Disable "hard" examples in CI

[qpms.git] / qpms / vectors.h

/*! \file vectors.h
 * \brief Coordinate transforms and vector arithmetics.
 */
#ifndef VECTORS_H
#define VECTORS_H
#include <math.h>
#ifndef M_PI_2
#define M_PI_2 (1.570796326794896619231321691639751442098584699687552910487)
#endif
#include "qpms_types.h"
#include "qpms_error.h"

//static inline double vectors_h_sq(double x) {return x*x;}

static const cart2_t CART2_ZERO = {0, 0};
static const cart3_t CART3_ZERO = {0, 0, 0};

/// 2D vector addition.
static inline cart2_t cart2_add(const cart2_t a, const cart2_t b) {
        cart2_t res = {a.x+b.x, a.y+b.y};
        return res;
}

/// 2D vector substraction.
static inline cart2_t cart2_substract(const cart2_t a, const cart2_t b) {
        cart2_t res = {a.x-b.x, a.y-b.y};
        return res;
}

/// 2D vector scaling.
static inline cart2_t cart2_scale(const double c, const cart2_t v) {
        cart2_t res = {c * v.x, c * v.y};
        return res;
}

/// 2D vector dot product.
static inline double cart2_dot(const cart2_t a, const cart2_t b) {
        return a.x * b.x + a.y * b.y;
}

static inline double cart2_normsq(const cart2_t a) {
        return cart2_dot(a, a);
}

/// 2D vector euclidian norm.
static inline double cart2norm(const cart2_t v) {
        return hypot(v.x, v.y); //sqrt(v.x*v.x + v.y*v.y);
}

/// 2D cartesian to polar coordinates conversion. See @ref coord_conversions.
static inline pol_t cart2pol(const cart2_t cart) {
        pol_t pol;
        pol.r = cart2norm(cart);
        pol.phi = atan2(cart.y, cart.x);
        return pol;
}

/// Polar to spherical coordinates conversion. See @ref coord_conversions.
static inline sph_t pol2sph_equator(const pol_t pol) {
        sph_t sph;
        sph.r = pol.r;
        sph.phi = pol.phi;
        sph.theta = M_PI_2;
        return sph;
}

/// 2D cartesian to spherical coordinates conversion. See @ref coord_conversions.
static inline sph_t cart22sph(const cart2_t cart) {
        sph_t sph;
        sph.r = cart2norm(cart);
        sph.theta = M_PI_2;
        sph.phi = atan2(cart.y, cart.x);
        return sph;
}

/// 1D cartesian to spherical coordinates conversion. See @ref coord_conversions.
static inline sph_t cart12sph_zaxis(double z) {
        sph_t sph = {fabs(z), z < 0 ? M_PI : 0, 0};
        return sph;
}

/// 1D to 3D cartesian coordinates conversion. See @ref coord_conversions.
static inline cart3_t cart12cart3z(double z) {
        cart3_t c = {0, 0, z};
        return c;
}

/// 2D to 3D cartesian coordinates conversion. See @ref coord_conversions.
static inline cart3_t cart22cart3xy(const cart2_t a) {
        cart3_t c;
        c.x = a.x;
        c.y = a.y;
        c.z = 0;
        return c;
}

static inline cart2_t cart3xy2cart2(const cart3_t a) {
        cart2_t c = {a.x, a.y};
        return c;
}

/// 3D vector dot product.
static inline double cart3_dot(const cart3_t a, const cart3_t b) {
        return a.x * b.x + a.y * b.y + a.z * b.z;
}


/// 3D vector product a.k.a. cross product.
static inline cart3_t cart3_vectorprod(const cart3_t a, const cart3_t b) {
        cart3_t c = {
                .x = a.y * b.z - a.z * b.y,
                .y = a.z * b.x - a.x * b.z,
                .z = a.x * b.y - a.y * b.x,
        };
        return c;
}

/// Scalar triple product \f$ a \cdot ( b \times c ) \f$.
static inline double cart3_tripleprod(const cart3_t a, const cart3_t b, const cart3_t c) {
        return cart3_dot(a, cart3_vectorprod(b, c));
}

/// 3D vector euclidian norm squared.
static inline double cart3_normsq(const cart3_t a) {
        return cart3_dot(a, a);
}

/// 3D vector euclidian norm.
static inline double cart3norm(const cart3_t v) {
        return sqrt(cart3_normsq(v));
}

/// 3D cartesian to spherical coordinates conversion. See @ref coord_conversions.
static inline sph_t cart2sph(const cart3_t cart) {
        sph_t sph;
        sph.r = cart3norm(cart);
        sph.theta = sph.r ? acos(cart.z / sph.r) : M_PI_2;
        sph.phi = atan2(cart.y, cart.x);
        return sph;
}

/// Spherical to 3D cartesian coordinates conversion. See @ref coord_conversions.
static inline cart3_t sph2cart(const sph_t sph) {
        cart3_t cart;
        double sin_th = 
#ifdef QPMS_VECTORS_NICE_TRANSFORMATIONS
           (sph.theta == M_PI) ? 0 :
#endif
                sin(sph.theta);
        cart.x = sph.r * sin_th * cos(sph.phi);
        cart.y = sph.r * sin_th * sin(sph.phi);
        cart.z = sph.r * cos(sph.theta);
        return cart;
}

/// Polar to 2D cartesian coordinates conversion. See @ref coord_conversions.
static inline cart2_t pol2cart(const pol_t pol) {
        cart2_t cart;
        cart.x = pol.r * cos(pol.phi);
        cart.y = pol.r * sin(pol.phi);
        return cart;
}

/// Polar to 3D cartesian coordinates conversion. See @ref coord_conversions.
static inline cart3_t pol2cart3_equator(const pol_t pol) {
        cart2_t c = pol2cart(pol);
        cart3_t cart3 = {c.x, c.y, 0};
        return cart3;
}


/// 3D vector addition.
static inline cart3_t cart3_add(const cart3_t a, const cart3_t b) {
        cart3_t res = {a.x+b.x, a.y+b.y, a.z+b.z};
        return res;
}

/// 3D vector substraction.
static inline cart3_t cart3_substract(const cart3_t a, const cart3_t b) {
        cart3_t res = {a.x-b.x, a.y-b.y, a.z-b.z};
        return res;
}

/// 3D vector scaling
static inline cart3_t cart3_scale(const double c, const cart3_t v) {
        cart3_t res = {c * v.x, c * v.y, c * v.z};
        return res;
}

/// 3D vector division by scalar (N.B. argument order).
static inline cart3_t cart3_divscale( const cart3_t v, const double c) {
        cart3_t res = {v.x / c, v.y / c, v.z / c};
        return res;
}

/// Euclidian distance between two 3D points.
static inline double cart3_dist(const cart3_t a, const cart3_t b) {
        return cart3norm(cart3_substract(a,b));
}

static inline bool cart3_isclose(const cart3_t a, const cart3_t b, double rtol, double atol) {
        return cart3_dist(a,b) <= atol + rtol * (cart3norm(b) + cart3norm(a)) * .5;
}

/// Complex 3D vector scaling.
static inline ccart3_t ccart3_scale(const complex double c, const ccart3_t v) {
        ccart3_t res = {c * v.x, c * v.y, c * v.z};
        return res;
}

/// Complex 3D vector adition.
static inline ccart3_t ccart3_add(const ccart3_t a, const ccart3_t b) {
        ccart3_t res = {a.x+b.x, a.y+b.y, a.z+b.z};
        return res;
}

/// Complex 3D vector substraction.
static inline ccart3_t ccart3_substract(const ccart3_t a, const ccart3_t b) {
        ccart3_t res = {a.x-b.x, a.y-b.y, a.z-b.z};
        return res;
}

/// Complex 3D cartesian vector "dot product" without conjugation.
static inline complex double ccart3_dotnc(const ccart3_t a, const ccart3_t b) {
        return a.x * b.x + a.y * b.y + a.z * b.z;
}

/// Convert cart3_t to ccart3_t.
static inline ccart3_t cart32ccart3(cart3_t c){
        ccart3_t res = {c.x, c.y, c.z};
        return res;
}

/// Complex 3D vector (geographic coordinates) addition.
static inline csphvec_t csphvec_add(const csphvec_t a, const csphvec_t b) {
        csphvec_t res = {a.rc + b.rc, a.thetac + b.thetac, a.phic + b.phic};
        return res;
}

/// Complex 3D vector (geographic coordinates) substraction.
static inline csphvec_t csphvec_substract(const csphvec_t a, const csphvec_t b) {
        csphvec_t res = {a.rc - b.rc, a.thetac - b.thetac, a.phic - b.phic};
        return res;
}

/// Complex 3D vector (geographic coordinates) scaling.
static inline csphvec_t csphvec_scale(complex double c, const csphvec_t v) {
        csphvec_t res = {c * v.rc, c * v.thetac, c * v.phic};
        return res;
}

/// Complex 3D vector (geographic coordinates) "dot product" without conjugation.
static inline complex double csphvec_dotnc(const csphvec_t a, const csphvec_t b) {
        //N.B. no complex conjugation done here
        return a.rc * b.rc + a.thetac * b.thetac + a.phic * b.phic;
}

/// Spherical coordinate system scaling.
static inline sph_t sph_scale(double c, const sph_t s) {
        sph_t res = {c * s.r, s.theta, s.phi};
        return res;
}

/// "Complex spherical" coordinate system scaling.
static inline csph_t sph_cscale(complex double c, const sph_t s) {
        csph_t res = {c * s.r, s.theta, s.phi};
        return res;
}

/// Coordinate transform of a vector in local geographic to global cartesian system.
// equivalent to sph_loccart2cart in qpms_p.py
static inline ccart3_t csphvec2ccart(const csphvec_t sphvec, const sph_t at) {
        const double st = sin(at.theta);
        const double ct = cos(at.theta);
        const double sf = sin(at.phi);
        const double cf = cos(at.phi);
        const double rx = st * cf;
        const double ry = st * sf;
        const double rz = ct;
        const double tx = ct * cf;
        const double ty = ct * sf;
        const double tz = -st;
        const double fx = -sf;
        const double fy = cf;
        const double fz = 0.;
        ccart3_t res;
        res.x = rx * sphvec.rc + tx * sphvec.thetac + fx * sphvec.phic;
        res.y = ry * sphvec.rc + ty * sphvec.thetac + fy * sphvec.phic;
        res.z = rz * sphvec.rc + tz * sphvec.thetac + fz * sphvec.phic;
        return res;
}

/// Coordinate transform of a vector in local geographic to global cartesian system.
/**
 *  Same as csphvec2ccart, but with csph_t as second argument.
 *  (The radial part (which is the only complex part of csph_t) 
 *  of the second argument does not play role in the
 *  transformation, so this is completely legit
 */
static inline ccart3_t csphvec2ccart_csph(const csphvec_t sphvec, const csph_t at) {
        const sph_t atreal = {0 /*not used*/, at.theta, at.phi};
        return csphvec2ccart(sphvec, atreal);
}

/// Coordinate transform of a vector in global cartesian to local geographic system.
static inline csphvec_t ccart2csphvec(const ccart3_t cartvec, const sph_t at) {
        // this chunk is copy-pasted from csphvec2cart, so there should be a better way...
        const double st = sin(at.theta);
        const double ct = cos(at.theta);
        const double sf = sin(at.phi);
        const double cf = cos(at.phi);
        const double rx = st * cf;
        const double ry = st * sf;
        const double rz = ct;
        const double tx = ct * cf;
        const double ty = ct * sf;
        const double tz = -st;
        const double fx = -sf;
        const double fy = cf;
        const double fz = 0.;
        csphvec_t res;
        res.rc     = rx * cartvec.x + ry * cartvec.y + rz * cartvec.z;
        res.thetac = tx * cartvec.x + ty * cartvec.y + tz * cartvec.z;
        res.phic   = fx * cartvec.x + fy * cartvec.y + fz * cartvec.z;
        return res;
}

/// Convert sph_t to csph_t.
static inline csph_t sph2csph(sph_t s) {
        csph_t cs = {s.r, s.theta, s.phi};
        return cs;
}

/// Convert csph_t to sph_t, discarding the imaginary part of radial component.
static inline sph_t csph2sph(csph_t s) {
        sph_t rs = {creal(s.r), s.theta, s.phi};
        return rs;
}

/// Lossy coordinate transform of ccart3_t to csph_t.
/** The angle and real part of the radial coordinate are determined
 *  from the real components of \a \cart. The imaginary part of the radial
 *  coordinate is then determined as the length of the imaginary 
 *  part of \a cart *projected onto* the real part of \a cart.
 *
 *  N.B. this obviously makes not much sense for purely imaginary vectors
 *  (and will cause NANs). TODO handle this better, as purely imaginary
 *  vectors could make sense e.g. for evanescent waves.
 */
static inline csph_t ccart2csph(const ccart3_t cart) {
        cart3_t rcart = {creal(cart.x), creal(cart.y), creal(cart.z)};
        cart3_t icart = {cimag(cart.x), cimag(cart.y), cimag(cart.z)};
        csph_t sph = sph2csph(cart2sph(rcart));
        sph.r += I * cart3_dot(icart,rcart) / cart3norm(rcart);
        return sph;
}

/// Real 3D cartesian to spherical (complex r) coordinates conversion. See @ref coord_conversions.
static inline csph_t cart2csph(const cart3_t cart) {
        csph_t sph;
        sph.r = cart3norm(cart);
        sph.theta = sph.r ? acos(cart.z / sph.r) : M_PI_2;
        sph.phi = atan2(cart.y, cart.x);
        return sph;
}

/// Coordinate transform of csph_t to ccart3_t
static inline ccart3_t csph2ccart(const csph_t sph) {
        ccart3_t cart;
        double sin_th = 
#ifdef QPMS_VECTORS_NICE_TRANSFORMATIONS
           (sph.theta == M_PI) ? 0 :
#endif
                sin(sph.theta);
        cart.x = sph.r * sin_th * cos(sph.phi);
        cart.y = sph.r * sin_th * sin(sph.phi);
        cart.z = sph.r * cos(sph.theta);
        return cart;
}


void print_csphvec(csphvec_t);
void print_ccart3(ccart3_t);
void print_cart3(cart3_t);
void print_sph(sph_t);

// kahan sums for various types... TODO make generic code using macros

/// Kanan sum initialisation for ccart3_t.
static inline void ccart3_kahaninit(ccart3_t *sum, ccart3_t *compensation) {
        sum->x = sum->y = sum->z = compensation->x = compensation->y = compensation->z = 0;
}
/// Kanan sum initialisation for csphvec_t.
static inline void csphvec_kahaninit(csphvec_t *sum, csphvec_t *compensation) {
        sum->rc = sum->thetac = sum->phic = compensation->rc = compensation->thetac = compensation->phic = 0;
}

/// Add element to Kahan sum (ccart3_t).
static inline void ccart3_kahanadd(ccart3_t *sum, ccart3_t *compensation, const ccart3_t input) {
        ccart3_t comped_input = ccart3_substract(input, *compensation);
        ccart3_t nsum = ccart3_add(*sum, comped_input);
        *compensation = ccart3_substract(ccart3_substract(nsum, *sum), comped_input);
        *sum = nsum;
}

/// Add element to Kahan sum (csphvec_t).
static inline void csphvec_kahanadd(csphvec_t *sum, csphvec_t *compensation, const csphvec_t input) {
        csphvec_t comped_input = csphvec_substract(input, *compensation);
        csphvec_t nsum = csphvec_add(*sum, comped_input);
        *compensation = csphvec_substract(csphvec_substract(nsum, *sum), comped_input);
        *sum = nsum;
}

/// Euclidian norm of a vector in geographic coordinates.
static inline double csphvec_norm(const csphvec_t a) {
        return  sqrt(creal(a.rc * conj(a.rc) + a.thetac * conj(a.thetac) + a.phic * conj(a.phic)));
}

static inline double csphvec_reldiff_abstol(const csphvec_t a, const csphvec_t b, double tolerance) {
        double anorm = csphvec_norm(a);
        double bnorm = csphvec_norm(b);
        if (anorm <= tolerance && bnorm <= tolerance) return 0;
        return csphvec_norm(csphvec_substract(a,b)) / (anorm + bnorm);
}

static inline double csphvec_reldiff(const csphvec_t a, const csphvec_t b) {
        return csphvec_reldiff_abstol(a, b, 0);
}


/*! \page coord_conversions Coordinate systems and default conversions
 *
 * The coordinate system transformations are defined as following:
 * 
 * \section coordtf_same_d Equal-dimension coordinate tranforms
 * \subsection sph_cart3 Spherical and 3D cartesian coordinates
 * * \f$ x = r \sin \theta \cos \phi \f$,
 * * \f$ y = r \sin \theta \sin \phi \f$,
 * * \f$ z = r \cos \theta \f$.
 * \subsection pol_cart2 Polar and 2D cartesian coordinates
 * * \f$ x = r \cos \phi \f$,
 * * \f$ y = r \sin \phi \f$.
 *
 * \section coordtf_123 Lower to higher dimension conversions.
 * * The 1D coordinate is identified with the \a z 3D cartesian coordinate.
 * * The 2D cartesian coordinates \a x, \a y are identified with the \a x, \a y
 *   3D cartesian coordinates.
 * * For the sake of consistency, default conversion between
 *   1D and 2D coordinates is not allowed and yields NAN values.
 *
 * \section coordtf_321 Higher to lower dimension conversions.
 * Default conversions from higher to lower-dimensional coordinate
 * systems are not allowed. Any projections have to be done explicitly.
 */

/// Conversion from anycoord_point_t to explicitly spherical coordinates.
/** See @ref coord_conversions for the conversion definitions.
 */ 
static inline sph_t anycoord2sph(anycoord_point_t p, qpms_coord_system_t t) {
        switch(t & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH:
                        return p.sph;
                        break;
                case QPMS_COORDS_POL:
                        return pol2sph_equator(p.pol);
                        break;
                case QPMS_COORDS_CART3:
                        return cart2sph(p.cart3);
                        break;
                case QPMS_COORDS_CART2:
                        return cart22sph(p.cart2);
                        break;
                case QPMS_COORDS_CART1:
                        return cart12sph_zaxis(p.z);
                        break;
        }
        QPMS_WTF;
}


/// Conversion from anycoord_point_t to explicitly 3D cartesian coordinates.
/** See @ref coord_conversions for the conversion definitions.
 */ 
static inline cart3_t anycoord2cart3(anycoord_point_t p, qpms_coord_system_t t) {
        switch(t & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH:
                        return sph2cart(p.sph);
                        break;
                case QPMS_COORDS_POL:
                        return pol2cart3_equator(p.pol);
                        break;
                case QPMS_COORDS_CART3:
                        return p.cart3;
                        break;
                case QPMS_COORDS_CART2:
                        return cart22cart3xy(p.cart2);
                        break;
                case QPMS_COORDS_CART1:
                        return cart12cart3z(p.z);
                        break;
        }
        QPMS_WTF;
}

/// Cartesian norm of anycoord_point_t.
// The implementation is simple and stupid, do not use for heavy computations.
static inline double anycoord_norm(anycoord_point_t p, qpms_coord_system_t t) {
        return cart3norm(anycoord2cart3(p, t));
}

#if 0
// Convenience identifiers for return values.
static const cart3_t CART3_INVALID = {NAN, NAN, NAN};
static const cart2_t CART2_INVALID = {NAN, NAN};
static const double CART1_INVALID = NAN;
static const sph_t SPH_INVALID = {NAN, NAN, NAN};
static const pol_t POL_INVALID = {NAN, NAN};
#endif

/// Conversion from anycoord_point_t to explicitly polar coordinates.
/** See @ref coord_conversions for the conversion definitions.
 */ 
static inline pol_t anycoord2pol(anycoord_point_t p, qpms_coord_system_t t) {
        switch(t & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH:
                case QPMS_COORDS_CART3:
                        QPMS_PR_ERROR("Implicit conversion from 3D to 2D"
                                        " coordinates not allowed");
                        break;
                case QPMS_COORDS_POL:
                        return p.pol;
                        break;
                case QPMS_COORDS_CART2:
                        return cart2pol(p.cart2);
                        break;
                case QPMS_COORDS_CART1:
                        QPMS_PR_ERROR("Implicit conversion from 1D to 2D"
                                        " coordinates not allowed");
                        break;
        }
        QPMS_WTF;
}


/// Conversion from anycoord_point_t to explicitly 2D cartesian coordinates.
/** See @ref coord_conversions for the conversion definitions.
 */ 
static inline cart2_t anycoord2cart2(anycoord_point_t p, qpms_coord_system_t t) {
        switch(t & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH:
                case QPMS_COORDS_CART3:
                        QPMS_PR_ERROR("Implicit conversion from 3D to 2D"
                                        " coordinates not allowed");
                        break;
                case QPMS_COORDS_POL:
                        return pol2cart(p.pol);
                        break;
                case QPMS_COORDS_CART2:
                        return p.cart2;
                        break;
                case QPMS_COORDS_CART1:
                        QPMS_PR_ERROR("Implicit conversion from 1D to 2D"
                                        " coordinates not allowed");
                        break;
        }
        QPMS_WTF;
}


/// Conversion from anycoord_point_t to explicitly 1D cartesian coordinates.
/** See @ref coord_conversions for the conversion definitions.
 */ 
static inline double anycoord2cart1(anycoord_point_t p, qpms_coord_system_t t) {
        if ((t & QPMS_COORDS_BITRANGE) == QPMS_COORDS_CART1) 
                        return p.z;
        else
                QPMS_PR_ERROR("Implicit conversion from nD (n > 1)"
                                " to 1D not allowed.");
}


/// Coordinate conversion of point arrays (something to something).
/** The dest and src arrays must not overlap */
static inline void qpms_array_coord_transform(void *dest, qpms_coord_system_t tdest,
                const void *src, qpms_coord_system_t tsrc, size_t nmemb) {
        switch(tdest & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH: 
                        {
                                sph_t *d = (sph_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH: {
                                                const sph_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = s[i];
                                                return; 
                                        } break;
                                        case QPMS_COORDS_CART3: {
                                                const cart3_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart2sph(s[i]);
                                                return; 
                                        } break;
                                        case QPMS_COORDS_POL: {
                                                const pol_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2sph_equator(s[i]);
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART2: {
                                                const cart2_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart22sph(s[i]);
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART1: {
                                                const double *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart12sph_zaxis(s[i]);
                                                return; 
                                        } break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART3:
                        {
                                cart3_t *d = (cart3_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH: {
                                                const sph_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = sph2cart(s[i]);
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART3: {
                                                const cart3_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = s[i];
                                                return;
                                        } break;
                                        case QPMS_COORDS_POL: {
                                                const pol_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2cart3_equator(s[i]);
                                                return; 
                                        } break;
                                        case QPMS_COORDS_CART2: {
                                                const cart2_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart22cart3xy(s[i]);
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART1: {
                                                const double *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart12cart3z(s[i]);
                                                return; 
                                        } break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_POL:
                        {
                                pol_t *d = (pol_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL: {
                                                const pol_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = s[i];
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART2: {
                                                const cart2_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart2pol(s[i]);
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART1:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed");
                                                break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART2:
                        {
                                cart2_t *d = (cart2_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL: {
                                                const pol_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2cart(s[i]);
                                                return; 
                                        } break;
                                        case QPMS_COORDS_CART2: {
                                                const cart2_t *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = s[i];
                                                return;
                                        } break;
                                        case QPMS_COORDS_CART1:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed");
                                                break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART1:
                        {
                                double *d = (double *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL:
                                        case QPMS_COORDS_CART2:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_CART1: {
                                                const double *s = src;
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = s[i];
                                                return; 
                                        } break;
                                }
                                QPMS_WTF;
                        }
                        break;
        }
        QPMS_WTF;
}


/// Coordinate conversion of point arrays (anycoord_point_t to something).
/** The dest and src arrays must not overlap */
static inline void anycoord_arr2something(void *dest, qpms_coord_system_t tdest,
                const anycoord_point_t *src, qpms_coord_system_t tsrc, size_t nmemb) {
  if(nmemb) {
        switch(tdest & QPMS_COORDS_BITRANGE) {
                case QPMS_COORDS_SPH: 
                        {
                                sph_t *d = (sph_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = src[i].sph;
                                                return; break;
                                        case QPMS_COORDS_CART3:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart2sph(src[i].cart3);
                                                return; break;
                                        case QPMS_COORDS_POL:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2sph_equator(src[i].pol);
                                                return; break;
                                        case QPMS_COORDS_CART2:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart22sph(src[i].cart2);
                                                return; break;
                                        case QPMS_COORDS_CART1:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart12sph_zaxis(src[i].z);
                                                return; break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART3:
                        {
                                cart3_t *d = (cart3_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = sph2cart(src[i].sph);
                                                return; break;
                                        case QPMS_COORDS_CART3:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = src[i].cart3;
                                                return; break;
                                        case QPMS_COORDS_POL:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2cart3_equator(src[i].pol);
                                                return; break;
                                        case QPMS_COORDS_CART2:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart22cart3xy(src[i].cart2);
                                                return; break;
                                        case QPMS_COORDS_CART1:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart12cart3z(src[i].z);
                                                return; break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_POL:
                        {
                                pol_t *d = (pol_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = src[i].pol;
                                                return; break;
                                        case QPMS_COORDS_CART2:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = cart2pol(src[i].cart2);
                                                return; break;
                                        case QPMS_COORDS_CART1:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed");
                                                break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART2:
                        {
                                cart2_t *d = (cart2_t *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = pol2cart(src[i].pol);
                                                return; break;
                                        case QPMS_COORDS_CART2:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = src[i].cart2;
                                                return; break;
                                        case QPMS_COORDS_CART1:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed");
                                                break;
                                }
                                QPMS_WTF;
                        }
                        break;
                case QPMS_COORDS_CART1:
                        {
                                double *d = (double *) dest;
                                switch (tsrc & QPMS_COORDS_BITRANGE) {
                                        case QPMS_COORDS_SPH:
                                        case QPMS_COORDS_CART3:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 2D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_POL:
                                        case QPMS_COORDS_CART2:
                                                QPMS_PR_ERROR("Implicit conversion from 3D to 1D coordinates not allowed"); 
                                                break;
                                        case QPMS_COORDS_CART1:
                                                for(size_t i = 0; i < nmemb; ++i)
                                                        d[i] = src[i].z;
                                                return; break;
                                }
                                QPMS_WTF;
                        }
                        break;
        }
        QPMS_WTF;
  }
}

/// Converts cart3_t to array of doubles.
static inline void cart3_to_double_array(double a[], cart3_t b) {
        a[0] = b.x; a[1] = b.y; a[2] = b.z;
}

/// Converts array of doubles to cart3_t.
static inline cart3_t cart3_from_double_array(const double a[]) {
        cart3_t b = {.x = a[0], .y = a[1], .z = a[1]};
        return b;
}

/// Converts cart2_t to array of doubles.
static inline void cart2_to_double_array(double a[], cart2_t b) {
        a[0] = b.x; a[1] = b.y;
}

/// Converts array of doubles to cart2_t
static inline cart2_t cart2_from_double_array(const double a[]) {
        cart2_t b = {.x = a[0], .y = a[1]};
        return b;
}


typedef double matrix3d[3][3];
typedef double matrix2d[2][2];
typedef complex double cmatrix3d[3][3];
typedef complex double cmatrix2d[2][2];
#endif //VECTORS_H