自学教程：C++ GSL_MAX函数代码示例

int bbfind_compute(bbfind*bbf, BB2 bbox) {	double ul[2], ur[2], ll[2], lr[2];		if(1) {		if(!getBoundingBox(bbf->buf, bbf->num, ul, ur, ll, lr)) {			sm_error("Could not compute bounding box./n");			return 0;		}		bbox->pose[0] = ll[0];		bbox->pose[1] = ll[1];		bbox->pose[2] = atan2(lr[1]-ll[1], lr[0]-ll[0]);		bbox->size[0] = distance_d(lr, ll);		bbox->size[1] = distance_d(ll, ul);	} else {		double bb_min[2] = {bbf->buf[0].x,bbf->buf[0].y}, 				bb_max[2] = {bbf->buf[0].x,bbf->buf[0].y};		int i; for(i=0;i<bbf->num; i++) {			bb_min[0] = GSL_MIN(bb_min[0], bbf->buf[i].x);			bb_min[1] = GSL_MIN(bb_min[1], bbf->buf[i].y);			bb_max[0] = GSL_MAX(bb_max[0], bbf->buf[i].x);			bb_max[1] = GSL_MAX(bb_max[1], bbf->buf[i].y);		}		bbox->pose[0] = bb_min[0];		bbox->pose[1] = bb_min[1];		bbox->pose[2] = 0;		bbox->size[0] = bb_max[0] - bb_min[0];		bbox->size[1] = bb_max[1] - bb_min[1];	}	return 1;}

/** Run the Kolmogorov-Smirnov test to determine whether two distributions are identical./param m1, m2  Two models, most likely of /ref apop_pmf type. I will ue the cdf method, so if your function doesn't have one, expect this to run the slow default. I run it for each row of each data set, so if your model has a /c NULL at the data, I won't know what to do.  /return An /ref apop_data set including the /f$p/f$-value from the Kolmogorov test that the two distributions are equal./li I assume that the data sets are sorted./include ks_tests.c/ingroup histograms*/apop_data *apop_test_kolmogorov(apop_model *m1, apop_model *m2){    //version for not a pair of histograms    Apop_assert(m1->data, "I will test the CDF at each point in the data set, but the first model has a NULL data set. "                          "Maybe generate, then apop_data_sort, a few thousand random draws?");    Apop_assert(m2->data, "I will test the CDF at each point in the data set, but the second model has a NULL data set. "                          "Maybe generate, then apop_data_sort, a few thousand random draws?");    int maxsize1, maxsize2;    {Get_vmsizes(m1->data); maxsize1 = maxsize;}//copy one of the macro's variables     {Get_vmsizes(m2->data); maxsize2 = maxsize;}//  to the full function's scope.    double largest_diff=GSL_NEGINF;    for (size_t i=0; i< maxsize1; i++){        Apop_data_row(m1->data, i, arow);        largest_diff = GSL_MAX(largest_diff, fabs(apop_cdf(arow, m1)-apop_cdf(arow, m2)));    }    for (size_t i=0; i< maxsize2; i++){     //There should be matched data rows, so there is redundancy.        Apop_data_row(m2->data, i, arow); // Feel free to submit a smarter version.        largest_diff = GSL_MAX(largest_diff, fabs(apop_cdf(arow, m1)-apop_cdf(arow, m2)));    }    apop_data *out = apop_data_alloc();    sprintf(out->names->title, "Kolmogorov-Smirnov test");    apop_data_add_named_elmt(out, "max distance", largest_diff);    double ps = psmirnov2x(largest_diff, maxsize1, maxsize2);    apop_data_add_named_elmt(out, "p value, 2 tail", 1-ps);    apop_data_add_named_elmt(out, "confidence, 2 tail", ps);    return out;}

inlinestatic double locMAX4(double x, double y, double z, double w){  double xy  = GSL_MAX(x,  y);  double xyz = GSL_MAX(xy, z);  return GSL_MAX(xyz, w);}

inlinestaticint locMax3(const int a, const int b, const int c){  int d = GSL_MAX(a, b);  return GSL_MAX(d, c);}

static intmagcal_init(const satdata_mag *data, magcal_workspace *w){  int s = 0;  size_t i;  size_t n = 0;  for (i = 0; i < data->n; ++i)    {      /* don't store flagged data */      if (data->flags[i])        continue;      /* don't process high latitude data */      if (fabs(data->latitude[i]) > MAGCAL_MAX_LATITUDE)        continue;      w->Ex[n] = SATDATA_VEC_X(data->B_VFM, i);      w->Ey[n] = SATDATA_VEC_Y(data->B_VFM, i);      w->Ez[n] = SATDATA_VEC_Z(data->B_VFM, i);      w->F[n] = data->F[i];      ++n;    }  if (n < 200)    {      fprintf(stderr, "magcal_init: insufficient data points for calibration: %zu/n",              n);      return -1;    }  if (n != w->n)    {      gsl_multifit_fdfsolver_free(w->fdf_s);      gsl_multifit_fdfridge_free(w->fdf_ridge);      w->fdf_s = gsl_multifit_fdfsolver_alloc(w->fdf_type, n, w->p);      w->fdf_ridge = gsl_multifit_fdfridge_alloc(w->fdf_type, n, w->p);      w->n = n;    }#if MAGCAL_SCALE  w->B_s = GSL_MAX(gsl_stats_sd(w->Ex, 1, n),                   GSL_MAX(gsl_stats_sd(w->Ey, 1, n),                           gsl_stats_sd(w->Ez, 1, n)));#endif  /* center and scale data arrays */  for (i = 0; i < n; ++i)    {      w->Ex[i] /= w->B_s;      w->Ey[i] /= w->B_s;      w->Ez[i] /= w->B_s;      w->F[i] /= w->B_s;    }  return s;} /* magcal_init() */

 apop_data * apop_bootstrap_cov_base(apop_data * data, apop_model *model, gsl_rng *rng, int iterations, char keep_boots, char ignore_nans, apop_data **boot_store){#endif    Get_vmsizes(data); //vsize, msize1, msize2    apop_model *e = apop_model_copy(model);    apop_data *subset = apop_data_copy(data);    apop_data *array_of_boots = NULL,              *summary;    //prevent and infinite regression of covariance calculation.    Apop_model_add_group(e, apop_parts_wanted); //default wants for nothing.    size_t i, nan_draws=0;    apop_name *tmpnames = (data && data->names) ? data->names : NULL; //save on some copying below.    if (data && data->names) data->names = NULL;    int height = GSL_MAX(msize1, GSL_MAX(vsize, (data?(*data->textsize):0)));	for (i=0; i<iterations && nan_draws < iterations; i++){		for (size_t j=0; j< height; j++){       //create the data set			size_t randrow	= gsl_rng_uniform_int(rng, height);            apop_data_memcpy(Apop_r(subset, j), Apop_r(data, randrow));		}		//get the parameter estimates.		apop_model *est = apop_estimate(subset, e);        gsl_vector *estp = apop_data_pack(est->parameters);        if (!gsl_isnan(apop_sum(estp))){            if (i==0){                array_of_boots	      = apop_data_alloc(iterations, estp->size);                apop_name_stack(array_of_boots->names, est->parameters->names, 'c', 'v');                apop_name_stack(array_of_boots->names, est->parameters->names, 'c', 'c');                apop_name_stack(array_of_boots->names, est->parameters->names, 'c', 'r');            }            gsl_matrix_set_row(array_of_boots->matrix, i, estp);        } else if (ignore_nans=='y'){            i--;             nan_draws++;        }        apop_model_free(est);        gsl_vector_free(estp);	}    if(data) data->names = tmpnames;    apop_data_free(subset);    apop_model_free(e);    int set_error=0;    Apop_stopif(i == 0 && nan_draws == iterations, apop_return_data_error(N),                1, "I ran into %i NaNs and no not-NaN estimations, and so stopped. "                       , iterations);    Apop_stopif(nan_draws == iterations,  set_error++;            apop_matrix_realloc(array_of_boots->matrix, i, array_of_boots->matrix->size2),                1, "I ran into %i NaNs, and so stopped. Returning results based "                       "on %zu bootstrap iterations.", iterations, i);	summary	= apop_data_covariance(array_of_boots);    if (boot_store) *boot_store = array_of_boots;    else            apop_data_free(array_of_boots);    if (set_error) summary->error = 'N';	return summary;}

static intsecs2d_green_df(const double r, const double theta, const double phi,                const double theta0, const double phi0,                double B[3], secs2d_state_t *state){  const double s = GSL_MIN(r, state->R) / GSL_MAX(r, state->R);  double thetap, stp, ctp;  size_t i;  secs2d_transform(theta0, phi0, theta, phi, &thetap);  stp = sin(thetap);  ctp = cos(thetap);  if (r >= state->R)    {      B[0] = ((1.0 - s * ctp) / sqrt(1 + s*s - 2.0*s*ctp) - 1.0) / stp;      B[1] = 0.0;      B[2] = -s * (1.0 / sqrt(1.0 + s*s - 2.0*s*ctp) - 1.0);    }  for (i = 0; i < 3; ++i)    B[i] *= MAGFIT_MU_0 / (4.0 * M_PI * r);  /* transform from SECS-centered system to geographic */  secs2d_transform_vec(theta0, phi0, theta, phi, B, B);  return GSL_SUCCESS;}

long AT_n_bins_for_DSB_distribution(const long n_bins_f,		const double f_d_Gy[],		const double f_dd_Gy[],		const double f[],		const double enhancement_factor[],		const double DSB_per_Gy_per_domain){	  //double* avg_DSB = (double*)calloc(n_bins_f, sizeof(double));	  double max_number_of_DSB = 0.0;	  for(long i = 0; i < n_bins_f; i++){		  max_number_of_DSB = GSL_MAX(max_number_of_DSB, f_d_Gy[i] * enhancement_factor[i] * DSB_per_Gy_per_domain);	  }	  if(isnan(max_number_of_DSB)){	    return(0);	  }	  // Use max + 5 * st.dev as safety margin	  max_number_of_DSB = floor(max_number_of_DSB) + 1.0;	  max_number_of_DSB += floor(5 * sqrt(max_number_of_DSB)) + 1;	  // Add one for zero bin	  return((long)max_number_of_DSB + 1);}

size_ttrack_flag_incomplete(const double qd_min, const double qd_max, satdata_mag *data, track_workspace *w){  size_t i;  size_t nflagged = 0;        /* number of points flagged */  size_t ntrack_flagged = 0;  /* number of entire tracks flagged for missing data */  if (data->n == 0)    return 0;  for (i = 0; i < w->n; ++i)    {      track_data *tptr = &(w->tracks[i]);      double qd0 = GSL_MIN(data->qdlat[tptr->start_idx], data->qdlat[tptr->end_idx]);      double qd1 = GSL_MAX(data->qdlat[tptr->start_idx], data->qdlat[tptr->end_idx]);      if (qd0 > qd_min || qd1 < qd_max)        {          nflagged += track_flag_track(i, TRACK_FLG_INCOMPLETE, data, w);          ++ntrack_flagged;        }    }  fprintf(stderr, "track_flag_incomplete: flagged %zu/%zu (%.1f%%) tracks due to missing data/n",          ntrack_flagged, w->n, (double) ntrack_flagged / (double) w->n * 100.0);  return nflagged;} /* track_flag_incomplete() */

intgsl_multifit_linear_lreg (const double smin, const double smax,                          gsl_vector * reg_param){  if (smax <= 0.0)    {      GSL_ERROR("smax must be positive", GSL_EINVAL);    }  else    {      const size_t N = reg_param->size;      /* smallest regularization parameter */      const double smin_ratio = 16.0 * GSL_DBL_EPSILON;      const double new_smin = GSL_MAX(smin, smax*smin_ratio);      double ratio;      size_t i;      gsl_vector_set(reg_param, N - 1, new_smin);      /* ratio so that reg_param(1) = s(1) */      ratio = pow(smax / new_smin, 1.0 / ((double)N - 1.0));      /* calculate the regularization parameters */      for (i = N - 1; i > 0 && i--; )        {          double rp1 = gsl_vector_get(reg_param, i + 1);          gsl_vector_set(reg_param, i, ratio * rp1);        }      return GSL_SUCCESS;    }}

/* interpolate Ne data near time t to latitude qdlat */doubleinterp_ne(const time_t t, const double qdlat, const satdata_mag *data){  double t_cdf = satdata_timet2epoch(t);  double Ne;  if (t_cdf >= data->t[0] && t_cdf <= data->t[data->n - 1])    {      int idx = (int) bsearch_double(data->t, t_cdf, 0, data->n - 1);      int half_window = 15; /* number of minutes in half time window */      int idx1 = GSL_MAX(0, idx - half_window*60*2);      int idx2 = GSL_MIN(data->n - 1, idx + half_window*60*2);      int qidx;            if (data->qdlat[idx1] < data->qdlat[idx2])        qidx = (int) bsearch_double(data->qdlat, qdlat, idx1, idx2);      else        qidx = (int) bsearch_desc_double(data->qdlat, qdlat, idx1, idx2);      Ne = interp1d(data->qdlat[qidx], data->qdlat[qidx + 1],                    data->ne[qidx], data->ne[qidx + 1], qdlat);    }  else    Ne = 0.0;  return Ne;}

intgsl_sf_pochrel_e(const double a, const double x, gsl_sf_result * result){  const double absx = fabs(x);  const double absa = fabs(a);  /* CHECK_POINTER(result) */  if(absx > 0.1*absa || absx*log(GSL_MAX(absa,2.0)) > 0.1) {    gsl_sf_result lnpoch;    double sgn;    int stat_poch = gsl_sf_lnpoch_sgn_e(a, x, &lnpoch, &sgn);    if(lnpoch.val > GSL_LOG_DBL_MAX) {      OVERFLOW_ERROR(result);    }    else {      const double el = exp(lnpoch.val);      result->val  = (sgn*el - 1.0)/x;      result->err  = fabs(result->val) * (lnpoch.err + 2.0 * GSL_DBL_EPSILON);      result->err += 2.0 * GSL_DBL_EPSILON * (fabs(sgn*el) + 1.0) / fabs(x);      return stat_poch;    }  }  else {    return pochrel_smallx(a, x, result);  }}

intgsl_sf_ellint_RC_e(double x, double y, gsl_mode_t mode, gsl_sf_result * result){  const double lolim = 5.0 * GSL_DBL_MIN;  const double uplim = 0.2 * GSL_DBL_MAX;  const gsl_prec_t goal = GSL_MODE_PREC(mode);  const double errtol = ( goal == GSL_PREC_DOUBLE ? 0.001 : 0.03 );  const double prec   = gsl_prec_eps[goal];  if(x < 0.0 || y < 0.0 || x + y < lolim) {    DOMAIN_ERROR(result);  }  else if(GSL_MAX(x, y) < uplim) {     const double c1 = 1.0 / 7.0;    const double c2 = 9.0 / 22.0;    double xn = x;    double yn = y;    double mu, sn, lamda, s;    while(1) {      mu = (xn + yn + yn) / 3.0;      sn = (yn + mu) / mu - 2.0;      if (fabs(sn) < errtol) break;      lamda = 2.0 * sqrt(xn) * sqrt(yn) + yn;      xn = (xn + lamda) * 0.25;      yn = (yn + lamda) * 0.25;    }    s = sn * sn * (0.3 + sn * (c1 + sn * (0.375 + sn * c2)));    result->val = (1.0 + s) / sqrt(mu);    result->err = prec * fabs(result->val);    return GSL_SUCCESS;  }  else {    DOMAIN_ERROR(result);  }}

static intlmniel_set(void *vstate, const gsl_vector *swts,           gsl_multifit_function_fdf *fdf, gsl_vector *x,           gsl_vector *f, gsl_vector *dx){  int status;  lmniel_state_t *state = (lmniel_state_t *) vstate;  const size_t p = x->size;  size_t i;  /* initialize counters for function and Jacobian evaluations */  fdf->nevalf = 0;  fdf->nevaldf = 0;  /* evaluate function and Jacobian at x and apply weight transform */  status = gsl_multifit_eval_wf(fdf, x, swts, f);  if (status)   return status;  if (fdf->df)    status = gsl_multifit_eval_wdf(fdf, x, swts, state->J);  else    status = gsl_multifit_fdfsolver_dif_df(x, swts, fdf, f, state->J);  if (status)    return status;  /* compute rhs = -J^T f */  gsl_blas_dgemv(CblasTrans, -1.0, state->J, f, 0.0, state->rhs);#if SCALE  gsl_vector_set_zero(state->diag);#else  gsl_vector_set_all(state->diag, 1.0);#endif  /* set default parameters */  state->nu = 2;#if SCALE  state->mu = state->tau;#else  /* compute mu_0 = tau * max(diag(J^T J)) */  state->mu = -1.0;  for (i = 0; i < p; ++i)    {      gsl_vector_view c = gsl_matrix_column(state->J, i);      double result; /* (J^T J)_{ii} */      gsl_blas_ddot(&c.vector, &c.vector, &result);      state->mu = GSL_MAX(state->mu, result);    }  state->mu *= state->tau;#endif  return GSL_SUCCESS;} /* lmniel_set() */

static void scaling(size_t const *elmts, size_t const n,  gsl_vector *weights, double const in_sum){    double fit_sum = 0;    for(size_t i=0; i < n; i ++)        fit_sum += weights->data[elmts[i]];    if (!fit_sum) return; //can happen if init table is very different from margins.    for(size_t i=0; i < n; i ++)        weights->data[elmts[i]] *= in_sum/fit_sum;	overall_max_dev = GSL_MAX(overall_max_dev, fabs(in_sum-fit_sum));}

lls_workspace *lls_alloc(const size_t max_block, const size_t p){  const gsl_multifit_robust_type *robust_t = gsl_multifit_robust_huber;  const size_t nblock = GSL_MAX(max_block, p);  lls_workspace *w;  w = calloc(1, sizeof(lls_workspace));  if (!w)    return 0;  /* A^T A matrix */  w->ATA = gsl_matrix_alloc(p, p);  w->work_A = gsl_matrix_alloc(p, p);  if (!w->ATA || !w->work_A)    {      lls_free(w);      return 0;    }  w->c = gsl_vector_alloc(p);  w->ATb = gsl_vector_alloc(p);  w->work_b = gsl_vector_alloc(p);  w->AF = gsl_matrix_alloc(p, p);  w->S = gsl_vector_alloc(p);  if (!w->ATb || !w->work_b)    {      lls_free(w);      return 0;    }  w->r = gsl_vector_alloc(nblock);  w->w_robust = gsl_vector_alloc(nblock);  w->robust_workspace_p = gsl_multifit_robust_alloc(robust_t, nblock, p);  if (!w->w_robust || !w->r)    {      lls_free(w);      return 0;    }  w->eigen_p = gsl_eigen_symm_alloc(p);  w->eval = gsl_vector_alloc(p);  w->p = p;  w->max_block = nblock;  w->residual = 0.0;  w->chisq = 0.0;  w->cond = -1.0;  w->niter = 0;  w->bTb = 0.0;  /* initialize matrices/vectors to 0 */  lls_reset(w);  return w;} /* lls_alloc() */

intgsl_multilarge_nlinear_test (const double xtol, const double gtol,                             const double ftol, int *info,                             const gsl_multilarge_nlinear_workspace * w){  int status;  double gnorm, fnorm, phi;  *info = 0;  status = gsl_multifit_test_delta(w->dx, w->x, xtol*xtol, xtol);  if (status == GSL_SUCCESS)    {      *info = 1;      return GSL_SUCCESS;    }  /* compute gnorm = max_i( g_i * max(x_i, 1) ) */  gnorm = scaled_infnorm(w->x, w->g);  /* compute fnorm = ||f|| */  fnorm = gsl_blas_dnrm2(w->f);  phi = 0.5 * fnorm * fnorm;#if 0  fprintf(stderr, "gnorm = %.12e fnorm = %.12e gnorm/phi = %.12e/n", gnorm, fnorm, gnorm / phi);#endif  if (gnorm <= gtol * GSL_MAX(phi, 1.0))    {      *info = 2;      return GSL_SUCCESS;    }#if 0  if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))    {      *info = 3;      return GSL_SUCCESS;    }#endif  return GSL_CONTINUE;}

static void_nc_cluster_mass_benson_p_limits (NcClusterMass *clusterm, NcHICosmo *model, const gdouble *xi, const gdouble *xi_params, gdouble *lnM_lower, gdouble *lnM_upper){  NcClusterMassBenson *msz = NC_CLUSTER_MASS_BENSON (clusterm);  const gdouble xil = GSL_MAX (xi[0] - 7.0, msz->signif_obs_min);  const gdouble zetal = _significance_to_zeta (clusterm, model, 2.0, xil) - 7.0 * D_SZ;  const gdouble lnMl = GSL_MAX (_zeta_to_mass (clusterm, model, 2.0, zetal), log (NC_CLUSTER_MASS_BENSON_M_LOWER_BOUND));  const gdouble xiu = xi[0] + 7.0;  const gdouble zetau = _significance_to_zeta (clusterm, model, 0.0, xiu) + 7.0 * D_SZ;  const gdouble lnMu = _zeta_to_mass (clusterm, model, 0.0, zetau);  NCM_UNUSED (xi_params);    *lnM_lower = lnMl;  *lnM_upper = lnMu;  return;}

static doublecholesky_LDLT_norm1(const gsl_matrix * LDLT, const gsl_permutation * p, gsl_vector * work){  const size_t N = LDLT->size1;  gsl_vector_const_view D = gsl_matrix_const_diagonal(LDLT);  gsl_vector_view diagA = gsl_vector_subvector(work, N, N);  double max = 0.0;  size_t i, j;  /* reconstruct diagonal entries of original matrix A */  for (j = 0; j < N; ++j)    {      double Ajj;      /* compute diagonal (j,j) entry of A */      Ajj = gsl_vector_get(&D.vector, j);      for (i = 0; i < j; ++i)        {          double Di = gsl_vector_get(&D.vector, i);          double Lji = gsl_matrix_get(LDLT, j, i);          Ajj += Di * Lji * Lji;        }      gsl_vector_set(&diagA.vector, j, Ajj);    }  gsl_permute_vector_inverse(p, &diagA.vector);  for (j = 0; j < N; ++j)    {      double sum = 0.0;      double Ajj = gsl_vector_get(&diagA.vector, j);      for (i = 0; i < j; ++i)        {          double *wi = gsl_vector_ptr(work, i);          double Aij = gsl_matrix_get(LDLT, i, j);          double absAij = fabs(Aij);          sum += absAij;          *wi += absAij;        }      gsl_vector_set(work, j, sum + fabs(Ajj));    }  for (i = 0; i < N; ++i)    {      double wi = gsl_vector_get(work, i);      max = GSL_MAX(max, wi);    }  return max;}

/** If there is an NaN anywhere in the row of data (including the matrix, the vector, the weights, and the text) then delete the row from the data set./li If every row has an NaN, then this returns /c NULL./li If /c apop_opts.db_nan is not /c NULL, then I will use that as a regular expression to check the text elements for bad data as well./li If /c inplace = 'y', then I'll free each element of the input data    set and refill it with the pruned elements. I'll still take up (up to)    twice the size of the data set in memory during the function. If    every row has an NaN, then your /c apop_data set will end up with    /c NULL vector, matrix, /dots. if /c inplace = 'n', then the original data set is left unmolested./li I only look at the first page of data (i.e. the /c more element is ignored)./li This function uses the /ref designated syntax for inputs.    /param d    The data, with NaNs    /param inplace If /c 'y', clear out the pointer-to-/ref apop_data that    you sent in and refill with the pruned data. If /c 'n', leave the    set alone and return a new data set.    /return     A (potentially shorter) copy of the data set, without    NaNs. If <tt>inplace=='y'</tt>, redundant with the input. If the entire data set is    cleared out, then this will be /c NULL.*/APOP_VAR_HEAD apop_data * apop_data_listwise_delete(apop_data *d, char inplace){    apop_data * apop_varad_var(d, NULL);    if (!d) return NULL;    char apop_varad_var(inplace, 'n');APOP_VAR_ENDHEAD    Get_vmsizes(d) //defines firstcol, vsize, wsize, msize1, msize2.    apop_assert_c(msize1 || vsize || d->textsize[0], NULL, 0,             "You sent to apop_data_listwise_delete a data set with NULL matrix, NULL vector, and no text. "            "Confused, it is returning NULL.");    //find out where the NaNs are    int len = GSL_MAX(vsize ? vsize : msize1, d->textsize[0]); //still some size assumptions here.    int not_empty = 0;    int *marked = calloc(len, sizeof(int));    for (int i=0; i< (vsize ? vsize: msize1); i++)        for (int j=firstcol; j <msize2; j++){            if (gsl_isnan(apop_data_get(d, i, j))){                    marked[i] = 1;                    break;            }        }    for (int i=0; i< wsize; i++)        if (gsl_isnan(gsl_vector_get(d->weights, i)))            marked[i] = 1;    if (d->textsize[0] && apop_opts.db_nan){        regex_t    rex;        int compiled_ok = !regcomp(&rex, apop_opts.db_nan, REG_EXTENDED +  REG_ICASE + REG_NOSUB);        apop_assert(compiled_ok, "apop_opts.db_nan needs to be a regular expression that "                                "I can use to check the text element of your data set for "                                "NaNs, But compiling %s into a regex failed. Or, set "                                "apop_opts.db_nan=NULL to bypass text checking.", apop_opts.db_nan);        for(int i=0; i< d->textsize[0]; i++)            if (!marked[i])                for(int j=0; j< d->textsize[1]; j++)                    if (!regexec(&rex, d->text[i][j], 0, 0, 0)){                        marked[i] ++;                        break;                    }        regfree(&rex);    }    //check that at least something isn't NULL.    for (int i=0; i< len; i++)        if (!marked[i]){            not_empty ++;            break;        }    if (!not_empty){        free(marked);        return NULL;    }    apop_data *out = (inplace=='y'|| inplace=='Y') ? d : apop_data_copy(d);    apop_data_rm_rows(out, marked);    free(marked);    return out;}

long  AT_n_bins_for_single_impact_local_dose_distrib(		const long    n,		const double  E_MeV_u[],		const long    particle_no[],		const long    material_no,		const long    rdd_model,		const double  rdd_parameter[],		const long    er_model,		const long    N2,		const long    stopping_power_source_no){	/* get lowest and highest dose */	double d_max_Gy    =  0.0;	double d_min_Gy    =  0.0;	// TODO think if d_min calculations can be done in smarter way. LET is only needed for Geiss RDD	long  i;	for (i = 0; i < n; i++){		double max_electron_range_m = AT_max_electron_range_m( E_MeV_u[i], (int)material_no, (int)er_model);		double LET_MeV_cm2_g        = AT_Stopping_Power_MeV_cm2_g_single( stopping_power_source_no, E_MeV_u[i], particle_no[i], material_no);		double norm_constant_Gy     = AT_RDD_precalculated_constant_Gy(max_electron_range_m, LET_MeV_cm2_g, E_MeV_u[i], particle_no[i], material_no, rdd_model, rdd_parameter, er_model);		double current_d_min_Gy     = AT_RDD_d_min_Gy( E_MeV_u[i], particle_no[i], material_no, rdd_model, rdd_parameter, er_model, norm_constant_Gy);		double current_d_max_Gy     = AT_RDD_d_max_Gy( E_MeV_u[i], particle_no[i], material_no, rdd_model, rdd_parameter, er_model, stopping_power_source_no);		if(i == 0){			d_min_Gy      =  current_d_min_Gy;			d_max_Gy      =  current_d_max_Gy;		}		else{			d_min_Gy      =  GSL_MIN(d_min_Gy, current_d_min_Gy);			d_max_Gy      =  GSL_MAX(d_max_Gy, current_d_max_Gy);		}	}	long n_bins_for_singe_impact_local_dose_ditrib = 0;	// get number of bins needed to span that dose range	if( (d_min_Gy > 0) && (d_max_Gy >0) ){		// OLD:		//		double tmp        =  log10(d_max_Gy/d_min_Gy) / log10(2.0) * ((double)N2);		//		n_bins_for_singe_impact_local_dose_ditrib        =  (long)(floor(tmp) + 1.0);		AT_histo_n_bins(     d_min_Gy,				d_max_Gy,				AT_N2_to_step(N2),				AT_histo_log,				&n_bins_for_singe_impact_local_dose_ditrib);	} else {#ifndef NDEBUG		printf("AT_n_bins_for_singe_impact_local_dose_ditrib: problem in evaluating n_bins_for_singe_impact_local_dose_ditrib: d_min = %g [Gy], d_max = %g [Gy] /n", d_min_Gy, d_max_Gy);		exit(EXIT_FAILURE);#endif	}	return n_bins_for_singe_impact_local_dose_ditrib + 1;}

static inttrust_init(void *vstate, const gsl_vector *swts,           gsl_multilarge_nlinear_fdf *fdf, const gsl_vector *x,           gsl_vector *f, gsl_vector *g, gsl_matrix *JTJ){  int status;  trust_state_t *state = (trust_state_t *) vstate;  const gsl_multilarge_nlinear_parameters *params = &(state->params);  double Dx;  /* evaluate function and Jacobian at x and apply weight transform */  status = gsl_multilarge_nlinear_eval_f(fdf, x, swts, f);  if (status)   return status;  /* compute g = J^T f and J^T J */  status = gsl_multilarge_nlinear_eval_df(CblasTrans, x, f, f,                                          swts, params->h_df, params->fdtype,                                          fdf, g, JTJ, state->workn);  if (status)    return status;  /* initialize diagonal scaling matrix D */  if (JTJ != NULL)    (params->scale->init)(JTJ, state->diag);  else    gsl_vector_set_all(state->diag, 1.0);  /* compute initial trust region radius */  Dx = trust_scaled_norm(state->diag, x);  state->delta = 0.3 * GSL_MAX(1.0, Dx);  /* initialize LM parameter */  nielsen_init(JTJ, state->diag, &(state->mu), &(state->nu));  /* initialize trust region method solver */  {    const gsl_multilarge_nlinear_trust_state trust_state = { x, f, g, JTJ, state->diag,                                                             swts, &(state->mu), params,                                                             state->solver_state, fdf,                                                             &(state->avratio) };    status = (params->trs->init)(&trust_state, state->trs_state);    if (status)      return status;  }  /* set default parameters */  state->avratio = 0.0;  return GSL_SUCCESS;}

doublegsl_hypot3(const double x, const double y, const double z){  double xabs = fabs(x);  double yabs = fabs(y);  double zabs = fabs(z);  double w = GSL_MAX(xabs, GSL_MAX(yabs, zabs));  if (w == 0.0)    {      return (0.0);    }  else    {      double r = w * sqrt((xabs / w) * (xabs / w) +                          (yabs / w) * (yabs / w) +                          (zabs / w) * (zabs / w));      return r;    }}

static double scale_factor(gsl_vector *scale){    double scale_factor;    size_t i;    scale_factor = 0.0;    for (i = 1; i < scale->size; i++)        scale_factor = GSL_MAX(scale_factor, gsl_vector_get(scale, i));    return scale_factor / gsl_vector_get(scale, 0);}

/** Give me a data set and a model, and I'll give you the jackknifed covariance matrix of the model parameters.The basic algorithm for the jackknife (glossing over the details): create a sequence of datasets, each with exactly one observation removed, and then produce a new set of parameter estimates using that slightly shortened data set. Then, find the covariance matrix of the derived parameters./li Jackknife or bootstrap? As a broad rule of thumb, the jackknife works best on models    that are closer to linear. The worse a linear approximation does (at the given data),    the worse the jackknife approximates the variance./param in	    The data set. An /ref apop_data set where each row is a single data point./param model    An /ref apop_model, that will be used internally by /ref apop_estimate.            /exception out->error=='n'   /c NULL input data./return         An /c apop_data set whose matrix element is the estimated covariance matrix of the parameters./see apop_bootstrap_covFor example:/include jack.c*/apop_data * apop_jackknife_cov(apop_data *in, apop_model *model){    Apop_stopif(!in, apop_return_data_error(n), 0, "The data input can't be NULL.");    Get_vmsizes(in); //msize1, msize2, vsize    apop_model *e = apop_model_copy(model);    int i, n = GSL_MAX(msize1, GSL_MAX(vsize, in->textsize[0]));    apop_model *overall_est = e->parameters ? e : apop_estimate(in, e);//if not estimated, do so    gsl_vector *overall_params = apop_data_pack(overall_est->parameters);    gsl_vector_scale(overall_params, n); //do it just once.    gsl_vector *pseudoval = gsl_vector_alloc(overall_params->size);    //Copy the original, minus the first row.    apop_data *subset = apop_data_copy(Apop_rs(in, 1, n-1));    apop_name *tmpnames = in->names;     in->names = NULL;  //save on some copying below.    apop_data *array_of_boots = apop_data_alloc(n, overall_params->size);    for(i = -1; i< n-1; i++){        //Get a view of row i, and copy it to position i-1 in the short matrix.        if (i >= 0) apop_data_memcpy(Apop_r(subset, i), Apop_r(in, i));        apop_model *est = apop_estimate(subset, e);        gsl_vector *estp = apop_data_pack(est->parameters);        gsl_vector_memcpy(pseudoval, overall_params);// *n above.        gsl_vector_scale(estp, n-1);        gsl_vector_sub(pseudoval, estp);        gsl_matrix_set_row(array_of_boots->matrix, i+1, pseudoval);        apop_model_free(est);        gsl_vector_free(estp);    }    in->names = tmpnames;    apop_data *out = apop_data_covariance(array_of_boots);    gsl_matrix_scale(out->matrix, 1./(n-1.));    apop_data_free(subset);    gsl_vector_free(pseudoval);    apop_data_free(array_of_boots);    if (e!=overall_est)        apop_model_free(overall_est);    apop_model_free(e);    gsl_vector_free(overall_params);    return out;}

static void scaling(size_t const *elmts, size_t const n,  gsl_vector *weights, double const in_sum, double *maxdev){    double fit_sum = 0, out_sum=0;    for(size_t i=0; i < n; i ++)        fit_sum += weights->data[elmts[i]];    if (!fit_sum) return; //can happen if init table is very different from margins.    for(size_t i=0; i < n; i ++){        out_sum +=        weights->data[elmts[i]] *= in_sum/fit_sum;    }    *maxdev = GSL_MAX(fabs(fit_sum - out_sum), *maxdev);}

/* [Carlson, p.109] says the error in truncating this asymptotic series * is less than the absolute value of the first neglected term. * * A termination argument is provided, so that the series will * be summed at most up to n=n_trunc. If n_trunc is set negative, * then the series is summed until it appears to start diverging. */intgsl_sf_hyperg_2F0_series_e(const double a, const double b, const double x,                           int n_trunc,                           gsl_sf_result * result                          ){    const int maxiter = 2000;    double an = a;    double bn = b;    double n   = 1.0;    double sum = 1.0;    double del = 1.0;    double abs_del = 1.0;    double max_abs_del = 1.0;    double last_abs_del = 1.0;    while(abs_del/fabs(sum) > GSL_DBL_EPSILON && n < maxiter) {        double u = an * (bn/n * x);        double abs_u = fabs(u);        if(abs_u > 1.0 && (max_abs_del > GSL_DBL_MAX/abs_u)) {            result->val = sum;            result->err = fabs(sum);            GSL_ERROR ("overflow", GSL_EOVRFLW);        }        del *= u;        sum += del;        abs_del = fabs(del);        if(abs_del > last_abs_del) break; /* series is probably starting to grow */        last_abs_del = abs_del;        max_abs_del  = GSL_MAX(abs_del, max_abs_del);        an += 1.0;        bn += 1.0;        n  += 1.0;        if(an == 0.0 || bn == 0.0) break;        /* series terminated */        if(n_trunc >= 0 && n >= n_trunc) break;  /* reached requested timeout */    }    result->val = sum;    result->err = GSL_DBL_EPSILON * n + abs_del;    if(n >= maxiter)        GSL_ERROR ("error", GSL_EMAXITER);    else        return GSL_SUCCESS;}

gsl_movstat_workspace *gsl_movstat_alloc_with_size(const size_t accum_state_size, const size_t H, const size_t J){  gsl_movstat_workspace *w;  size_t state_size = accum_state_size;  w = calloc(1, sizeof(gsl_movstat_workspace));  if (w == 0)    {      GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);    }  w->H = H;  w->J = J;  w->K = H + J + 1;  if (state_size == 0)    {      /*       * determine maximum number of bytes needed for the various accumulators;       * the accumulators will all share the same workspace       */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_mad->size)(w->K));    /* MAD accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_mean->size)(w->K));   /* mean/variance/sd accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_min->size)(w->K));    /* min/max accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_sum->size)(w->K));    /* sum accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_median->size)(w->K)); /* median accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_Qn->size)(w->K));     /* Q_n accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_qqr->size)(w->K));    /* QQR accumulator */      state_size = GSL_MAX(state_size, (gsl_movstat_accum_Sn->size)(w->K));     /* S_n accumulator */    }  w->state = malloc(state_size);  if (w->state == 0)    {      gsl_movstat_free(w);      GSL_ERROR_NULL ("failed to allocate space for accumulator state", GSL_ENOMEM);    }  w->work = malloc(w->K * sizeof(double));  if (w->work == 0)    {      gsl_movstat_free(w);      GSL_ERROR_NULL ("failed to allocate space for work", GSL_ENOMEM);    }  w->state_size = state_size;  return w;}

/* WKB evaluation of F, G. Assumes  0 < x < turning point. * Overflows are trapped, GSL_EOVRFLW is signalled, * and an exponent is returned such that: * *   result_F = fjwkb * exp(-exponent) *   result_G = gjwkb * exp( exponent) * * See [Biedenharn et al. Phys. Rev. 97, 542-554 (1955), Section IV] * * Unfortunately, this is not very accurate in general. The * test cases typically have 3-4 digits of precision. One could * argue that this is ok for general use because, for instance, * F is exponentially small in this region and so the absolute * accuracy is still roughly acceptable. But it would be better * to have a systematic method for improving the precision. See * the Abad+Sesma method discussion below. */staticintcoulomb_jwkb(const double lam, const double eta, const double x,             gsl_sf_result * fjwkb, gsl_sf_result * gjwkb,	     double * exponent){  const double llp1      = lam*(lam+1.0) + 6.0/35.0;  const double llp1_eff  = GSL_MAX(llp1, 0.0);  const double rho_ghalf = sqrt(x*(2.0*eta - x) + llp1_eff);  const double sinh_arg  = sqrt(llp1_eff/(eta*eta+llp1_eff)) * rho_ghalf / x;  const double sinh_inv  = log(sinh_arg + sqrt(1.0 + sinh_arg*sinh_arg));  const double phi = fabs(rho_ghalf - eta*atan2(rho_ghalf,x-eta) - sqrt(llp1_eff) * sinh_inv);  const double zeta_half = pow(3.0*phi/2.0, 1.0/3.0);  const double prefactor = sqrt(M_PI*phi*x/(6.0 * rho_ghalf));    double F = prefactor * 3.0/zeta_half;  double G = prefactor * 3.0/zeta_half; /* Note the sqrt(3) from Bi normalization */  double F_exp;  double G_exp;    const double airy_scale_exp = phi;  gsl_sf_result ai;  gsl_sf_result bi;  gsl_sf_airy_Ai_scaled_e(zeta_half*zeta_half, GSL_MODE_DEFAULT, &ai);  gsl_sf_airy_Bi_scaled_e(zeta_half*zeta_half, GSL_MODE_DEFAULT, &bi);  F *= ai.val;  G *= bi.val;  F_exp = log(F) - airy_scale_exp;  G_exp = log(G) + airy_scale_exp;  if(G_exp >= GSL_LOG_DBL_MAX) {    fjwkb->val = F;    gjwkb->val = G;    fjwkb->err = 1.0e-3 * fabs(F); /* FIXME: real error here ... could be smaller */    gjwkb->err = 1.0e-3 * fabs(G);    *exponent = airy_scale_exp;    GSL_ERROR ("error", GSL_EOVRFLW);  }  else {    fjwkb->val = exp(F_exp);    gjwkb->val = exp(G_exp);    fjwkb->err = 1.0e-3 * fabs(fjwkb->val);    gjwkb->err = 1.0e-3 * fabs(gjwkb->val);    *exponent = 0.0;    return GSL_SUCCESS;  }}