2 constrained-breaking.cc -- implement a line breaker that
3 support limits on the number of systems
5 source file of the GNU LilyPond music typesetter
7 (c) 2006--2007 Joe Neeman <joeneeman@gmail.com>
10 #include "constrained-breaking.hh"
12 #include "international.hh"
14 #include "output-def.hh"
15 #include "paper-column.hh"
16 #include "paper-score.hh"
17 #include "simple-spacer.hh"
22 We use the following optimal substructure. Let W(A) be our weight function.
24 Let A_{k,n} = (a_{k,n,1}, ... a_{k,n,k}) be the optimal set of line breaks
25 for k systems and n potential breakpoints. a_{k,n,k} = n (it is the end of
28 Then A_{k+1, m} is contructed from
29 min_ {k < j < m} ( W(A_{k,j} :: m) )
30 where by A::m we denote appending m to the list A
34 The above algorithm makes it easy to end at a point before the end of the
35 score (just find A_{k,m} for some m < breaks_.size () - 1). However, we must
36 add information for starting at a point after the beginning. One constructor
37 allows the specification of a list of starting columns, start_. We then have
38 start_.size () different solution arrays. state_[i] is the array for the
39 solution starting at column number start_[i].
41 The indices "start" and "end" refer to the index in the start_ array of the
42 desired starting and ending columns.
44 each solution array looks like
45 a_{1,1,1} a_{2,1,2} a_{3,1,3} . . .
46 X a_{2,2,2} a_{3,2,3} . . .
50 where the X's mark invalid solutions (can't have more systems than
51 breakpoints). Note that each value is of the form a_{x,n,x}. This is because
52 a breakpoint of the form a_{x,n,x-1} will also be called a_{x-1,m,x-1} for
53 some m < n. Each cell in the array stores the value of its m (ie. the
54 ending breakpoint of the previous line) as "prev_".
56 For finding A_{sys, brk}, let "me" be the (sys_count,brk) cell in our
57 solution array (state_[start][sys * rank + brk]).
59 Then A_{sys, brk} = A_{sys - 1, me.prev_} :: me
63 start and sys here are indexed from 0.
64 brk is indexed from starting_breakpoints_[start]
65 (for brk, starting_breakpoints_[start] is the beginning
66 of the piece; the smallest value we should ever see here is
67 starting_breakpoints_[start] + 1) */
69 Constrained_breaking::calc_subproblem (vsize start, vsize sys, vsize brk)
71 assert (sys < systems_);
72 assert (start < start_.size ());
73 assert (brk < breaks_.size ());
75 bool found_something = false;
76 vsize start_col = starting_breakpoints_[start];
77 Matrix<Constrained_break_node> &st = state_[start];
78 vsize max_index = brk - start_col;
79 for (vsize j=max_index; j-- > sys;)
81 if (0 == sys && j > 0)
82 continue; /* the first line cannot have its first break after the beginning */
84 Line_details const &cur = lines_.at (brk, j + start_col);
85 if (isinf (cur.force_))
93 prev_f = st.at (j, sys-1).details_.force_;
94 prev_dem = st.at (j, sys-1).demerits_;
99 Real dem = combine_demerits (cur.force_, prev_f) + prev_dem + cur.break_penalty_;
100 Constrained_break_node &n = st.at (max_index, sys);
101 if (dem < n.demerits_)
103 found_something = true;
109 return found_something;
112 vector<Column_x_positions>
113 Constrained_breaking::solve ()
116 return get_best_solution (0, VPOS);
119 return get_solution(0, VPOS, systems_);
123 Constrained_breaking::space_line (vsize i, vsize j)
125 bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
126 bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
127 Column_x_positions col;
129 vector<Grob*> line (all_.begin () + breaks_[i],
130 all_.begin() + breaks_[j] + 1);
131 Interval line_dims = line_dimensions_int (pscore_->layout (), i);
132 bool last = j == breaks_.size () - 1;
133 bool ragged = ragged_right || (last && ragged_last);
135 return get_line_configuration (line, line_dims[RIGHT] - line_dims[LEFT], line_dims[LEFT], ragged);
139 Constrained_breaking::resize (vsize systems)
143 if (pscore_ && systems_ > valid_systems_)
145 for (vsize i = 0; i < state_.size (); i++)
146 state_[i].resize (breaks_.size () - starting_breakpoints_[i], systems_, Constrained_break_node ());
148 /* fill out the matrices */
149 for (vsize i = 0; i < state_.size (); i++)
150 for (vsize j = valid_systems_; j < systems_; j++)
151 for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
152 if (!calc_subproblem (i, j, k))
153 break; /* if we couldn't break this, it is too cramped already */
154 valid_systems_ = systems_;
158 vector<Column_x_positions>
159 Constrained_breaking::get_solution (vsize start, vsize end, vsize sys_count)
161 vsize start_brk = starting_breakpoints_[start];
162 vsize end_brk = prepare_solution (start, end, sys_count);
164 Matrix<Constrained_break_node> const &st = state_[start];
165 vector<Column_x_positions> ret;
167 /* find the first solution that satisfies constraints */
168 for (vsize sys = sys_count-1; sys != VPOS; sys--)
170 for (vsize brk = end_brk; brk != VPOS; brk--)
172 if (!isinf (st.at (brk, sys).details_.force_))
176 warning (_ ("cannot find line breaking that satisfies constraints" ));
177 ret.push_back (space_line (brk, end_brk));
179 /* build up the good solution */
180 for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
182 vsize prev_brk = st.at (brk, cur_sys).prev_;
183 assert (brk != VPOS);
184 ret.push_back (space_line (prev_brk + start_brk, brk + start_brk));
192 /* if we get to here, just put everything on one line */
193 warning (_ ("cannot find line breaking that satisfies constraints" ));
194 ret.push_back (space_line (0, end_brk));
198 vector<Column_x_positions>
199 Constrained_breaking::get_best_solution (vsize start, vsize end)
201 vsize min_systems = get_min_systems (start, end);
202 vsize max_systems = get_max_systems (start, end);
203 Real best_demerits = infinity_f;
204 vector<Column_x_positions> best_so_far;
206 for (vsize i = min_systems; i <= max_systems; i++)
208 vsize brk = prepare_solution (start, end, i);
209 Real dem = state_[start].at (brk, i-1).demerits_;
211 if (dem < best_demerits)
214 best_so_far = get_solution (start, end, i);
218 vector<Column_x_positions> cur = get_solution (start, end, i);
219 bool too_many_lines = true;
221 for (vsize j = 0; j < cur.size (); j++)
222 if (cur[j].force_ < 0)
224 too_many_lines = false;
231 if (best_so_far.size ())
233 return get_solution (start, end, max_systems);
236 std::vector<Line_details>
237 Constrained_breaking::get_details (vsize start, vsize end, vsize sys_count)
239 vsize brk = prepare_solution (start, end, sys_count);
240 Matrix<Constrained_break_node> const &st = state_[start];
241 vector<Line_details> ret;
243 for (int sys = sys_count-1; sys >= 0 && brk != VPOS; sys--)
245 ret.push_back (st.at (brk, sys).details_);
246 brk = st.at (brk, sys).prev_;
253 Constrained_breaking::get_min_systems (vsize start, vsize end)
256 vsize brk = prepare_solution (start, end, 1);
257 vsize rank = breaks_.size () - starting_breakpoints_[start];
258 Matrix<Constrained_break_node> const &st = state_[start];
260 /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
261 for (sys_count = 0; sys_count < rank; sys_count++)
263 if (sys_count >= valid_systems_)
265 resize (sys_count + 3);
267 if (!isinf (st.at (brk, sys_count).details_.force_))
268 return sys_count + 1;
270 /* no possible breaks satisfy constraints */
275 Constrained_breaking::get_max_systems (vsize start, vsize end)
277 vsize brk = (end >= start_.size ()) ? breaks_.size () - 1 : starting_breakpoints_[end];
278 return brk - starting_breakpoints_[start];
282 Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count)
284 assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
285 assert (start < end);
288 if (end == start_.size ())
292 brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
293 brk -= starting_breakpoints_[start];
297 Constrained_breaking::Constrained_breaking (Paper_score *ps)
299 valid_systems_ = systems_ = 0;
300 start_.push_back (0);
305 Constrained_breaking::Constrained_breaking (Paper_score *ps, vector<vsize> const &start)
308 valid_systems_ = systems_ = 0;
313 /* find the forces for all possible lines and cache ragged_ and ragged_right_ */
315 Constrained_breaking::initialize ()
320 ragged_right_ = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
321 ragged_last_ = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
323 Output_def *l = pscore_->layout ();
324 System *sys = pscore_->root_system ();
325 Real space = robust_scm2double (l->c_variable ("ideal-system-space"), 0);
326 SCM padding_scm = l->c_variable ("page-breaking-between-system-padding");
327 if (!scm_is_number (padding_scm))
328 padding_scm = l->c_variable ("between-system-padding");
329 Real padding = robust_scm2double (padding_scm, 0.0);
331 Interval first_line = line_dimensions_int (pscore_->layout (), 0);
332 Interval other_lines = line_dimensions_int (pscore_->layout (), 1);
333 /* do all the rod/spring problems */
334 breaks_ = pscore_->find_break_indices ();
335 all_ = pscore_->root_system ()->used_columns ();
336 lines_.resize (breaks_.size (), breaks_.size (), Line_details ());
337 vector<Real> forces = get_line_forces (all_,
338 other_lines.length (),
339 other_lines.length () - first_line.length (),
341 for (vsize i = 0; i + 1 < breaks_.size (); i++)
344 for (vsize j = i + 1; j < breaks_.size (); j++)
346 int start = Paper_column::get_rank (all_[breaks_[i]]);
347 int end = Paper_column::get_rank (all_[breaks_[j]]);
348 Interval extent = sys->pure_height (sys, start, end);
349 bool last = j == breaks_.size () - 1;
350 bool ragged = ragged_right_ || (last && ragged_last_);
351 Line_details &line = lines_.at (j, i);
353 line.force_ = forces[i*breaks_.size () + j];
354 if (ragged && last && !isinf (line.force_))
356 if (isinf (line.force_))
359 Grob *c = all_[breaks_[j]];
360 line.break_penalty_ = robust_scm2double (c->get_property ("line-break-penalty"), 0);
361 line.page_penalty_ = robust_scm2double (c->get_property ("page-break-penalty"), 0);
362 line.turn_penalty_ = robust_scm2double (c->get_property ("page-turn-penalty"), 0);
363 line.break_permission_ = c->get_property ("line-break-permission");
364 line.page_permission_ = c->get_property ("page-break-permission");
365 line.turn_permission_ = c->get_property ("page-turn-permission");
367 max_ext = max (max_ext, extent.length ());
368 line.extent_ = extent;
369 line.padding_ = padding;
371 line.inverse_hooke_ = extent.length () + space;
375 /* work out all the starting indices */
376 for (vsize i = 0; i < start_.size (); i++)
379 for (j = 0; j + 1 < breaks_.size () && breaks_[j] < start_[i]; j++)
381 starting_breakpoints_.push_back (j);
382 start_[i] = breaks_[j];
384 state_.resize (start_.size ());
388 Constrained_breaking::combine_demerits (Real force, Real prev_force)
391 return force * force;
393 return force * force + (prev_force - force) * (prev_force - force);