checks if a given position (row, col) is within the banded structure. For uplo = "U" the position is within the band if for uplo = "L" the position is within the band if with $kd$ the number of sub/superdiagonals and $n$ the number of rows/columns.

is_within_bandmod_banded_matrixFunction

Checks if a given position (row, col) is within the banded structure, i.e. with $ku$ the number of superdiagonals and $kl$ the number of subdiagonals.

is_zeromod_check_valuesInterface

interface to check if values/arrays are zero

isothermal_atmosphere_eqmod_equilibriumInterface

interface to the different equilibrium submodules

kh_cd_instability_eqmod_equilibriumInterface

interface to the different equilibrium submodules

KHI_eqmod_equilibriumInterface

interface to the different equilibrium submodules

Loads a previously calculated profile and uses that to set the resolution, density and density derivatives.

log_equilibrium_infomod_consoleSubroutine
log_grid_infomod_consoleSubroutine
log_io_infomod_consoleSubroutine
log_physics_infomod_consoleSubroutine
log_solver_infomod_consoleSubroutine
logical_tostringmod_loggingFunction
lookup_table_valuemod_interpolationFunction

Function for fast table-lookup, returns the corresponding y-value in y_values based on a given based on a given $x0$. If the allow_outside flag is given as .true. then values on the edge of the table are returned when the lookup value is outside the array. Uses simple linear interpolation.

magnetothermal_instability_eqmod_equilibriumInterface

interface to the different equilibrium submodules

matrix_to_arraymod_transform_matrixInterface
matrix_to_bandedmod_transform_matrixInterface
matrix_to_complex_arraymod_transform_matrixSubroutine

Converts a given matrix data structure with complex nodes to a 2D complex array.

matrix_to_complex_bandedmod_transform_matrixSubroutine

Converts a matrix data structure into a complex banded matrix.

matrix_to_complex_hermitian_bandedmod_transform_matrixSubroutine

Converts a matrix data structure into a complex Hermitian banded matrix.

matrix_to_hermitian_bandedmod_transform_matrixInterface
MRI_accretion_eqmod_equilibriumInterface

interface to the different equilibrium submodules

multiplymod_banded_operationsInterface
needs_resamplingmod_integrationFunction

Checks if an array needs resampling.

new_arpack_configmod_arpack_typeFunction

Constructor for a new ARPACK configuration based on the dimension of the eigenvalue problem, mode of the solver and type of the B-matrix. Initialises required variables and allocates work arrays to be used when calling the solvers.

new_banded_matrixmod_banded_matrixFunction

Constructor for a new banded matrix with a given number of rows, columns, subdiagonals and superdiagonals. Allocates and initialises the datatype.

new_block_dimsmod_dimsFunction
new_conduction_settingsmod_conduction_settingsFunction
new_cooling_settingsmod_cooling_settingsFunction
new_eigenfunctionsmod_eigenfunctionsFunction
new_equilibrium_settingsmod_equilibrium_settingsFunction
new_flow_settingsmod_flow_settingsFunction
new_gravity_settingsmod_gravity_settingsFunction
new_grid_settingsmod_grid_settingsFunction
new_hall_settingsmod_hall_settingsFunction
new_hermitian_banded_matrixmod_banded_matrix_hermitianFunction

Constructor for a new Hermitian banded matrix with a given number of rows and diagonals. Allocates and initialises the datatype. initialise all to zero

new_io_settingsmod_io_settingsFunction
new_matrixmod_matrix_structureFunction

Constructor for a new matrix matrix with a given number of rows. Allocates and initialises the matrix datatype.

new_matrix_element_nodemod_matrix_element_nodeFunction
new_matrix_elementsmod_matrix_elementsFunction
new_nodemod_matrix_nodeFunction

Constructor for a new node, sets the column and element attributes. The element passed is polymorphic, but will be cast to complex in the node itself. No nodes are linked yet; the pointer to the next node is initialised to null().

new_physics_settingsmod_physics_settingsFunction
new_resistivity_settingsmod_resistivity_settingsFunction
new_rowmod_matrix_rowFunction

Constructor for a new row, initialises the linked list datastructure and sets the current head and tail pointers to null().

new_settingsmod_settingsFunction
new_solver_settingsmod_solver_settingsFunction
new_timermod_timingFunction
new_unit_systemmod_unitsFunction
new_viscosity_settingsmod_viscosity_settingsFunction
on_exception_raisedmod_exceptionsSubroutine

Workflow that is executed by default when an exception is raised. The argument message is printed to the console and program execution is terminated.

open_filemod_outputSubroutine
paint_stringmod_paintingFunction

Subroutine to paint a given string to the desired colour, returns a new string with ANSI escape sequences prepended and appended. If the 'colour' argument is not known, simply returns the string itself.

parse_finished_statsmod_arpack_typeSubroutine

Parses the statistics that come out of ARPACK when the run is finished. Displays the number of OPX and BX operations and the number of re-orthogonalisation steps that were needed.

parse_io_infomod_inputSubroutine
parse_znaupd_infomod_arpack_typeSubroutine

Parses the info parameter that comes out of ARPACK's znaupd method. If info = 0, everything behaved nicely and the reverse communication subroutines exited properly. If info is any other value something went wrong and we handle it accordingly.

parse_zneupd_infomod_arpack_typeSubroutine

Parses the info parameter that comes out of ARPACK's zneupd method. If info = 0, the eigenvalues extraction routines exited properly, if info is any other value something went wrong and we handle it accordingly.

perform_NaN_and_negative_checksmod_inspectionsSubroutine

General routine to do initial sanity checks on the various equilibrium attributes. We check the equilibrium arrays for NaN and see if all density and temperature values are positive.

perform_sanity_checksmod_inspectionsSubroutine

General routine to do sanity checks on the different equilibrium types. We check the wavenumbers and on-axis values, as well as standard and non-adiabatic equilibrium force balance.

photospheric_flux_tube_eqmod_equilibriumInterface

interface to the different equilibrium submodules

print_console_infomod_consoleSubroutine

Prints various console messages showing geometry, grid parameters, equilibrium parameters etc. Only for logging level "info" or above.

print_logomod_consoleSubroutine

Prints the Legolas logo to the console. The logo is wrapped in 1 whitespace at the top and two at the bottom. Only for logging level 'warning' (1) and above

print_timeloglegolasSubroutine
print_whitespacemod_consoleSubroutine

Prints an empty line to the console. Only if logging level is 'warning' or above.

qr_choleskymod_solversInterface

interface to the different solution methods implemented in submodules

qr_invertmod_solversInterface

interface to the different solution methods implemented in submodules

Calculates the derivatives of the quadratic basis functions.

qz_directmod_solversInterface

interface to the different solution methods implemented in submodules

Cleanup routine, deallocates all variables allocated at module-scope.

raise_exceptionmod_exceptionsSubroutine

Raises an exception with a given message. By default, exceptions terminate program execution. Calls the initialisation routine if not already done.

real_array_is_constantmod_check_valuesFunction

Check if an array has constant values

real_is_equalmod_check_valuesFunction

Equality check between real values

real_is_negativemod_check_valuesFunction

Check if values are or contain negative numbers

real_is_zeromod_check_valuesFunction

Checks if real values are zero

real_tostringmod_loggingFunction
resistive_homo_eqmod_equilibriumInterface

interface to the different equilibrium submodules

resistive_tearing_modes_eqmod_equilibriumInterface

interface to the different equilibrium submodules

resistive_tearing_modes_flow_eqmod_equilibriumInterface

interface to the different equilibrium submodules

resonant_absorption_eqmod_equilibriumInterface

interface to the different equilibrium submodules

retransform_eigenfunctionmod_ef_assemblyFunction
rk45mod_integrationSubroutine

Calculates the Runge-Kutta coefficients and calculates the fourth and fifth order solutions for step i+1 based on the values at step i.

rotating_plasma_cyl_eqmod_equilibriumInterface

interface to the different equilibrium submodules

RTI_eqmod_equilibriumInterface

interface to the different equilibrium submodules

RTI_KHI_eqmod_equilibriumInterface

interface to the different equilibrium submodules

RTI_theta_pinch_eqmod_equilibriumInterface

interface to the different equilibrium submodules

save_profile_to_filemod_solar_atmosphereSubroutine

Saves the density and density derivatives to the given filename. These can be used later on to set the values instead of solving the differential equation.

select_eigenfunctions_to_savemod_eigenfunctionsSubroutine
set_all_io_to_falsemod_io_settingsSubroutine
set_arpack_modemod_solver_settingsSubroutine
set_basename_datfilemod_io_settingsSubroutine
set_basis_functionssmod_natural_boundariesSubroutine
set_block_dimsmod_dimsSubroutine
set_bmatmod_arpack_typeSubroutine

Sets the type of B-matrix.

set_boundary_flagsmod_boundary_managerSubroutine
set_boundary_typemod_equilibrium_settingsSubroutine
set_conduction_prefactormod_thermal_conductionSubroutine

Sets the thermal conduction prefactor, given by . The radial derivative of the prefactor is also set, given by

set_conduction_valuesmod_thermal_conductionSubroutine

This routines sets all thermal conduction values in kappa_field, and calls all other relevant subroutines defined in this module.

set_cooling_curvemod_cooling_settingsSubroutine
set_derived_state_vectormod_settingsSubroutine
set_electron_fractionmod_hall_settingsSubroutine
set_elementmod_banded_matrix_hermitianSubroutine

Sets the element $a_{ij}$ of the original array into the banded structure. The row and col arguments refer to the row and column indices of the element in the original array. This routine has no effect if the location falls outside of the banded structure.

set_elementmod_banded_matrixSubroutine

Sets the element $a_{ij}$ of the original array into the banded structure. The row and col arguments refer to the row and column indices of the element in the original array. This routine has no effect if the location falls outside of the banded structure.

set_energy_balancemod_inspectionsSubroutine

Enforces the non-adiabatic force-balance equation for the equilibrium state. This is given by This subroutine essentially sets $\mathscr{L}0$ in such a way that this equation is satisfied. If the heating is assumed to only depend on the equilibrium, and if there is no $B$, $v_{01}$ or perpendicular thermal conduction, then $\mathscr{L}_0 = 0$. If one (or more) of these effects are present, then $\mathscr{L}_0 = 0$ is no longer true. The rc_field % heat_loss attribute is modified on exit.

set_equilibriummod_equilibriumSubroutine

Calls the routine to set the equilibrium pointer, then calls the correct submodule. Performs some sanity checks (negative values, NaNs etc.) when the equilibrium is set, then calls additional physics modules if needed.

set_equilibrium_arrays_on_ef_gridmod_derived_efsSubroutine
set_equilibrium_pointermod_equilibriumSubroutine

Selects the submodule based on the specified equilibrium in the parfile. Works on a case-select basis.

set_equilibrium_typemod_equilibrium_settingsSubroutine
set_eta_dropoffmod_resistivitySubroutine

Sets a hyperbolic tangent profile for the resistivity so it goes smoothly to zero near the edges. The location and width of the dropoff profile can be controlled through dropoff_edge_dist and dropoff_width.

set_fixed_resistivitymod_resistivity_settingsSubroutine
set_fixed_tc_paramod_conduction_settingsSubroutine
set_fixed_tc_perpmod_conduction_settingsSubroutine
set_function_pointermod_derived_efsSubroutine
set_gammamod_physics_settingsSubroutine
set_geometrymod_grid_settingsSubroutine
set_grid_boundariesmod_grid_settingsSubroutine
set_grid_gaussmod_gridSubroutine

Sets up grid_gauss, that is, the grid evaluated in the four Gaussian points. This is done by evaluating the weights at the four Gaussian nodes.

set_gridptsmod_grid_settingsSubroutine
set_hall_factorsmod_hallSubroutine

Retrieves the normalised Hall factor as described by Porth et al. (2014), with a dropoff at the boundary, if desired. Additionally, defines the electron inertia factor if included, with a dropoff profile, if desired.

set_incompressiblemod_physics_settingsSubroutine
set_interpolation_pointsmod_cooling_settingsSubroutine
set_kappa_paramod_thermal_conductionSubroutine

Calculates the parallel thermal conduction. Returns either the full parallel thermal conduction based on the equilibrium parameters, or a fixed value if specified in the global variables module.

set_kappa_para_derivativesmod_thermal_conductionSubroutine

Calculates the temperature derivative of the parallel thermal conduction component.

set_kappa_perpmod_thermal_conductionSubroutine

Calculates the perpendicular thermal conduction. Returns either the full perpendicular thermal conduction based on the equilibrium parameters, or a fixed value if specified in the global variables module.

set_kappa_perp_derivativesmod_thermal_conductionSubroutine

Calculates the thermal conduction derivatives. Returns the derivative of the perpendicular thermal conduction with respect to density, magnetic field squared and temperature.

Sets the radial derivative of the perpendicular thermal conduction coefficient. This is defined as

set_labelmod_matrix_structureSubroutine

Sets the label of the current matrix.

set_logging_levelmod_loggingSubroutine
set_maxitermod_arpack_typeSubroutine

Sets the maximum number of iterations that ARPACK is allowed to take, defaults to max(100, 10 * k) with k the number of eigenvalues.

set_mean_molecular_weightmod_unitsSubroutine
set_modemod_arpack_typeSubroutine

Sets the mode for the solver.

set_nb_eqsmod_settingsSubroutine
set_ncvmod_arpack_typeSubroutine

Setter for ncv, the number of Arnoldi basis vectors to calculate. This should satisfy 1 <= ncv - nev and ncv <= evpdim, with recommended value ncv = 2 * nev (see arpack docs).

set_nevmod_arpack_typeSubroutine

Setter for number of eigenvalues to calculate.

set_output_foldermod_io_settingsSubroutine

Sets the radiative cooling attributes of the corresponding types. This is called after the equilibrium is initialised in the submodule.

set_raise_methodmod_exceptionsSubroutine

Subroutine meant to be publicly called, sets the routine to be used when raising exceptions. Calls the initialisation routine if not already done.

set_residualmod_arpack_typeSubroutine

Setter for the residual vector, allocates and manually initialises the residual (= starting) vector using a uniform distribution on (-1, 1) for both the real and imaginary parts. Relies on the LAPACK routine zlarnv.

set_resistivity_valuesmod_resistivitySubroutine

This routines sets all resistivity values in \p eta_field, and calls all other relevant subroutines defined in this module.

set_scale_factormod_gridSubroutine

The scale factor to switch between Cartesian and cylindrical geometries is set here, along with its derivative. For cylindrical the scale factor is simply equal to the Gaussian grid, and its derivative is unity. For Cartesian the scale factor is unity and its derivative is zero.

set_small_values_to_zeromod_check_valuesInterface

interface to check for small values

set_solar_atmospheremod_solar_atmosphereSubroutine

Sets the density, temperature, gravity and magnetic field attributes of the respective fields to a realistic solar atmosphere profile. This routine first interpolates the temperature and numberdensity table at n_interp resolution, then solves the following ODE for the density: using a fifth order Runge-Kutta method. If the optional argument save_to is provided then the density profiles are saved to that file, which can be loaded back in on subsequent runs through the optional argument load_from. The integration is done over the entire table, the curve is sampled on the Gaussian grid, meaning that grid variations can all use the same result.

set_solvermod_solver_settingsSubroutine
set_state_vectormod_settingsSubroutine
set_units_from_densitymod_unitsSubroutine
set_units_from_temperaturemod_unitsSubroutine
set_viscosity_valuemod_viscosity_settingsSubroutine
set_whichmod_arpack_typeSubroutine

Setter for the "which" argument of ARPACK routines.

should_compute_eigenvectorsmod_io_settingsFunction
small_values_complexmod_check_valuesSubroutine

Small value checks for a complex variable/array/matrix, with the real and imaginary parts checked separately. Values that are smaller than the specified tolerance tol are set to zero. If tol is not present, DP_LIMIT is used as tolerance.

small_values_realmod_check_valuesSubroutine

Small value checks for a real variable/array/matrix. Values that are smaller than the specified tolerance tol are set to zero. If tol is not present, DP_LIMIT is used as tolerance.

solve_arpack_generalsmod_arpack_mainInterface
solve_arpack_shift_invertsmod_arpack_mainInterface

Main subroutine to solve the eigenvalue problem. Depending on the solvelist passed in the parfile, different solvers are called.

solve_linear_system_complex_bandedmod_linear_systemsFunction

Calculates the solution $X$ to a system of linear equations $AX = B$ where $A$ is a complex banded matrix and $B$ is a complex vector.

solve_linear_system_complex_banded_LUmod_linear_systemsFunction

Calculates the solution $X$ to a system of linear equations $AX = B$ where $A$ is a complex banded matrix and $B$ is a complex vector. Uses the LU factorisation of $A$ and pivoting information from zgbtrf.

spline_sizes_are_validmod_matrix_elementsFunction
standard_equil_conditionsmod_inspectionsSubroutine

Checks the standard force-balance equation for the equilibrium state. This results in three expressions, and they should all be fulfilled.

start_timermod_timingSubroutine
state_vector_is_setmod_settingsFunction
strmod_loggingInterface
suydam_cluster_eqmod_equilibriumInterface

interface to the different equilibrium submodules

taylor_couette_eqmod_equilibriumInterface

interface to the different equilibrium submodules

tc_pinch_eqmod_equilibriumInterface

interface to the different equilibrium submodules

throw_info_nonzero_warningmod_linear_systemsSubroutine
ticmod_timingSubroutine

Subroutine to start a wall clock timer.

tocmod_timingSubroutine

Subroutine to end a wall clock timer.

transform_state_variable_to_subblock_indexmod_get_indicesFunction

Transforms a given array of state variables to subblock indices. If odd is .true. returns the odd indices, otherwise the even indices. If edge equals "left", returns the indices corresponding to the left boundary block, if edge equals "right" returns indices for the right boundary block.

update_block_dimensionsmod_settingsSubroutine
update_dependent_unitsmod_unitsSubroutine
uplo_is_validmod_banded_matrix_hermitianFunction

Checks whether the given uplo parameter is valid.

user_defined_eqmod_equilibriumInterface

interface to the different equilibrium submodules

viscosity_boundariesmod_viscositySubroutine

Creates a quadblock for the A matrix containing the natural boundary conditions coming from the viscosity terms, depending on the supplied edge.

warningmod_loggingSubroutine
write_base_eigenfunction_datamod_outputSubroutine
write_derived_eigenfunction_datamod_outputSubroutine
write_eigenvector_datamod_outputSubroutine
write_equilibrium_datamod_outputSubroutine
write_equilibrium_infomod_outputSubroutine
write_equilibrium_namesmod_outputSubroutine
write_grid_infomod_outputSubroutine
Zeroes out the row and column corresponding to the given indices. Afterwards diagonal_factor is introduced in that row/column on the main diagonal.