BmnMeasureLin6.h

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/*
    BM@N alignment routine
    BM@N experiment at NICA complex, JINR, 2025
 
    Department: Math & Soft Group of HEP lab
    Author:     Igor Polev, polev@jinr.int
 
    BmnMeasureLin6 class header-only implementation
    Linearized measurement model with 6 alignment parameters per detector
    (3 shifts + 3 rotations) and 4 local parameters per straight track.
 
    Reference: 16-th BM@N Collaboration Meeting report by I. Polev,
    Appendix A (alignment transformation) and Appendix B (measurement model).
*/
 
#ifndef BMNMEASURELIN6_H
#define BMNMEASURELIN6_H
 
#include "BmnMeasureModel.h"
 
/*
 * Alignment transformation:
 *
 *      | x_m |           | x      |   | dx      |
 *      | y_m | = R_zyx * | y      | + | dy      |
 *      | z0  |           | z - z0 |   | dz + z0 |
 *
 *      R_zyx =  | 1     -psi   theta |  (linearized rotation)
 *               | psi    1    -phi   |
 *               |-theta  phi   1     |
 *
 * Linearized measurement model, with `bar` denoting the latest
 * approximation of the local parameters:
 *
 *      x_m   = alpha_x + beta_x * z0 + dx - dz * beta_x_bar - psi * y_bar - phi * beta_x_bar * y_bar + theta *
 * beta_x_bar * x_bar y_m   = alpha_y + beta_y * z0 + dy - dz * beta_y_bar + psi * x_bar - phi * beta_y_bar * y_bar +
 * theta * beta_y_bar * x_bar x_bar = alpha_x_bar + beta_x_bar * z0 y_bar = alpha_y_bar + beta_y_bar * z0
 */
 
class BmnMeasureLin6 : public BmnMeasureModel
{
  public:
    const char* Description() const noexcept override;   // out of line: anchors the vtable
 
    inline Double_t X(Double_t z0, const SVectGL& gl, const SVectLC& lc) const noexcept override
    {
        const Double_t beta_x{lc(iX1)}, x_bar{lc(iX0) + beta_x * z0}, y_bar{lc(iY0) + lc(iY1) * z0};
        return x_bar + gl(idX) - gl(idZ) * beta_x - gl(iPsi) * y_bar - gl(iPhi) * beta_x * y_bar
               + gl(iTheta) * beta_x * x_bar;
    }
 
    inline Double_t Y(Double_t z0, const SVectGL& gl, const SVectLC& lc) const noexcept override
    {
        const Double_t beta_y{lc(iY1)}, x_bar{lc(iX0) + lc(iX1) * z0}, y_bar{lc(iY0) + beta_y * z0};
        return y_bar + gl(idY) - gl(idZ) * beta_y + gl(iPsi) * x_bar - gl(iPhi) * beta_y * y_bar
               + gl(iTheta) * beta_y * x_bar;
    }
 
    inline SVectGL dXdA(Double_t z0, const SVectLC& lc) const noexcept override
    {
        const Double_t beta_x{lc(iX1)}, beta_x_m{-beta_x}, y_bar{lc(iY0) + lc(iY1) * z0};
        return SVectGL{1.0, 0.0, beta_x_m, beta_x_m * y_bar, beta_x * (lc(iX0) + beta_x * z0), -y_bar};
    }
 
    inline SVectGL dYdA(Double_t z0, const SVectLC& lc) const noexcept override
    {
        const Double_t beta_y{lc(iY1)}, beta_y_m{-beta_y}, x_bar{lc(iX0) + lc(iX1) * z0};
        return SVectGL{0.0, 1.0, beta_y_m, beta_y_m * (lc(iY0) + beta_y * z0), beta_y * x_bar, x_bar};
    }
 
    inline Bool_t AlignHit(FairHit& hit, const SVectGL& a) const noexcept override
    {
        SMatr3x3 rot{RM::SMatrixIdentity()};
        rot(2, 1) = a(iPhi);
        rot(1, 2) = -a(iPhi);
        rot(0, 2) = a(iTheta);
        rot(2, 0) = -a(iTheta);
        rot(1, 0) = a(iPsi);
        rot(0, 1) = -a(iPsi);
 
        Int_t ifail;
        SVect3 hitAligned{rot.InverseFast(ifail) * SVect3(hit.GetX() - a(idX), hit.GetY() - a(idY), -a(idZ))};
        if (ifail)
            return kFALSE;
 
        hit.SetXYZ(hitAligned(iX), hitAligned(iY), hitAligned(iZ) + hit.GetZ());
        return kTRUE;
    }
 
    inline void AlignHitApproximately(SVect3& hit, const SVectGL& a) const noexcept override
    {
        // First order approximate correction
        const Double_t x_m{hit(iX)}, y_m{hit(iY)};
        hit(iX) -= a(iX) - a(iPsi) * y_m;
        hit(iY) -= a(iY) + a(iPsi) * x_m;
        hit(iZ) -= a(iZ) + a(iPhi) * y_m - a(iTheta) * x_m;
    }
};
 
#endif   // BMNMEASURELIN6_H