vectors.h

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#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};
 
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;
}
 
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;
}
 
static inline cart2_t cart2_scale(const double c, const cart2_t v) {
    cart2_t res = {c * v.x, c * v.y};
    return res;
}
 
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);
}
 
static inline double cart2norm(const cart2_t v) {
    return hypot(v.x, v.y); //sqrt(v.x*v.x + v.y*v.y);
}
 
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;
}
 
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;
}
 
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;
}
 
static inline sph_t cart12sph_zaxis(double z) {
    sph_t sph = {fabs(z), z < 0 ? M_PI : 0, 0};
    return sph;
}
 
static inline cart3_t cart12cart3z(double z) {
    cart3_t c = {0, 0, z};
    return c;
}
 
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;
}
 
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;
}
 
 
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;
}
 
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));
}
 
static inline double cart3_normsq(const cart3_t a) {
    return cart3_dot(a, a);
}
 
static inline double cart3norm(const cart3_t v) {
    return sqrt(cart3_normsq(v));
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
static inline ccart3_t cart32ccart3(cart3_t c){
    ccart3_t res = {c.x, c.y, c.z};
    return res;
}
 
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;
}
 
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;
}
 
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;
}
 
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;
}
 
static inline sph_t sph_scale(double c, const sph_t s) {
    sph_t res = {c * s.r, s.theta, s.phi};
    return res;
}
 
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;
}
 
// 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;
}
 
 
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);
}
 
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;
}
 
static inline csph_t sph2csph(sph_t s) {
    csph_t cs = {s.r, s.theta, s.phi};
    return cs;
}
 
static inline sph_t csph2sph(csph_t s) {
    sph_t rs = {creal(s.r), s.theta, s.phi};
    return rs;
}
 
 
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;
}
 
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;
}
 
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
 
static inline void ccart3_kahaninit(ccart3_t *sum, ccart3_t *compensation) {
    sum->x = sum->y = sum->z = compensation->x = compensation->y = compensation->z = 0;
}
static inline void csphvec_kahaninit(csphvec_t *sum, csphvec_t *compensation) {
    sum->rc = sum->thetac = sum->phic = compensation->rc = compensation->thetac = compensation->phic = 0;
}
 
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;
}
 
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;
}
 
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);
}
 
 
 
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;
}
 
 
 
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;
}
 
// 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
 
 
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;
}
 
 
 
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;
}
 
 
 
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.");
}
 
 
 
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;
}
 
 
 
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;
  }
}
 
static inline void cart3_to_double_array(double a[], cart3_t b) {
    a[0] = b.x; a[1] = b.y; a[2] = b.z;
}
 
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;
}
 
static inline void cart2_to_double_array(double a[], cart2_t b) {
    a[0] = b.x; a[1] = b.y;
}
 
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