qpms/qpms/tmatrices.h

/*! \file tmatrices.h
 * \brief T-matrices for scattering systems.
 */
#ifndef TMATRICES_H
#define TMATRICES_H
#ifdef __cplusplus
extern "C" {
#endif

// #include "qpms_types.h" // included via materials.h
// #include <gsl/gsl_spline.h> // included via materials.h
#include "materials.h"
#include <stdio.h>



struct qpms_finite_group_t;
typedef struct qpms_finite_group_t qpms_finite_group_t;

/// Returns a pointer to the beginning of the T-matrix row \a rowno.
static inline _Complex double *qpms_tmatrix_row(qpms_tmatrix_t *t, size_t rowno){
	return t->m + (t->spec->n * rowno);
}

/// Initialises a zero T-matrix.
/** \sa qpms_tmatrix_init_from_generator() 
 *  \sa qpms_tmatrix_init_from_function() */
qpms_tmatrix_t *qpms_tmatrix_init(const qpms_vswf_set_spec_t *bspec);


/// Copies a T-matrix, allocating new array for the T-matrix data.
qpms_tmatrix_t *qpms_tmatrix_copy(const qpms_tmatrix_t *T);

/// Copies a T-matrix contents between two pre-allocated T-matrices.
/** orig->spec and dest->spec must be identical.
 *
 * \returns \a dest 
 */ 
qpms_tmatrix_t *qpms_tmatrix_mv(qpms_tmatrix_t *dest, const qpms_tmatrix_t *orig);

/// Destroys a T-matrix.
void qpms_tmatrix_free(qpms_tmatrix_t *t);

/// Check T-matrix equality/similarity.
/** 
 *  This function actually checks for identical vswf specs.
 * TODO define constants with "default" atol, rtol for this function.
 */
_Bool qpms_tmatrix_isclose(const qpms_tmatrix_t *T1, const qpms_tmatrix_t *T2,
		const double rtol, const double atol);

/// Creates a T-matrix from another matrix and a symmetry operation.
/** The symmetry operation is expected to be a unitary (square) 
 *  matrix \a M with the same
 *  VSWF basis spec as the T-matrix (i.e. \a t->spec). The new T-matrix will then
 *  correspond to CHECKME \f[ T' = MTM^\dagger \f] 
 */
qpms_tmatrix_t *qpms_tmatrix_apply_symop(
		const qpms_tmatrix_t *T, ///< the original T-matrix
		const _Complex double *M ///< the symmetry op matrix in row-major format
		);

/// Applies a symmetry operation onto a T-matrix, rewriting the original T-matrix data.
/** The symmetry operation is expected to be a unitary (square) 
 *  matrix \a M with the same
 *  VSWF basis spec as the T-matrix (i.e. \a t->spec). The new T-matrix will then
 *  correspond to CHECKME \f[ T' = MTM^\dagger \f] 
 */
qpms_tmatrix_t *qpms_tmatrix_apply_symop_inplace(
		qpms_tmatrix_t *T, ///< the original T-matrix
		const _Complex double *M ///< the symmetry op matrix in row-major format
		);

/// Symmetrizes a T-matrix with an involution symmetry operation.
/** The symmetry operation is expected to be a unitary (square) 
 *  matrix \a M with the same
 *  VSWF basis spec as the T-matrix (i.e. \a t->spec). The new T-matrix will then
 *  correspond to CHECKME \f[ T' = \frac{T + MTM^\dagger}{2} \f] 
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_involution(
		const qpms_tmatrix_t *T, ///< the original T-matrix
		const _Complex double *M ///< the symmetry op matrix in row-major format
		);

/// Creates a \f$ C_\infty \f$ -symmetrized version of a T-matrix.
/**
 *  \f[ {T'}_{tlm}^{\tau\lambda\mu} = T_{tlm}^{\tau\lambda\mu} \delta_{m\mu} \f]
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_inf(
		const qpms_tmatrix_t *T ///< the original T-matrix
		);
/// Creates a \f$ C_N \f$ -symmetrized version of a T-matrix.
/**
 *  \f[ {T'}_{tlm}^{\tau\lambda\mu} = \begin{cases}
 *  T{}_{lm}^{\lambda\mu} & (m-\mu)\mod N=0\\
 *  0 & (m-\mu)\mod N\ne0
 *  \end{cases} . \f]
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_N(
		const qpms_tmatrix_t *T, ///< the original T-matrix
		int N ///< number of z-axis rotations in the group
		);

/// Symmetrizes a T-matrix with an involution symmetry operation, rewriting the original one.
/** The symmetry operation is expected to be a unitary (square) 
 *  matrix \a M with the same
 *  VSWF basis spec as the T-matrix (i.e. \a t->spec). The new T-matrix will then
 *  correspond to CHECKME \f[ T' = \frac{T + MTM^\dagger}{2} \f] 
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_involution_inplace(
		qpms_tmatrix_t *T, ///< the original T-matrix
		const _Complex double *M ///< the symmetry op matrix in row-major format
		);

/// Creates a \f$ C_\infty \f$ -symmetrized version of a T-matrix, rewriting the original one.
/**
 *  \f[ {T'}_{tlm}^{\tau\lambda\mu} = T_{tlm}^{\tau\lambda\mu} \delta_{m\mu} \f]
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_inf_inplace(
		qpms_tmatrix_t *T ///< the original T-matrix
		);
/// Creates a \f$ C_N \f$ -symmetrized version of a T-matrix, rewriting the original one.
/**
 *  \f[ {T'}_{tlm}^{\tau\lambda\mu} = \begin{cases}
 *  T{}_{lm}^{\lambda\mu} & (m-\mu)\mod N=0\\
 *  0 & (m-\mu)\mod N\ne0
 *  \end{cases} . \f]
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_C_N_inplace(
		qpms_tmatrix_t *T, ///< the original T-matrix
		int N ///< number of z-axis rotations in the group
		);

/// Reads an open scuff-tmatrix generated file.
/** 
 * \a *freqs, \a *freqs_su, \a *tmatrices_array and \a *tmdata 
 * arrays are allocated by this function
 * and have to be freed by the caller after use.
 * \a freqs_su and \a tmatrices_array can be NULL, in that case
 * the respective arrays are not filled nor allocated.
 *
 * The contents of tmatrices_array is NOT 
 * supposed to be freed element per element.
 *
 * TODO more checks and options regarding NANs etc.
 *
 */
qpms_errno_t qpms_load_scuff_tmatrix(
		const char *path, ///< Path to the TMatrix file
		const qpms_vswf_set_spec_t *bspec, ///< VSWF set spec
		size_t *n, ///< Number of successfully loaded t-matrices
		double **freqs, ///< Frequencies in SI units..
		double **freqs_su, ///< Frequencies in SCUFF units (optional).
		/// The resulting T-matrices (optional).
		qpms_tmatrix_t **tmatrices_array, 
		_Complex double **tmdata ///< The T-matrices raw contents
		);

/// Tells whether qpms_load_scuff_tmatrix should crash if fopen() fails.
/** If true (default), the function causes the program
 * die e.g. when the tmatrix file
 * does not exists.
 *
 * If false, it does nothing and returns an appropriate error value instead.
 * This is desirable e.g. when used in Python (so that proper exception can
 * be thrown).
 */
extern _Bool qpms_load_scuff_tmatrix_crash_on_failure;

/// Loads a scuff-tmatrix generated file.
/** A simple wrapper over qpms_read_scuff_tmatrix() that needs a 
 * path instead of open FILE.
 *
 * The T-matrix is transformed from the VSWF basis defined by
 * QPMS_NORMALISATION_CONVENTION_SCUFF into the basis defined
 * by convention bspec->norm.
 * 
 * Right now, bspec->norm with real or "reversed complex" spherical
 * harmonics are not supported.
 */
qpms_errno_t qpms_read_scuff_tmatrix(
		FILE *f, ///< An open stream with the T-matrix data.
		const qpms_vswf_set_spec_t *bspec, ///< VSWF set spec
		size_t *n, ///< Number of successfully loaded t-matrices
		double **freqs, ///< Frequencies in SI units.
		double **freqs_su, ///< Frequencies in SCUFF units (optional).
		/// The resulting T-matrices (optional).
		qpms_tmatrix_t **tmatrices_array, 
		/// The T-matrices raw contents. 
		/** The coefficient of outgoing wave defined by 
		 * \a bspec->ilist[desti] as a result of incoming wave
		 * \a bspec->ilist[srci] at frequency \a (*freqs)[fi]
		 * is accessed via
		 * (*tmdata)[bspec->n*bspec->n*fi + desti*bspec->n + srci].
		 */
		_Complex double ** tmdata 
		);

/// In-place application of point group elements on raw T-matrix data.
/** \a tmdata can be e.g. obtained by qpms_load_scuff_tmatrix().
 * The \a symops array should always contain all elements of a finite
 * point (sub)group, including the identity operation.
 *
 * TODO more doc.
 */
qpms_errno_t qpms_symmetrise_tmdata_irot3arr(
		_Complex double *tmdata, const size_t tmcount,
		const qpms_vswf_set_spec_t *bspec,
		size_t n_symops,
		const qpms_irot3_t *symops
		);

/// In-place application of a point group on raw T-matrix data.
/** This does the same as qpms_symmetrise_tmdata_irot3arr(),
 * but takes a valid finite point group as an argument.
 *
 * TODO more doc.
 */
qpms_errno_t qpms_symmetrise_tmdata_finite_group(
		_Complex double *tmdata, const size_t tmcount,
		const qpms_vswf_set_spec_t *bspec,
		const qpms_finite_group_t *pointgroup
		);

/// In-place application of point group elements on a T-matrix.
/** The \a symops array should always contain all elements of a finite
 * point (sub)group, including the identity operation.
 *
 * TODO more doc.
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_irot3arr_inplace(
		qpms_tmatrix_t *T,
		size_t n_symops,
		const qpms_irot3_t *symops
		);

/// In-place application of point group elements on a T-matrix.
/** This does the same as qpms_tmatrix_symmetrise_irot3arr(),
 * but takes a valid finite point group as an argument.
 *
 * TODO more doc.
 */
qpms_tmatrix_t *qpms_tmatrix_symmetrise_finite_group_inplace(
		qpms_tmatrix_t *T,
		const qpms_finite_group_t *pointgroup
		);

/// Application of T-matrix on a vector of incident field coefficients, \f$ f = Ta \f$.
_Complex double *qpms_apply_tmatrix(
		_Complex double *f_target, ///< Scattered field coefficient array of size T->spec->n; if NULL, a new one is allocated.
		const _Complex double *a, ///< Incident field coefficient array of size T->spec->n.
		const qpms_tmatrix_t *T ///< T-matrix \a T to apply.
		);

/// Generic T-matrix generator function that fills a pre-initialised qpms_tmatrix_t given a frequency.
/** Implemented by: 
 * qpms_tmatrix_generator_axialsym()
 * qpms_tmatrix_generator_interpolator()
 * qpms_tmatrix_generator_sphere()
 * qpms_tmatrix_generator_constant()
 * qpms_tmatrix_generator_zero()
 */
typedef struct qpms_tmatrix_generator_t {
	qpms_errno_t (*function) (qpms_tmatrix_t *t, ///< T-matrix to fill.
			_Complex double omega, ///< Angular frequency.
			const void *params ///< Implementation dependent parameters.
			);
	const void *params; ///< Parameter pointer passed to the function.
} qpms_tmatrix_generator_t;

/// Initialises and evaluates a new T-matrix using a generator.
qpms_tmatrix_t *qpms_tmatrix_init_from_generator(
		const qpms_vswf_set_spec_t *bspec,
		qpms_tmatrix_generator_t gen,
		_Complex double omega);


/// Implementation of qpms_matrix_generator_t that just copies a constant matrix.
/** N.B. this does almost no checks at all, so use it only for t-matrices with
 * the same base spec.
 */
qpms_errno_t qpms_tmatrix_generator_constant(qpms_tmatrix_t *t,
		_Complex double omega_ignored,
		/// Source T-matrix, real type is (const qpms_tmatrix_t*).
		const void *tmatrix_orig
		);

/// Dummy implementation of qpms_tmatrix_generator_t, yielding a zero matrix.
/**
 * This effectively represents a part of the background medium without
 * any scatterer present.
 */
qpms_errno_t qpms_tmatrix_generator_zero(qpms_tmatrix_t *t,
    _Complex double omega_ignored,
    const void *params_ignored);

/* Fuck this, include the whole <gsl/gsl_spline.h>
typedef struct gsl_spline gsl_spline; // Forward declaration for the interpolator struct
typedef struct gsl_interp_type gsl_interp_type;
extern const gsl_interp_type * gsl_interp_linear;
extern const gsl_interp_type * gsl_interp_polynomial;
extern const gsl_interp_type * gsl_interp_cspline;
extern const gsl_interp_type * gsl_interp_cspline_periodic;
extern const gsl_interp_type * gsl_interp_akima;
extern const gsl_interp_type * gsl_interp_akima_periodic;
extern const gsl_interp_type * gsl_interp_steffen;
*/

// struct gsl_interp_accel; // use if lookup proves to be too slow
typedef struct qpms_tmatrix_interpolator_t {
	const qpms_vswf_set_spec_t *bspec;
	//_Bool owns_bspec;
	gsl_spline **splines_real; ///< There will be a spline object for each nonzero element
	gsl_spline **splines_imag; ///< There will be a spline object for each nonzero element
	// gsl_interp_accel **accel_real;
	// gsl_interp_accel **accel_imag;
} qpms_tmatrix_interpolator_t;

/// Free a T-matrix interpolator.
void qpms_tmatrix_interpolator_free(qpms_tmatrix_interpolator_t *interp);

/// Fills an existing T-matrix with new interpolated values.
qpms_errno_t qpms_tmatrix_interpolator_eval_fill(qpms_tmatrix_t *target, ///< T-matrix to be updated, not NULL.
		const qpms_tmatrix_interpolator_t *interp, double freq);

/// Evaluate a T-matrix interpolated value.
/** The result is to be freed using qpms_tmatrix_free().*/
qpms_tmatrix_t *qpms_tmatrix_interpolator_eval(const qpms_tmatrix_interpolator_t *interp, double freq);

/// Create a T-matrix interpolator from frequency and T-matrix arrays.
qpms_tmatrix_interpolator_t *qpms_tmatrix_interpolator_create(size_t n, ///< Number of freqs and T-matrices provided.
		const double *freqs, const qpms_tmatrix_t *tmatrices_array, ///< N.B. array of qpms_tmatrix_t, not pointers!
		const gsl_interp_type *iptype
	       //, _Bool copy_bspec ///< if true, copies its own copy of basis spec from the first T-matrix.
       	       /*, ...? */);


/// qpms_tmatrix_interpolator for qpms_tmatrix_generator_t.
/** As in qpms_tmatrix_interpolator_eval(), the imaginary part of frequency is discarded!
 */
qpms_errno_t qpms_tmatrix_generator_interpolator(qpms_tmatrix_t *t, ///< T-matrix to fill.
			_Complex double omega, ///< Angular frequency.
			const void *interpolator ///< Parameter of type qpms_tmatrix_interpolator_t *.
);

/// Calculates the reflection Mie-Lorentz coefficients for a spherical particle.
/**
 * This function is based on the previous python implementation mie_coefficients() from qpms_p.py,
 * so any bugs therein should affect this function as well and perhaps vice versa.
 *
 * Most importantly, the case of magnetic material, \a mu_i != 0 or \a mu_e != 0 has never been tested
 * and might give wrong results.
 *
 * \return Array with the Mie-Lorentz reflection coefficients in the order determined by bspec.
 * If \a target was not NULL, this is target, otherwise a newly allocated array.
 *
 * TODO better doc.
 */
_Complex double *qpms_mie_coefficients_reflection(
                _Complex double *target, ///< Target array of length bspec->n. If NULL, a new one will be allocated.
                const qpms_vswf_set_spec_t *bspec, ///< Defines which of the coefficients are calculated.
                double a, ///< Radius of the sphere.
                _Complex double k_i, ///< Wave number of the internal material of the sphere.
                _Complex double k_e, ///< Wave number of the surrounding medium.
                _Complex double mu_i, ///< Relative permeability of the sphere material.
                _Complex double mu_e, ///< Relative permeability of the surrounding medium.
                qpms_bessel_t J_ext, ///< Kind of the "incoming" waves. Most likely QPMS_BESSEL_REGULAR.
                qpms_bessel_t J_scat ///< Kind of the "scattered" waves. Most likely QPMS_HANKEL_PLUS.
                );

/// Replaces the contents of an existing T-matrix with that of a spherical nanoparticle calculated using the Lorentz-mie theory.
qpms_errno_t qpms_tmatrix_spherical_fill(qpms_tmatrix_t *t, ///< T-matrix whose contents are to be replaced. Not NULL.
		double a, ///< Radius of the sphere.
		_Complex double k_i, ///< Wave number of the internal material of the sphere.
		_Complex double k_e, ///< Wave number of the surrounding medium.
		_Complex double mu_i, ///< Relative permeability of the sphere material.
		_Complex double mu_e ///< Relative permeability of the surrounding medium.
		);

/// Parameter structure for qpms_tmatrix_generator_sphere().
typedef struct qpms_tmatrix_generator_sphere_param_t {
	qpms_epsmu_generator_t outside;
	qpms_epsmu_generator_t inside;
	double radius;
} qpms_tmatrix_generator_sphere_param_t;

/// T-matrix generator for spherical particles using Lorentz-Mie solution.
qpms_errno_t qpms_tmatrix_generator_sphere(qpms_tmatrix_t *t,
		_Complex double omega,
		const void *params ///< Of type qpms_tmatrix_generator_sphere_param_t.
		);

/// Creates a new T-matrix of a spherical particle using the Lorentz-Mie theory.
static inline qpms_tmatrix_t *qpms_tmatrix_spherical(
		const qpms_vswf_set_spec_t *bspec,
		double a, ///< Radius of the sphere.
		_Complex double k_i, ///< Wave number of the internal material of the sphere.
		_Complex double k_e, ///< Wave number of the surrounding medium.
		_Complex double mu_i, ///< Relative permeability of the sphere material.
		_Complex double mu_e ///< Relative permeability of the surrounding medium.
		) {
	qpms_tmatrix_t *t = qpms_tmatrix_init(bspec);
	qpms_tmatrix_spherical_fill(t, a, k_i, k_e, mu_i, mu_e);
	return t;
}

/// Convenience function to calculate T-matrix of a non-magnetic spherical particle using the permittivity values, replacing existing T-matrix data.
qpms_errno_t qpms_tmatrix_spherical_mu0_fill(
		qpms_tmatrix_t *t, ///< T-matrix whose contents are to be replaced. Not NULL.
		double a, ///< Radius of the sphere.
		double omega, ///< Angular frequency.
		_Complex double epsilon_fg, ///< Relative permittivity of the sphere.
		_Complex double epsilon_bg ///< Relative permittivity of the background medium.
		); 

/// Convenience function to calculate T-matrix of a non-magnetic spherical particle using the permittivity values.
static inline qpms_tmatrix_t *qpms_tmatrix_spherical_mu0(
		const qpms_vswf_set_spec_t *bspec,
		double a, ///< Radius of the sphere.
		double omega, ///< Angular frequency.
		_Complex double epsilon_fg, ///< Relative permittivity of the sphere.
		_Complex double epsilon_bg ///< Relative permittivity of the background medium.
		) {
	qpms_tmatrix_t *t = qpms_tmatrix_init(bspec);
	qpms_tmatrix_spherical_mu0_fill(t, a, omega, epsilon_fg, epsilon_bg);
	return t;
};

/// Return value type for qpms_arc_function_t.
typedef struct qpms_arc_function_retval_t {
	double r; ///< Distance from the origin.
	double beta; ///< Angle between surface normal and radial direction.
} qpms_arc_function_retval_t;

/// Prototype for general parametrisation of \f$ C_\infty \f$-symmetric particle's surface.
typedef struct qpms_arc_function_t {
	/// Arc parametrisation function.
	/** TODO link to notes.
	 *
	 * Implemented by:
	 * qpms_arc_cylinder(),
	 * qpms_arc_sphere().
	 */
	qpms_arc_function_retval_t (*function) (
			double theta, ///< Polar angle from interval \f$ [0, \pi] \f$. 
			const void *params ///< Pointer to implementation specific parameters.
			);
	const void *params;
} qpms_arc_function_t;

/// Parameter structure for qpms_arc_cylinder().
typedef struct qpms_arc_cylinder_params_t {
	double R; ///< Cylinder radius.
	double h; ///< Cylinder height.
} qpms_arc_cylinder_params_t;

/// Arc parametrisation of cylindrical particle; for qpms_arc_function_t.
qpms_arc_function_retval_t qpms_arc_cylinder(double theta,
		const void *params ///< Points to qpms_arc_cylinder_params_t
		);

/// Arc parametrisation of spherical particle; for qpms_arc_function_t.
/** Useful mostly only for benchmarks or debugging, as one can use the Mie-Lorentz solution. */
qpms_arc_function_retval_t qpms_arc_sphere(double theta,
		const void *R ///< Points to double containing particle's radius.
		);


/// Replaces T-matrix contents with those of a particle with \f$ C_\infty \f$ symmetry.
/** 
 * N.B. currently, this might crash for higher values of lMax (lMax > 5).
 * Also, it seems that I am doing something wrong, as the result is accurate for sphere
 * with lMax = 1 and for higher l the accuracy decreases.
 */
qpms_errno_t qpms_tmatrix_axialsym_fill(
		qpms_tmatrix_t *t, ///< T-matrix whose contents are to be replaced. Not NULL.
		_Complex double omega, ///< Angular frequency.
		qpms_epsmu_t outside, ///< Optical properties of the outside medium.
		qpms_epsmu_t inside, ///< Optical properties of the particle's material.
		qpms_arc_function_t shape, ///< Particle surface parametrisation.
		/** If `lMax_extend > t->bspec->lMax`, then the internal \a Q, \a R matrices will be 
		 * trimmed at this larger lMax; the final T-matrix will then be trimmed
		 * according to bspec.
		 */
		qpms_l_t lMax_extend 
		);

/// Creates a new T-matrix of a particle with \f$ C_\infty \f$ symmetry.
static inline qpms_tmatrix_t *qpms_tmatrix_axialsym(
		const qpms_vswf_set_spec_t *bspec,
		_Complex double omega, ///< Angular frequency.
		qpms_epsmu_t outside, ///< Optical properties of the outside medium.
		qpms_epsmu_t inside, ///< Optical properties of the particle's material.
		qpms_arc_function_t shape, ///< Particle surface parametrisation.
		/// Internal lMax to improve precision of the result.
		/** If `lMax_extend > bspec->lMax`, then the internal \a Q, \a R matrices will be 
		 * trimmed at this larger lMax; the final T-matrix will then be trimmed
		 * according to bspec.
		 */
		qpms_l_t lMax_extend 
		) {
	qpms_tmatrix_t *t = qpms_tmatrix_init(bspec);
	qpms_tmatrix_axialsym_fill(t, omega, outside, inside, shape, lMax_extend);
	return t;
}

/// Parameter structure for qpms_tmatrix_generator_axialsym.
typedef struct qpms_tmatrix_generator_axialsym_param_t {
	qpms_epsmu_generator_t outside;
	qpms_epsmu_generator_t inside;
	qpms_arc_function_t shape;
	qpms_l_t lMax_extend;
} qpms_tmatrix_generator_axialsym_param_t;


/// qpms_tmatrix_axialsym for qpms_tmatrix_generator_t
qpms_errno_t qpms_tmatrix_generator_axialsym(qpms_tmatrix_t *t, ///< T-matrix to fill.
			_Complex double omega, ///< Angular frequency.
			const void *params ///< Parameters of type qpms_tmatrix_generator_axialsym_param_t.
);


/// Computes the (reduced) transposed R or Q matrix for axially symmetric particle (useful for debugging).
qpms_errno_t qpms_tmatrix_generator_axialsym_RQ_transposed_fill(_Complex double *target,
		_Complex double omega,
		const qpms_tmatrix_generator_axialsym_param_t *param,
		qpms_normalisation_t norm,
		qpms_bessel_t J
		);

/// Computes the (reduced) transposed R or Q matrix for axially symmetric particle (useful mostly for debugging).
qpms_errno_t qpms_tmatrix_axialsym_RQ_transposed_fill(_Complex double *target,
		_Complex double omega, qpms_epsmu_t outside, qpms_epsmu_t inside,
		qpms_arc_function_t shape, qpms_l_t lMaxQR, qpms_normalisation_t norm,
		qpms_bessel_t J ///< Use QPMS_BESSEL_REGULAR to calculate \f$ R^T\f$ or QPMS_HANKEL_PLUS to calculate \f$ Q^T\f$.
		);


/// An "abstract" T-matrix, contains a T-matrix generator instead of actual data.
typedef struct qpms_tmatrix_function_t {
        /** \brief VSWF basis specification, NOT owned by qpms_tmatrix_t by default.
         *
         *  Usually not checked for meaningfulness by the functions (methods),
         *  so the caller should take care that \a spec->ilist does not
         *  contain any duplicities and that for each wave with order \a m
         *  there is also one with order \a −m.
         */
        const qpms_vswf_set_spec_t *spec;
        const qpms_tmatrix_generator_t *gen; ///< A T-matrix generator function.
} qpms_tmatrix_function_t;

/// Convenience function to create a new T-matrix from qpms_tmatrix_function_t.
// FIXME the name is not very intuitive.
static inline qpms_tmatrix_t *qpms_tmatrix_init_from_function(qpms_tmatrix_function_t f, _Complex double omega) {
	return qpms_tmatrix_init_from_generator(f.spec, *f.gen, omega);
}

/// Specifies different kinds of operations done on T-matrices
typedef enum {
	QPMS_TMATRIX_OPERATION_NOOP, ///< Identity operation.
	QPMS_TMATRIX_OPERATION_LRMATRIX, ///< General matrix transformation \f$ T' = MTM^\dagger \f$; see @ref qpms_tmatrix_operation_lrmatrix.
	QPMS_TMATRIX_OPERATION_IROT3, ///< Single rotoreflection specified by a qpms_irot3_t.
	QPMS_TMATRIX_OPERATION_IROT3ARR, ///< Symmetrise using an array of rotoreflection; see @ref qpms_tmatrix_operation_irot3arr.
	QPMS_TMATRIX_OPERATION_COMPOSE_SUM, ///< Apply several transformations and sum the results, see @ref qpms_tmatrix_operation_compose_sum.
	QPMS_TMATRIX_OPERATION_COMPOSE_CHAIN, ///< Chain several different transformations; see @ref qpms_tmatrix_operation_compose_chain.
	QPMS_TMATRIX_OPERATION_SCMULZ, ///< Elementwise scalar multiplication with a complex matrix; see @ref qpms_tmatrix_operation_scmulz.
	//QPMS_TMATRIX_OPERATION_POINTGROUP, ///< TODO the new point group in pointgroup.h
	QPMS_TMATRIX_OPERATION_FINITE_GROUP_SYMMETRISE ///< Legacy qpms_finite_group_t with filled rep3d; see @ref qpms_tmatrix_operation_finite_group.
} qpms_tmatrix_operation_kind_t;

/// General matrix transformation \f[ T' = MTM^\dagger \f] spec for qpms_tmatrix_operation_t.
struct qpms_tmatrix_operation_lrmatrix {
	/// Raw matrix data of \a M in row-major order.
	/** The matrix must be taylored for the given bspec! */
	_Complex double *m; 
        size_t m_size; ///< Total size of \a m matrix in terms of sizeof(_Complex double).
	_Bool owns_m; ///< Whether \a m is owned by this;
};

struct qpms_tmatrix_operation_t; // Forward declaration for the composed operations.

/// Specifies a composed operation of type \f$ T' = c\sum_i f_i'(T) \f$ for qpms_tmatrix_operation_t.
struct qpms_tmatrix_operation_compose_sum {
	size_t n; ///< Number of operations in ops;
	const struct qpms_tmatrix_operation_t **ops; ///< Operations array. (Pointers array \a ops[] always owned by this.)
	double factor; ///< Overall factor \a c.
	/// (Optional) operations buffer into which elements of \a ops point.
	/** Owned by this or NULL. If not NULL, all \a ops members are assumed to point into 
	 * the memory held by \a opmem and to be properly initialised.
	 * Each \a ops member has to point to _different_ elements of \a opmem.
	 */ 
	struct qpms_tmatrix_operation_t *opmem; 
};

/// Specifies a composed operation of type \f$ T' =  f_{n-1}(f_{n-2}(\dots f_0(T)\dots))) \f$ for qpms_tmatrix_operation_t.
struct qpms_tmatrix_operation_compose_chain {
	size_t n; ///< Number of operations in ops;
	const struct qpms_tmatrix_operation_t **ops; ///< Operations array. (Pointers owned by this.)
	struct qpms_tmatrix_operation_t *opmem; ///< (Optional) operations buffer into which elements of \a ops point. (Owned by this or NULL.)
	size_t opmem_size; ///< Length of the opmem array.
	_Bool *ops_owned; ///< True for all sub operations owned by this and saved in opmem. NULL if opmem is NULL.
};

/// Specifies an elementwise complex multiplication of type \f$ T'_{ij} = M_{ij}T_{ij} \f$ for qpms_tmatrix_operation_t.
struct qpms_tmatrix_operation_scmulz {
	/// Raw matrix data of \a M in row-major order.
	/** The matrix must be taylored for the given bspec! */
	_Complex double *m;
        size_t m_size; ///< Total size of \a m matrix in terms of sizeof(_Complex double).
	_Bool owns_m; ///< Whether \a m is owned by this.
};

/// Specifies a symmetrisation using a set of rotoreflections (with equal weights) for qpms_tmatrix_operation_t.
/** Internally, this is evaluated using a call to qpms_symmetrise_tmdata_irot3arr()
 * or qpms_symmetrise_tmdata_irot3arr_inplace(). */
struct qpms_tmatrix_operation_irot3arr {
	size_t n; ///< Number of rotoreflections;
	qpms_irot3_t *ops; ///< Rotoreflection array of size \a n.
	_Bool owns_ops; ///< Whether \a ops array is owned by this.
};

/// A generic T-matrix transformation operator.
typedef struct qpms_tmatrix_operation_t {
	/// Specifies the operation kind to be performed and which type \op actually contains.
	qpms_tmatrix_operation_kind_t typ;
	union {
		struct qpms_tmatrix_operation_lrmatrix lrmatrix;
		struct qpms_tmatrix_operation_scmulz scmulz;
		qpms_irot3_t irot3; ///< Single rotoreflection; \a typ = QPMS_TMATRIX_OPERATION_IROT3
		struct qpms_tmatrix_operation_irot3arr irot3arr;
		struct qpms_tmatrix_operation_compose_sum compose_sum;
		struct qpms_tmatrix_operation_compose_chain compose_chain;
		/// Finite group for QPMS_TMATRIX_OPERATION_FINITE_GROUP_SYMMETRISE.
		/** Not owned by this; \a rep3d must be filled. */
		const qpms_finite_group_t *finite_group; 
	} op; ///< Operation data; actual type is determined by \a typ.
} qpms_tmatrix_operation_t;

static const qpms_tmatrix_operation_t qpms_tmatrix_operation_noop = {.typ = QPMS_TMATRIX_OPERATION_NOOP};

/// Apply an operation on a T-matrix, returning a newly allocated result.
qpms_tmatrix_t *qpms_tmatrix_apply_operation(const qpms_tmatrix_operation_t *op, const qpms_tmatrix_t *orig);

/// Apply an operation on a T-matrix and replace it with the result.
qpms_tmatrix_t *qpms_tmatrix_apply_operation_inplace(const qpms_tmatrix_operation_t *op, qpms_tmatrix_t *orig);

/// Apply an operation on a T-matrix and replace another one it with the result.
qpms_tmatrix_t *qpms_tmatrix_apply_operation_replace(qpms_tmatrix_t *dest, 
		const qpms_tmatrix_operation_t *op, const qpms_tmatrix_t *orig);

/// (Recursively) deallocates internal data of qpms_tmatrix_operation_t.
/** It does NOT clear the memory pointed to by op it self, but only
 * heap-allocated data of certain operations, if labeled as owned by it.
 * In case of compose operations, the recursion stops if the children are
 * not owned by them (the opmem pointer is NULL).
 */
void qpms_tmatrix_operation_clear(qpms_tmatrix_operation_t *f);

/// (Recursively) copies an qpms_tmatrix_operation_t.
/** Makes copies of all the internal data and takes ownership over them if needed */
void qpms_tmatrix_operation_copy(qpms_tmatrix_operation_t *target, const qpms_tmatrix_operation_t *src);

/// Inits a new "chain" of composed operations, some of which might be owned.
void qpms_tmatrix_operation_compose_chain_init(
		qpms_tmatrix_operation_t *target, ///< The operation structure that will be set to the chain.
		size_t nops, ///< Number of chained operations (length of the \a ops array)
		size_t opmem_size ///< Size of the own operations buffer (length of the \a opmem array)
		);

#if 0
// Abstract types that describe T-matrix/particle/scatsystem symmetries
// To be implemented later. See also the thoughts in the beginning of groups.h.

typedef *char qpms_tmatrix_id_t; ///< Maybe I want some usual integer type instead.

///Abstract T-matrix type draft.
/**
 * TODO.
 */
typedef struct qpms_abstract_tmatrix_t{
	qpms_tmatrix_id_t id;
	/// Generators of the discrete point group under which T-matrix is invariant.
	qpms_irot3_t *invar_gens;
	/// Length of invar_gens.
	qpms_gmi_t invar_gens_size;

} qpms_abstract_tmatrix_t;


typedef struct qpms_abstract_particle_t{
} qpms_abstract_particle_t;

/// An abstract particle, defined by its position and abstract T-matrix.
typedef struct qpms_abstract_particle_t {
	cart3_t pos; ///< Particle position in cartesian coordinates.
	const qpms_abstract_tmatrix_t *tmatrix; ///< T-matrix; not owned by this.
} qpms_abstract_particle_t;


/** This is just an alias, as the same index can be used for 
 * abstract T-matrices as well.
 */
typedef qpms_particle_tid_t qpms_abstract_particle_tid_t;
#endif // 0

#ifdef __cplusplus
}
#endif
#endif //TMATRICES_H