X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Foptim-1.2.0%2Fprivate%2F__nonlin_residmin__.m;fp=octave_packages%2Foptim-1.2.0%2Fprivate%2F__nonlin_residmin__.m;h=63eabdd813b2c0bcde3738f15fbc2d2d6412723a;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05

diff --git a/octave_packages/optim-1.2.0/private/__nonlin_residmin__.m b/octave_packages/optim-1.2.0/private/__nonlin_residmin__.m
new file mode 100644
index 0000000..63eabdd
--- /dev/null
+++ b/octave_packages/optim-1.2.0/private/__nonlin_residmin__.m
@@ -0,0 +1,1032 @@
+## Copyright (C) 2010, 2011 Olaf Till <olaf.till@uni-jena.de>
+##
+## 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/>.
+
+## Internal function, called by nonlin_residmin --- see there --- and
+## others. Calling __nonlin_residmin__ indirectly hides the argument
+## "hook", usable by wrappers, from users. Currently, hook can contain
+## the field "observations", so that dimensions of observations and
+## returned values of unchanged model function can be checked against
+## each other exactly one time.
+
+## disabled PKG_ADD: __all_opts__ ("__nonlin_residmin__");
+
+function [p, resid, cvg, outp] = \
+      __nonlin_residmin__ (f, pin, settings, hook)
+
+  if (compare_versions (version (), "3.3.55", "<"))
+    ## optimset mechanism was fixed for option names with underscores
+    ## sometime in 3.3.54+, if I remember right
+    optimget = @ __optimget__;
+  endif
+
+  if (compare_versions (version (), "3.2.4", "<="))
+    ## For bug #31484; but Octave 3.6... shows bug #36288 due to this
+    ## workaround. Octave 3.7... seems to be all right.
+    __dfdp__ = @ __dfdp__;
+  endif
+
+  ## some scalar defaults; some defaults are backend specific, so
+  ## lacking elements in respective constructed vectors will be set to
+  ## NA here in the frontend
+  diffp_default = .001;
+  stol_default = .0001;
+  cstep_default = 1e-20;
+
+  if (nargin == 1 && ischar (f) && strcmp (f, "defaults"))
+    p = optimset ("param_config", [], \
+		  "param_order", [], \
+		  "param_dims", [], \
+		  "f_inequc_pstruct", false, \
+		  "f_equc_pstruct", false, \
+		  "f_pstruct", false, \
+		  "df_inequc_pstruct", false, \
+		  "df_equc_pstruct", false, \
+		  "dfdp_pstruct", false, \
+		  "lbound", [], \
+		  "ubound", [], \
+		  "dfdp", [], \
+		  "cpiv", @ cpiv_bard, \
+		  "max_fract_change", [], \
+		  "fract_prec", [], \
+		  "diffp", [], \
+		  "diff_onesided", [], \
+		  "complex_step_derivative_f", false, \
+		  "complex_step_derivative_inequc", false, \
+		  "complex_step_derivative_equc", false, \
+		  "cstep", cstep_default, \
+		  "fixed", [], \
+		  "inequc", [], \
+		  "equc", [], \
+                  "inequc_f_idx", false, \
+                  "inequc_df_idx", false, \
+                  "equc_f_idx", false, \
+                  "equc_df_idx", false, \
+		  "weights", [], \
+		  "TolFun", stol_default, \
+		  "MaxIter", [], \
+		  "Display", "off", \
+		  "Algorithm", "lm_svd_feasible", \
+		  "plot_cmd", @ (f) 0, \
+		  "debug", false, \
+		  "lm_svd_feasible_alt_s", false);
+    return;
+  endif
+
+  assign = @ assign; # Is this faster in repeated calls?
+
+  if (nargin != 4)
+    error ("incorrect number of arguments");
+  endif
+
+  if (ischar (f))
+    f = str2func (f);
+  endif
+
+  if (! (pin_struct = isstruct (pin)))
+    if (! isvector (pin) || columns (pin) > 1)
+      error ("initial parameters must be either a structure or a column vector");
+    endif
+  endif
+
+  #### processing of settings and consistency checks
+
+  pconf = optimget (settings, "param_config");
+  pord = optimget (settings, "param_order");
+  pdims = optimget (settings, "param_dims");
+  f_inequc_pstruct = optimget (settings, "f_inequc_pstruct", false);
+  f_equc_pstruct = optimget (settings, "f_equc_pstruct", false);
+  f_pstruct = optimget (settings, "f_pstruct", false);
+  dfdp_pstruct = optimget (settings, "dfdp_pstruct", f_pstruct);
+  df_inequc_pstruct = optimget (settings, "df_inequc_pstruct", \
+				f_inequc_pstruct);
+  df_equc_pstruct = optimget (settings, "df_equc_pstruct", \
+			      f_equc_pstruct);
+  lbound = optimget (settings, "lbound");
+  ubound = optimget (settings, "ubound");
+  dfdp = optimget (settings, "dfdp");
+  if (ischar (dfdp)) dfdp = str2func (dfdp); endif
+  max_fract_change = optimget (settings, "max_fract_change");
+  fract_prec = optimget (settings, "fract_prec");
+  diffp = optimget (settings, "diffp");
+  diff_onesided = optimget (settings, "diff_onesided");
+  fixed = optimget (settings, "fixed");
+  do_cstep = optimget (settings, "complex_step_derivative_f", false);
+  cstep = optimget (settings, "cstep", cstep_default);
+  if (do_cstep && ! isempty (dfdp))
+    error ("both 'complex_step_derivative_f' and 'dfdp' are set");
+  endif
+  do_cstep_inequc = \
+      optimget (settings, "complex_step_derivative_inequc", false);
+  do_cstep_equc = optimget (settings, "complex_step_derivative_equc", false);
+
+  any_vector_conf = ! (isempty (lbound) && isempty (ubound) && \
+		       isempty (max_fract_change) && \
+		       isempty (fract_prec) && isempty (diffp) && \
+		       isempty (diff_onesided) && isempty (fixed));
+
+  ## collect constraints
+  [mc, vc, f_genicstr, df_gencstr, user_df_gencstr] = \
+      __collect_constraints__ (optimget (settings, "inequc"), \
+			       do_cstep_inequc, "inequality constraints");
+  [emc, evc, f_genecstr, df_genecstr, user_df_genecstr] = \
+      __collect_constraints__ (optimget (settings, "equc"), \
+			       do_cstep_equc, "equality constraints");
+  mc_struct = isstruct (mc);
+  emc_struct = isstruct (emc);
+
+  ## correct "_pstruct" settings if functions are not supplied, handle
+  ## constraint functions not honoring indices
+  if (isempty (dfdp)) dfdp_pstruct = false; endif
+  if (isempty (f_genicstr))
+    f_inequc_pstruct = false;
+  elseif (! optimget (settings, "inequc_f_idx", false))
+    f_genicstr = @ (p, varargin) apply_idx_if_given \
+        (f_genicstr (p, varargin{:}), varargin{:});
+  endif
+  if (isempty (f_genecstr))
+    f_equc_pstruct = false;
+  elseif (! optimget (settings, "equc_f_idx", false))
+    f_genecstr = @ (p, varargin) apply_idx_if_given \
+        (f_genecstr (p, varargin{:}), varargin{:});
+  endif
+  if (user_df_gencstr)
+    if (! optimget (settings, "inequc_df_idx", false))
+      df_gencstr = @ (varargin) df_gencstr (varargin{:})(varargin{2}, :);
+    endif
+  else
+    df_inequc_pstruct = false;
+  endif
+  if (user_df_genecstr)
+    if (! optimget (settings, "equc_df_idx", false))
+      df_genecstr = @ (varargin) df_genecstr (varargin{:})(varargin{2}, :);
+    endif
+  else
+    df_equc_pstruct = false;
+  endif
+
+  ## some settings require a parameter order
+  if (pin_struct || ! isempty (pconf) || f_inequc_pstruct || \
+      f_equc_pstruct || f_pstruct || dfdp_pstruct || \
+      df_inequc_pstruct || df_equc_pstruct || mc_struct || \
+      emc_struct)
+    if (isempty (pord))
+      if (pin_struct)
+	if (any_vector_conf || \
+	    ! (f_pstruct && \
+	       (f_inequc_pstruct || isempty (f_genicstr)) && \
+	       (f_equc_pstruct || isempty (f_genecstr)) && \
+	       (dfdp_pstruct || isempty (dfdp)) && \
+	       (df_inequc_pstruct || ! user_df_gencstr) && \
+	       (df_equc_pstruct || ! user_df_genecstr) && \
+	       (mc_struct || isempty (mc)) && \
+	       (emc_struct || isempty (emc))))
+	  error ("no parameter order specified and constructing a parameter order from the structure of initial parameters can not be done since not all configuration or given functions are structure based");
+	else
+	  pord = fieldnames (pin);
+	endif
+      else
+	error ("given settings require specification of parameter order or initial parameters in the form of a structure");
+      endif
+    endif
+    pord = pord(:);
+    if (pin_struct && ! all (isfield (pin, pord)))
+      error ("some initial parameters lacking");
+    endif
+    if ((nnames = rows (unique (pord))) < rows (pord))
+      error ("duplicate parameter names in 'param_order'");
+    endif
+    if (isempty (pdims))
+      if (pin_struct)
+	pdims = cellfun \
+	    (@ size, fields2cell (pin, pord), "UniformOutput", false);
+      else
+	pdims = num2cell (ones (nnames, 2), 2);
+      endif
+    else
+      pdims = pdims(:);
+      if (pin_struct && \
+	  ! all (cellfun (@ (x, y) prod (size (x)) == prod (y), \
+			  struct2cell (pin), pdims)))
+	error ("given param_dims and dimensions of initial parameters do not match");
+      endif
+    endif
+    if (nnames != rows (pdims))
+      error ("lengths of 'param_order' and 'param_dims' not equal");
+    endif
+    pnel = cellfun (@ prod, pdims);
+    ppartidx = pnel;
+    if (any (pnel > 1))
+      pnonscalar = true;
+      cpnel = num2cell (pnel);
+      prepidx = cat (1, cellfun \
+		     (@ (x, n) x(ones (1, n), 1), \
+		      num2cell ((1:nnames).'), cpnel, \
+		      "UniformOutput", false){:});
+      epord = pord(prepidx, 1);
+      psubidx = cat (1, cellfun \
+		     (@ (n) (1:n).', cpnel, \
+		      "UniformOutput", false){:});
+    else
+      pnonscalar = false; # some less expensive interfaces later
+      prepidx = (1:nnames).';
+      epord = pord;
+      psubidx = ones (nnames, 1);
+    endif
+  else
+    pord = []; # spares checks for given but not needed
+  endif
+
+  if (pin_struct)
+    np = sum (pnel);
+  else
+    np = length (pin);
+    if (! isempty (pord) && np != sum (pnel))
+      error ("number of initial parameters not correct");
+    endif
+  endif
+
+  plabels = num2cell (num2cell ((1:np).'));
+  if (! isempty (pord))
+    plabels = cat (2, plabels, num2cell (epord), \
+		   num2cell (num2cell (psubidx)));
+  endif
+
+  ## some useful vectors
+  zerosvec = zeros (np, 1);
+  NAvec = NA (np, 1);
+  Infvec = Inf (np, 1);
+  falsevec = false (np, 1);
+  sizevec = [np, 1];
+
+  ## collect parameter-related configuration
+  if (! isempty (pconf))
+    ## use supplied configuration structure
+
+    ## parameter-related configuration is either allowed by a structure
+    ## or by vectors
+    if (any_vector_conf)
+      error ("if param_config is given, its potential items must not \
+	  be configured in another way");
+    endif
+
+    ## supplement parameter names lacking in param_config
+    nidx = ! isfield (pconf, pord);
+    pconf = cell2fields ({struct()}(ones (1, sum (nidx))), \
+			 pord(nidx), 2, pconf);
+
+    pconf = structcat (1, fields2cell (pconf, pord){:});
+
+    ## in the following, use reshape with explicit dimensions (instead
+    ## of x(:)) so that errors are thrown if a configuration item has
+    ## incorrect number of elements
+
+    lbound = - Infvec;
+    if (isfield (pconf, "lbound"))
+      idx = ! fieldempty (pconf, "lbound");
+      if (pnonscalar)
+	lbound (idx(prepidx), 1) = \
+	    cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     {pconf(idx).lbound}.', \
+			     cpnel(idx), "UniformOutput", false){:});
+      else
+	lbound(idx, 1) = cat (1, pconf.lbound);
+      endif
+    endif
+
+    ubound = Infvec;
+    if (isfield (pconf, "ubound"))
+      idx = ! fieldempty (pconf, "ubound");
+      if (pnonscalar)
+	ubound (idx(prepidx), 1) = \
+	    cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     {pconf(idx).ubound}.', \
+			     cpnel(idx), "UniformOutput", false){:});
+      else
+	ubound(idx, 1) = cat (1, pconf.ubound);
+      endif
+    endif
+
+    max_fract_change = fract_prec = NAvec;
+
+    if (isfield (pconf, "max_fract_change"))
+      idx = ! fieldempty (pconf, "max_fract_change");
+      if (pnonscalar)
+	max_fract_change(idx(prepidx)) = \
+	    cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     {pconf(idx).max_fract_change}.', \
+			     cpnel(idx), \
+			     "UniformOutput", false){:});
+      else
+	max_fract_change(idx) = [pconf.max_fract_change];
+      endif
+    endif
+
+    if (isfield (pconf, "fract_prec"))
+      idx = ! fieldempty (pconf, "fract_prec");
+      if (pnonscalar)
+	fract_prec(idx(prepidx)) = \
+	    cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     {pconf(idx).fract_prec}.', cpnel(idx), \
+			     "UniformOutput", false){:});
+      else
+	fract_prec(idx) = [pconf.fract_prec];
+      endif
+    endif
+
+    diffp = zerosvec;
+    diffp(:) = diffp_default;
+    if (isfield (pconf, "diffp"))
+      idx = ! fieldempty (pconf, "diffp");
+      if (pnonscalar)
+	diffp(idx(prepidx)) = \
+	    cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     {pconf(idx).diffp}.', cpnel(idx), \
+			     "UniformOutput", false){:});
+      else
+	diffp(idx) = [pconf.diffp];
+      endif
+    endif
+
+    diff_onesided = fixed = falsevec;
+
+    if (isfield (pconf, "diff_onesided"))
+      idx = ! fieldempty (pconf, "diff_onesided");
+      if (pnonscalar)
+	diff_onesided(idx(prepidx)) = \
+	    logical \
+	    (cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			      {pconf(idx).diff_onesided}.', cpnel(idx), \
+			     "UniformOutput", false){:}));
+      else
+	diff_onesided(idx) = logical ([pconf.diff_onesided]);
+      endif
+    endif
+
+    if (isfield (pconf, "fixed"))
+      idx = ! fieldempty (pconf, "fixed");
+      if (pnonscalar)
+	fixed(idx(prepidx)) = \
+	    logical \
+	    (cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			      {pconf(idx).fixed}.', cpnel(idx), \
+			     "UniformOutput", false){:}));
+      else
+	fixed(idx) = logical ([pconf.fixed]);
+      endif
+    endif
+  else
+    ## use supplied configuration vectors
+
+    if (isempty (lbound))
+      lbound = - Infvec;
+    elseif (any (size (lbound) != sizevec))
+      error ("bounds: wrong dimensions");
+    endif
+
+    if (isempty (ubound))
+      ubound = Infvec;
+    elseif (any (size (ubound) != sizevec))
+      error ("bounds: wrong dimensions");
+    endif
+
+    if (isempty (max_fract_change))
+      max_fract_change = NAvec;
+    elseif (any (size (max_fract_change) != sizevec))
+      error ("max_fract_change: wrong dimensions");
+    endif
+
+    if (isempty (fract_prec))
+      fract_prec = NAvec;
+    elseif (any (size (fract_prec) != sizevec))
+      error ("fract_prec: wrong dimensions");
+    endif
+
+    if (isempty (diffp))
+      diffp = zerosvec;
+      diffp(:) = diffp_default;
+    else
+      if (any (size (diffp) != sizevec))
+	error ("diffp: wrong dimensions");
+      endif
+      diffp(isna (diffp)) = diffp_default;
+    endif
+
+    if (isempty (diff_onesided))
+      diff_onesided = falsevec;
+    else
+      if (any (size (diff_onesided) != sizevec))
+	error ("diff_onesided: wrong dimensions")
+      endif
+      diff_onesided(isna (diff_onesided)) = false;
+      diff_onesided = logical (diff_onesided);
+    endif
+
+    if (isempty (fixed))
+      fixed = falsevec;
+    else
+      if (any (size (fixed) != sizevec))
+	error ("fixed: wrong dimensions");
+      endif
+      fixed(isna (fixed)) = false;
+      fixed = logical (fixed);
+    endif
+  endif
+
+  ## guaranty all (lbound <= ubound)
+  if (any (lbound > ubound))
+    error ("some lower bounds larger than upper bounds");
+  endif
+
+  #### consider whether initial parameters and functions are based on
+  #### parameter structures or parameter vectors; wrappers for call to
+  #### default function for jacobians
+
+  ## initial parameters
+  if (pin_struct)
+    if (pnonscalar)
+      pin = cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+			     fields2cell (pin, pord), cpnel, \
+			     "UniformOutput", false){:});
+    else
+      pin = cat (1, fields2cell (pin, pord){:});
+    endif
+  endif
+
+  ## model function
+  if (f_pstruct)
+    if (pnonscalar)
+      f = @ (p, varargin) \
+	  f (cell2struct \
+	     (cellfun (@ reshape, mat2cell (p, ppartidx), \
+		       pdims, "UniformOutput", false), \
+	      pord, 1), varargin{:});
+    else
+      f = @ (p, varargin) \
+	  f (cell2struct (num2cell (p), pord, 1), varargin{:});
+    endif
+  endif
+  f_pin = f (pin);
+  if (isfield (hook, "observations"))
+    if (any (size (f_pin) != size (obs = hook.observations)))
+      error ("dimensions of observations and values of model function must match");
+    endif
+    f = @ (p) f (p) - obs;
+    f_pin -= obs;
+  endif
+
+  ## jacobian of model function
+  if (isempty (dfdp))
+    if (do_cstep)
+      dfdp = @ (p, hook) jacobs (p, f, hook);
+    else
+      dfdp = @ (p, hook) __dfdp__ (p, f, hook);
+    endif
+  endif
+  if (dfdp_pstruct)
+    if (pnonscalar)
+      dfdp = @ (p, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (dfdp (cell2struct \
+		      (cellfun (@ reshape, mat2cell (p, ppartidx), \
+				pdims, "UniformOutput", false), \
+		       pord, 1), hook), \
+		pord){:});
+    else
+      dfdp = @ (p, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (dfdp (cell2struct (num2cell (p), pord, 1), hook), \
+		pord){:});
+    endif
+  endif
+
+  ## function for general inequality constraints
+  if (f_inequc_pstruct)
+    if (pnonscalar)
+      f_genicstr = @ (p, varargin) \
+	  f_genicstr (cell2struct \
+		      (cellfun (@ reshape, mat2cell (p, ppartidx), \
+				pdims, "UniformOutput", false), \
+		       pord, 1), varargin{:});
+    else
+      f_genicstr = @ (p, varargin) \
+	  f_genicstr \
+	  (cell2struct (num2cell (p), pord, 1), varargin{:});
+    endif
+  endif
+
+  ## note this stage
+  possibly_pstruct_f_genicstr = f_genicstr;
+
+  ## jacobian of general inequality constraints
+  if (df_inequc_pstruct)
+    if (pnonscalar)
+      df_gencstr = @ (p, func, idx, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (df_gencstr \
+		(cell2struct \
+		 (cellfun (@ reshape, mat2cell (p, ppartidx), \
+			   pdims, "UniformOutput", false), pord, 1), \
+		 func, idx, hook), \
+		pord){:});
+    else
+      df_gencstr = @ (p, func, idx, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (df_gencstr (cell2struct (num2cell (p), pord, 1), \
+			    func, idx, hook), \
+		pord){:});
+    endif
+  endif
+
+  ## function for general equality constraints
+  if (f_equc_pstruct)
+    if (pnonscalar)
+      f_genecstr = @ (p, varargin) \
+	  f_genecstr (cell2struct \
+		      (cellfun (@ reshape, mat2cell (p, ppartidx), \
+				pdims, "UniformOutput", false), \
+		       pord, 1), varargin{:});
+    else
+      f_genecstr = @ (p, varargin) \
+	  f_genecstr \
+	  (cell2struct (num2cell (p), pord, 1), varargin{:});
+    endif
+  endif
+
+  ## note this stage
+  possibly_pstruct_f_genecstr = f_genecstr;
+
+  ## jacobian of general equality constraints
+  if (df_equc_pstruct)
+    if (pnonscalar)
+      df_genecstr = @ (p, func, idx, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (df_genecstr \
+		(cell2struct \
+		 (cellfun (@ reshape, mat2cell (p, ppartidx), \
+			   pdims, "UniformOutput", false), pord, 1), \
+		 func, idx, hook), \
+		pord){:});
+    else
+      df_genecstr = @ (p, func, idx, hook) \
+	  cat (2, \
+	       fields2cell \
+	       (df_genecstr (cell2struct (num2cell (p), pord, 1), \
+			     func, idx, hook), \
+		pord){:});
+    endif
+  endif
+
+  ## linear inequality constraints
+  if (mc_struct)
+    idx = isfield (mc, pord);
+    if (rows (fieldnames (mc)) > sum (idx))
+      error ("unknown fields in structure of linear inequality constraints");
+    endif
+    smc = mc;
+    mc = zeros (np, rows (vc));
+    mc(idx(prepidx), :) = cat (1, fields2cell (smc, pord(idx)){:});
+  endif
+
+  ## linear equality constraints
+  if (emc_struct)
+    idx = isfield (emc, pord);
+    if (rows (fieldnames (emc)) > sum (idx))
+      error ("unknown fields in structure of linear equality constraints");
+    endif
+    semc = emc;
+    emc = zeros (np, rows (evc));
+    emc(idx(prepidx), :) = cat (1, fields2cell (semc, pord(idx)){:});
+  endif
+
+  ## parameter-related configuration for jacobian functions
+  if (dfdp_pstruct || df_inequc_pstruct || df_equc_pstruct)
+    if(pnonscalar)
+      s_diffp = cell2struct \
+	  (cellfun (@ reshape, mat2cell (diffp, ppartidx), \
+		    pdims, "UniformOutput", false), pord, 1);
+      s_diff_onesided = cell2struct \
+	  (cellfun (@ reshape, mat2cell (diff_onesided, ppartidx), \
+		    pdims, "UniformOutput", false), pord, 1);
+      s_orig_lbound = cell2struct \
+	  (cellfun (@ reshape, mat2cell (lbound, ppartidx), \
+		    pdims, "UniformOutput", false), pord, 1);
+      s_orig_ubound = cell2struct \
+	  (cellfun (@ reshape, mat2cell (ubound, ppartidx), \
+		    pdims, "UniformOutput", false), pord, 1);
+      s_plabels = cell2struct \
+	  (num2cell \
+	   (cat (2, cellfun \
+		 (@ (x) cellfun \
+		  (@ reshape, mat2cell (cat (1, x{:}), ppartidx), \
+		   pdims, "UniformOutput", false), \
+		  num2cell (plabels, 1), "UniformOutput", false){:}), \
+	    2), \
+	   pord, 1);
+      s_orig_fixed = cell2struct \
+	  (cellfun (@ reshape, mat2cell (fixed, ppartidx), \
+		    pdims, "UniformOutput", false), pord, 1);
+    else
+      s_diffp = cell2struct (num2cell (diffp), pord, 1);
+      s_diff_onesided = cell2struct (num2cell (diff_onesided), pord, 1);
+      s_orig_lbound = cell2struct (num2cell (lbound), pord, 1);
+      s_orig_ubound = cell2struct (num2cell (ubound), pord, 1);
+      s_plabels = cell2struct (num2cell (plabels, 2), pord, 1);
+      s_orig_fixed = cell2struct (num2cell (fixed), pord, 1);
+    endif
+  endif
+
+  #### some further values and checks
+
+  if (any (fixed & (pin < lbound | pin > ubound)))
+    warning ("some fixed parameters outside bounds");
+  endif
+
+  ## dimensions of linear constraints
+  if (isempty (mc))
+    mc = zeros (np, 0);
+    vc = zeros (0, 1);
+  endif
+  if (isempty (emc))
+    emc = zeros (np, 0);
+    evc = zeros (0, 1);
+  endif
+  [rm, cm] = size (mc);
+  [rv, cv] = size (vc);
+  if (rm != np || cm != rv || cv != 1)
+    error ("linear inequality constraints: wrong dimensions");
+  endif
+  [erm, ecm] = size (emc);
+  [erv, ecv] = size (evc);
+  if (erm != np || ecm != erv || ecv != 1)
+    error ("linear equality constraints: wrong dimensions");
+  endif
+
+  ## check weights dimensions
+  weights = optimget (settings, "weights", ones (size (f_pin)));
+  if (any (size (weights) != size (f_pin)))
+    error ("dimension of weights and residuals must match");
+  endif
+
+  ## note initial values of linear constraits
+  pin_cstr.inequ.lin_except_bounds = mc.' * pin + vc;
+  pin_cstr.equ.lin = emc.' * pin + evc;
+
+  ## note number and initial values of general constraints
+  if (isempty (f_genicstr))
+    pin_cstr.inequ.gen = [];
+    n_genicstr = 0;
+  else
+    n_genicstr = length (pin_cstr.inequ.gen = f_genicstr (pin));
+  endif
+  if (isempty (f_genecstr))
+    pin_cstr.equ.gen = [];
+    n_genecstr = 0;
+  else
+    n_genecstr = length (pin_cstr.equ.gen = f_genecstr (pin));
+  endif
+
+  #### collect remaining settings
+  hook.TolFun = optimget (settings, "TolFun", stol_default);
+  hook.MaxIter = optimget (settings, "MaxIter");
+  if (ischar (hook.cpiv = optimget (settings, "cpiv", @ cpiv_bard)))
+    hook.cpiv = str2func (hook.cpiv);
+  endif
+  hook.Display = optimget (settings, "Display", "off");
+  hook.plot_cmd = optimget (settings, "plot_cmd", @ (f) 0);
+  hook.testing = optimget (settings, "debug", false);
+  hook.new_s = optimget (settings, "lm_svd_feasible_alt_s", false);
+  backend = optimget (settings, "Algorithm", "lm_svd_feasible");
+  backend = map_matlab_algorithm_names (backend);
+  backend = map_backend (backend);
+
+  #### handle fixing of parameters
+  orig_lbound = lbound;
+  orig_ubound = ubound;
+  orig_fixed = fixed;
+  if (all (fixed))
+    error ("no free parameters");
+  endif
+
+  nonfixed = ! fixed;
+  if (any (fixed))
+    ## backend (returned values and initial parameters)
+    backend = @ (f, pin, hook) \
+	backend_wrapper (backend, fixed, f, pin, hook);
+
+    ## model function
+    f = @ (p, varargin) f (assign (pin, nonfixed, p), varargin{:});
+
+    ## jacobian of model function
+    dfdp = @ (p, hook) \
+	dfdp (assign (pin, nonfixed, p), hook)(:, nonfixed);
+    
+    ## function for general inequality constraints
+    f_genicstr = @ (p, varargin) \
+	f_genicstr (assign (pin, nonfixed, p), varargin{:});
+    
+    ## jacobian of general inequality constraints
+    df_gencstr = @ (p, func, idx, hook) \
+	df_gencstr (assign (pin, nonfixed, p), func, idx, hook) \
+	(:, nonfixed);
+
+    ## function for general equality constraints
+    f_genecstr = @ (p, varargin) \
+	f_genecstr (assign (pin, nonfixed, p), varargin{:});
+
+    ## jacobian of general equality constraints
+    df_genecstr = @ (p, func, idx, hook) \
+	df_genecstr (assign (pin, nonfixed, p), func, idx, hook) \
+	(:, nonfixed);
+
+    ## linear inequality constraints
+    vc += mc(fixed, :).' * (tp = pin(fixed));
+    mc = mc(nonfixed, :);
+
+    ## linear equality constraints
+    evc += emc(fixed, :).' * tp;
+    emc = emc(nonfixed, :);
+
+    ## _last_ of all, vectors of parameter-related configuration,
+    ## including "fixed" itself
+    lbound = lbound(nonfixed, :);
+    ubound = ubound(nonfixed, :);
+    max_fract_change = max_fract_change(nonfixed);
+    fract_prec = fract_prec(nonfixed);
+    fixed = fixed(nonfixed);
+  endif
+
+  #### supplement constants to jacobian functions
+
+  ## jacobian of model function
+  if (dfdp_pstruct)
+    dfdp = @ (p, hook) \
+	dfdp (p, cell2fields \
+	      ({s_diffp, s_diff_onesided, s_orig_lbound, \
+		s_orig_ubound, s_plabels, \
+		cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+			    1, s_orig_fixed), cstep}, \
+	       {"diffp", "diff_onesided", "lbound", "ubound", \
+		"plabels", "fixed", "h"}, \
+	       2, hook));
+  else
+    dfdp = @ (p, hook) \
+	dfdp (p, cell2fields \
+	      ({diffp, diff_onesided, orig_lbound, orig_ubound, \
+		plabels, assign(orig_fixed, nonfixed, hook.fixed), \
+		cstep}, \
+	       {"diffp", "diff_onesided", "lbound", "ubound", \
+		"plabels", "fixed", "h"}, \
+	       2, hook));
+  endif
+
+  ## jacobian of general inequality constraints
+  if (df_inequc_pstruct)
+    df_gencstr = @ (p, func, idx, hook) \
+	df_gencstr (p, func, idx, cell2fields \
+		    ({s_diffp, s_diff_onesided, s_orig_lbound, \
+		      s_orig_ubound, s_plabels, \
+		      cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+				  1, s_orig_fixed), cstep}, \
+		     {"diffp", "diff_onesided", "lbound", "ubound", \
+		      "plabels", "fixed", "h"}, \
+		     2, hook));
+  else
+    df_gencstr = @ (p, func, idx, hook) \
+	df_gencstr (p, func, idx, cell2fields \
+		    ({diffp, diff_onesided, orig_lbound, \
+		      orig_ubound, plabels, \
+		      assign(orig_fixed, nonfixed, hook.fixed), cstep}, \
+		     {"diffp", "diff_onesided", "lbound", "ubound", \
+		      "plabels", "fixed", "h"}, \
+		     2, hook));
+  endif
+
+  ## jacobian of general equality constraints
+  if (df_equc_pstruct)
+    df_genecstr = @ (p, func, idx, hook) \
+	df_genecstr (p, func, idx, cell2fields \
+		     ({s_diffp, s_diff_onesided, s_orig_lbound, \
+		       s_orig_ubound, s_plabels, \
+		       cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+				   1, s_orig_fixed), cstep}, \
+		      {"diffp", "diff_onesided", "lbound", "ubound", \
+		       "plabels", "fixed", "h"}, \
+		      2, hook));
+  else
+    df_genecstr = @ (p, func, idx, hook) \
+	df_genecstr (p, func, idx, cell2fields \
+		     ({diffp, diff_onesided, orig_lbound, \
+		       orig_ubound, plabels, \
+		       assign(orig_fixed, nonfixed, hook.fixed), cstep}, \
+		      {"diffp", "diff_onesided", "lbound", "ubound", \
+		       "plabels", "fixed", "h"}, \
+		      2, hook));
+  endif
+
+  #### interfaces to constraints
+  
+  ## include bounds into linear inequality constraints
+  tp = eye (sum (nonfixed));
+  lidx = lbound != - Inf;
+  uidx = ubound != Inf;
+  mc = cat (2, tp(:, lidx), - tp(:, uidx), mc);
+  vc = cat (1, - lbound(lidx, 1), ubound(uidx, 1), vc);
+
+  ## concatenate linear inequality and equality constraints
+  mc = cat (2, mc, emc);
+  vc = cat (1, vc, evc);
+  n_lincstr = rows (vc);
+
+  ## concatenate general inequality and equality constraints
+  if (n_genecstr > 0)
+    if (n_genicstr > 0)
+      nidxi = 1 : n_genicstr;
+      nidxe = n_genicstr + 1 : n_genicstr + n_genecstr;
+      f_gencstr = @ (p, idx, varargin) \
+	  cat (1, \
+	       f_genicstr (p, idx(nidxi), varargin{:}), \
+	       f_genecstr (p, idx(nidxe), varargin{:}));
+      df_gencstr = @ (p, idx, hook) \
+	  cat (1, \
+	       df_gencstr (p, @ (p, varargin) \
+			   possibly_pstruct_f_genicstr \
+			   (p, idx(nidxi), varargin{:}), \
+			   idx(nidxi), \
+			   setfield (hook, "f", \
+				     hook.f(nidxi(idx(nidxi))))), \
+	       df_genecstr (p, @ (p, varargin) \
+			    possibly_pstruct_f_genecstr \
+			    (p, idx(nidxe), varargin{:}), \
+			    idx(nidxe), \
+			    setfield (hook, "f", \
+				      hook.f(nidxe(idx(nidxe))))));
+    else
+      f_gencstr = f_genecstr;
+      df_gencstr = @ (p, idx, hook) \
+	  df_genecstr (p, \
+		       @ (p, varargin) \
+		       possibly_pstruct_f_genecstr \
+		       (p, idx, varargin{:}), \
+		       idx, \
+		       setfield (hook, "f", hook.f(idx)));
+    endif
+  else
+    f_gencstr = f_genicstr;
+    df_gencstr = @ (p, idx, hook) \
+	df_gencstr (p, \
+		    @ (p, varargin) \
+		    possibly_pstruct_f_genicstr (p, idx, varargin{:}), \
+		    idx, \
+		    setfield (hook, "f", hook.f(idx)));
+  endif    
+  n_gencstr = n_genicstr + n_genecstr;
+
+  ## concatenate linear and general constraints, defining the final
+  ## function interfaces
+  if (n_gencstr > 0)
+    nidxl = 1:n_lincstr;
+    nidxh = n_lincstr + 1 : n_lincstr + n_gencstr;
+    f_cstr = @ (p, idx, varargin) \
+	cat (1, \
+	     mc(:, idx(nidxl)).' * p + vc(idx(nidxl), 1), \
+	     f_gencstr (p, idx(nidxh), varargin{:}));
+    df_cstr = @ (p, idx, hook) \
+	cat (1, \
+	     mc(:, idx(nidxl)).', \
+	     df_gencstr (p, idx(nidxh), \
+			 setfield (hook, "f", \
+				   hook.f(nidxh))));
+  else
+    f_cstr = @ (p, idx, varargin) mc(:, idx).' * p + vc(idx, 1);
+    df_cstr = @ (p, idx, hook) mc(:, idx).';
+  endif
+
+  ## define eq_idx (logical index of equality constraints within all
+  ## concatenated constraints
+  eq_idx = false (n_lincstr + n_gencstr, 1);
+  eq_idx(n_lincstr + 1 - rows (evc) : n_lincstr) = true;
+  n_cstr = n_lincstr + n_gencstr;
+  eq_idx(n_cstr + 1 - n_genecstr : n_cstr) = true;
+
+  #### prepare interface hook
+
+  ## passed constraints
+  hook.mc = mc;
+  hook.vc = vc;
+  hook.f_cstr = f_cstr;
+  hook.df_cstr = df_cstr;
+  hook.n_gencstr = n_gencstr;
+  hook.eq_idx = eq_idx;
+  hook.lbound = lbound;
+  hook.ubound = ubound;
+
+  ## passed values of constraints for initial parameters
+  hook.pin_cstr = pin_cstr;
+
+  ## passed function for derivative of model function
+  hook.dfdp = dfdp;
+
+  ## passed function for complementary pivoting
+  ## hook.cpiv = cpiv; # set before
+
+  ## passed value of residual function for initial parameters
+  hook.f_pin = f_pin;
+
+  ## passed options
+  hook.max_fract_change = max_fract_change;
+  hook.fract_prec = fract_prec;
+  ## hook.TolFun = ; # set before
+  ## hook.MaxIter = ; # set before
+  hook.weights = weights;
+  hook.fixed = fixed;
+
+  #### call backend
+
+  [p, resid, cvg, outp] = backend (f, pin, hook);
+
+  if (pin_struct)
+    if (pnonscalar)
+      p = cell2struct \
+	  (cellfun (@ reshape, mat2cell (p, ppartidx), \
+		    pdims, "UniformOutput", false), \
+	   pord, 1);
+    else
+      p = cell2struct (num2cell (p), pord, 1);
+    endif
+  endif
+
+endfunction
+
+function backend = map_matlab_algorithm_names (backend)
+
+  switch (backend)
+    case "levenberg-marquardt"
+      backend = "lm_svd_feasible";
+      warning ("algorithm 'levenberg-marquardt' mapped to 'lm_svd_feasible'");
+  endswitch
+
+endfunction
+
+function backend = map_backend (backend)
+
+  switch (backend)
+    case "lm_svd_feasible"
+      backend = "__lm_svd__";
+    otherwise
+      error ("no backend implemented for algorithm '%s'", backend);
+  endswitch
+
+  backend = str2func (backend);
+
+endfunction
+
+function [p, resid, cvg, outp] = backend_wrapper (backend, fixed, f, p, hook)
+
+  [tp, resid, cvg, outp] = backend (f, p(! fixed), hook);
+
+  p(! fixed) = tp;
+
+endfunction
+
+function lval = assign (lval, lidx, rval)
+
+  lval(lidx) = rval;
+
+endfunction
+
+function ret = __optimget__ (s, name, default)
+
+  if (isfield (s, name))
+    ret = s.(name);
+  elseif (nargin > 2)
+    ret = default;
+  else
+    ret = [];
+  endif
+
+endfunction
+
+function ret = apply_idx_if_given  (ret, varargin)
+
+  if (nargin > 1)
+    ret = ret(varargin{1});
+  endif
+
+endfunction