# Parameter definitions for thorn AHFinderDirect
# $Header$

################################################################################

# we may need to look at grid::domain to choose our patch system symmetries
shares: grid
USES KEYWORD domain

# we need to look at ADMBase::metric_type and StaticConformal::conformal_state
# to check physical/conformal metric
shares: ADMBase
USES KEYWORD metric_type

# all remaining parameters are private to this thorn
private:
################################################################################

#
# overall parameters for the apparent horizon finding algorithm itself
#

boolean find_AHs_at_postinitial \
  "should we try to find apparent horizons at CCTK_POSTINITIAL?"
{
} "true"

boolean find_AHs_at_poststep \
  "should we try to find apparent horizons at CCTK_POSTSTEP?"
{
} "true"

keyword method "top-level method used to find the apparent horizon"
{
# these options are mostly for testing/debugging
"horizon function"  :: "evaluate the LHS function H(h)"
"Jacobian test"	    :: \
  "compute/print the J[H(h)] Jacobian matrix by all possible methods"
"Jacobian test (NP only)" :: \
  "compute/print the J[H(h)] Jacobian matrix by numerical perturbation only"

# this is for normal apparent horizon finding
"Newton solve"	    :: "find the horizon via Newton's method"
} "Newton solve"

#
# We support searching for up to N_horizons distinct apparent horizons
# (some of which may be nested inside others) in a slice.  We number
# these 1, 2, 3, ... (this seems a bit more user-friendly than Cactus's
# native 0-origin numbering).  Since Cactus arrays are 0-origin, we
# make the arrays be of size N_horizons+1, and don't use the [0] array
# elements.
#
# To change the N_horizons limit, just change the upper limit for
# N_horizons itself, change all the [N_horizons+1] array sizes in this
# paramter file, and recompile your configuration.  No changes are
# needed to the source code.
#
int N_horizons "number of apparent horizons to search for"
{
0   :: "turn this thorn into a fancy no-op :)"
1:4 :: "search for this many apparent horizons"
} 1

#
# This parameter controls which (how many) informational (non-error)
# messages are printed describing the operation of the apparent horizon
# finder.  This is analogous to the -W Cactus command-line option, except
# that this parameter controls (only) *non*-error messages.
#
keyword verbose_level \
  "controls which (how many) messages to print describing AH finding"
{
# 1 line each time step giving number of horizons found and their masses
# ... this doesn't work yet :(
"physics highlights"   :: "just a few physics messages"

# 1 line for each horizon giving position/mass/area, + a summary line or two
"physics details"      :: "more detailed physics messages"

# 1 line giving H(h) norms at each Newton iteration
"algorithm highlights" :: \
  "physics details + a few messages about the AH-finding algorithm"

# lots of details tracing what the code is doing
"algorithm details"    :: \
  "physics details + lots of messages about the AH-finding algorithm"
} "algorithm highlights"

# n.b. printing timing stats is independent of  verbose_level
boolean print_timing_stats \
  "should we print timing stats for the whole apparent-horizon-finding process?"
{
} "false"

################################################################################

#
# parameters for the Jacobian matrix
#

keyword Jacobian_method "how do we compute the Jacobian matrix?"
{
# for debugging only"
"numerical perturbation"    :: "n.b. this is *very* slow"

# use this for normal apparent horizon finding
"symbolic differentiation with finite diff d/dr" :: \
  "fast, tricky programming, uses only gij, dx gij, Kij"

# alas, this isn't implemented yet :(
"symbolic differentiation"  :: \
  "fast, tricky programming, uses gij, dx gij, dxx gij, Kij, dx Kij"
} "symbolic differentiation with finite diff d/dr"

#
# This parameter lists all known storage methods.  See
# "src/include/config.hh" for which of these are actually compiled in at
# the moment.  N.b. each compiled-in method requires linking with the
# corresponding linear-solver library; see "src/make.configuration.defn"
# for details on these libraries.
#
keyword Jacobian_storage_method "how do we store the Jacobian matrix?"
{
# at present this is the only option
"dense matrix"	:: "dense matrix (inefficient at high angular resolution)"
} "dense matrix"

#
# This parameter controls two different sorts of one-sided finite
# differencing:
# - numerical-perturbation Jacobian computations
# - the finite differencing part of the "symbolic differentiation
#   with finite diff d/dr" Jacobian computation
#
# Notes on this parameter:
# - don't set it too small or roundoff errors will become large
# - don't set it too large or finite differencing errors will become large
# In practice the default value should be fine
#
real Jacobian_perturbation_amplitude \
  "perturbation amplitude for 1-sided finite differencing for Jacobians"
{
(0.0:* :: "any real number > 0"
} 1.0e-6

################################################################################

#
# parameters for the Newton's-method solution of H(h) = 0
#

#
# The first time we (try to) find a given horizon, our initial guess
# is likely to be rather inaccurate, so we may need a larger number of
# iterations.  But if we've found this horizon before, then we have its
# previous position as an initial guess, so (assuming that we've been
# scheduled at each time step) we shouldn't need as many iterations.
#
int max_Newton_iterations__initial \
  "maximum number of Newton iterations before giving up \
   when initially finding a given horizon"
{
(0:* :: "any positive integer"
} 20
int max_Newton_iterations__subsequent \
  "maximum number of Newton iterations before giving up \
   when re-finding a given horizon after finding it before"
{
(0:* :: "any positive integer"
} 10

#
# To avoid the Newton iteration diverging if there is no horizon present
# or if the initial guess is bad, we limit the distance the horizon may
# move in any single Newton iteration (i.e. the infinity-norm of Delta_h)
# to <= this fraction of the mean horizon radius
#
real max_Delta_h_over_h \
  "don't let horizon move > this fraction of mean radius in a Newton iteration"
{
(0.0:* :: "any positive real number"
} 0.1

#
# we declare convergence if *either* of the following two criteria are met
#
real H_norm_for_convergence "declare convergence if ||H||_inf <= this"
{
(0.0:* :: "any positive real number"
} 1.0e-8
real Delta_h_norm_for_convergence \
  "declare convergence after any Newton step with ||Delta_h||_inf <= this"
{
(0.0:* :: "any positive real number"
} 1.0e-8

#
# This only needs to be set to true for very careful convergence studies
# etc.  On the other hand, setting it to true probably only slows down
# the apparent horizon finder by a few percent.
#
boolean final_H_update_if_exit_x_H_small \
  "should we do a final H(h) update after a h += Delta_h update which is\
   so small it meets the Delta_h_norm_for_convergence convergence criterion?"
{
} "false"

################################################################################

#
# input/output parameters
#

# this is mainly useful for debugging purposes
boolean output_initial_guess \
  "should we output the initial guess back to the h data file?"
{
} "false"

# for debugging convergence failures, we can optionally output
# h, H, and delta_h at each Newton iteration
# (the file names are the usual ones with ".it%d" appended)
boolean debugging_output_at_each_Newton_iteration \
  "should we output {h, H, delta_h} at each Newton iteration?"
{
} "false"

# the next two parameters control how often we write full-sized
# output files (format controlled by  file_format ); we still *find*
# apparent horizons at each time step, and compute/print small-sized
# diagnostics, but this parameter may be used to reduce the number
# and size of output files
int how_often_to_output_h \
  "how often (in Cactus time steps) should we output h (0 to disable)?"
{
0   :: "don't output h at all"
1:* :: "any integer >= 1"
} 1

# setting this > 0 is probably only of interest if the Newton iteration
# fails to converge, or if you're debugging AHFinderDirect internals
int how_often_to_output_H_of_h \
  "how often (in Cactus time steps) should we output the H(h) functions?"
{
0   :: "don't output H(h) at all"
1:* :: "any integer >= 1"
} 0

keyword file_format \
  "what file format should we use for h and H(h) data files?"
{
"ASCII (gnuplot)"	:: "simple ASCII format, directly readable by gnuplot"
"HDF5"			:: "HDF5 surface format (alas not implemented yet)"
} "ASCII (gnuplot)"

boolean output_ghost_zones_for_h \
  "should we include the ghost zones in h data files?"
{
} "false"

string ASCII_gnuplot_file_name_extension \
  "extension for ASCII (gnuplot) data files"
{
.* :: "any string"
} "gnuplot"
string HDF5_file_name_extension "extension for HDF5 data files"
{
.* :: "any string"
} "hdf5"

#
# These file names are actually just "base" file names, with the full
# file names being given by a printf() format "%s.t%d.ah%d[.it%d].%s",
# where
# - the first %s is the base file name,
# - the first %d is the global Cactus time iteration number,
# - the second %d is the apparent horizon number, ande
# - the optional third %d is the horizon finder iteration number
# - the second %s is the file name extension as set by the
#   {ASCII,HDF5}_data_file_name_extension
#

string h_base_file_name \
  "base file name for horizon shape h input/output file(s)"
{
.+ :: "any nonempty string"
} "h.dat"

string H_of_h_base_file_name "base file name for H(h) output file(s)"
{
.+ :: "any nonempty string"
} "H.dat"

string Delta_h_base_file_name \
  "base file name for horizon-shape-update Delta_h output file(s)"
{
.+ :: "any nonempty string"
} "Delta_h.dat"

string Jacobian_base_file_name "base file name for Jacobian output file(s)"
{
.+ :: "any valid file name"
} "Jacobian.dat"

################################################################################

#
# parameters to define the patch systems
#
private:

#
# For each apparent horizon, you need to set these parameters to the
# Cactus xyz coordinates of a "local origin point" inside the horizon,
# which will serve as the origin for the apparent horizon finder's
# local angular coordinate system.
#
# The apparent horizon surface (and in fact all the trial surfaces the
# apparent horizon finder generates while iteratively solving the apparent
# horizon equation) is restricted to being a Strahlkoerper ("star-shaped
# region") about the origin point.  That is, each surface must be of
# the form r = h(angle) with h a single-valued function.
#
# If the origin point is too far from the actual horizon centroid, i.e.
# if it's too close to the horizon surface itself, then the apparent
# horizon finder's Newton iteration won't converge as quickly or robustly.
# However, in practice the tolerances on this are quite loose -- 1/4
# of the horizon radius is no problem, and even 1/2 the horizon radius
# only slows the convergence by an extra iteration or two.
#
real origin_x[5] "global x coordinate of patch system origin"
{
*:* :: "any real number"
} 0.0
real origin_y[5] "global y coordinate of patch system origin"
{
*:* :: "any real number"
} 0.0
real origin_z[5] "global z coordinate of patch system origin"
{
*:* :: "any real number"
} 0.0

keyword patch_system_type "what type of patch system should we use?"
{
# choose this for normal use
"match Cactus grid symmetry" :: \
  "choose automagically based on grid symmetries and the patch system's origin"

# these are also fully supported
"full sphere"	:: "full sphere, no symmetries"
"+z hemisphere"	:: "mirror symmetry across z=0 plane"

# these don't fully work yet for apparent horizon finding
# (the Jacobian computation doesn't grok them properly)
"+xy quadrant"	:: "90 degree periodic rotation symmetry about z axis"
"+xz quadrant"	:: "mirror symmetry across z=0 plane *and* \
		    180 degree periodic rotation symmetry about z axis"
"+xyz octant"	:: "mirror symmetry across z=0 plane *and* \
		    90 degree periodic rotation symmetry about z axis"
} "match Cactus grid symmetry"

#
# This parameter sets the width of the interpatch ghost zones in the
# patch system.  Note that this thorn uses the terminology "ghost zone"
# for any of what Cactus in general now calls a "boundary zone" or a
# "symmetry zone" or a "patch zone".
#
# This parameter must be at least
# ... 2 if FINITE_DIFF_ORDER is set to 4 in "src/include/config.hh"
# ... 1 if FINITE_DIFF_ORDER is set to 2 in "src/include/config.hh"
# The code checks for this being too small, and reports a fatal error if so.
#
int N_ghost_points "number of ghost zones on each side of a patch"
{
0:* :: "any integer >= 0"
} 2

int N_overlap_points \
  "number of grid points that nominally-just-touching patches should overlap"
{
1:*:2 :: "any integer >= 0; current implementation requires that it be odd"
} 1

#
# In practice the error in the horizon position is usually dominated
# by the errors from interpolating the Cactus gij and Kij to the horizon
# position, not by the angular finite differencing or interpatch interpolation
# errors.  Thus this parameter can be made quite large (low resolution)
# for better performance, without seriously affecting the accuracy
# with which we can locate the horizon.
#
# This spacing must integrally divide 90 degrees for full sphere patch
# systems, or 45 degrees for other patch systems.
#
# Also, the computation of surface integrals over the horizon (for horizon
# areas, masses, and centroids) is most accurate if the number of angular
# grid zones (i.e. the patch size divided by this parameter) is even or
# >= 7 (or both) for both coordinates of all patches.
#
# If you are thinking of setting this to a small value (high resolution),
# note also that with the current dense-matrix storage of the Jacobian,
# the memory/running time of the LAPACK linear system solve scales as
# the inverse 4th/6th power of this parameter!
#
real delta_drho_dsigma "angular grid spacing of patches, in degrees"
{
(0.0:* :: "any real number > 0.0"
} 7.5

################################################################################

#
# parameters for how we compute surface integrals over the horizon
#

# ... N is the number of grid zones in a patch, in either direction
keyword surface_integral_method \
  "how do we compute surface integrals over the horizon?"
{
"trapezoid"		:: "alternate name for trapezoid rule"
"trapezoid rule"	:: "trapezoid rule (2nd order for smooth functions)"
"Simpson"		:: "alternate name for Simpson's rule"
"Simpson's rule"	:: \
  "Simpson's rule (4th order for smooth fns, requires N to be even)"
"Simpson (variant)"	:: "alternate name for Simpson's rule variant"
"Simpson's rule (variant)":: \
  "Simpson's rule variant (4th order for smooth fns, requires N >= 7)"

# choose this for normal use (assuming FINITE_DIFF_ORDER is set to 4
# in "src/include/config.hh")
"automatic choice"	:: \
  "choose Simpson's rule or variant if applicable, otherwise trapezoid rule"
} "automatic choice"

################################################################################

#
# parameters for how we compute the slice's geometry
# (gij, Kij, partial_k gij)
#

keyword geometry_method "how do we compute the slice's geometry?"
{
# for normal use
"interpolate from Cactus grid" :: "interpolate gij and Kij from Cactus grid"

# for testing/debugging
"Schwarzschild/EF"             :: \
  "hard-wire to Schwarzschild spacetime / Eddington-Finkelstein slice"
} "interpolate from Cactus grid"

########################################

#
# parameters for geometry_method = "interpolate from Cactus grid"
#
# This 3D interpolator is used to interpolate gij and Kij from the
# Cactus grid to the position of each trial horizon surface, giving
# gij, Kij, and partial_x gij as outputs.  This interpolator must have
# the following properties:
# - It must be able to accept the Cactus grid as an input domain.  The
#   current implementation uses the  CCTK_InterpLocalUniform()  API; this
#   is processor-local and so restricts the whole apparent horizon finder
#   to single-processor operation.
# - It must support taking at least 1st derivatives as part of the
#   interpolation.
# - It should give at least $C^1$ interpolants for smooth data, otherwise
#   the H(h) function will have "spikes" and the Newton iteration may
#   fail to converge all the way down to tight error tolerances.  $C^2$
#   would be even better, but in practice a ($C^1$) Hermite interpolant
#   works well.
# In practice the default values for these parameters should work fine
# (so long as you compile with CactusBase/LocalInterp and activate that
# thorn).
#

string geometry_interpolator_name \
  "name under which the geometry interpolation operator is registered in Cactus"
{
.* :: "any string"
} "Hermite polynomial interpolation"

string geometry_interpolator_pars \
  "parameters for the geometry interpolator"
{
.* :: "any string acceptable to Util_TableSetFromString() and to the interpolator"
} "order=3"

########################################

#
# parameters for geometry_method = "Schwarzschild/EF"
#

real geometry__Schwarzschild_EF__mass "mass of Schwarzschild BH"
{
(0.0:*		:: "BH mass = any real number > 0"
} 1.0

real geometry__Schwarzschild_EF__x_posn "x coordinate of Schwarzschild BH"
{
*:* :: "any real number"
} 0.0
real geometry__Schwarzschild_EF__y_posn "y coordinate of Schwarzschild BH"
{
*:* :: "any real number"
} 0.0
real geometry__Schwarzschild_EF__z_posn "z coordinate of Schwarzschild BH"
{
*:* :: "any real number"
} 0.0

# some of the formulas have 0/0 limits on the z axis; this parameter controls
# where we switch from the generic formulas to the L'Hopital's-rule z axis
# limits
# - don't set this parameter too small or roundoff errors will be excessive
# - don't set this parameter too large or finite differencing errors will
#   be excessive
# in practice the default value should be fine
# n.b. this is used for centered finite differencing, unlike the Jacobian
real geometry__Schwarzschild_EF__epsilon \
  "threshold for sin^2 theta = (x^2+y^2)/r^2 below which we use z axis limits"
{
(0.0:*	:: "this should be somewhat above the floating-point roundoff level"
} 1.0e-9

# we compute partial_k g_ij by numerical finite differencing of the exact
# analytical g_ij values; this parameter sets the "grid spacing" for this
# - don't set this parameter too small or roundoff errors will be excessive
# - don't set this parameter too large or finite differencing errors will
#   be excessive
# in practice the default value should be fine
# ... n.b. this finite differencing is *centered*, unlike that in the
#          Jacobian computation
real geometry__Schwarzschild_EF__Delta_xyz \
  "finite diff pseuo-grid spacing for computing partial_k g_ij"
{
(0.0:* :: "any real number > 0"
} 1.0e-6

########################################

#
# These tests control whether we check that various angular gridfns
# are finite (neither NaN nor infinity) at various points in evaluating
# the H(h) function.  These are pretty cheap tests, and they're quite
# useful in catching assorted wierdness, so it's probably worth leaving
# them enabled unless you're trying to squeeze every last nanosecond...
#
boolean check_that_h_is_finite \
  "should we check that horizon shape function h is finite?"
{
} "true"
boolean check_that_geometry_is_finite \
  "should we check the interpolated geometry variables are finite?"
{
} "true"

################################################################################

#
# parameters for the interpatch interpolator
#
# This 1D interpolator is used to interpolate the h function between
# angular patches.  Because any given patch boundary only interpolates
# from a single neighboring patch (this is to simplify the bookkeeping),
# near the patch corners this interpolator will have to be used off-centered.
# Thus it's desirable to use an interpolator which retains reasonable
# accuracy right up to the edge of the data range.  In practice a Lagrange
# polynomial interpolant works well.
#

string interpatch_interpolator_name \
  "name under which the interpatch interpolation operator is registered in Cactus"
{
.* :: "any string"
} "Lagrange polynomial interpolation"

string interpatch_interpolator_pars \
  "parameters for the interpatch interpolator"
{
.* :: "any string acceptable to Util_TableSetFromString() and to the interpolator"
} "order=5"

################################################################################

#
# parameters specifying the initial guess for the apparent horizon shape
# (Note that if at any time we fail to find the (an) apparent horizon,
# then we reset our trial horizon surface to this initial guess before
# next attempting to find this horizon.)
#

# n.b. Schwarzschild/EF is the special case spin=0 of Kerr/Kerr
keyword initial_guess_method \
  "method used to set up initial guess for apparent horizon shape"
{
"read from file"	:: "read from input file"
"Kerr/Kerr"		:: \
  "set to the (analytical) horizon of Kerr spacetime in Kerr coordinates"
"Kerr/Kerr-Schild"	:: \
  "set to the (analytical) horizon of Kerr spacetime in Kerr-Schild coordinates"
"coordinate sphere"	:: "set to a coordinate sphere"
"coordinate ellipsoid"	:: "set to a coordinate ellipsoid"
} "coordinate sphere"

# parameters for initial_guess_method = "Kerr/Kerr"
real initial_guess__Kerr_Kerr__x_posn[5] "x coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_Kerr__y_posn[5] "y coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_Kerr__z_posn[5] "z coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_Kerr__mass[5] "mass of Kerr BH"
{
(0.0:*		:: "BH mass = any real number > 0"
} 1.0
# n.b. my convention is that a=J/m^2 is dimensionless,
#      while MTW take a=J/m=m * (my a)
real initial_guess__Kerr_Kerr__spin[5] "dimensionless spin a=J/m^2 of Kerr BH"
{
(-1.0:1.0)	:: \
  "dimensionless BH spin = J/m^2 = any real number with absolute value < 1"
} 0.6

# parameters for initial_guess_method = "Kerr/Kerr-Schild"
real initial_guess__Kerr_KerrSchild__x_posn[5] "x coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_KerrSchild__y_posn[5] "y coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_KerrSchild__z_posn[5] "z coordinate of Kerr BH"
{
*:* :: "any real number"
} 0.0
real initial_guess__Kerr_KerrSchild__mass[5] "mass of Kerr BH"
{
(0.0:*		:: "BH mass = any real number > 0"
} 1.0
# n.b. my convention is that a=J/m^2 is dimensionless,
#      while MTW take a=J/m=m * (my a)
real initial_guess__Kerr_KerrSchild__spin[5] "dimensionless spin a=J/m^2 of Kerr BH"
{
(-1.0:1.0)	:: \
  "dimensionless BH spin = J/m^2 = any real number with absolute value < 1"
} 0.6

# parameters for initial_guess_method = "sphere"
real initial_guess__coord_sphere__x_center[5] "x coordinate of sphere center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_sphere__y_center[5] "y coordinate of sphere center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_sphere__z_center[5] "z coordinate of sphere center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_sphere__radius[5] "radius of sphere"
{
(0.0:* :: "any real number > 0.0"
} 2.0

# parameters for initial_guess_method = "ellipsoid"
real initial_guess__coord_ellipsoid__x_center[5] \
  "x coordinate of ellipsoid center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_ellipsoid__y_center[5] \
  "y coordinate of ellipsoid center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_ellipsoid__z_center[5] \
  "z coordinate of ellipsoid center"
{
*:* :: "any real number"
} 0.0
real initial_guess__coord_ellipsoid__x_radius[5] "x radius of ellipsoid"
{
(0.0:* :: "any real number > 0.0"
} 2.0
real initial_guess__coord_ellipsoid__y_radius[5] "y radius of ellipsoid"
{
(0.0:* :: "any real number > 0.0"
} 2.0
real initial_guess__coord_ellipsoid__z_radius[5] "z radius of ellipsoid"
{
(0.0:* :: "any real number > 0.0"
} 2.0

################################################################################

#
# parameters for the test driver "src/patch/test_patch_system.cc"
#
# By default this test driver isn't compiled into the cactus executable,
# and these parameters are ignored.  To compile this test driver into
# the cactus executable (and have these parameters used),
# - edit the list of "source files in this directory" in
#   "src/patch/make.code.defn" to add  test_patch_system.cc
# - comment out the list of "subdirectories containing source files" in
#   "src/make.code.defn", and uncomment the alternate list which is
#   normally commented out there (this omits the higher-level directories
#   src/elliptic/, src/gr/, and src/driver/)
#
keyword which_test "which test should we do?"
{
"gridfn"	:: "set up test fn(x,y,z), print it"
"read gridfn"	:: "read in ghosted test fn(x,y,z), print it"
"synchronize"	:: "set up test fn(x,y,z), synchronize it, print errors"
"ghost zone Jacobian":: \
  "set up test fn(x,y,z), compute Jacobian of gz.synchronize(), compare with NP"
"derivatives"	:: "set up test fn(rho,sigma), take derivs, print errors"
} "gridfn"

int which_derivs "bit flags to specify which derivatives to test"
{
0:63 :: "any set of bit flags"
} 63

# true ==> gives a more thorough test of the Jacobian,
#          but makes the test run much slower
# false ==> gives a slightly less thorough test, but runs faster
boolean NP_Jacobian__perturb_all_y_patch_points \
  "should we perturb at *all* points in the y patch, or just those with the \
   iperp which is (supposedly) involved in the interpatch interpolation?"
{
} "true"

################################################################################