reconstruction::reconstruction_class Type Reference

Base class containing all the data needed to reconstruct a model. More...

Public Member Functions
FINAL	reconstruction_destruct (this)
	Deconstruct a reconstruction_class object.
procedure	get_k_use (this, num_sv)
	Get the number of singular values to use.
procedure	get_exp_dg2 (this, delta_a)
	Get the expected dg^2 size.
procedure	get_exp_g2 (this, delta_a)
	Get the expected g^2 size.
procedure	get_g2 (this)
	Get the current g^2.
procedure	get_lastg2 (this)
	Get the last g^2.
procedure	get_dg2 (this)
	Get the change in g^2.
procedure	eval_e (this, signals, a_model, gaussp, eq_steps, iou, eq_comm)
	Evaluate the e vector for a reconstruction step.
procedure	eval_f (this, derived_params, a_model)
	Evaluate the f vector for a reconstruction step.
procedure	eval_jacobians (this, signals, derived_params, locks, a_model, gaussp, params, eq_steps, iou, recon_comm, eq_comm)
	Evaluate the jacobian.
procedure	eval_step (this, signals, derived_params, locks, a_model, gaussp, params, eq_steps, iou, recon_comm, eq_comm)
	Evaluate the proper quasi-Newton step.
procedure	sl_step (this, k_use, step_size, delta_a)
	Take a straight line step.
procedure	seg_step (this, k_use, step_size, delta_a)
	Take a segmented path step.
procedure	lm_step (this, k_use, step_size, delta_a)
	Take a Levenberg-Marquardt step.
procedure	lm_rootfind (this, k_use, lambda_default, step_size, utdote)
	Root find for Levenberg-Marquardt step.
procedure	lm_function (this, f_sqrd, step_size_sqrd, lambda)
	Levenberg-Marquardt function.
procedure	step (this, signals, derived_params, locks, a_model, gaussp, params, eq_steps, iou, recon_comm, eq_comm)
	Step the reconstruction.
procedure	try_step (this, signals, derived_params, locks, a_model, gaussp, params, eq_steps, max_step, iou, recon_comm, eq_comm)
	Try step size.
procedure	eval_sem (this, params, signals, derived_params)
	Evaluate the parameter covariance and signal effectiveness.
procedure	invert_matrix (this, matrix, sub, name)
	Invert an M x N matrix.
procedure	write (this, iou)
	Write out a reconstruction.
procedure	write_step1 (this, step_type, iou)
	Write out a reconstruction step attempt.
procedure	write_step2 (this, iou)
	Write out a final reconstruction step.
GENERIC	write_step write_step1, write_step2
procedure	restart (this, result_ncid, current_step, signals, derived_params, a_model)
	Restart from result file.
procedure	sync_state (this, recon_comm)
	Syncronize state to children.
procedure	sync_svd (this, recon_comm)
	Syncronize svd.
procedure	sync_parent (this, params, num_signal, num_derived_params, stride, offset, recon_comm)
	Syncronize child state back to parent.

Public Attributes
integer	step_type = reconstruction_no_step_type
	Type descriptor of the boundry type for the lower(1) and upper(2) ranges.
real(rprec)	step_max
	Maximum number of reconstruction steps.
logical	use_central = .false.
	Controls if central differencing is used.
integer	current_step = 0
	Counter to track the step number.
integer	last_para_signal = 0
	Index of the last parallelable signal.
real(rprec), dimension(:,:), pointer	e => null()
	Array of all e vectors for each reconstruction step.
real(rprec), dimension(:,:), pointer	f => null()
	Array of all f vectors for each reconstruction step. The f vector contains the initial value of the derived parameter.
real(rprec), dimension(:,:), pointer	jacobian => null()
	The normalized jacobian for the current step.
real(rprec), dimension(:,:), pointer	derived_jacobian => null()
	The normalized derived jacobian for the current step.
real(rprec), dimension(:,:), pointer	hessian => null()
	The normalized hessian for the current step.
real(rprec), dimension(:), pointer	gradient => null()
	The normalized gradient for the current step.
real(rprec), dimension(:,:), pointer	delta_a => null()
	The normalized parameter step for each sigular value.
real(rprec), dimension(:), pointer	j_svd_w => null()
	The matrix of singular value decomposition singular values.
real(rprec), dimension(:,:), pointer	j_svd_u => null()
	The U matrix of singular value decomposition.
real(rprec), dimension(:,:), pointer	j_svd_vt => null()
	The tansposed V matrix of singular value decomposition.
real(rprec), dimension(:), pointer	delta_a_len => null()
	The normalized step length for each sigular value.
real(rprec), dimension(:), pointer	svd_w => null()
	The singular values used in inverting parameter covariance matrix.
real(rprec), dimension(:), pointer	exp_g2 => null()
	The expected g^2 for each reconstruction step.
real(rprec), dimension(:), pointer	step_size => null()
	The normalized step size for each reconstruction step.
integer, dimension(:), pointer	num_sv => null()
	The number of sigular values used for each reconstruction step.
real(rprec)	cut_svd
	Cutoff value for relative singular values.
real(rprec)	cut_eff
	Cutoff value for expected step efficiency.
real(rprec)	cut_marg_eff
	Cutoff value for expected marginal step efficiency.
real(rprec)	cut_delta_a
	Cutoff value for expected step size.
real(rprec)	cut_dg2
	Cutoff value for expected change in g^2.
real(rprec)	cut_inv_svd
	Cutoff value for pseudo inverse singular values.
real(rprec), dimension(:,:), pointer	lm_ratio => null()
	Ratio of singular values to the Levenberg-Marquardt lambda.
real(rprec), dimension(:,:), pointer	last_values => null()
	Last signals.

Detailed Description

Base class containing all the data needed to reconstruct a model.

Member Function/Subroutine Documentation

eval_e()

procedure reconstruction::reconstruction_class::eval_e	(	class (reconstruction_class), intent(inout)	this,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		class (model_class), pointer	a_model,
		type (gaussp_class_pointer), dimension(:), intent(inout)	gaussp,
		integer, intent(inout)	eq_steps,
		integer, intent(in)	iou,
		integer, intent(in)	eq_comm
	)

Evaluate the e vector for a reconstruction step.

Evaluates the e vector after soving the equilibrium.

See also

signal::signal_get_e

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	signals	Array of signal objects.
[in,out]	a_model	A model instance.
[in,out]	gaussp	Array of guassian_process::gaussp_class objects.
[in,out]	eq_steps	Number of steps for the equilibrium to take.
[in]	iou	Input/output file to write log messages to.
[in]	eq_comm	MPI communicator for the child equilibrium processes.

Returns

True if the equilibrium converged and false if otherwise.

eval_f()

procedure reconstruction::reconstruction_class::eval_f	(	class (reconstruction_class), intent(inout)	this,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		class (model_class), intent(inout)	a_model
	)

Evaluate the f vector for a reconstruction step.

Evaluates the f vector after soving the equilibrium.

See also

param::param_get_value

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	derived_params	Array of param objects.
[in,out]	a_model	A model instance.

eval_jacobians()

procedure reconstruction::reconstruction_class::eval_jacobians	(	class (reconstruction_class), intent(inout)	this,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		type (param_pointer), dimension(:), intent(in)	locks,
		class (model_class), pointer	a_model,
		type (gaussp_class_pointer), dimension(:), intent(inout)	gaussp,
		type (param_pointer), dimension(:), intent(inout)	params,
		integer, intent(inout)	eq_steps,
		integer, intent(in)	iou,
		integer, intent(in)	recon_comm,
		integer, intent(in)	eq_comm
	)

Evaluate the jacobian.

Evaluates the jacobian. When using MPI, reach row of the jacobian is evaluated in parallel.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	signals	Array of signal objects.
[in]	derived_params	Array of derived param objects.
[in,out]	a_model	A model instance.
[in,out]	params	Array of parameter objects.
[in,out]	eq_steps	Number of steps for the equilibrium to take.
[in]	iou	Input/output file to write log messages to.
[in]	recon_comm	MPI communicator for the child jacobian processes.
[in]	eq_comm	MPI communicator for the child equilibrium processes.

eval_sem()

procedure reconstruction::reconstruction_class::eval_sem	(	class (reconstruction_class), intent(inout)	this,
		type (param_pointer), dimension(:), intent(inout)	params,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(inout)	derived_params
	)

Evaluate the parameter covariance and signal effectiveness.

Calculates the signal effectiveness matrix. This value is stored in parameter::param_class::sem. To find the signal effectiveness, an intermediate step computes the parameter covariance. Computes the derived parameter covariance matrix also.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	params	Array of parameter objects.
[in,out]	signals	Array of signal objects.
[in,out]	derived_params	Array of parameter objects.

eval_step()

procedure reconstruction::reconstruction_class::eval_step	(	class (reconstruction_class), intent(inout)	this,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		type (param_pointer), dimension(:), intent(in)	locks,
		class (model_class), pointer	a_model,
		type (gaussp_class_pointer), dimension(:), intent(inout)	gaussp,
		type (param_pointer), dimension(:), intent(inout)	params,
		integer, intent(inout)	eq_steps,
		integer, intent(in)	iou,
		integer, intent(in)	recon_comm,
		integer, intent(in)	eq_comm
	)

Evaluate the proper quasi-Newton step.

Evaluates the jacobian, performs the SVD and computes the quasi-Newton step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	signals	Array of signal objects.
[in]	derived_params	Array of derived param objects.
[in,out]	a_model	A model instance.
[in,out]	params	Array of parameter objects.
[in,out]	eq_steps	Number of steps for the equilibrium to take.
[in]	iou	Input/output file to write log messages to.
[in]	recon_comm	MPI communicator for the child jacobian processes.
[in]	eq_comm	MPI communicator for the child equilibrium processes.

Returns

The number of singular values to use.

get_dg2()

procedure reconstruction::reconstruction_class::get_dg2

(

class (reconstruction_class), intent(in)

this

)

Get the change in g^2.

Gets the change in g^2 from the last reconstruction step to the current step.

Parameters

[in]

this

A reconstruction_class instance.

Returns

The last g^2.

get_exp_dg2()

procedure reconstruction::reconstruction_class::get_exp_dg2	(	class (reconstruction_class), intent(in)	this,
		real (rprec), dimension(:), intent(in)	delta_a
	)

Get the expected dg^2 size.

Estimates the change in g^2. Equation 22 in Hanson et. al. doi:10.1088/0029-5515/49/7/075031 Note: there is a typo in equation 22. The - sign in the last term should be a plus sign.

Parameters

[in]	this	A reconstruction_class instance.
[in]	delta_a	The normalized parameter step.

Returns

Change expected change in g^2.

get_exp_g2()

procedure reconstruction::reconstruction_class::get_exp_g2	(	class (reconstruction_class), intent(in)	this,
		real (rprec), dimension(:), intent(in)	delta_a
	)

Get the expected g^2 size.

Estimates the g^2. Equation 22 in Hanson et. al. doi:10.1088/0029-5515/49/7/075031

Parameters

[in]	this	A reconstruction_class instance.
[in]	delta_a	The normalized parameter step.

Returns

Expected g^2.

get_g2()

procedure reconstruction::reconstruction_class::get_g2

(

class (reconstruction_class), intent(in)

this

)

Get the current g^2.

Gets the g^2 value for the current reconstruction step.

Parameters

[in]

this

A reconstruction_class instance.

Returns

Current g^2.

get_k_use()

procedure reconstruction::reconstruction_class::get_k_use	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	num_sv
	)

Get the number of singular values to use.

Number of sigular values to uses is determined by the various cutoffs.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	num_sv	Total number of sigular values.

Returns

The number of sigular values to use.

get_lastg2()

procedure reconstruction::reconstruction_class::get_lastg2

(

class (reconstruction_class), intent(in)

this

)

Get the last g^2.

Gets the g^2 value for the last reconstruction step.

Parameters

[in]

this

A reconstruction_class instance.

Returns

The last g^2.

invert_matrix()

procedure reconstruction::reconstruction_class::invert_matrix	(	class (reconstruction_class), intent(inout)	this,
		real (rprec), dimension(:,:), pointer	matrix,
		character (len=*), intent(in)	sub,
		character (len=*), intent(in)	name
	)

Invert an M x N matrix.

Perform a pseudo-inversion using a singular value decomposition. This subroutine destroys the original matrix.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	matrix	The matrix to invert.
[in]	sub	The subroutine of the matrix this was called from.
[in]	name	The name of the matrix to be inverted.

lm_function()

procedure reconstruction::reconstruction_class::lm_function	(	class (reconstruction_class), intent(inout)	this,
		real (rprec), dimension(:), intent(in)	f_sqrd,
		real (rprec), intent(in)	step_size_sqrd,
		real (rprec), intent(in)	lambda
	)

Levenberg-Marquardt function.

Function used by reconstruction_lm_rootfind for a Levenberg-Marquardt step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	f_sqrd	f^2
[in]	step_size_sqrd	Square of the current step size.
[in]	lambda	Lambda value.

Returns

F(lambda)

lm_rootfind()

procedure reconstruction::reconstruction_class::lm_rootfind	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	k_use,
		real (rprec), intent(in)	lambda_default,
		real (rprec), intent(in)	step_size,
		real (rprec), dimension(:), intent(in)	utdote
	)

Root find for Levenberg-Marquardt step.

Find the root of the reconstruction_lm_function for a Levenberg-Marquardt step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	k_use	Number of singular values to use.
[in]	lambda_default	The default lambda.
[in]	step_size	Current step size limit.
[in]	utdote	Vector of U^T * e

Returns

The root lambda.

lm_step()

procedure reconstruction::reconstruction_class::lm_step	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	k_use,
		real (rprec), intent(in)	step_size,
		real (rprec), dimension(:), intent(out)	delta_a
	)

Take a Levenberg-Marquardt step.

Determines the normalized change in parameters for a Levenberg-Marquardt step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	k_use	Number of singular values to use.
[in]	step_size	Current step size limit.
[out]	delta_a	Normalized change in parameter.

Returns

The step size used.

reconstruction_destruct()

FINAL reconstruction::reconstruction_class::reconstruction_destruct ( type (reconstruction_class), intent(inout)  this )

final

Deconstruct a reconstruction_class object.

Deallocates memory and uninitializes a reconstruction_class object.

Parameters

[in,out]

this

A reconstruction_class instance.

restart()

procedure reconstruction::reconstruction_class::restart	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	result_ncid,
		integer, intent(in)	current_step,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		class (model_class), pointer	a_model
	)

Restart from result file.

Restarts the reconstruction from the result file. Note, that there is an external step counter and an internal step counter. Internally we will restart current step at zero.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	result_ncid	NetCDF file id of the result file.
[in]	current_step	Step index to read variables from.
[in,out]	a_model	A model instance.

seg_step()

procedure reconstruction::reconstruction_class::seg_step	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	k_use,
		real (rprec), intent(in)	step_size,
		real (rprec), dimension(:), intent(out)	delta_a
	)

Take a segmented path step.

Determines the normalized change in parameters for a segmented path step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	k_use	Number of singular values to use.
[in]	step_size	Current step size limit.
[out]	delta_a	Normalized change in parameter.

Returns

The step size used.

sl_step()

procedure reconstruction::reconstruction_class::sl_step	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	k_use,
		real (rprec), intent(in)	step_size,
		real (rprec), dimension(:), intent(out)	delta_a
	)

Take a straight line step.

Determines the normalized change in parameters for a straight line step.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	k_use	Number of singular values to use.
[in]	step_size	Current step size limit.
[out]	delta_a	Normalized change in parameter.

Returns

The step size used.

step()

procedure reconstruction::reconstruction_class::step	(	class (reconstruction_class), intent(inout)	this,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		type (param_pointer), dimension(:), intent(in)	locks,
		class (model_class), pointer	a_model,
		type (gaussp_class_pointer), dimension(:), intent(inout)	gaussp,
		type (param_pointer), dimension(:), intent(inout)	params,
		integer, intent(inout)	eq_steps,
		integer, intent(in)	iou,
		integer, intent(in)	recon_comm,
		integer, intent(in)	eq_comm
	)

Step the reconstruction.

Advance the reconstruction by a single step. This is the main V3FIT algorithm.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	signals	Array of signal objects.
[in,out]	locks	Array of lock objects.
[in,out]	a_model	A model instance.
[in,out]	gaussp	Array of guassian_process::gaussp_class objects.
[in,out]	params	Array of v3fit_params::param_class objects.
[in,out]	eq_steps	Number of steps the equilibrium took.
[in]	iou	Input/output file to write log messages to.
[in]	recon_comm	MPI communicator for the child jacobian processes.
[in]	eq_comm	MPI communicator for the child equilibrium processes.

Returns

True if the step was successfull and false otherwise.

sync_parent()

procedure reconstruction::reconstruction_class::sync_parent	(	class (reconstruction_class), intent(inout)	this,
		type (param_pointer), dimension(:), intent(inout)	params,
		integer, intent(in)	num_signal,
		integer, intent(in)	num_derived_params,
		integer, dimension(:), intent(in)	stride,
		integer, dimension(:), intent(in)	offset,
		integer, intent(in)	recon_comm
	)

Syncronize child state back to parent.

Syncs data between the parent and child processes. If MPI support is not compiled in this subroutine reduces to a no op.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	num_params	Number of reconstruction parameters.
[in]	num_signal	Number of signals.
[in]	num_derived_params	Number of derived parameters.
[in]	stride	Length work size for each process.
[in]	offset	Start offset for each process.
[in]	recon_comm	A MPI recon_comm handle.

sync_state()

procedure reconstruction::reconstruction_class::sync_state	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	recon_comm
	)

Syncronize state to children.

Syncs data between the parent and child processes. If MPI support is not compiled in this subroutine reduces to a no op.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	recon_comm	A MPI recon_comm handle.

sync_svd()

procedure reconstruction::reconstruction_class::sync_svd	(	class (reconstruction_class), intent(inout)	this,
		integer, intent(in)	recon_comm
	)

Syncronize svd.

Syncs the svd information to the child processes so these processes can sample parameter space for the step sizes.

Parameters

[in,out]	this	A reconstruction_class instance.
[in]	recon_comm	A MPI recon_comm handle.

try_step()

procedure reconstruction::reconstruction_class::try_step	(	class (reconstruction_class), intent(inout)	this,
		type (signal_pointer), dimension(:), intent(inout)	signals,
		type (param_pointer), dimension(:), intent(in)	derived_params,
		type (param_pointer), dimension(:), intent(in)	locks,
		class (model_class), pointer	a_model,
		type (gaussp_class_pointer), dimension(:), intent(inout)	gaussp,
		type (param_pointer), dimension(:), intent(inout)	params,
		integer, intent(inout)	eq_steps,
		real (rprec), intent(inout)	max_step,
		integer, intent(in)	iou,
		integer, intent(in)	recon_comm,
		integer, intent(in)	eq_comm
	)

Try step size.

Sample reconstruction by trying to take a specified step size.

Parameters

[in,out]	this	A reconstruction_class instance.
[in,out]	signals	Array of signal objects.
[in,out]	locks	Array of lock objects.
[in,out]	a_model	A model instance.
[in,out]	params	Array of parameter objects.
[in,out]	eq_steps	Number of steps for the equilibrium to take.
[in]	max_step	Upper limit of the step size to attemp.
[in]	iou	Input/output file to write log messages to.
[in]	recon_comm	MPI communicator for the child jacobian processes.
[in]	eq_comm	MPI communicator for the child equilibrium processes.
[out]	param_value	Parameter corresponding to the smallest g^2 value.

Returns

The lowest q^2 value.

write()

procedure reconstruction::reconstruction_class::write	(	class (reconstruction_class), intent(in)	this,
		integer, intent(in)	iou
	)

Write out a reconstruction.

Write out the final information about a reconstruction. This writes out a table of the g^2, expected g^2, number of sigular values used and the normalized step size used.

Parameters

[in]	this	A reconstruction_class instance.
[in]	iou	Input/output file to write final result to.

write_step1()

procedure reconstruction::reconstruction_class::write_step1	(	class (reconstruction_class), intent(in)	this,
		character (len=*), intent(in)	step_type,
		integer, intent(in)	iou
	)

Write out a reconstruction step attempt.

Write out information about a reconstruction step. This writes the number of singular values use, the step type, the normalized step size and the expected g^2.

Parameters

[in]	this	A reconstruction_class instance.
[in]	step_type	The step type used.
[in]	iou	Input/output file to write final result to.

write_step2()

procedure reconstruction::reconstruction_class::write_step2	(	class (reconstruction_class), intent(in)	this,
		integer, intent(in)	iou
	)

Write out a final reconstruction step.

Write out information about a reconstruction step. This writes the number of singular values use, the step type, the normalized step size and the expected g^2.

Parameters

[in]	this	A reconstruction_class instance.
[in]	iou	Input/output file to write final result to.

Member Data Documentation

cut_delta_a

real (rprec) reconstruction::reconstruction_class::cut_delta_a

Cutoff value for expected step size.

See also

v3fit_input::cut_delta_a

cut_dg2

real (rprec) reconstruction::reconstruction_class::cut_dg2

Cutoff value for expected change in g^2.

See also

v3fit_input::cut_dg2

cut_eff

real (rprec) reconstruction::reconstruction_class::cut_eff

Cutoff value for expected step efficiency.

See also

v3fit_input::cut_eff

cut_inv_svd

real (rprec) reconstruction::reconstruction_class::cut_inv_svd

Cutoff value for pseudo inverse singular values.

See also

v3fit_input::cut_inv_svd

cut_marg_eff

real (rprec) reconstruction::reconstruction_class::cut_marg_eff

Cutoff value for expected marginal step efficiency.

See also

v3fit_input::cut_marg_eff

cut_svd

real (rprec) reconstruction::reconstruction_class::cut_svd

Cutoff value for relative singular values.

See also

v3fit_input::cut_svd

e

real (rprec), dimension(:,:), pointer reconstruction::reconstruction_class::e => null()

Array of all e vectors for each reconstruction step.

See also

signal::signal_get_e

step_max

real (rprec) reconstruction::reconstruction_class::step_max

Maximum number of reconstruction steps.

See also

v3fit_input::nrstep

step_type

integer reconstruction::reconstruction_class::step_type = reconstruction_no_step_type

Type descriptor of the boundry type for the lower(1) and upper(2) ranges.

Possible values are:

• reconstruction_no_step_type
• reconstruction_sl_step_type
• reconstruction_lm_step_type
• reconstruction_seg_step_type

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The documentation for this type was generated from the following file:

• V3FIT/Sources/reconstruction.f