/*
 * zernike.c
 *
 * Copyright 2016 Edward V. Emelianov <eddy@sao.ru, edward.emelianoff@gmail.com>
 *
 * 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 2 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, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 * MA 02110-1301, USA.
 */

#ifndef _GNU_SOURCE
#define _GNU_SOURCE  (1)  // for math.h
#endif
#include <math.h>
#include <strings.h>
#include <limits.h> // INT_MAX
#include "zernike.h"
#include "usefull_macros.h"
#include "saveimg.h"

#ifndef iabs
#define iabs(a)  (((a)<(0)) ? (-a) : (a))
#endif

// scaling factor
static double zscale = 1.;
// coordinate step on a grid
static double coord_step = DEFAULT_CRD_STEP;
// default wavelength for wavefront (650nm) in meters
static double wavelength = DEFAULT_WAVELENGTH;
// default coefficient to transform vawefront from wavelengths into user value
static double wf_coeff = 1.;
// array of factorials 1..100
static double *FK = NULL;
// unit for WF measurement
static char *outpunit = DEFAULT_WF_UNIT;
// amount of first polynomials to reset
static int Zern_zero = 0;
// array with indexes to be reset to 0 (copy of G.tozero)
static int* tozero = NULL;
static int tozerosz = 0; // size of array

// list of additional coefficients
static coeff *addcoefflist = NULL;
static int addcoefsz = 0; // its size
// matrix rotation angle (in radians)
static double rotangle = 0.;

/**
 * setter & getter for zscale
 */
void z_set_scale(double s){zscale = s;}
double z_get_scale(){return zscale;}

/**
 * Set/get value of Zern_zero
 */
int z_set_Nzero(int val){
    if(val > 0) Zern_zero  = val;
    return Zern_zero;
}
/**
 * Fill list of coefficients to be reset
 */
void z_set_tozero(int **val){
    if(!val) return;
    size_t cur = tozerosz;
    while(val[tozerosz]) ++tozerosz;
    //printf("2zero: %zd\n", tozerosz);
    tozero = realloc(tozero, tozerosz*sizeof(int));
    if(!tozero) ERR("realloc()");
    while(*val){
        tozero[cur++] = **val++;
    }
    //for(cur = 0; cur < tozerosz; ++cur) printf(":: %d\n", tozero[cur]);
}
/**
 * @return size of `tozero` array
 * @param idxs (o) - `tozero` itself
 */
int z_get_tozero(int **idxs){
    if(!idxs) return -1;
    *idxs = tozero;
    return tozerosz;
}

// parse additional coefficient record (N=val) and fill data
void parse_coeff(char *rec, coeff *c){
    if(!rec) ERRX(_("Empty record"));
    char *s = strdup(rec);
    if(!s) ERR("strdup()");
    char *eq = strchr(s, '=');
    if(!eq || *rec == '=')
        ERRX(_("Coefficients' records should be like N=val, where N is Znumber, val is its additional value"));
    *eq++ = 0;
    char *endptr;
    long tmp = strtol(s, &endptr, 0);
    //printf("tmp=%ld, eptr=%s\n", tmp, endptr);
    if(endptr == rec || *endptr != '\0' || tmp < 0 || tmp > INT_MAX)
        ERRX(_("Coefficient's index should be a non-negative integer"));
    c->idx = (int) tmp;
    if(!str2double(&c->addval, eq)) 
        ERRX(_("Wrong coefficient"));
    free(s);
}
/**
 * Fill list of additional coefficients
 */
void z_set_addcoef(char **list){
    if(!list || !*list) return;
    size_t cur = addcoefsz;
    while(list[addcoefsz]) ++addcoefsz;
    //printf("add coeffs: %zd\n", addcoefsz);
    addcoefflist = realloc(addcoefflist, addcoefsz*sizeof(coeff));
    if(!addcoefflist) ERR("realloc()");
    while(*list){
        parse_coeff(*list++, &addcoefflist[cur++]);
    }
    //for(cur = 0; cur < addcoefsz; ++cur) printf("coeff %d += %g\n", addcoefflist[cur].idx, addcoefflist[cur].addval);
}

/**
 * @return length of `addcoeflist` array
 * @param vals (o) - `addcoeflist` itself
 */
int z_get_addcoef(coeff **vals){
    if(!vals) return -1;
    *vals = addcoefflist;
    return addcoefsz;
}

/**
 * Set default coordinate grid step on an unity circle
 * @param step - new step
 * @return 0 if all OK, -1 or 1 if `step` bad
 */
int z_set_step(double step){
    printf("Set step to %g\n", step);
    if(step < DBL_EPSILON) return -1;
    if(step > 1.) return 1;
    coord_step = step;
    return 0;
}

double z_get_step(){
    return coord_step;
}

/**
 * Set value of default wavelength
 * @param w - new wavelength (from 100nm to 10um) in meters, microns or nanometers
 * @return 0 if all OK
 */
int z_set_wavelength(double w){
    if(w > 1e-7 && w < 1e-5) // meters
        wavelength = w;
    else if(w > 0.1 && w < 10.) // micron
        wavelength = w * 1e-6;
    else if(w > 100. && w < 10000.) // nanometer
        wavelength = w * 1e-9;
    else return 1;
    return 0;
}

double z_get_wavelength(){
    return wavelength;
}

static wf_units wfunits[] = {
    { 1.    , (const char * const []){"meter", "m", NULL}},
    {1e3    , (const char * const []){"millimeter", "mm", NULL}},
    {1e6    , (const char * const []){"micrometer", "um", "u", NULL}},
    {1e9    , (const char * const []){"nanometer", "nm", "n", NULL}},
    {-1.    , (const char * const []){"wavelength", "wave", "lambda", "w", "l", NULL}},
    {0.     , (const char * const []){NULL}}
};

/**
 * Set coefficient `wf_coeff` to user defined unit
 */
int z_set_wfunit(char *U){
    wf_units *u = wfunits;
    while(u->units[0]){
        const char * const * unit = u->units;
        while(*unit){
            if(strcasecmp(*unit, U) == 0){
                wf_coeff = u->wf_coeff;
                if(wf_coeff < 0.){ // wavelengths
                    wf_coeff = 1./wavelength; // in wavelengths
                }
                outpunit = (char*)u->units[0];
                printf("wf_coeff = %g\n", wf_coeff);
                return 0;
            }
            ++unit;
        }
        ++u;
    }
    return 1;
}

char *z_get_wfunit(){
    return outpunit;
}

double z_get_wfcoeff(){
    return wf_coeff;
}

/**
 * Print all wf_units available
 */
void z_print_wfunits(){
    wf_units *u = wfunits;
    printf(_("Unit (meters)\tAvailable values\n"));
    do{
        const char * const*unit = u->units;
        double val = 1./u->wf_coeff;
        if(val > 0.)
            printf("%-8g\t", val);
        else
            printf("(wavelength)\t");
        do{
            printf("%s  ", *unit);
        }while(*(++unit));
        printf("\n");
    }while((++u)->units[0]);
    printf("\n");
}

/**
 * Convert polynomial order in Noll notation into n/m
 * @param p (i) - order of Zernike polynomial in Noll notation
 * @param N (o) - order of polynomial
 * @param M (o) - angular parameter
 */
void convert_Zidx(int p, int *N, int *M){
    int n = (int) floor((-1.+sqrt(1.+8.*p)) / 2.);
    if(M) *M = (int)(2.0*(p - n*(n+1.)/2. - 0.5*(double)n));
    if(N) *N = n;
}

/**
 * Build array with R powers (from 0 to n inclusive)
 * @param n     - power of Zernike polinomial (array size = n+1)
 * @param Sz    - size of P array
 * @param P (i) - polar coordinates of points
 */
double **build_rpow(int n, int Sz, polar *P){
    int i, j, N = n + 1;
    double **Rpow = MALLOC(double*, N);
    Rpow[0] = MALLOC(double, Sz);
    for(i = 0; i < Sz; i++) Rpow[0][i] = 1.; // zero's power
    for(i = 1; i < N; i++){ // Rpow - is quater I of cartesian coordinates ('cause other are fully simmetrical)
        Rpow[i] = MALLOC(double, Sz);
        double *rp = Rpow[i], *rpo = Rpow[i-1];
        polar *p = P;
        for(j = 0; j < Sz; j++, rp++, rpo++, p++){
            *rp = (*rpo) * p->r;
        }
    }
    return Rpow;
}

/**
 * Free array of R powers with power n
 * @param Rpow (i) - array to free
 * @param n        - power of Zernike polinomial for that array (array size = n+1)
 */
void free_rpow(double ***Rpow, int n){
    int i, N = n+1;
    for(i = 0; i < N; i++) FREE((*Rpow)[i]);
    FREE(*Rpow);
}

/**
 * Free array of coordinates
 */
void free_coords(polcrds *p){
    FREE(p->P);
    free_rpow(&p->Rpow, p->N);
    free(p);
}
/**
 * Generate polar coordinates for grid [-1..1] by both coordinates
 *   with default step. Correct to rotangle
 * @return array of coordinates  **without any point outside unitary circle**
 */
polcrds *gen_coords(){
    int WH = 1 + (int)(2. / coord_step), max_sz = WH * WH, L = 0, idx = -1;
    polar *coordinates = malloc(max_sz * sizeof(polar)), *cptr = coordinates;
    if(!cptr) return NULL;
    double x, y, cmax = 1. + coord_step/2.;
    for(y = -1.; y < cmax; y += coord_step){
        for(x = -1.; x < cmax; x += coord_step){
            double R = sqrt(x*x + y*y);
            ++idx;
            if(R > 1.) continue;
            cptr->r = R;
            cptr->theta = atan2(y, x) + rotangle;
            cptr->idx = idx;
            ++cptr;
            ++L;
        }
    }
    DBG("%d points outside circle (ratio = %g, ideal = %g)", max_sz - L, ((double)L)/max_sz, M_PI/4.);
    polcrds *crds = MALLOC(polcrds, 1);
    crds->P = coordinates;
    crds->Sz = L;
    crds->N = 40; // start from 40
    crds->Rpow = build_rpow(crds->N, L, coordinates);
    crds->WH = WH;
    return crds;
}

/**
 * Build pre-computed array of factorials from 1 to 100
 */
void build_factorial(){
    double F = 1.;
    int i;
    if(FK) return;
    FK = MALLOC(double, ZERNIKE_MAX_POWER);
    FK[0] = 1.;
    for(i = 1; i < ZERNIKE_MAX_POWER; i++)
        FK[i] = (F *= (double)i);
}

/**
 * Validation check of zernfun parameters
 * return 1 in case of error
 */
int check_parameters(int n, int m, polcrds *P){
    if(!P || P->Sz < 3 || !P->P || !P->Rpow){
        WARNX(_("Size of matrix must be > 2!"));
        return 1;
    }
    if(n > ZERNIKE_MAX_POWER){
        WARNX(_("Order of Zernike polynomial must be <= %d!"), ZERNIKE_MAX_POWER);
        return 1;
    }
    int erparm = 0;
    if(n < 0) erparm = 1;
    if(n < iabs(m)) erparm = 1; // |m| must be <= n
    if((n - m) % 2) erparm = 1; // n-m must differ by a prod of 2
    if(erparm)
        WARNX(_("Wrong parameters of Zernike polynomial (%d, %d)"), n, m);
    else
        if(!FK) build_factorial();
    return erparm;
}



/**
 * Zernike function for scattering data
 * @param n,m     - orders of polynomial
 * @param P(i)    - array with points coordinates (polar, r<=1)
 * @param norm(o) - (optional) norm coefficient
 * @return dynamically allocated array with Z(n,m) for given array P
 */
double *zernfun(int n, int m, polcrds *P, double *norm){
    if(check_parameters(n, m, P)) return NULL;
    int j, k, m_abs = iabs(m), iup = (n-m_abs)/2, Sz = P->Sz;
    if(n > P->N){
        free_rpow(&P->Rpow, P->N);
        P->N = n+10;
        P->Rpow = build_rpow(P->N, Sz, P->P);
    }
    double ZSum = 0.;
    // now fill output matrix
    double *Zarr = MALLOC(double, Sz); // output matrix
    double *Zptr = Zarr;
    polar *p = P->P;
    double **Rpow = P->Rpow;
    for(j = 0; j < Sz; j++, p++, Zptr++){
        double Z = 0.;
        if(p->r > 1.) continue; // throw out points with R>1
        // calculate R_n^m
        for(k = 0; k <= iup; k++){ // Sum
            double z = (1. - 2. * (k % 2)) * FK[n - k]        //       (-1)^k * (n-k)!
                /(//----------------------------------- -----   -------------------------------
                    FK[k]*FK[(n+m_abs)/2-k]*FK[(n-m_abs)/2-k] // k!((n+|m|)/2-k)!((n-|m|)/2-k)!
                );
            Z += z * Rpow[n-2*k][j];  // *R^{n-2k}
        }
        // normalize
        double eps_m = (m) ? 1. : 2.;
        Z *= sqrt(2.*(n+1.) / M_PI / eps_m  );
        double m_theta = (double)m_abs * p->theta;
        // multiply to angular function:
        if(m){
            if(m > 0)
                Z *= cos(m_theta);
            else
                Z *= sin(m_theta);
        }
        *Zptr = Z;
        ZSum += Z*Z;
    }
    if(norm) *norm = ZSum;
    return Zarr;
}

/**
 * Restoration of image in points P by Zernike polynomials' coefficients
 * @param Zsz  (i) - number of actual elements in coefficients array
 * @param Zidxs(i) - array with Zernike coefficients
 * @param P(i)     - points coordinates & R powers
 * @return restored image
 */
double *Zcompose(int Zsz, double *Zidxs, polcrds *P){
    if(!P || !P->P || !P->Rpow) return NULL;
    int i, Sz = P->Sz;
    for(i = 0; i < Zern_zero; ++i) Zidxs[i] = 0.;
    for(i = 0; i < tozerosz; i++){
        int C = tozero[i];
        if(C > -1 && C < Zsz) Zidxs[C] = 0.;
        else WARNX(_("Not zero idx %d (should be from 0 to %d)"), C, Zsz-1);
    }
    for(i = 0; i < addcoefsz; i++){
        int C = addcoefflist[i].idx;
        if(C > -1 && C < Zsz) Zidxs[C] += addcoefflist[i].addval;
        else WARNX(_("Not change idx %d (should be from 0 to %d)"), C, Zsz-1);
    }
    double *image = MALLOC(double, Sz);
    for(i = 0; i < Zsz; i++){ // now we fill array
        double K = Zidxs[i];
        //printf("Z[%d]=%g\n", i, K);
        if(fabs(K) < DBL_EPSILON) continue; // 0.0m
        int n, m;
        convert_Zidx(i, &n, &m);
        double *Zcoeff = zernfun(n, m, P, NULL);
        if(!Zcoeff){
            WARNX(_("Can't compute coefficients for n=%d, m=%d!"), n,m);
            continue;
        }
        int j;
        double *iptr = image, *zptr = Zcoeff;
        for(j = 0; j < Sz; j++, iptr++, zptr++)
            *iptr += K * (*zptr); // add next Zernike polynomial
        FREE(Zcoeff);
    }
    return image;
}

/**
 * Save restored wavefront into file `filename`
 * @param P         (i) - points coordinates & R powers
 * @param Z         (i) - wavefront shift (in lambdas)
 * @param std       (i) - std of shift in each point
 * @param filename  (i) - name of output file
 * @return 1 if failed
 */
int z_save_wavefront(polcrds *P, double *Z, double *std, char *fprefix){
    int Sz = P->Sz, i, ret = 1;
    polar *p = P->P;
    if(!P  || !p || !Z || Sz < 0 || !fprefix) return 1;
    /*************** Step 1 - save points coordinates table ***************/
    char *filename = MALLOC(char, strlen(fprefix) + 10);
    sprintf(filename, "%s.points", fprefix);
    printf("try to save to %s\n", filename);
    FILE *f = fopen(filename, "w");
    if(!f) goto returning;
    int WH = P->WH, max_sz = WH * WH;
    double *WF = calloc(max_sz, sizeof(double));
    if(!WF) goto returning;
    // calculate std & scope by all wavefront
    double *z = Z, sum = 0., sum2 = 0., min = 1e12, max = -1e12;
    for(i = 0; i < Sz; ++i, ++z){
        double pt = *z;
        if(pt < min) min = pt;
        if(pt > max) max = pt;
        sum += pt;
        sum2 += pt*pt;
    }
    double coef = wf_coeff * zscale;
    sum2 *= coef, sum *= coef, max *= coef, min *= coef;
    fprintf(f, "# Wavefront units: %ss, wavelength: %gnm, std by all WF: %g, Scope: %g, max: %g, min: %g\n",
        outpunit, wavelength*1e9, sum2/Sz + sum*sum/Sz/Sz, max - min, max, min);
    if(Zern_zero) fprintf(f, "# First %d coefficients were cleared\n", Zern_zero);
    fprintf(f, "# X (-1..1)\tY (-1..1)\tZ \tstd_Z\n");
    for(i = 0, z = Z; i < Sz; ++i, ++p, ++z, ++std){
        double x, y, s, c, r = p->r, zdat = (*z) * coef;
        sincos(p->theta - rotangle, &s, &c);
        x = r * c, y = r * s;
        fprintf(f, "%6.3f\t%6.3f\t%9.3g\t%9.3g\n", x, y, zdat, (*std) * coef);
        WF[p->idx] = zdat;
        //DBG("WF[%d] = %g; x=%.1f, y=%.1f", p->idx, zdat,x,y);
    }
    fclose(f);
    /*************** Step 2 - save matrix of data ***************/
    sprintf(filename, "%s.matrix", fprefix);
    printf("try to save to %s\n", filename);
    f = fopen(filename, "w");
    if(!f) goto returning;
    fprintf(f, "# Wavefront data\n# Units: %ss, wavelength: %gnm\n# Step: %g\n",
        outpunit, wavelength*1e9, coord_step);
    int x, y;
    // Invert Y axe to have matrix with right Y direction (towards up)
    for(y = WH-1; y > -1; --y){
        double *wptr = &WF[y*WH];
        for(x = 0; x < WH; ++x, ++wptr)
            fprintf(f, "%6.3g\t", *wptr);
        fprintf(f, "\n");
    }
    writeimg(fprefix, WH, WF);
    ret = 0;
returning:
    FREE(filename);
    return ret;
}


/**
 * change rotation angle (0..2pi)
 */
void z_set_rotangle(double angle){
    angle -= floor(angle/360.) * 360.;
    rotangle = angle * M_PI/180.;
    printf("angle: %g\n", rotangle*180/M_PI);
}

double z_get_rotangle(){
    return rotangle;
}