GWcsMOL.cpp

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/***************************************************************************
 *                 GWcsMOL.cpp - Mollweide's projection class              *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2015-2021 by Juergen Knoedlseder                         *
 * ----------------------------------------------------------------------- *
 *                                                                         *
 *  This program is free software: you can redistribute it and/or modify   *
 *  it under the terms of the GNU General Public License as published by   *
 *  the Free Software Foundation, either version 3 of the License, or      *
 *  (at your option) any later version.                                    *
 *                                                                         *
 *  This program is distributed in the hope that it will be useful,        *
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of         *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the          *
 *  GNU General Public License for more details.                           *
 *                                                                         *
 *  You should have received a copy of the GNU General Public License      *
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.  *
 *                                                                         *
 ***************************************************************************/
/**
 * @file GWcsMOL.cpp
 * @brief Mollweide's projection class implementation
 * @author Juergen Knoedlseder
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include "GException.hpp"
#include "GMath.hpp"
#include "GTools.hpp"
#include "GWcsMOL.hpp"
#include "GWcsRegistry.hpp"

/* __ Method name definitions ____________________________________________ */
#define G_PRJ_X2S    "GWcsMOL::prj_x2s(int, int, int, int, double*, double*,"\
                                                   " double*, double*, int*)"
#define G_PRJ_S2X    "GWcsMOL::prj_s2x(int, int, int, int, double*, double*,"\
                                                   " double*, double*, int*)"

/* __ Macros _____________________________________________________________ */
#define copysign(X, Y) ((Y) < 0.0 ? -fabs(X) : fabs(X))

/* __ Coding definitions _________________________________________________ */

/* __ Debug definitions __________________________________________________ */
//#define G_DEBUG_PRJ                             //!< Debug GWcsMOL::prj_x2s

/* __ Local prototypes ___________________________________________________ */

/* __ Constants __________________________________________________________ */

/* __ Globals ____________________________________________________________ */
const GWcsMOL      g_wcs_mol_seed;
const GWcsRegistry g_wcs_mol_registry(&g_wcs_mol_seed);


/*==========================================================================
 =                                                                         =
 =                         Constructors/destructors                        =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Void constructor
 ***************************************************************************/
GWcsMOL::GWcsMOL(void) : GWcs()
{
    // Initialise class members
    init_members();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Constructor
 *
 * @param[in] coords Coordinate system.
 * @param[in] crval1 X value of reference pixel.
 * @param[in] crval2 Y value of reference pixel.
 * @param[in] crpix1 X index of reference pixel (starting from 1).
 * @param[in] crpix2 Y index of reference pixel (starting from 1).
 * @param[in] cdelt1 Increment in x direction at reference pixel [deg].
 * @param[in] cdelt2 Increment in y direction at reference pixel [deg].
 ***************************************************************************/
GWcsMOL::GWcsMOL(const std::string& coords,
                 const double& crval1, const double& crval2,
                 const double& crpix1, const double& crpix2,
                 const double& cdelt1, const double& cdelt2) :
                 GWcs(coords, crval1, crval2, crpix1, crpix2, cdelt1, cdelt2)

{
    // Initialise class members
    init_members();

    // Setup WCS derived parameters
    wcs_set();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy constructor
 *
 * @param[in] wcs World Coordinate System.
 ***************************************************************************/
GWcsMOL::GWcsMOL(const GWcsMOL& wcs) : GWcs(wcs)
{
    // Initialise class members for clean destruction
    init_members();

    // Copy members
    copy_members(wcs);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Destructor
 ***************************************************************************/
GWcsMOL::~GWcsMOL(void)
{
    // Free members
    free_members();

    // Return
    return;
}


/*==========================================================================
 =                                                                         =
 =                               Operators                                 =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Assignment operator
 *
 * @param[in] wcs World Coordinate System.
 * @return World Coordinate System.
 ***************************************************************************/
GWcsMOL& GWcsMOL::operator=(const GWcsMOL& wcs)
{
    // Execute only if object is not identical
    if (this != &wcs) {

        // Copy base class members
        this->GWcs::operator=(wcs);

        // Free members
        free_members();

        // Initialise private members for clean destruction
        init_members();

        // Copy members
        copy_members(wcs);

    } // endif: object was not identical

    // Return this object
    return *this;
}


/*==========================================================================
 =                                                                         =
 =                             Public methods                              =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Clear instance
 *
 * This method properly resets the object to an initial state.
 ***************************************************************************/
void GWcsMOL::clear(void)
{
    // Free class members (base and derived classes, derived class first)
    free_members();
    this->GWcs::free_members();
    this->GSkyProjection::free_members();

    // Initialise members
    this->GSkyProjection::init_members();
    this->GWcs::init_members();
    init_members();

    // Return
    return;
}


/***********************************************************************//**
 * @brief Clone instance
 *
 * @return Pointer to deep copy of Mollweide projection.
 ***************************************************************************/
GWcsMOL* GWcsMOL::clone(void) const
{
    return new GWcsMOL(*this);
}



/***********************************************************************//**
 * @brief Print WCS information
 *
 * @param[in] chatter Chattiness (defaults to NORMAL).
 * @return String containing WCS information.
 ***************************************************************************/
std::string GWcsMOL::print(const GChatter& chatter) const
{
    // Initialise result string
    std::string result;

    // Continue only if chatter is not silent
    if (chatter != SILENT) {

        // Append header
        result.append("=== GWcsMOL ===");

        // Append information
        result.append(wcs_print(chatter));

    } // endif: chatter was not silent

    // Return result
    return result;
}


/*==========================================================================
 =                                                                         =
 =                             Private methods                             =
 =                                                                         =
 ==========================================================================*/

/***********************************************************************//**
 * @brief Initialise class members
 ***************************************************************************/
void GWcsMOL::init_members(void)
{
    // Return
    return;
}


/***********************************************************************//**
 * @brief Copy class members
 *
 * @param[in] wcs World Coordinate System.
 ***************************************************************************/
void GWcsMOL::copy_members(const GWcsMOL& wcs)
{
    // Return
    return;
}


/***********************************************************************//**
 * @brief Delete class members
 ***************************************************************************/
void GWcsMOL::free_members(void)
{
    // Return
    return;
}


/***********************************************************************//**
 * @brief Setup of projection
 *
 * This method sets up the projection information. The method has been
 * adapted from the wcslib function prj.c::molset (version 4.20).
 *
 *   Given and/or returned:
 *      m_r0      Reset to 180/pi if 0.
 *      m_phi0    Reset to  0.0 if undefined.
 *      m_theta0  Reset to  0.0 if undefined.
 *
 *   Returned:
 *      m_x0      Fiducial offset in x.
 *      m_y0      Fiducial offset in y.
 *      m_w[0]    sqrt(2)*r0
 *      m_w[1]    sqrt(2)*r0/90
 *      m_w[2]    1/(sqrt(2)*r0)
 *      m_w[3]    90/r0
 *      m_w[4]    2/pi
 ***************************************************************************/
void GWcsMOL::prj_set(void) const
{
    // Signal that projection has been set (needs to be done before calling
    // the prj_off() method to avoid an endless loop)
    m_prjset = true;

    // Initialise projection parameters
    m_w.assign(5, 0.0);
    
    // Set undefined parameters
    if (m_r0 == 0.0) {
        m_r0 = gammalib::rad2deg;
    }
    
    // Precompute 
    m_w[0] = gammalib::sqrt_two * m_r0;
    m_w[1] = m_w[0]/90.0;
    m_w[2] = 1.0/m_w[0];
    m_w[3] = 90.0/m_r0;
    m_w[4] = 2.0/gammalib::pi;
    
    // Compute fiducial offset
    prj_off(0.0, 0.0);
    
    // Return
    return;
}


/***********************************************************************//**
 * @brief Pixel-to-spherical deprojection
 *
 * @param[in] nx X vector length.
 * @param[in] ny Y vector length (0=no replication).
 * @param[in] sxy Input vector step.
 * @param[in] spt Output vector step.
 * @param[in] x Vector of projected x coordinates.
 * @param[in] y Vector of projected y coordinates.
 * @param[out] phi Longitude of the projected point in native spherical
 *                 coordinates [deg].
 * @param[out] theta Latitude of the projected point in native spherical
 *                   coordinates [deg].
 * @param[out] stat Status return value for each vector element
 *
 * Deproject pixel (x,y) coordinates in the plane of projection to native
 * spherical coordinates (phi,theta).
 *
 * This method has been adapted from the wcslib function prj.c::molx2s()
 * (version 4.20). The interface follows very closely that of wcslib. In
 * contrast to the wcslib routine, however, the method assumes that the
 * projection has been setup previously (as this will be done by the
 * constructor).
 ***************************************************************************/
void GWcsMOL::prj_x2s(int nx, int ny, int sxy, int spt, 
                      const double* x, const double* y,
                      double* phi, double* theta, int* stat) const
{
    // Set tolerance
    const double tol = 1.0e-12;

    // Initialize projection if required
    if (!m_prjset) {
        prj_set();
    }

    // Set value replication length mx,my
    int mx;
    int my;
    if (ny > 0) {
        mx = nx;
        my = ny;
    } 
    else {
        mx = 1;
        my = 1;
        ny = nx;
    }

    // Initialise status code and statistics
    int status    = 0;
    int n_invalid = 0;
    
    // Do x dependence
    const double* xp     = x;
    int           rowoff = 0;
    int           rowlen = nx * spt;
    for (int ix = 0; ix < nx; ++ix, rowoff += spt, xp += sxy) {
        double  xj     = *xp + m_x0;
        double  s      = m_w[3] * xj;
        double  t      = std::abs(xj) - tol;
        double* phip   = phi   + rowoff;
        double* thetap = theta + rowoff;
        for (int iy = 0; iy < my; ++iy, phip += rowlen, thetap += rowlen) {
            *phip   = s;
            *thetap = t;
        }
    }

    // Do y dependence
    const double* yp     = y;
    double*       phip   = phi;
    double*       thetap = theta;
    int*          statp  = stat;
    for (int iy = 0; iy < ny; ++iy, yp += sxy) {

        // Initialise status
        int istat = 0;

        // Compute some stuff
        double yj  = *yp + m_y0;
        double y0  = yj / m_r0;
        double r   = 2.0 - y0 * y0;
        double s   = 0.0;

        // Check limits
        if (r <= tol) {
            if (r < -tol) {
                istat  = 1;
                status = 3;
                n_invalid++;
                #if defined(G_DEBUG_PRJ)
                std::cout << "prj_x2s(Phi)..:";
                std::cout << " nx=" << nx;
                std::cout << " ny=" << ny;
                std::cout << " iy=" << iy;
                std::cout << " yp=" << *yp;
                std::cout << " yj=" << yj;
                std::cout << " y0=" << y0;
                std::cout << " phip=" << *phip;
                std::cout << " r=" << r;
                std::cout << " s=" << s;
                std::cout << std::endl;
                #endif
            }
            else {
                istat = -1; // OK if fabs(x) < tol whence phi = 0.0
            }
            r = 0.0;
            s = 0.0;
        }
        else {
            r = std::sqrt(r);
            s = 1.0 / r;
        }

        // Compute z and t
        double z = yj * m_w[2];
        if (std::abs(z) > 1.0) {
            if (std::abs(z) > 1.0+tol) {
                istat  = 1;
                status = 3;
                n_invalid++;
                #if defined(G_DEBUG_PRJ)
                std::cout << "prj_x2s(Phi)..:";
                std::cout << " nx=" << nx;
                std::cout << " ny=" << ny;
                std::cout << " iy=" << iy;
                std::cout << " yp=" << *yp;
                std::cout << " yj=" << yj;
                std::cout << " y0=" << y0;
                std::cout << " phip=" << *phip;
                std::cout << " r=" << r;
                std::cout << " s=" << s;
                std::cout << " z=" << z;
                std::cout << std::endl;
                #endif
                z = 0.0;
            }
            else {
                z = copysign(1.0, z) + y0 * r / gammalib::pi;
            }
        }
        else {
            z = std::asin(z) * m_w[4] + y0 * r / gammalib::pi;
        }
        if (std::abs(z) > 1.0) {
            if (std::abs(z) > 1.0+tol) {
                istat  = 1;
                status = 3;
                n_invalid++;
                #if defined(G_DEBUG_PRJ)
                std::cout << "prj_x2s(Phi)..:";
                std::cout << " nx=" << nx;
                std::cout << " ny=" << ny;
                std::cout << " iy=" << iy;
                std::cout << " yp=" << *yp;
                std::cout << " yj=" << yj;
                std::cout << " y0=" << y0;
                std::cout << " phip=" << *phip;
                std::cout << " r=" << r;
                std::cout << " s=" << s;
                std::cout << " z=" << z;
                std::cout << std::endl;
                #endif
                z = 0.0;
            }
            else {
                z = copysign(1.0, z);
            }
        }
        double t = std::asin(z) * gammalib::rad2deg;

        // Do ...
        for (int ix = 0; ix < mx; ++ix, phip += spt, thetap += spt, statp += spt) {

            // Set status flag
            if (istat < 0 && *thetap >= 0.0) {
                *statp = 1;
                status = 3;
                n_invalid++;
            }
            else {
                *statp = 0;
            }

            // Set values
            *phip  *= s;
            *thetap = t;
            
        }

    } // endfor: did y dependence

    // Check status code
    gammalib::check_prj_x2s_status(G_PRJ_X2S, status, n_invalid);

    // Do boundary checking
    status = prj_bchk(1.0e-11, nx, my, spt, phi, theta, stat);
    
    // Check status code
    gammalib::check_prj_x2s_status(G_PRJ_X2S, status, 1);

    // Return
    return;
}


/***********************************************************************//**
 * @brief Generic spherical-to-pixel projection
 *
 * @param[in] nphi Longitude vector length.
 * @param[in] ntheta Latitude vector length (0=no replication).
 * @param[in] spt Input vector step.
 * @param[in] sxy Output vector step.
 * @param[in] phi Longitude vector of the projected point in native spherical
 *                coordinates [deg].
 * @param[in] theta Latitude vector of the projected point in native spherical
 *                  coordinates [deg].
 * @param[out] x Vector of projected x coordinates.
 * @param[out] y Vector of projected y coordinates.
 * @param[out] stat Status return value for each vector element (always 0)
 *
 * Project native spherical coordinates (phi,theta) to pixel (x,y)
 * coordinates in the plane of projection.
 *
 * This method has been adapted from the wcslib function prj.c::mols2x()
 * (version 4.20). The interface follows very closely that of wcslib. In
 * contrast to the wcslib routine, however, the method assumes that the
 * projection has been setup previously (as this will be done by the
 * constructor).
 ***************************************************************************/
void GWcsMOL::prj_s2x(int nphi, int ntheta, int spt, int sxy,
                      const double* phi, const double* theta,
                      double* x, double* y, int* stat) const
{
    // Set tolerance
    const double tol = 1.0e-13;

    // Initialize projection if required
    if (!m_prjset) {
        prj_set();
    }

    // Set value replication length mphi,mtheta
    int mphi;
    int mtheta;
    if (ntheta > 0) {
        mphi   = nphi;
        mtheta = ntheta;
    } 
    else {
        mphi   = 1;
        mtheta = 1;
        ntheta = nphi;
    }

    // Initialise status code and statistics
    int status    = 0;
    int n_invalid = 0;
    
    // Do phi dependence
    const double* phip   = phi;
    int           rowoff = 0;
    int           rowlen = nphi * sxy;
    for (int iphi = 0; iphi < nphi; ++iphi, rowoff += sxy, phip += spt) {
        double  xi = m_w[1] * (*phip);
        double* xp = x + rowoff;
        for (int itheta = 0; itheta < mtheta; ++itheta) {
            *xp = xi;
            xp += rowlen;
        }
    }

    // Do theta dependence
    const double* thetap = theta;
    double*       xp     = x;
    double*       yp     = y;
    int*          statp  = stat;
    for (int itheta = 0; itheta < ntheta; ++itheta, thetap += spt) {

        // Compute xi and eta
        double xi  = 0.0;
        double eta = 0.0;
        if (std::abs(*thetap) == 90.0) {
            xi  = 0.0;
            eta = copysign(m_w[0], *thetap);
        }
        else if (*thetap == 0.0) {
            xi  = 1.0;
            eta = 0.0;
        }
        else {
            double u  =  gammalib::pi * std::sin(*thetap * gammalib::deg2rad);
            double v0 = -gammalib::pi;
            double v1 =  gammalib::pi;
            double v  = u;
            for (int k = 0; k < 100; ++k) {
                double resid = (v - u) + std::sin(v);
                if (resid < 0.0) {
                    if (resid > -tol) {
                        break;
                    }
                    v0 = v;
                }
                else {
                    if (resid < tol) {
                        break;
                    }
                    v1 = v;
                }
                v = 0.5 * (v0 + v1);
            }
            double gamma = 0.5 * v;
            xi           = std::cos(gamma);
            eta          = std::sin(gamma) * m_w[0];
        }
        eta -= m_y0;

        // Do ...
        for (int iphi = 0; iphi < mphi; ++iphi, xp += sxy, yp += sxy, statp += sxy) {
            *xp    = xi * (*xp) - m_x0;
            *yp    = eta;
            *statp = 0;
        }

    } // endfor: theta dependence
  
    // Check status code
    gammalib::check_prj_s2x_status(G_PRJ_S2X, status, n_invalid);

    // Return
    return;
}