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 Han-Wen Nienhuys <hanwen@xs4all.nl>
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 indicies "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 vector<Constrained_break_node> &st = state_[start];
78 vsize rank = breaks_.size () - start_col;
79 vsize max_index = brk - start_col;
80 for (vsize j=sys; j < max_index; j++)
82 if (0 == sys && j > 0)
83 break; /* the first line cannot have its first break after the beginning */
85 Line_details const &cur = lines_[(j + start_col)*lines_rank_ + brk];
91 prev_f = st[(sys-1) * rank + j].details_.force_;
92 prev_dem = st[(sys-1) * rank + j].demerits_;
97 Real dem = combine_demerits (cur.force_, prev_f) + prev_dem + cur.break_penalty_;
101 int k = sys*rank + max_index;
102 if (isinf (st[k].demerits_) || dem < st[k].demerits_)
104 found_something = true;
105 st[k].demerits_ = dem;
106 st[k].details_ = cur;
110 return found_something;
113 vector<Column_x_positions>
114 Constrained_breaking::solve ()
118 programming_error (_f ("no system number set in constrained-breaking"));
119 systems_ = breaks_.size () / 4;
123 return get_solution(0, VPOS, systems_);
127 Constrained_breaking::space_line (vsize i, vsize j)
129 bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
130 bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
131 Column_x_positions col;
133 vector<Grob*> line (all_.begin () + breaks_[i],
134 all_.begin() + breaks_[j] + 1);
135 Interval line_dims = line_dimensions_int (pscore_->layout (), i);
136 bool last = j == breaks_.size () - 1;
137 bool ragged = ragged_right || (last && ragged_last);
139 return get_line_configuration (line, line_dims[RIGHT] - line_dims[LEFT], line_dims[LEFT], ragged);
143 Constrained_breaking::resize (vsize systems)
147 if (!breaks_.size () && pscore_)
149 Output_def *l = pscore_->layout ();
150 Real extent = scm_to_double (l->c_variable ("system-height"));
151 Real padding = scm_to_double (l->c_variable ("between-system-padding"));
152 Real space = scm_to_double (l->c_variable ("between-system-space"));
153 bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
154 bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
156 Interval first_line = line_dimensions_int (pscore_->layout (), 0);
157 Interval other_lines = line_dimensions_int (pscore_->layout (), 1);
158 /* do all the rod/spring problems */
159 breaks_ = pscore_->find_break_indices ();
160 lines_rank_ = breaks_.size ();
161 all_ = pscore_->root_system ()->columns ();
162 lines_.resize (breaks_.size () * breaks_.size ());
163 vector<Real> forces = get_line_forces (all_,
165 other_lines.length (),
166 other_lines.length () - first_line.length (),
168 for (vsize i = 0; i < breaks_.size () - 1; i++)
170 for (vsize j = i + 1; j < breaks_.size (); j++)
172 bool last = j == breaks_.size () - 1;
173 bool ragged = ragged_right || (last && ragged_last);
174 int k = i*lines_rank_ + j;
175 SCM pen = all_[breaks_[j]]->get_property ("penalty");
176 if (scm_is_number (pen))
177 lines_[k].break_penalty_ = scm_to_double (pen);
179 lines_[k].force_ = forces[k];
180 lines_[k].extent_ = extent;
181 lines_[k].padding_ = padding;
182 lines_[k].space_ = space;
183 lines_[k].inverse_hooke_ = 3; // FIXME: somewhat arbitrary
184 if (ragged && lines_[k].force_ < 0)
185 lines_[k].force_ = infinity_f;
186 if (isinf (lines_[k].force_))
191 /* work out all the starting indices */
192 for (vsize i = 0; i < start_.size (); i++)
195 for (j = 0; j < breaks_.size () - 1 && breaks_[j] < start_[i]; j++)
197 starting_breakpoints_.push_back (j);
198 start_[i] = breaks_[j];
200 state_.resize (start_.size ());
203 if (pscore_ && systems_ > valid_systems_)
205 for (vsize i = 0; i < state_.size (); i++)
206 state_[i].resize((breaks_.size () - starting_breakpoints_[i]) * systems_);
208 /* fill out the matrices */
209 for (vsize i = 0; i < state_.size (); i++)
210 for (vsize j = valid_systems_; j < systems_; j++)
211 for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
212 if (!calc_subproblem (i, j, k))
213 break; /* if we couldn't break this, it is too cramped already */
214 valid_systems_ = systems_;
218 vector<Column_x_positions>
219 Constrained_breaking::get_solution (vsize start, vsize end, vsize sys_count)
223 vsize start_brk = starting_breakpoints_[start];
224 prepare_solution (start, end, sys_count, &rank, &end_brk);
226 vector<Constrained_break_node> const &st = state_[start];
227 vector<Column_x_positions> ret;
229 /* find the first solution that satisfies constraints */
230 for (vsize sys = sys_count-1; sys != VPOS; sys--)
232 for (vsize brk = end_brk; brk != VPOS; brk--)
234 if (!isinf (st[sys*rank + brk].details_.force_))
238 warning ( _("couldn't find line breaking that satisfies constraints" ));
239 ret.push_back (space_line (brk, end_brk));
241 /* build up the good solution */
242 for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
244 vsize prev_brk = st[cur_sys*rank + brk].prev_;
245 assert (brk != VPOS);
246 ret.push_back (space_line (prev_brk + start_brk, brk + start_brk));
254 /* if we get to here, just put everything on one line */
255 warning ( _("couldn't find line breaking that satisfies constraints" ));
256 ret.push_back (space_line (0, end_brk));
260 std::vector<Line_details>
261 Constrained_breaking::get_details (vsize start, vsize end, vsize sys_count)
265 prepare_solution (start, end, sys_count, &rank, &brk);
266 vector<Constrained_break_node> const &st = state_[start];
267 vector<Line_details> ret;
269 for (int sys = sys_count-1; sys >= 0 && brk != VPOS; sys--)
271 ret.push_back (st[sys*rank + brk].details_);
272 brk = st[sys*rank + brk].prev_;
278 Constrained_breaking::get_min_systems (vsize start, vsize end)
284 prepare_solution (start, end, 1, &rank, &brk);
285 vector<Constrained_break_node> const &st = state_[start];
287 /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
288 for (sys_count = 0; sys_count < rank; sys_count++)
290 if (sys_count >= valid_systems_)
292 resize (sys_count + 3);
294 if (!isinf (st[sys_count*rank + brk].details_.force_))
295 return sys_count + 1;
297 /* no possible breaks satisfy constraints */
302 Constrained_breaking::get_max_systems (vsize start, vsize end)
304 vsize brk = (end >= start_.size ()) ? breaks_.size () - 1 : starting_breakpoints_[end];
305 return brk - starting_breakpoints_[start];
309 Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count, vsize *rank, vsize *brk)
311 assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
312 assert (start < end);
315 if (end == start_.size ())
318 *rank = breaks_.size () - starting_breakpoints_[start];
319 *brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
320 *brk -= starting_breakpoints_[start];
323 Constrained_breaking::Constrained_breaking ()
325 valid_systems_ = systems_ = 0;
326 start_.push_back (0);
329 Constrained_breaking::Constrained_breaking (vector<vsize> const &start)
332 valid_systems_ = systems_ = 0;
336 Constrained_breaking::combine_demerits (Real force, Real prev_force)
338 return force * force + fabs (prev_force - force);