WIP data structure redefinitions.

[qpms.git] / qpms / scatsystem.h

/*! \file scatsystem.h
 * \brief Modern interface for finite lattice calculations, including symmetries.
 *
 * N.B. Only "reasonably normalised" waves are supported now in most of the
 * functions defined here, i.e. those that can be rotated by the usual
 * Wigner matrices, i.e. the "power" or "spharm" -normalised ones.
 * 
 * TODO FIXME check whether Condon-Shortley phase can have some nasty influence
 * here; I fear that yes.
 */
#ifndef QPMS_SCATSYSTEM_H
#define QPMS_SCATSYSTEM_H
#include "qpms_types.h"
#include "vswf.h"
#include <stdbool.h>

/// Overrides the number of threads spawned by the paralellized functions.
/** TODO MORE DOC which are those? */
void qpms_scatsystem_set_nthreads(long n);

/// A particle, defined by its T-matrix and position.
typedef struct qpms_particle_t {
        // Does it make sense to ever use other than cartesian coords for this?
        cart3_t pos; ///< Particle position in cartesian coordinates.
        const qpms_tmatrix_t *tmatrix; ///< T-matrix; not owned by qpms_particle_t.
} qpms_particle_t;

struct qpms_finite_group_t;
typedef struct qpms_finite_group_t qpms_finite_group_t;

/// A particle, defined by its T-matrix INDEX and position, to be used in qpms_scatsys_t.
typedef struct qpms_particle_tid_t {
        // Does it make sense to ever use other than cartesian coords for this?
        cart3_t pos; ///< Particle position in cartesian coordinates.
        qpms_ss_tmi_t tmatrix_id; ///< T-matrix index
} qpms_particle_tid_t;


typedef qpms_gmi_t qpms_ss_orbit_pi_t; ///< Auxilliary type used in qpms_ss_orbit_type_t for labeling particles inside orbits.
typedef qpms_ss_tmi_t qpms_ss_oti_t; ///< Auxilliary type used for labeling orbit types.

/// Structure describing a particle's "orbit type" under symmetry group actions in a system.
/**
 * Each particle has its orbit with respect to a symmetry group of the system in which the particle lies,
 * i.e. a set of particles onto which the group operations map the original particle.
 * 
 * (TODO DOC improve the following explanation:)
 * Typically, there will be only a small number of different (T-matrix, particle 
 * <a href="https://en.wikipedia.org/wiki/Group_action#Fixed_points_and_stabilizer_subgroups">stabiliser</a>)
 * pairs in the system. We can group the particles accordingly, into the same "orbit types"
 * that will allow to do certain operations only once for each "orbit type", saving memory and (perhaps) time.
 *
 * Each particle will then have assigned:
 *   1. an orbit type,
 *   2. an ID inside that orbit.
 *
 *
 * TODO DOC how the process of assigning the particle IDs actually work, orbit type (non-)uniqueness.
 *
 *
 * Memory is managed by qpms_scatspec_t; qpms_ss_orbit_type_t does not own anything.
 *
 */
typedef struct qpms_ss_orbit_type_t {
        qpms_ss_orbit_pi_t size; ///< Size of the orbit (a divisor of the group order), i.e. number of particles on the orbit.
        size_t bspecn; ///< Individual particle's coefficient vector length. The same as ss->tm[this.tmatrices[0]]->spec->n.
        /// Action of the group elements onto the elements in this orbit.
        /** Its size is sym->order * this.size
         *  and its values lie between 0 and \a this.size − 1.
         *
         *  Action of the group element g onto the pi-th particle
         *  is given by action[g + pi*sym->order].
         *  
         */
        qpms_ss_orbit_pi_t *action;
        /// T-matrix IDs of the particles on this orbit (type).
        /**
         * We save all the tmi's of the particles on the orbit here to make the number of array lookups
         * and pointer dereferences constant.
         *
         * The size of this array is \a size.
         */
        qpms_ss_tmi_t *tmatrices;
        /// Sizes of the per-orbit irrep bases. 
        /**
         * The order of the irreps corresponds to the order in \a ss->sym->irreps.
         * The size of this array is (obviously) \a ss->sym->nirreps.
         *
         * TODO different type? 
         * TODO doc.
         */
        size_t *irbase_sizes;
        //The following are pretty redundant, TODO reduce them at some point.
        /// Cumulative sums of irbase_sizes.
        size_t *irbase_cumsizes;
        /// TODO doc.
        size_t *irbase_offsets;
        /// Per-orbit irreducible representation orthonormal bases.
        /** This also defines the unitary operator that transforms the orbital excitation coefficients
         * in the symmetry-adapted basis.
         *
         * The size is (\a this->size * \a this->tmatrices[0].spec->n)**2.
         *
         * TODO doc.
         */
        complex double *irbases;
        /// TODO doc.
        size_t instance_count;
        /// Cumulative sum of the preceding ot->siza * ot->instance_count;
        qpms_ss_pi_t p_offset;
} qpms_ss_orbit_type_t;


typedef ptrdiff_t qpms_ss_osn_t; ///< "serial number" of av orbit in a given type.

/// Auxillary type used in qpms_scatsys_t that identifies the particle's orbit and its id inside that orbit.
typedef struct qpms_ss_particle_orbitinfo {
        qpms_ss_oti_t t; ///< Orbit type.
#define QPMS_SS_P_ORBITINFO_UNDEF (-1) ///< This labels that the particle has not yet been assigned to an orbit.
        qpms_ss_osn_t osn; ///< "Serial number" of the orbit in the given type. TODO type and more doc.
        qpms_ss_orbit_pi_t p; ///< Order (sija, ei rankki) of the particle inside that orbit type.
} qpms_ss_particle_orbitinfo_t;

struct qpms_trans_calculator;

typedef struct qpms_scatsys_t {
        qpms_qpms_epsmu_generator_t *medium; ///< Optical properties of the background medium.
        qpms_abstract_tmatrix_t **tm; ///< T-matrices in the system
        qpms_ss_tmi_t tm_count; ///< Number of all different T-matrices
        qpms_ss_tmi_t tm_capacity; ///< Capacity of tm[].
        qpms_particle_tid_t *p; ///< Particles.
        qpms_ss_pi_t p_count; ///< Size of particles array.
        qpms_ss_pi_t p_capacity; ///< Capacity of p[].

        //TODO the index types do not need to be so big.
        const struct qpms_finite_group_t *sym; ///< Symmetry group of the array
        qpms_ss_pi_t *p_sym_map; ///< Which particles map onto which by the symmetry ops.
        ///< p_sym_map[idi + pi * sym->order] gives the index of pi-th particle under the idi'th sym op.
        qpms_ss_tmi_t *tm_sym_map; ///< Which t-matrices map onto which by the symmetry ops. Lookup by tm_sum_map[idi + tmi * sym->order].

        qpms_ss_oti_t orbit_type_count;
        qpms_ss_orbit_type_t *orbit_types; ///< (Array length is \a orbit_type_count.)

        qpms_ss_particle_orbitinfo_t *p_orbitinfo; ///< Orbit type identification of each particle. (Array length is \a p_count.)

        size_t fecv_size; ///< Number of elements of a full excitation coefficient vector size. 
        size_t *saecv_sizes; ///< Number of elements of symmetry-adjusted coefficient vector sizes (order as in sym->irreps).

        size_t *fecv_pstarts; ///< Indices of where pi'th particle's excitation coeffs start in a full excitation coefficient vector.
        size_t *saecv_ot_offsets; ///< TODO DOC. In the packed vector, saecv_ot_offsets[iri * orbit_type_count + oti] indicates start of ot
        /**< TODO maybe move it to qpms_ss_orbit_type_t, ffs. */
        //size_t **saecv_pstarts; ///< NI. Indices of where pi'th particle's excitation coeff start in a symmetry-adjusted e.c.v.
        ///**< First index is irrep index as in sym->irreps, second index is particle index. */

        // TODO shifted origin of the symmetry group etc.
        // TODO some indices for fast operations here.
        // private
        size_t max_bspecn; ///< Maximum tm[...]->spec->n. Mainly for workspace allocation.
        
        /// Particles grouped by orbit (in the order corresponding to the packed memory layout).
        qpms_ss_pi_t *p_by_orbit;

        // We keep the p_orbitinfo arrays in this chunk in order to avoid memory fragmentation
        char *otspace;
        char *otspace_end;
        double lenscale; // radius of the array, used as a relative tolerance measure
        struct qpms_trans_calculator *c;
} qpms_scatsys_t;


typedef struct qpms_scatsys_at_omega_t {
        const qpms_scatsys_t *ss; ///< Parent scattering system.
        /// T-matrices from \a ss, evaluated at \a omega.
        /** The T-matrices are in the same order as in \a ss,
         * i.e in the order corresponding to TODO WHAT E7ACTLY??
         */
        qpms_tmatrix_t **tm;
        complex double omega; ///< Angular frequency
        complex double eps; ///< Background medium relative electric permittivity
        complex double mu; ///< Background medium relative magnetic permeability
        complex double wavenumber; ///< Background medium wavenumber
        complex double refractive_index; ///< Background medium refractive index
} qpms_scatsys_at_omega_t;

void qpms_scatsys_at_omega_free(qpms_scatsys_at_omega_t *);

/// Convenience function to access pi'th particle's bspec.
static inline const qpms_vswf_set_spec_t *qpms_ss_bspec_pi(const qpms_scatsys_t *ss, qpms_ss_pi_t pi) {
        return ss->tm[ss->p[pi].tmatrix_id]->spec;
}

/// Creates a new scatsys by applying a symmetry group, copying particles if needed.
/** In fact, it copies everything except the vswf set specs, so keep them alive until scatsys is destroyed.
 * The following fields must be filled:
 * orig->tm
 * orig->tm_count
 * orig->p
 * orig->p_count
 */
qpms_scatsys_t *qpms_scatsys_apply_symmetry(const qpms_scatsys_t *orig, const struct qpms_finite_group_t *sym);
/// Destroys the result of qpms_scatsys_apply_symmetry or qpms_scatsys_load.
void qpms_scatsys_free(qpms_scatsys_t *s);

/// Creates a "full" transformation matrix U that takes a full vector and projects it onto an symmetry adapted basis.
/** Mostly as a reference and a debugging tool, as multiplicating these big matrices would be inefficient.
 * 
 * TODO doc about shape etc.
 */
complex double *qpms_scatsys_irrep_transform_matrix(complex double *target_U,
                const qpms_scatsys_t *ss, qpms_iri_t iri);

/// Projects a "big" matrix onto an irrep (slow reference implementation).
/** TODO doc */
complex double *qpms_scatsys_irrep_pack_matrix_stupid(complex double *target_packed,
                const complex double *orig_full, const qpms_scatsys_t *ss,
                qpms_iri_t iri);

/// Transforms a big "packed" matrix into the full basis (slow reference implementation).
/** TODO doc */
complex double *qpms_scatsys_irrep_unpack_matrix_stupid(complex double *target_full,
                const complex double *orig_packed, const qpms_scatsys_t *ss,
                qpms_iri_t iri, bool add);

/// Projects a "big" matrix onto an irrep.
/** TODO doc */
complex double *qpms_scatsys_irrep_pack_matrix(complex double *target_packed,
                const complex double *orig_full, const qpms_scatsys_t *ss,
                qpms_iri_t iri);

/// Transforms a big "packed" matrix into the full basis.
/** TODO doc */
complex double *qpms_scatsys_irrep_unpack_matrix(complex double *target_full,
                const complex double *orig_packed, const qpms_scatsys_t *ss,
                qpms_iri_t iri, bool add);

/// Projects a "big" vector onto an irrep.
/** TODO doc */
complex double *qpms_scatsys_irrep_pack_vector(complex double *target_packed,
                const complex double *orig_full, const qpms_scatsys_t *ss,
                qpms_iri_t iri);

/// Transforms a big "packed" vector into the full basis.
/** TODO doc */
complex double *qpms_scatsys_irrep_unpack_vector(complex double *target_full,
                const complex double *orig_packed, const qpms_scatsys_t *ss,
                qpms_iri_t iri, bool add);

/// Global translation matrix.
/**
 * The diagonal (particle self-) block are filled with zeros (even for regular Bessel waves).
 * This may change in the future.
 */
complex double *qpms_scatsys_build_translation_matrix_full(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss,
                complex double k ///< Wave number to use in the translation matrix.
                );

/// As qpms_scatsys_build_translation_full() but with choice of Bessel function type.
/** Might be useful for evaluation of cross sections and testing.
 */
complex double *qpms_scatsys_build_translation_matrix_e_full(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss,
                complex double k, ///< Wave number to use in the translation matrix.
                qpms_bessel_t J
                );

/// Global translation matrix with selectable Bessel function, projected on an irrep.
/**
 * The diagonal (particle self-) blocks are currently filled with zeros.
 * This may change in the future.
 */
complex double *qpms_scatsys_build_translation_matrix_e_irrep_packed(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss,
                qpms_iri_t iri,
                complex double k, ///< Wave number to use in the translation matrix.
                qpms_bessel_t J
                );

/// Creates the full \f$ (I - TS) \f$ matrix of the scattering system.
complex double *qpms_scatsys_build_modeproblem_matrix_full(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss,
                complex double k ///< Wave number to use in the translation matrix.
                );
/// Creates the mode problem matrix \f$ (I - TS) \f$ directly in the irrep-packed form.
complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss, qpms_iri_t iri,
                complex double k ///< Wave number to use in the translation matrix.
                );
/// Alternative implementation of qpms_scatsys_build_modeproblem_matrix_irrep_packed().
complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss, qpms_iri_t iri,
                complex double k ///< Wave number to use in the translation matrix.
                );
/// Alternative (serial reference) implementation of qpms_scatsys_build_modeproblem_matrix_irrep_packed().
complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorder_serial(
                /// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
                complex double *target,
                const qpms_scatsys_t *ss, qpms_iri_t iri,
                complex double k ///< Wave number to use in the translation matrix.
                );

/// LU factorisation (LAPACKE_zgetrf) result holder.
typedef struct qpms_ss_LU {
        const qpms_scatsys_t *ss;
        bool full; ///< true if full matrix; false if irrep-packed.
        qpms_iri_t iri; ///< Irrep index if `full == false`.
        /// LU decomposition array.
        complex double *a;
        /// Pivot index array, size at least max(1,min(m, n)).
        int *ipiv; 
} qpms_ss_LU;
void qpms_ss_LU_free(qpms_ss_LU);

/// Builds an LU-factorised mode/scattering problem \f$ (I - TS) \f$ matrix from scratch.
qpms_ss_LU qpms_scatsys_build_modeproblem_matrix_full_LU(
                complex double *target, ///< Pre-allocated target array. Optional (if NULL, new one is allocated).
                int *target_piv, ///< Pre-allocated pivot array. Optional (if NULL, new one is allocated).
                const qpms_scatsys_t *ss,
                complex double k ///< Wave number to use in the translation matrix.
                );

/// Builds an irrep-packed LU-factorised mode/scattering problem matrix from scratch.
qpms_ss_LU qpms_scatsys_build_modeproblem_matrix_irrep_packed_LU(
                complex double *target, ///< Pre-allocated target array. Optional (if NULL, new one is allocated).
                int *target_piv, ///< Pre-allocated pivot array. Optional (if NULL, new one is allocated).
                const qpms_scatsys_t *ss, qpms_iri_t iri,
                complex double k ///< Wave number to use in the translation matrix.
                );

/// Computes LU factorisation of a pre-calculated mode/scattering problem matrix, replacing its contents.
qpms_ss_LU qpms_scatsys_modeproblem_matrix_full_factorise(
                complex double *modeproblem_matrix_full, ///< Pre-calculated mode problem matrix (I-TS). Mandatory.
                int *target_piv, ///< Pre-allocated pivot array. Optional (if NULL, new one is allocated).
                const qpms_scatsys_t *ss
                );

/// Computes LU factorisation of a pre-calculated irrep-packed mode/scattering problem matrix, replacing its contents.
qpms_ss_LU qpms_scatsys_modeproblem_matrix_irrep_packed_factorise(
                complex double *modeproblem_matrix_irrep_packed, ///< Pre-calculated mode problem matrix (I-TS). Mandatory.
                int *target_piv, ///< Pre-allocated pivot array. Optional (if NULL, new one is allocated).
                const qpms_scatsys_t *ss, qpms_iri_t iri
                );

/// Solves a (possibly partial, irrep-packed) scattering problem \f$ (I-TS)f = Ta_\mathrm{inc} \f$ using a pre-factorised \f$ (I-TS) \f$.
complex double *qpms_scatsys_scatter_solve(
                complex double *target_f, ///< Target (full or irrep-packed, depending on `ludata.full`) array for \a f. If NULL, a new one is allocated.
                const complex double *a_inc, ///< Incident field expansion coefficient vector \a a (full or irrep-packed, depending on `ludata.full`).
                qpms_ss_LU ludata ///< Pre-factorised \f$ I - TS \f$ matrix data.
                );


/// NOT IMPLEMENTED Dumps a qpms_scatsys_t structure to a file.
qpms_errno_t qpms_scatsys_dump(qpms_scatsys_t *ss, char *path);

/// NOT IMPLEMENTED Reads a qpms_scatsys_t structure from a file.
qpms_scatsys_t *qpms_scatsys_load(char *path);

struct qpms_finite_group_t;

/// Constructs a "full matrix action" of a point group element for an orbit type.
/** TODO detailed doc */
complex double *qpms_orbit_action_matrix(
                /// Target array. If NULL, a new one is allocated.
                /** The size of the array is (orbit->size * bspec->n)**2
                 * (it makes sense to assume all the T-matrices share their spec).
                 */
                complex double *target,
                /// The orbit (type).
                const qpms_ss_orbit_type_t *orbit,
                /// Base spec of the t-matrices (we don't know it from orbit, as it has 
                /// only T-matrix indices.
                const qpms_vswf_set_spec_t *bspec,
                /// The symmetry group used to generate the orbit (must have rep3d filled).
                const struct qpms_finite_group_t *sym,
                /// The index of the operation in sym to represent.
                const qpms_gmi_t g);

/// Constructs a dense matrix representation of a irrep projector for an orbit type.
/** TODO detailed doc */
complex double *qpms_orbit_irrep_projector_matrix(
                /// Target array. If NULL, a new one is allocated.
                /** The size of the array is (orbit->size * bspec->n)**2
                 * (it makes sense to assume all the T-matrices share their spec).
                 */
                complex double *target,
                /// The orbit (type).
                const qpms_ss_orbit_type_t *orbit,
                /// Base spec of the t-matrices (we don't know it from orbit, as it has 
                /// only T-matrix indices.
                const qpms_vswf_set_spec_t *bspec,
                /// The symmetry group used to generate the orbit (must have rep3d filled).
                const struct qpms_finite_group_t *sym,
                /// The index of the irreducible representation of sym.
                const qpms_iri_t iri);

/// TODO DOC!!!!!
complex double *qpms_orbit_irrep_basis(
                /// Here theh size of theh basis shall be saved,
                size_t *basis_size,
                /// Target array. If NULL, a new one is allocated.
                /** The size of the array is basis_size * (orbit->size * bspec->n)
                 * (it makes sense to assume all the T-matrices share their spec).
                 */
                complex double *target,
                /// The orbit (type).
                const qpms_ss_orbit_type_t *orbit,
                /// Base spec of the t-matrices (we don't know it from orbit, as it has 
                /// only T-matrix indices.
                const qpms_vswf_set_spec_t *bspec,
                /// The symmetry group used to generate the orbit (must have rep3d filled).
                const struct qpms_finite_group_t *sym,
                /// The index of the irreducible representation of sym.
                const qpms_iri_t iri);


/// Creates an incident field vector in the full basis, given a function that evaluates the field expansions at points.
/** TODO detailed doc!
 * \returns target_full if target_full was not NULL, otherwise the newly allocated array. */
complex double *qpms_scatsys_incident_field_vector_full(
                /// Target array. If NULL, a new one is allocated.
                /** The length of the array is ss->fecv_size. */
                complex double *target_full,
                const qpms_scatsys_t *ss,
                qpms_incfield_t field_at_point,
                const void *args, ///< Pointer passed as the last argument to (*field_at_point)()
                bool add ///< If true, add to target_full; rewrite target_full if false.
                );

/// Applies T-matrices onto an incident field vector in the full basis.
complex double *qpms_scatsys_apply_Tmatrices_full(
                complex double *target_full, /// Target vector array. If NULL, a new one is allocated.
                const complex double *inc_full, /// Incident field coefficient vector. Must not be NULL.
                const qpms_scatsys_t *ss
                );


#if 0
/// Creates a (partial) incident field vector in the symmetry-adapted basis, given a function that evaluates the field expansions at points.
/** TODO detailed doc! */
complex double *qpms_scatsys_incident_field_vector_irrep_packed(
                /// Target array. If NULL, a new one is allocated.
                /** The length of the array is ss->fecv_size. */
                complex double *target_full,
                const qpms_scatsys_t *ss,
                const qpms_iri_t iri, ///< The index of given irreducible representation of ss->sym.
                qpms_incfield_t field_at_point,
                const void *args, ///< Pointer passed as the last argument to (*field_at_point)()
                bool add ///< If true, add to target_full; rewrite target_full if false.
                );
#endif

/// Evaluates scattered fields (corresponding to a given excitation vector) at a given point.
/**
 * By scattered field, one assumes a linear combination of positive-Hankel-type
 * spherical waves.
 *
 * \return Complex electric field at the point defined by \a where.
 */
ccart3_t qpms_scatsys_eval_E(const qpms_scatsys_t *ss,
                const complex double *coeff_vector, ///< A full-length excitation vector (outgoing wave coefficients).
                cart3_t where, ///< Evaluation point.
                complex double k ///< Wave number.
                );


#if 0
/** Evaluates partial scattered fields (corresponding to a given irrep-reduced excitation vector)
 * at a given point.
 *
 * \return Complex electric field at the point defined by \a where.
 */
ccart3_t qpms_scatsys_eval_E_irrep(const qpms_scatsys_t *ss,
                qpms_iri_t iri, ///< Irreducible representation
                const complex double *coeff_vector, ///< A reduced excitation vector, corresponding to \a iri.
                cart3_t where, ///< Evaluation point.
                complex double k ///< Wave number.
                );
#endif

#endif //QPMS_SCATSYSTEM_H