Discrete.m 83.2 KB
Newer Older
1
classdef  (InferiorClasses = {?quantity.Symbolic}) Discrete < handle & matlab.mixin.Copyable & matlab.mixin.CustomDisplay
2

3
4
5
6
7
8
9
10
11
12
	properties (SetAccess = protected)
		% Discrete evaluation of the continuous quantity
		valueDiscrete double;
	end
	
	properties (Hidden, Access = protected, Dependent)
		doNotCopy;
	end
	
	properties
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
		% ID of the figure handle in which the handle is plotted
		figureID double = 1;
		
		% Name of this object
		name char;
		
		% domain
		domain;
	end
	
	properties ( Dependent )
		
		% Name of the domains that generate the grid.
		gridName {mustBe.unique};
		
28
29
30
31
32
33
34
		% Grid for the evaluation of the continuous quantity. For the
		% example with the function f(x,t), the grid would be
		%   {[<spatial domain>], [<temporal domain>]}
		% whereas <spatial domain> is the discret description of the
		% spatial domain and <temporal domain> the discrete description of
		% the temporal domain.
		grid; % in set.grid it is ensured that, grid is a (1,:)-cell-array
35
36
37
38
39
40
41
	end
	
	methods
		%--------------------
		% --- Constructor ---
		%--------------------
		function obj = Discrete(valueOriginal, varargin)
42
43
44
45
			% DISCRETE a quantity, represented by discrete values.
			%	obj = Discrete(valueOriginal, varargin) initializes a
			%	quantity. The parameters to be set are:
			% 'valueOrigin' must be
46
47
48
			% 1) a cell-array of double arrays with
			%	size(valueOriginal) == size(obj) and
			%	size(valueOriginal{it}) == gridSize
49
50
51
52
53
			%	Example: valueOrigin = { f(Z, T), g(Z, T) } is a cell array
			%	wich contains the functions f(z,t) and g(z,t) evaluated on
			%	the discrete domain (Z x T). Then, the name-value-pair
			%	parameter 'domain' must be set with quantity.Domain
			%	objects, according to the domains Z and T.
54
55
			% OR
			% 2) adouble-array with
56
			%	size(valueOriginal) == [gridSize, size(quantity)]
57
58
59
60
61
			% Furthermore, 'gridName' must be part of the name-value-pairs
			% in varargin. Additional parameters can be specified using
			% name-value-pair-syntax in varargin.
			
			% to allow the initialization as object array, the constructor
62
63
64
65
66
			% must be allowed to be called without arguments, i.e. nargin == 0.
			% Then no parameters are set.
			if nargin == 1
				% if nargin == 1 it can be a conversion of child-classes or an empty
				% object
67
68
69
70
71
				if isa(valueOriginal, 'quantity.Discrete')
					% allows the conversion of a quantity object without
					% extra check if the object is already from class
					% quantity.Discrete
					obj = valueOriginal;
72
				else
73
					% empty object. this is needed for instance, to create
74
					% quantity.Discrete([]), which is useful for creating default
75
76
					% values.
					obj = quantity.Discrete.empty(size(valueOriginal));
77
				end
78
			elseif nargin > 1
79
80
81
				
				%% input parser
				myParser = misc.Parser();
82
83
				myParser.addParameter('name', string(), @isstr);
				myParser.addParameter('figureID', 1, @isnumeric);
84
85
				myParser.parse(varargin{:});
				
86
				%% domain parser
87
				myDomain = quantity.Domain.parser(varargin{:});
88
89
90
91
92
93
94
95
96
97
98
99
100
101
												
				%% get the sizes of obj and grid
				gridLength = myDomain.gridLength;

				% convert double valued valueOriginal to cell-valued value
				% original
				if ~iscell(valueOriginal)
					valueOriginal = quantity.Discrete.value2cell(valueOriginal, gridLength);
				end
				
				% Check if the grid fits to the values. In addition, catch
				% the case if all values are empty. This is required for
				% the initialization of quantity.Function and
				% quantity.Symbolic objects
102
103
				assert( misc.alln( cellfun(@isempty, valueOriginal ) ) || ...
					numGridElements(myDomain) == numel(valueOriginal{1}), ...
104
105
106
					'grids do not fit to valueOriginal');				
				
				% allow initialization of empty objects
107
108
109
110
111
112
				valueOriginalSize = size(valueOriginal);
				if any(valueOriginalSize == 0)
					% If the size is specified in the arguements, it should
					% be chosen instead of the default size from the
					% valueOriginal.
					myParser = misc.Parser();
113
					myParser.addParameter('size', valueOriginalSize((1+ndims(myDomain)):end));
114
115
116
117
118
					myParser.parse(varargin{:});
					obj = quantity.Discrete.empty(myParser.Results.size);
					return;
				end
				
119
120
121
				% set valueDiscrete
				for k = 1:numel(valueOriginal)
					if numel(myDomain) == 1
122
123
124
						% for quantities on a single domain, ensure that
						% the discrete values are stored as column-vector
						% by using the (:) operator.
125
						obj(k).valueDiscrete = valueOriginal{k}(:); %#ok<AGROW>
126
					else
127
						obj(k).valueDiscrete = valueOriginal{k}; %#ok<AGROW>
128
129
130
131
					end
				end
				
				%% set further properties
132
				[obj.domain] = deal(myDomain);
133
134
135
136
				[obj.name] = deal(myParser.Results.name);
				[obj.figureID] = deal(myParser.Results.figureID);
				
				%% reshape object from vector to matrix
137
				obj = reshape(obj, size(valueOriginal));
138
139
			end
		end% Discrete() constructor
140
		
141
142
		%---------------------------
		% --- getter and setters ---
143
144
		%---------------------------
		function gridName = get.gridName(obj)
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
145
146
147
148
149
			if isempty(obj.domain)
				gridName = {};
			else
				gridName = {obj.domain.name};
			end
150
151
152
		end
		
		function grid = get.grid(obj)
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
153
154
155
156
157
			if isempty(obj.domain)
				grid = {};
			else
				grid = {obj.domain.grid};
			end
158
159
		end
		
Jakob Gabriel's avatar
Jakob Gabriel committed
160
		function itIs = isConstant(obj)
Ferdinand Fischer's avatar
Ferdinand Fischer committed
161
			% the quantity is interpreted as constant if it has no grid or
162
			% it has a grid that is only defined at one point.
163
			itIs = isempty(obj(1).domain);
164
165
		end % isConstant()
		
166
167
168
169
		function doNotCopy = get.doNotCopy(obj)
			doNotCopy = obj.doNotCopyPropertiesName();
		end
		function valueDiscrete = get.valueDiscrete(obj)
170
171
			% check if the value discrete for this object
			% has already been computed.
172
			empty = isempty(obj.valueDiscrete);
173
			if any(empty(:))
174
				obj.valueDiscrete = obj.obj2value(obj.domain, true);
175
176
177
178
			end
			valueDiscrete = obj.valueDiscrete;
		end
		
179
180
181
182
183
184
185
186
187
188
189
		%-------------------
		% --- converters ---
		%-------------------
		function exportData = exportData(obj, varargin)
			
			% make the object names:
			if obj.nargin == 1
				headers = cell(1, numel(obj) + 1);
				headers{1} = obj(1).gridName{1};
				for i= 1:numel(obj) %TODO use easier to read headers
					headers{i+1} = [obj(i).name '' num2str(i)];
190
				end
191
192
193
194
195
196
197
198
199
				exportData = export.dd(...
					'M', [obj.grid{:}, obj.valueDiscrete], ...
					'header', headers, varargin{:});
			elseif obj.nargin == 2
				error('Not yet implemented')
			else
				error('Not yet implemented')
			end
		end
200
201
202
		function d = double(obj)
			d = obj.on();
		end
203
204
		function o = quantity.Function(obj)
			props = nameValuePair( obj(1) );
205
			
206
207
208
209
210
			for k = 1:numel(obj)
				F = griddedInterpolant(obj(k).grid{:}', obj(k).on());
				o(k) = quantity.Function(@(varargin) F(varargin{:}), ...
					props{:});
			end
211
212
			
			o = reshape(o, size(obj));
213
		end
214
		function o = signals.PolynomialOperator(obj)
215
			A = cell(size(obj, 3), 1);
Ferdinand Fischer's avatar
Ferdinand Fischer committed
216
217
218
			for k = 1:size(obj, 3)
				A{k} = obj(:,:,k);
			end
219
			o = signals.PolynomialOperator(A);
Ferdinand Fischer's avatar
Ferdinand Fischer committed
220
221
222
223
224
225
226
227
228
		end
		
		function o = quantity.Symbolic(obj)
			if isempty(obj)
				o = quantity.Symbolic.empty(size(obj));
			else
				error('Not yet implemented')
			end
		end
229
		
230
		function obj = setName(obj, newName)
231
232
233
			% Function to set all names of all elements of the quantity obj to newName.
			[obj.name] = deal(newName);
		end % setName()
234
235
236
	end
	
	methods (Access = public)
237
		function [d, I, d_size] = compositionDomain(obj, domainName)
238
			
239
240
241
			assert(isscalar(obj));
					
			d = obj.on();
242
243
			
			% the evaluation of obj.on( compositionDomain ) is done by:
244
			d_size = size(d);
245
246
			
			% 1) vectorization of the n-d-grid: compositionDomain	
247
			d = d(:);
248
249

			% 2) then it is sorted in ascending order
250
			[d, I] = sort(d);			
251
252
			
			% verify the domain to be monotonical increasing
253
			deltaCOD = diff(d);
254
255
			assert(misc.alln(deltaCOD >= 0), 'The domain for the composition f(g(.)) must be monotonically increasing');

256
			d = quantity.Domain(domainName, d);
257
258
		end
		
259
		function obj_hat = compose(obj, g, optionalArgs)
260
261
262
			% COMPOSE compose two functions
			%	OBJ_hat = compose(obj, G, varargin) composes the function
			%	defined by OBJ with the function given by G. In particular,
263
			%		f_hat(z,t) = f( z, g(z,t) )
264
			%	if f(t) = obj, g is G and f_hat is OBJ_hat.
265
266
267
268
269
270
271
			arguments
				obj
				g quantity.Discrete;
				optionalArgs.domain quantity.Domain = obj(1).domain;
			end
			myCompositionDomain = optionalArgs.domain;
			originalDomain = obj(1).domain;
272
			
273
274
275
276
277
			assert( length( myCompositionDomain ) == 1 );
			[idx, logOfDomain] = originalDomain.gridIndex(myCompositionDomain);
			assert( isequal( originalDomain(idx), myCompositionDomain ), ...
				'Composition of functions: The domains for the composition must be equal. A grid join is not implemented yet.');
			assert( any( logOfDomain )  )
278
			
279
280
281
282
			% 2) get the composition domain:
			%	For the argument y of a function f(y) which should be
			%	composed by y = g(z,t) a new dommain will be created on the
			%	basis of evaluation of g(z,t).
283
			[composeOnDomain, I, domainSize] = ...
284
285
				g.compositionDomain(myCompositionDomain.name);
			
286
287
			% check if the composition domain is in the range of definition
			% of obj.
288
			if ~composeOnDomain.isSubDomainOf( myCompositionDomain )
289
290
				warning('quantity:Discrete:compose', ....
					'The composition domain is not a subset of obj.domain! The missing values will be extrapolated.');
291
			end			
292
293
			
			% 3) evaluation on the new grid:
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
			%	the order of the domains is important. At first, the
			%	domains which will not be replaced are taken. The last
			%	domain must be the composed domain. For example: a function
			%	f(x, y, z, t), where y should be composed with g(z, t) will
			%	be resorted to f_(x, z, t, y) and then evaluated with y =
			%	g(z,t)
			evaluationDomain = [originalDomain( ~logOfDomain ), composeOnDomain ];
			newValues = obj.on( evaluationDomain );
			
			% reshape the new values into a 2-d array so that the first
			% dimension is any domain but the composition domain and the
			% last dimension is the composition domain
			sizeOldDomain = prod( [originalDomain( ~logOfDomain ).n] );
			sizeComposeDomain = composeOnDomain.gridLength;
			newValues = reshape(newValues, [sizeOldDomain, sizeComposeDomain]);
309
310
			
			% 4) reorder the computed values, dependent on the sort
311
312
			% position fo the new domain
			newValues(:,I) = newValues(:,:);
313
314
315
			
			% 5) rearrange the computed values, to have the same dimension
			% as the required domain
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
			% *) consider the domain 
			%		f( z, g(z,t) ) = f(z, g(zeta,t) )|_{zeta = z}
			tmpDomain = [originalDomain( ~logOfDomain ), g(1).domain ];
			% newValues will be reshaped into the form
			%	f(z, t, zeta)
			newValues = reshape( newValues, [tmpDomain.gridLength, 1] );
			% *) now the common domains, i.e., zeta = z must be merged:
			%	for this, find the index of the common domain in list of
			%	temporary combined domain
			
			intersectDomain = intersect( {originalDomain( ~logOfDomain ).name}, ...
				{g(1).domain.name} );
			
			if ~isempty(intersectDomain)
				
				idx = 1:length(tmpDomain);
				idxCommon = idx(strcmp({tmpDomain.name}, intersectDomain));

				% take the diagonal values of the common domain, i.e., z = zeta
				newValues = misc.diagNd( newValues, idxCommon );
			end
337
			
338
			% *) build a new valueDiscrete on the correct grid.		
339
340
341
			obj_hat = quantity.Discrete( newValues, ...
				'name', [obj.name '°' g.name], ...
				'size', size(obj), ...
342
				'domain', tmpDomain.join);
343
344
345
			
		end
		
346
347
348
349
350
351
352
353
354
355
356
357
358
359
		function value = on(obj, myDomain, gridNames)
			% ON evaluation of the quantity on a certain domain.
			%	value = on(obj) or value = obj.on(); evaluates the quantity
			%	on its standard grid. 
			%	value = obj.on( myDomain ) evalutes the quantity on the
			%	grid specified by myDomain. The order of the domains in
			%	domain, will be the same as from myDomain. 
			%	value = obj.on( grid ) evaluates the quantity specified by
			%	grid. Grid must be a cell-array with the grids as elements.
			%	value = obj.on( grid, gridName ) evaluates the quantity
			%	specified by grid. Grid must be a cell-aary with the grids
			%	as elements. By the gridName parameter the order of the
			%	grid can be specified.

360
361
362
			if isempty(obj)
				value = zeros(size(obj));
			else
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
				if nargin == 1
					% case 0: no domain was specified, hence the value is requested
					% on the default grid defined by obj(1).domain.
					value = obj.obj2value(obj(1).domain);
					
				elseif nargin == 2 && (iscell(myDomain) || isnumeric(myDomain))
					% case 1: a domain is specified by myDomain == grid(-cell)
					myDomain = misc.ensureIsCell(myDomain);
					newGrid = myDomain;
					myDomain = quantity.Domain.empty();

					if obj(1).isConstant()
						gridNames = repmat({''}, length(newGrid));
					else
						gridNames = {obj(1).domain.name};
					end

					for k = 1:length(newGrid)
						myDomain(k) = quantity.Domain(gridNames{k}, newGrid{k});
					end
					value = reshape(obj.obj2value(myDomain), ...
						[myDomain.gridLength, size(obj)]);
				else
					% Since in the remaining cases the order of the domains is not 
					% neccessarily equal to the order in obj(1).domain, this is 
					% more involved:
					if nargin == 2
						% case 2: a domain is specified by a myDomain = domain-array
						% nothing has to be done to obtain the domain.

					elseif nargin == 3
						% case 3: a domain is specified by a grid and a grid
						% name. Then, the first input parameter is the grid,
						% i.e., myGrid = myDomain and the second is the grid
						% name.
						% Since the order of the domains is not neccessarily equal to the
						% order in obj(1).domain, this is more involved:
400
						myDomain = misc.ensureIsCell(myDomain);
401
402
403
404
405
406
407
408
409
						gridNames = misc.ensureIsCell(gridNames);

						assert(all(cellfun(@(v)isvector(v), myDomain)), ...
							'The cell entries for a new grid have to be vectors')
						assert(iscell(gridNames), ...
							'The gridNames parameter must be cell array')
						assert(all(cellfun(@ischar, gridNames)), ...
							'The gridNames must be strings')

410
411
412
						newGrid = myDomain;
						myDomain = quantity.Domain.empty();
						for k = 1:length(newGrid)
413
							myDomain(k) = quantity.Domain(gridNames{k}, newGrid{k});
414
						end
415
416
					else
						error('wrong number of input arguments')
417
					end
418

419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
					% verify the domain
					if obj(1).isConstant
						gridPermuteIdx = 1:length(myDomain);
					else
						assert(numel(myDomain) == numel(obj(1).domain), ...
							'Wrong grid for the evaluation of the object');
						% compute the permutation index, in order to bring the
						% new domain in the same order as the original one.
						gridPermuteIdx = obj(1).domain.getPermutationIdx(myDomain);
					end			
					% get the valueDiscrete data for this object. Apply the
					% permuted myDomain. Then the obj2value will be evaluated
					% in the order of the original domain. The permutation to
					% the new order will be done in the next step.
					originalOrderedDomain(gridPermuteIdx) = myDomain;
					value = obj.obj2value(originalOrderedDomain);
					value = permute(reshape(value, [originalOrderedDomain.gridLength, size(obj)]), ...
						[gridPermuteIdx, numel(gridPermuteIdx)+(1:ndims(obj))]);
437
				end
438
439
			end % if isempty(obj)
		end % on()
440
		
441
442
443
444
445
446
		function interpolant = interpolant(obj)
			% get the interpolant of the obj;
			if isempty(obj)
				value = zeros(size(obj));
				indexGrid = arrayfun(@(s)linspace(1,s,s), size(obj), 'UniformOutput', false);
				interpolant = numeric.interpolant(...
447
					[indexGrid{:}], value);
448
			else
449
				myGrid = obj(1).grid;
450
451
452
				value = obj.obj2value();
				indexGrid = arrayfun(@(s)linspace(1,s,s), size(obj), 'UniformOutput', false);
				interpolant = numeric.interpolant(...
453
					[myGrid, indexGrid{:}], value);
454
455
456
457
			end
		end
		
		
Jakob Gabriel's avatar
Jakob Gabriel committed
458
459
460
		function assertSameGrid(a, varargin)
			% check if all elements of a have same grid and gridName. If
			% further quantites are inputs via varargin, it is verified if
461
462
			% that quantity has same grid and gridName as quantity a as
			% well.
Ferdinand Fischer's avatar
Ferdinand Fischer committed
463
			if isempty(a)
464
465
				if nargin > 1
					varargin{1}.assertSameGrid(varargin{2:end});
466
				end
467
				return;
Ferdinand Fischer's avatar
Ferdinand Fischer committed
468
469
470
471
			else
				referenceGridName = a(1).gridName;
				referenceGrid= a(1).grid;
			end
Jakob Gabriel's avatar
Jakob Gabriel committed
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
			for it = 1 : numel(a)
				assert(isequal(referenceGridName, a(it).gridName), ...
					'All elements of a quantity must have same gridNames');
				assert(isequal(referenceGrid, a(it).grid), ...
					'All elements of a quantity must have same grid');
			end
			if nargin > 1
				b = varargin{1};
				for it = 1 : numel(b)
					assert(isequal(referenceGridName, b(it).gridName), ...
						'All elements of a quantity must have same gridNames');
					assert(isequal(referenceGrid, b(it).grid), ...
						'All elements of a quantity must have same grid');
				end
			end
			if nargin > 2
				% if more then 1 quantity is in varargin, they are checked
				% iteratively by calling assertSameGrid() again.
				assertSameGrid(varargin{:});
			end
		end
		
		function [referenceGrid, referenceGridName] = getFinestGrid(a, varargin)
			% find the finest grid of all input quantities by comparing
			% gridSize for each iteratively.
Ferdinand Fischer's avatar
Ferdinand Fischer committed
497
			
498
			if isempty(a) || isempty(a(1).grid)
499
500
501
502
				if nargin > 1
					[referenceGrid, referenceGridName] = varargin{1}.getFinestGrid(varargin{2:end});
				else
					referenceGrid = {};
503
					referenceGridName = '';
504
505
				end
				return;
Ferdinand Fischer's avatar
Ferdinand Fischer committed
506
507
508
			else
				referenceGridName = a(1).gridName;
				referenceGrid = a(1).grid;
509
				referenceGridSize = [a(1).domain.n];
Ferdinand Fischer's avatar
Ferdinand Fischer committed
510
			end
511
			
Jakob Gabriel's avatar
Jakob Gabriel committed
512
			for it = 1 : numel(varargin)
513
				if isempty(varargin{it}) || isempty(varargin{it}(1).domain)
Ferdinand Fischer's avatar
Ferdinand Fischer committed
514
515
					continue;
				end
Jakob Gabriel's avatar
Jakob Gabriel committed
516
517
518
519
				assert(numel(referenceGridName) == numel(varargin{it}(1).gridName), ...
					['For getFinestGrid, the gridName of all objects must be equal', ...
					'. Maybe gridJoin() does what you want?']);
				for jt = 1 : numel(referenceGridName)
520
					comparisonGridSize = varargin{it}(1).domain.find(referenceGridName{jt}).n;
Jakob Gabriel's avatar
Jakob Gabriel committed
521
522
523
					comparisonGrid = varargin{it}.gridOf(referenceGridName{jt});
					assert(referenceGrid{jt}(1) == comparisonGrid(1), 'Grids must have same domain for combining them')
					assert(referenceGrid{jt}(end) == comparisonGrid(end), 'Grids must have same domain for combining them')
524
					if comparisonGridSize > referenceGridSize(jt)
Jakob Gabriel's avatar
Jakob Gabriel committed
525
						referenceGrid{jt} = comparisonGrid;
526
						referenceGridSize(jt) = comparisonGridSize;
Jakob Gabriel's avatar
Jakob Gabriel committed
527
528
529
530
531
					end
				end
			end
		end
		
532
533
		function obj = sort(obj, varargin)
			%SORT sorts the grid of the object in a desired order
534
			% obj = sortGrid(obj) sorts the grid in alphabetical order.
535
536
			% obj = sort(obj, 'descend') sorts the grid in descending
			% alphabetical order.
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
537
						
538
539
			% only sort the grids if there is something to sort
			if obj(1).nargin > 1
540
				
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
541
542
				[sortedDomain, I] = obj(1).domain.sort(varargin{:});
				[obj.domain] = deal(sortedDomain);
543
				
544
545
				for k = 1:numel(obj)
					obj(k).valueDiscrete = permute(obj(k).valueDiscrete, I);
546
				end
547
548
			end
		end% sort()
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
549
		
Jakob Gabriel's avatar
Jakob Gabriel committed
550
		function c = horzcat(a, varargin)
551
			%HORZCAT Horizontal concatenation.
552
553
554
555
556
557
			%   [A B] is the horizontal concatenation of objects A and B
			%   from the class quantity.Discrete. A and B must have the
			%   same number of rows and the same grid. [A,B] is the same
			%   thing. Any number of matrices can be concatenated within
			%   one pair of brackets. Horizontal and vertical concatenation
			%   can be combined together as in [1 2;3 4].
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
			%
			%   [A B; C] is allowed if the number of rows of A equals the
			%   number of rows of B and the number of columns of A plus the
			%   number of columns of B equals the number of columns of C.
			%   The matrices in a concatenation expression can themselves
			%   by formed via a concatenation as in [A B;[C D]].  These
			%   rules generalize in a hopefully obvious way to allow fairly
			%   complicated constructions.
			%
			%   N-D arrays are concatenated along the second dimension. The
			%   first and remaining dimensions must match.
			%
			%   C = HORZCAT(A,B) is called for the syntax '[A  B]' when A
			%   or B is an object.
			%
			%   Y = HORZCAT(X1,X2,X3,...) is called for the syntax '[X1 X2
			%   X3 ...]' when any of X1, X2, X3, etc. is an object.
			%
			%	See also HORZCAT, CAT.
577
			c = cat(2, a, varargin{:});
Jakob Gabriel's avatar
Jakob Gabriel committed
578
579
		end
		function c = vertcat(a, varargin)
580
581
582
583
			%VERTCAT Vertical concatenation.
			%   [A;B] is the vertical concatenation of objects A and B from
			%   the class quantity.Discrete. A and B must have the same
			%   number of columns and the same grid. Any number of matrices
584
585
586
			%   can be concatenated within one pair of brackets. Horizontal
			%   and vertical concatenation can be combined together as in
			%   [1 2;3 4].
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
			%
			%   [A B; C] is allowed if the number of rows of A equals the
			%   number of rows of B and the number of columns of A plus the
			%   number of columns of B equals the number of columns of C.
			%   The matrices in a concatenation expression can themselves
			%   by formed via a concatenation as in [A B;[C D]].  These
			%   rules generalize in a hopefully obvious way to allow fairly
			%   complicated constructions.
			%
			%   N-D arrays are concatenated along the first dimension. The
			%   remaining dimensions must match.
			%
			%   C = VERTCAT(A,B) is called for the syntax '[A; B]' when A
			%   or B is an object.
			%
			%   Y = VERTCAT(X1,X2,X3,...) is called for the syntax '[X1;
			%   X2; X3; ...]' when any of X1, X2, X3, etc. is an object.
			%
			%   See also HORZCAT, CAT.
606
			c = cat(1, a, varargin{:});
Jakob Gabriel's avatar
Jakob Gabriel committed
607
		end
608
		function c = cat(dim, a, varargin)
609
610
611
			%CAT Concatenate arrays.
			%   CAT(DIM,A,B) concatenates the arrays of objects A and B
			%   from the class quantity.Discrete along the dimension DIM.
612
613
			%   CAT(2,A,B) is the same as [A,B]. CAT(1,A,B) is the same as
			%   [A;B].
614
			%
615
616
			%   B = CAT(DIM,A1,A2,A3,A4,...) concatenates the input arrays
			%   A1, A2, etc. along the dimension DIM.
617
			%
618
619
620
621
			%   When used with comma separated list syntax, CAT(DIM,C{:})
			%   or CAT(DIM,C.FIELD) is a convenient way to concatenate a
			%   cell or structure array containing numeric matrices into a
			%   single matrix.
622
623
			%
			%   Examples:
624
			%     a = magic(3); b = pascal(3);
625
626
627
			%     c = cat(4,a,b)
			%   produces a 3-by-3-by-1-by-2 result and
			%     s = {a b};
628
			%     for i=1:length(s),
629
630
631
632
			%       siz{i} = size(s{i});
			%     end
			%     sizes = cat(1,siz{:})
			%   produces a 2-by-2 array of size vectors.
633
			
Jakob Gabriel's avatar
Jakob Gabriel committed
634
			if nargin == 1
635
				objCell = {a};
Jakob Gabriel's avatar
Jakob Gabriel committed
636
			else
637
				objCell = [{a}, varargin(:)'];
638
				
639
640
641
				% this function has the very special thing that it a does
				% not have to be an quantity.Discrete object. So it has to
				% be checked which of the input arguments is an
642
				% quantity.Discrete object. This is considered to give
643
644
645
				% the basic values for the initialization of new
				% quantity.Discrete values
				isAquantityDiscrete = cellfun(@(o) isa(o, 'quantity.Discrete'), objCell);
646
647
				isEmpty = cellfun(@(o) isempty(o), objCell);
				objIdx = find(isAquantityDiscrete & (~isEmpty), 1);
648
				
649
650
651
652
				if all(isEmpty)
					% if there are only empty entries, nothing can be
					% concatenated, so a new empty object is initialized.
					s = cellfun(@(o) size(o), objCell, 'UniformOutput', false);
653
					if dim == 1
654
						S = sum(cat(3, s{:}), 3);
655
656
657
658
659
					elseif dim == 2
						S = s{1};
					else
						error('Not implemented')
					end
660
661
662
					c = quantity.Discrete.empty(S);
					return
				else
663
					obj = objCell{objIdx};
664
665
666
				end
				
				for k = 1:numel(objCell(~isEmpty))
667
					
668
669
					if isa(objCell{k}, 'quantity.Discrete')
						o = objCell{k};
670
					else
671
						value = objCell{k};
672
						for l = 1:numel(value)
673
							M(:,l) = repmat(value(l), prod(obj(1).domain.gridLength), 1);
674
675
						end
						if isempty(value)
676
							M = zeros([prod(obj(1).domain.gridLength), size(value(l))]);
677
						end
678
						M = reshape(M, [obj(1).domain.gridLength, size(value)]);
679
						o = quantity.Discrete( M, ...
680
							'size', size(value), ...
681
682
							'gridName', obj(1).gridName, ...
							'grid', obj(1).grid);
683
684
					end
					
685
					objCell{k} = o;
686
687
				end
				
Jakob Gabriel's avatar
Jakob Gabriel committed
688
			end
689
			
690
691
692
693
694
			% sort the grid names of each quantity
			for it = 1: (numel(varargin) + 1)
				objCell{it} = objCell{it}.sort;
			end
			
695
			[fineGrid, fineGridName] = getFinestGrid(objCell{~isEmpty});
696
			for it = 1 : (numel(varargin) + 1)  % +1 because the first entry is a
697
				% change the grid to the finest
698
				objCell{it} = objCell{it}.changeGrid(fineGrid, fineGridName);
699
			end
Jakob Gabriel's avatar
Jakob Gabriel committed
700
			assertSameGrid(objCell{:});
701
702
			argin = [{dim}, objCell(:)'];
			c = builtin('cat', argin{:});
Jakob Gabriel's avatar
Jakob Gabriel committed
703
704
		end
		
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
		function Y = blkdiag(A, varargin)
			% blkdiag  Block diagonal concatenation of matrix input arguments.
			%									|A 0 .. 0|
			% Y = blkdiag(A,B,...)  produces	|0 B .. 0|
			%									|0 0 ..  |
			% Yet, A, B, ... must have the same gridName and grid.
			if nargin == 1
				Y = copy(A);
			else
				B = varargin{1};
				if isempty(B)
					Y = A;
				else
					assert(isequal(A(1).gridName, B(1).gridName), 'only implemented for same grid and gridName');
					assert(isequal(A(1).grid, B(1).grid), 'only implemented for same grid and gridName');
					Y = [A, zeros(size(A, 1), size(B, 2)); ...
						zeros(size(B, 1), size(A, 2)), B];
				end
				if nargin > 2
					Y = blkdiag(Y, varargin{2:end});
				end
			end
		end % blkdiag()
		
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
		function solution = solveAlgebraic(obj, rhs, gridName, objLimit)
			%% this method solves
			%	obj(gridName) == rhs
			% for the variable specified by gridName.
			% rhs must be of apropriate size and gridName must
			% be an gridName of obj. If the result is constant (i.e., if
			% obj only depends on variable, then a double array is
			% returned. Else the solution is of the type as obj.
			% Yet, this is only implemented for obj with one variable
			% (grid) (see quantity.invert-method).
			% The input objLimit specifies minimum and maximum of the
			% values of obj, between which the solution should be searched.
			assert(numel(obj(1).gridName) == 1);
			assert(isequal(size(obj), [1, 1]));
			
			if ~isequal(size(rhs), size(obj))
				error('rhs has not the same size as quantity');
			end
			if ~iscell(gridName)
				gridName = {gridName};
			end
			if numel(gridName) ~= 1
				error('this function can only solve for one variable');
			end
			if isempty(strcmp(obj(1).gridName, gridName{1}))
				error('quantity does not depend on variable');
			end
			
			if nargin == 4
				assert(numel(objLimit)==2, 'a lower and upper limit must be specified (or neither)');
				objValueTemp = obj.on();
				gridSelector = (objValueTemp >= objLimit(1)) & (objValueTemp <= objLimit(2));
761
762
				gridSelector([max(1, find(gridSelector, 1, 'first')-1), ...
					min(find(gridSelector, 1, 'last')+1, numel(gridSelector))]) = 1;
763
764
				limitedGrid = obj(1).grid{1}(gridSelector);
				objCopy = obj.copy();
Jakob Gabriel's avatar
Jakob Gabriel committed
765
				objCopy = objCopy.changeGrid({limitedGrid}, gridName);
766
767
768
769
770
771
				objInverseTemp = objCopy.invert(gridName);
			else
				objInverseTemp = obj.invert(gridName);
			end
			
			solution = objInverseTemp.on(rhs);
772
773
774
775
776
777
778
			
			% 			solution = zeros(numel(obj), 1);
			% 			for it = 1 : numel(obj)
			% 				objInverseTemp = obj(it).invert(gridName);
			% 				solution(it) = objInverseTemp.on(rhs(it));
			% 			end
			% 			solution = reshape(solution, size(obj));
779
780
781
782
783
784
785
786
		end
		
		function inverse = invert(obj, gridName)
			% inverse solves the function representet by the quantity for
			% its variable, for instance, if obj represents y = f(x), then
			% invert returns an object containing x = f^-1(y).
			% Yet, this is only implemented for obj with one variable
			% (grid).
787
788
789
790
791
792
793
			if iscell(gridName)
				% fixme: by default the first gridName is chosen as new
				% name. This works because the functions is only written
				% for quantities with one variable.
				gridName = gridName{1};
			end
			
794
795
			assert(numel(obj(1).gridName) == 1);
			assert(isequal(size(obj), [1, 1]));
796
			inverse = quantity.Discrete(repmat(obj(1).grid{obj(1).domain.gridIndex(gridName)}(:), [1, size(obj)]), ...
797
				'size', size(obj), 'domain', quantity.Domain([obj(1).name], obj.on()), ...
798
				'name', gridName);
799
800
801
802
			
		end
		
		function solution = solveDVariableEqualQuantity(obj, varargin)
803
			% solves the first order ODE
804
			%	dvar / ds = obj(var(s))
805
806
807
808
809
810
			%	var(0) = ic
			% to obtain var(s, ic) depending on both the argument s and the initial 
			% condition ic. Herein, obj may only depend on one variable / gridName / ...
			% domain.
			assert(numel(obj(1).domain) == 1, ...
				'this method is only implemented for quanitities with one domain');
811
812
813
814
815
816
817
			
			myParser = misc.Parser();
			myParser.addParameter('initialValueGrid', obj(1).grid{1});
			myParser.addParameter('variableGrid', obj(1).grid{1});
			myParser.addParameter('newGridName', 's');
			myParser.parse(varargin{:});
			
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
818
			variableGrid = myParser.Results.variableGrid(:);
819
			myGridSize = [numel(variableGrid), ...
820
821
				numel(myParser.Results.initialValueGrid)];
			
822
823
			% the time (s) vector has to start at 0, to ensure the IC. If
			% variableGrid does not start with 0, it is separated in
824
			% negative and positive parts and later combined again.
Ferdinand Fischer's avatar
tmp    
Ferdinand Fischer committed
825
826
			positiveVariableGrid = [0; variableGrid(variableGrid > 0)];
			negativeVariableGrid = [0; flip(variableGrid(variableGrid < 0))];
827
828
829
830
831
832
833
834
835
836
837
838
			
			% solve ode for every entry in obj and for every initial value
			odeSolution = zeros([myGridSize, numel(obj)]);
			for it = 1:numel(obj)
				for icIdx = 1:numel(myParser.Results.initialValueGrid)
					resultGridPositive = [];
					odeSolutionPositive = [];
					resultGridNegative = [];
					odeSolutionNegative = [];
					if numel(positiveVariableGrid) > 1
						[resultGridPositive, odeSolutionPositive] = ...
							ode45(@(y, z) obj(it).on(z), ...
839
							positiveVariableGrid, ...
840
							myParser.Results.initialValueGrid(icIdx));
841
842
843
844
					end
					if numel(negativeVariableGrid) >1
						[resultGridNegative, odeSolutionNegative] = ...
							ode45(@(y, z) obj(it).on(z), ...
845
							negativeVariableGrid, ...
846
							myParser.Results.initialValueGrid(icIdx));
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
					end
					if any(variableGrid == 0)
						resultGrid = [flip(resultGridNegative(2:end)); 0 ; resultGridPositive(2:end)];
						odeSolution(:, icIdx, it) = [flip(odeSolutionNegative(2:end)); ...
							myParser.Results.initialValueGrid(icIdx); odeSolutionPositive(2:end)];
					else
						resultGrid = [flip(resultGridNegative(2:end)); resultGridPositive(2:end)];
						odeSolution(:, icIdx, it) = [flip(odeSolutionNegative(2:end)); ...
							odeSolutionPositive(2:end)];
					end
					assert(isequal(resultGrid(:), variableGrid(:)));
				end
			end
			
			% return result as quantity-object
			solution = quantity.Discrete(...
				reshape(odeSolution, [myGridSize, size(obj)]), ...
864
865
				'domain', [quantity.Domain(myParser.Results.newGridName, variableGrid), ...
					quantity.Domain('ic', myParser.Results.initialValueGrid)], ...
866
				'size', size(obj), 'name', ['solve(', obj(1).name, ')']);
867
		end % solveDVariableEqualQuantity()
868
		
869
		function solution = subs(obj, gridName2Replace, values)
870
			% SUBS substitute variables of a quantity
871
872
873
874
875
876
877
878
879
880
881
882
			%	solution = SUBS(obj, NEWDOMAIN), replaces the original
			%	domain of the object with the new domain specified by
			%	NEWDOMAIN. NEWDOMAIN must have the same grid name as the
			%	original domain.
			%
			%	solution = SUBS(obj, GRIDNAMES2REPLACE, VALUES) replaces
			%	the domains which are specified by GRIDNAMES2REPLACE by
			%	VALUES. GRIDNAMES2REPLACE must be a cell-array with the
			%	names of the domains or an object-array with
			%	quantity.Domain objects which should be replaced by VALUES.
			%	VALUES must be a cell-array of the new values or new grid
			%	names.
883
884
885
886
887
888
889
890
			%
			%	Example: 
			%		q = q.subs('z', 't')
			%		will replace the domain with the name 'z' by a domain
			%		with the name 't' but with the same discretization.
			%		q = q.subs('z', linspace(0,1)')
			%		will replace the grid of domain with the name 'z' by
			%		the new grid specified by linspace.
891
892
893
			if nargin == 1 || isempty(gridName2Replace)
				% if gridName2Replace is empty, then nothing must be done.
				solution = obj;
894
			elseif isempty(obj)
Ferdinand Fischer's avatar
Ferdinand Fischer committed
895
896
				% if the object is empty, nothing must be done.
				solution = obj;
897
898
			else
				% input checks
899
900
901
902
903
904
905
906
907
908
				if nargin == 2
					assert(isa(gridName2Replace, 'quantity.Domain'), 'If only two parameters are specified, the second parameter must be a quantiy.Domain');

					values = {gridName2Replace.grid};
					gridName2Replace = {gridName2Replace.name};
					
				elseif nargin == 3
					
					gridName2Replace = misc.ensureIsCell(gridName2Replace);
					values = misc.ensureIsCell(values);
909
				end
910
				
Jakob Gabriel's avatar
Jakob Gabriel committed
911
912
				assert(numel(values) == numel(gridName2Replace), ...
					'gridName2Replace and values must be of same size');
913
				
914
915
				% here substitution starts:
				% The first (gridName2Replace{1}, values{1})-pair is
916
917
918
919
920
921
922
923
924
925
				% replaced. If there are more cell-elements in those inputs
				% then subs() is called again for the remaining pairs
				% (gridName2Replace{2:end}, values{2:end}).
				if ischar(values{1})
					% if values{1} is a char-array, then the gridName is
					% replaced
					if any(strcmp(values{1}, gridName2Replace(2:end)))
						% in the case if a quantity f(z, zeta) should be
						% substituted like subs(f, {z, zeta}, {zeta, z})
						% this would cause an error, since after the first
926
927
						% substituion subs(f, z, zeta) the result would be
						% f(zeta, zeta) -> the 2nd subs(f, zeta, z) will
928
929
930
931
932
933
934
						% result in f(z, z) and not in f(zeta, z) as
						% intended. This is solved, by an additonal
						% substitution:
						values{end+1} = values{1};
						gridName2Replace{end+1} = [gridName2Replace{1}, 'backUp'];
						values{1} = [gridName2Replace{1}, 'backUp'];
					end
Jakob Gabriel's avatar
Jakob Gabriel committed
935
936
937
938
939
940
941
					if isequal(values{1}, gridName2Replace{1})
						% replace with same variable... everything stay the
						% same.
						newGrid = obj(1).grid;
						newGridName = obj(1).gridName;
						newValue = obj.on();
					elseif any(strcmp(values{1}, obj(1).gridName))
942
						% if for a quantity f(z, zeta) this method is
943
944
945
						% called with subs(f, zeta, z), then g(z) = f(z, z)
						% results, hence the dimensions z and zeta are
						% merged.
946
947
						gridIndices = [obj(1).domain.gridIndex(gridName2Replace{1}), ...
							obj(1).domain.gridIndex(values{1})];
948
949
950
951
952
953
954
955
						newGridForOn = obj(1).grid;
						if numel(obj(1).grid{gridIndices(1)}) > numel(obj(1).grid{gridIndices(2)})
							newGridForOn{gridIndices(2)} = newGridForOn{gridIndices(1)};
						else
							newGridForOn{gridIndices(1)} = newGridForOn{gridIndices(2)};
						end
						newValue = misc.diagNd(obj.on(newGridForOn), gridIndices);
						newGrid = {newGridForOn{gridIndices(1)}, ...
Jakob Gabriel's avatar
Jakob Gabriel committed
956
							newGridForOn{1:1:numel(newGridForOn) ~= gridIndices(1) ...
957
							& 1:1:numel(newGridForOn) ~= gridIndices(2)}};
958
						newGridName = {values{1}, ...
Jakob Gabriel's avatar
Jakob Gabriel committed
959
							obj(1).gridName{1:1:numel(obj(1).gridName) ~= gridIndices(1) ...
960
							& 1:1:numel(obj(1).gridName) ~= gridIndices(2)}};
961
962
963
964
965
					else
						% this is the default case. just grid name is
						% changed.
						newGrid = obj(1).grid;
						newGridName = obj(1).gridName;
966
						newGridName{obj(1).domain.gridIndex(gridName2Replace{1})} ...
967
968
969
970
971
972
973
974
975
976
977
978
979
							= values{1};
						newValue = obj.on();
					end
					
				elseif isnumeric(values{1}) && numel(values{1}) == 1
					% if values{1} is a scalar, then obj is evaluated and
					% the resulting quantity loses that spatial grid and
					% gridName
					newGridName = obj(1).gridName;
					newGridName = newGridName(~strcmp(newGridName, gridName2Replace{1}));
					% newGrid is the similar to the original grid, but the
					% grid of gridName2Replace is removed.
					newGrid = obj(1).grid;
980
					newGrid = newGrid((1:1:numel(newGrid)) ~= obj(1).domain.gridIndex(gridName2Replace{1}));
981
					newGridSize = cellfun(@(v) numel(v), newGrid);
982
983
984
					% newGridForOn is the similar to the original grid, but
					% the grid of gridName2Replace is set to values{1} for
					% evaluation of obj.on().
985
					newGridForOn = obj(1).grid;
986
					newGridForOn{obj(1).domain.gridIndex(gridName2Replace{1})} = values{1};
987
988
989
990
991
992
					newValue = reshape(obj.on(newGridForOn), [newGridSize, size(obj)]);
					
				elseif isnumeric(values{1}) && numel(values{1}) > 1
					% if values{1} is a double vector, then the grid is
					% replaced.
					newGrid = obj(1).grid;
993
					newGrid{obj(1).domain.gridIndex(gridName2Replace{1})} = values{1};
994
995
996
997
998
999
1000
					newGridName = obj(1).gridName;
					newValue = obj.on(newGrid);
				else
					error('value must specify a gridName or a gridPoint');
				end
				if isempty(newGridName)
					solution = newValue;
For faster browsing, not all history is shown. View entire blame