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35
36
37 #ifndef VIGRA_MATRIX_HXX
38 #define VIGRA_MATRIX_HXX
39
40 #include <cmath>
41 #include <iosfwd>
42 #include <iomanip>
43 #include "multi_array.hxx"
44 #include "mathutil.hxx"
45 #include "numerictraits.hxx"
46 #include "multi_pointoperators.hxx"
47
48
49 namespace vigra
50 {
51
52 /** \defgroup LinearAlgebraModule Linear Algebra
53
54 \brief Classes and functions for matrix algebra, linear equations systems, eigen systems, least squares etc.
55 */
56
57 /** \ingroup LinearAlgebraModule
58
59 \brief Linear algebra functions.
60
61 Namespace <tt>vigra/linalg</tt> hold VIGRA's linear algebra functionality. But most of its contents
62 is exported into namespace <tt>vigra</tt> via <tt>using</tt> directives.
63 */
64 namespace linalg
65 {
66
67 template <class T, class C>
68 inline MultiArrayIndex
69 rowCount(const MultiArrayView<2, T, C> &x);
70
71 template <class T, class C>
72 inline MultiArrayIndex
73 columnCount(const MultiArrayView<2, T, C> &x);
74
75 template <class T, class C>
76 inline MultiArrayView <2, T, C>
77 rowVector(MultiArrayView <2, T, C> const & m, MultiArrayIndex d);
78
79 template <class T, class C>
80 inline MultiArrayView <2, T, C>
81 columnVector(MultiArrayView<2, T, C> const & m, MultiArrayIndex d);
82
83 template <class T, class ALLOC = std::allocator<T> >
84 class TemporaryMatrix;
85
86 template <class T, class C1, class C2>
87 void transpose(const MultiArrayView<2, T, C1> &v, MultiArrayView<2, T, C2> &r);
88
89 template <class T, class C>
90 bool isSymmetric(const MultiArrayView<2, T, C> &v);
91
92 enum RawArrayMemoryLayout { RowMajor, ColumnMajor };
93
94 /********************************************************/
95 /* */
96 /* Matrix */
97 /* */
98 /********************************************************/
99
100 /** Matrix class.
101
102 \ingroup LinearAlgebraModule
103
104 This is the basic class for all linear algebra computations. Matrices are
105 stored in a <i>column-major</i> format, i.e. the row index is varying fastest.
106 This is the same format as in the lapack and gmm++ libraries, so it will
107 be easy to interface these libraries. In fact, if you need optimized
108 high performance code, you should use them. The VIGRA linear algebra
109 functionality is provided for smaller problems and rapid prototyping
110 (no one wants to spend half the day installing a new library just to
111 discover that the new algorithm idea didn't work anyway).
112
113 <b>See also:</b>
114 <ul>
115 <li> \ref LinearAlgebraFunctions
116 </ul>
117
118 <b>\#include</b> <vigra/matrix.hxx> or<br>
119 <b>\#include</b> <vigra/linear_algebra.hxx><br>
120 Namespaces: vigra and vigra::linalg
121 */
122 template <class T, class ALLOC = std::allocator<T> >
123 class Matrix
124 : public MultiArray<2, T, ALLOC>
125 {
126 typedef MultiArray<2, T, ALLOC> BaseType;
127
128 public:
129 typedef Matrix<T, ALLOC> matrix_type;
130 typedef TemporaryMatrix<T, ALLOC> temp_type;
131 typedef MultiArrayView<2, T> view_type;
132 typedef typename BaseType::value_type value_type;
133 typedef typename BaseType::pointer pointer;
134 typedef typename BaseType::const_pointer const_pointer;
135 typedef typename BaseType::reference reference;
136 typedef typename BaseType::const_reference const_reference;
137 typedef typename BaseType::difference_type difference_type;
138 typedef typename BaseType::difference_type_1 difference_type_1;
139 typedef ALLOC allocator_type;
140
141 /** default constructor
142 */
143 Matrix()
144 {}
145
146 /** construct with given allocator
147 */
148 explicit Matrix(ALLOC const & alloc)
149 : BaseType(alloc)
150 {}
151
152 /** construct with given shape and init all
153 elements with zero. Note that the order of the axes is
154 <tt>difference_type(rows, columns)</tt> which
155 is the opposite of the usual VIGRA convention.
156 */
157 explicit Matrix(const difference_type &aShape,
158 ALLOC const & alloc = allocator_type())
159 : BaseType(aShape, alloc)
160 {}
161
162 /** construct with given shape and init all
163 elements with zero. Note that the order of the axes is
164 <tt>(rows, columns)</tt> which
165 is the opposite of the usual VIGRA convention.
166 */
167 Matrix(difference_type_1 rows, difference_type_1 columns,
168 ALLOC const & alloc = allocator_type())
169 : BaseType(difference_type(rows, columns), alloc)
170 {}
171
172 /** construct with given shape and init all
173 elements with the constant \a init. Note that the order of the axes is
174 <tt>difference_type(rows, columns)</tt> which
175 is the opposite of the usual VIGRA convention.
176 */
177 Matrix(const difference_type &aShape, const_reference init,
178 allocator_type const & alloc = allocator_type())
179 : BaseType(aShape, init, alloc)
180 {}
181
182 /** construct with given shape and init all
183 elements with the constant \a init. Note that the order of the axes is
184 <tt>(rows, columns)</tt> which
185 is the opposite of the usual VIGRA convention.
186 */
187 Matrix(difference_type_1 rows, difference_type_1 columns, const_reference init,
188 allocator_type const & alloc = allocator_type())
189 : BaseType(difference_type(rows, columns), init, alloc)
190 {}
191
192 /** construct with given shape and copy data from C-style array \a init.
193 Unless \a layout is <tt>ColumnMajor</tt>, the elements in this array
194 are assumed to be given in row-major order (the C standard order) and
195 will automatically be converted to the required column-major format.
196 Note that the order of the axes is <tt>difference_type(rows, columns)</tt> which
197 is the opposite of the usual VIGRA convention.
198 */
199 Matrix(const difference_type &shape, const_pointer init, RawArrayMemoryLayout layout = RowMajor,
200 allocator_type const & alloc = allocator_type())
201 : BaseType(shape, alloc) // FIXME: this function initializes the memory twice
202 {
203 if(layout == RowMajor)
204 {
205 difference_type trans(shape[1], shape[0]);
206 linalg::transpose(MultiArrayView<2, T>(trans, const_cast<pointer>(init)), *this);
207 }
208 else
209 {
210 std::copy(init, init + elementCount(), this->data());
211 }
212 }
213
214 /** construct with given shape and copy data from C-style array \a init.
215 Unless \a layout is <tt>ColumnMajor</tt>, the elements in this array
216 are assumed to be given in row-major order (the C standard order) and
217 will automatically be converted to the required column-major format.
218 Note that the order of the axes is <tt>(rows, columns)</tt> which
219 is the opposite of the usual VIGRA convention.
220 */
221 Matrix(difference_type_1 rows, difference_type_1 columns, const_pointer init, RawArrayMemoryLayout layout = RowMajor,
222 allocator_type const & alloc = allocator_type())
223 : BaseType(difference_type(rows, columns), alloc) // FIXME: this function initializes the memory twice
224 {
225 if(layout == RowMajor)
226 {
227 difference_type trans(columns, rows);
228 linalg::transpose(MultiArrayView<2, T>(trans, const_cast<pointer>(init)), *this);
229 }
230 else
231 {
232 std::copy(init, init + elementCount(), this->data());
233 }
234 }
235
236 /** copy constructor. Allocates new memory and
237 copies tha data.
238 */
239 Matrix(const Matrix &rhs)
240 : BaseType(rhs)
241 {}
242
243 /** construct from temporary matrix, which looses its data.
244
245 This operation is equivalent to
246 \code
247 TemporaryMatrix<T> temp = ...;
248
249 Matrix<T> m;
250 m.swap(temp);
251 \endcode
252 */
253 Matrix(const TemporaryMatrix<T, ALLOC> &rhs)
254 : BaseType(rhs.allocator())
255 {
256 this->swap(const_cast<TemporaryMatrix<T, ALLOC> &>(rhs));
257 }
258
259 /** construct from a MultiArrayView. Allocates new memory and
260 copies tha data. \a rhs is assumed to be in column-major order already.
261 */
262 template<class U, class C>
263 Matrix(const MultiArrayView<2, U, C> &rhs)
264 : BaseType(rhs)
265 {}
266
267 /** assignment.
268 If the size of \a rhs is the same as the matrix's old size, only the data
269 are copied. Otherwise, new storage is allocated, which invalidates
270 all objects (array views, iterators) depending on the matrix.
271 */
272 Matrix & operator=(const Matrix &rhs)
273 {
274 BaseType::operator=(rhs); // has the correct semantics already
275 return *this;
276 }
277
278 /** assign a temporary matrix. If the shapes of the two matrices match,
279 only the data are copied (in order to not invalidate views and iterators
280 depending on this matrix). Otherwise, the memory is swapped
281 between the two matrices, so that all depending objects
282 (array views, iterators) ar invalidated.
283 */
284 Matrix & operator=(const TemporaryMatrix<T, ALLOC> &rhs)
285 {
286 if(this->shape() == rhs.shape())
287 this->copy(rhs);
288 else
289 this->swap(const_cast<TemporaryMatrix<T, ALLOC> &>(rhs));
290 return *this;
291 }
292
293 /** assignment from arbitrary 2-dimensional MultiArrayView.<br>
294 If the size of \a rhs is the same as the matrix's old size, only the data
295 are copied. Otherwise, new storage is allocated, which invalidates
296 all objects (array views, iterators) depending on the matrix.
297 \a rhs is assumed to be in column-major order already.
298 */
299 template <class U, class C>
300 Matrix & operator=(const MultiArrayView<2, U, C> &rhs)
301 {
302 BaseType::operator=(rhs); // has the correct semantics already
303 return *this;
304 }
305
306 /** assignment from scalar.<br>
307 Equivalent to Matrix::init(v).
308 */
309 Matrix & operator=(value_type const & v)
310 {
311 return init(v);
312 }
313
314 /** init elements with a constant
315 */
316 template <class U>
317 Matrix & init(const U & init)
318 {
319 BaseType::init(init);
320 return *this;
321 }
322
323 /** reshape to the given shape and initialize with zero.
324 */
325 void reshape(difference_type_1 rows, difference_type_1 columns)
326 {
327 BaseType::reshape(difference_type(rows, columns));
328 }
329
330 /** reshape to the given shape and initialize with \a init.
331 */
332 void reshape(difference_type_1 rows, difference_type_1 columns, const_reference init)
333 {
334 BaseType::reshape(difference_type(rows, columns), init);
335 }
336
337 /** reshape to the given shape and initialize with zero.
338 */
339 void reshape(difference_type const & newShape)
340 {
341 BaseType::reshape(newShape);
342 }
343
344 /** reshape to the given shape and initialize with \a init.
345 */
346 void reshape(difference_type const & newShape, const_reference init)
347 {
348 BaseType::reshape(newShape, init);
349 }
350
351 /** Create a matrix view that represents the row vector of row \a d.
352 */
353 view_type rowVector(difference_type_1 d) const
354 {
355 return vigra::linalg::rowVector(*this, d);
356 }
357
358 /** Create a matrix view that represents the column vector of column \a d.
359 */
360 view_type columnVector(difference_type_1 d) const
361 {
362 return vigra::linalg::columnVector(*this, d);
363 }
364
365 /** number of rows (height) of the matrix.
366 */
367 difference_type_1 rowCount() const
368 {
369 return this->m_shape[0];
370 }
371
372 /** number of columns (width) of the matrix.
373 */
374 difference_type_1 columnCount() const
375 {
376 return this->m_shape[1];
377 }
378
379 /** number of elements (width*height) of the matrix.
380 */
381 difference_type_1 elementCount() const
382 {
383 return rowCount()*columnCount();
384 }
385
386 /** check whether the matrix is symmetric.
387 */
388 bool isSymmetric() const
389 {
390 return vigra::linalg::isSymmetric(*this);
391 }
392
393 /** sums over the matrix.
394 */
395 TemporaryMatrix<T> sum() const
396 {
397 TemporaryMatrix<T> result(1, 1);
398 vigra::transformMultiArray(srcMultiArrayRange(*this),
399 destMultiArrayRange(result),
400 vigra::FindSum<T>() );
401 return result;
402 }
403
404 /** sums over dimension \a d of the matrix.
405 */
406 TemporaryMatrix<T> sum(difference_type_1 d) const
407 {
408 difference_type shape(d==0 ? 1 : this->m_shape[0], d==0 ? this->m_shape[1] : 1);
409 TemporaryMatrix<T> result(shape);
410 vigra::transformMultiArray(srcMultiArrayRange(*this),
411 destMultiArrayRange(result),
412 vigra::FindSum<T>() );
413 return result;
414 }
415
416 /** sums over the matrix.
417 */
418 TemporaryMatrix<T> mean() const
419 {
420 TemporaryMatrix<T> result(1, 1);
421 vigra::transformMultiArray(srcMultiArrayRange(*this),
422 destMultiArrayRange(result),
423 vigra::FindAverage<T>() );
424 return result;
425 }
426
427 /** calculates mean over dimension \a d of the matrix.
428 */
429 TemporaryMatrix<T> mean(difference_type_1 d) const
430 {
431 difference_type shape(d==0 ? 1 : this->m_shape[0], d==0 ? this->m_shape[1] : 1);
432 TemporaryMatrix<T> result(shape);
433 vigra::transformMultiArray(srcMultiArrayRange(*this),
434 destMultiArrayRange(result),
435 vigra::FindAverage<T>() );
436 return result;
437 }
438
439
440 #ifdef DOXYGEN
441 // repeat the following functions for documentation. In real code, they are inherited.
442
443 /** read/write access to matrix element <tt>(row, column)</tt>.
444 Note that the order of the argument is the opposite of the usual
445 VIGRA convention due to column-major matrix order.
446 */
447 value_type & operator()(difference_type_1 row, difference_type_1 column);
448
449 /** read access to matrix element <tt>(row, column)</tt>.
450 Note that the order of the argument is the opposite of the usual
451 VIGRA convention due to column-major matrix order.
452 */
453 value_type operator()(difference_type_1 row, difference_type_1 column) const;
454
455 /** squared Frobenius norm. Sum of squares of the matrix elements.
456 */
457 typename NormTraits<Matrix>::SquaredNormType squaredNorm() const;
458
459 /** Frobenius norm. Root of sum of squares of the matrix elements.
460 */
461 typename NormTraits<Matrix>::NormType norm() const;
462
463 /** create a transposed view of this matrix.
464 No data are copied. If you want to transpose this matrix permanently,
465 you have to assign the transposed view:
466
467 \code
468 a = a.transpose();
469 \endcode
470 */
471 MultiArrayView<2, vluae_type, StridedArrayTag> transpose() const;
472 #endif
473
474 /** add \a other to this (sizes must match).
475 */
476 template <class U, class C>
477 Matrix & operator+=(MultiArrayView<2, U, C> const & other)
478 {
479 BaseType::operator+=(other);
480 return *this;
481 }
482
483 /** subtract \a other from this (sizes must match).
484 */
485 template <class U, class C>
486 Matrix & operator-=(MultiArrayView<2, U, C> const & other)
487 {
488 BaseType::operator-=(other);
489 return *this;
490 }
491
492 /** multiply \a other element-wise with this matrix (sizes must match).
493 */
494 template <class U, class C>
495 Matrix & operator*=(MultiArrayView<2, U, C> const & other)
496 {
497 BaseType::operator*=(other);
498 return *this;
499 }
500
501 /** divide this matrix element-wise by \a other (sizes must match).
502 */
503 template <class U, class C>
504 Matrix & operator/=(MultiArrayView<2, U, C> const & other)
505 {
506 BaseType::operator/=(other);
507 return *this;
508 }
509
510 /** add \a other to each element of this matrix
511 */
512 Matrix & operator+=(T other)
513 {
514 BaseType::operator+=(other);
515 return *this;
516 }
517
518 /** subtract \a other from each element of this matrix
519 */
520 Matrix & operator-=(T other)
521 {
522 BaseType::operator-=(other);
523 return *this;
524 }
525
526 /** scalar multiply this with \a other
527 */
528 Matrix & operator*=(T other)
529 {
530 BaseType::operator*=(other);
531 return *this;
532 }
533
534 /** scalar divide this by \a other
535 */
536 Matrix & operator/=(T other)
537 {
538 BaseType::operator/=(other);
539 return *this;
540 }
541 };
542
543 // TemporaryMatrix is provided as an optimization: Functions returning a matrix can
544 // use TemporaryMatrix to make explicit that it was allocated as a temporary data structure.
545 // Functions receiving a TemporaryMatrix can thus often avoid to allocate new temporary
546 // memory.
547 template <class T, class ALLOC> // default ALLOC already declared above
548 class TemporaryMatrix
549 : public Matrix<T, ALLOC>
550 {
551 typedef Matrix<T, ALLOC> BaseType;
552 public:
553 typedef Matrix<T, ALLOC> matrix_type;
554 typedef TemporaryMatrix<T, ALLOC> temp_type;
555 typedef MultiArrayView<2, T, StridedArrayTag> view_type;
556 typedef typename BaseType::value_type value_type;
557 typedef typename BaseType::pointer pointer;
558 typedef typename BaseType::const_pointer const_pointer;
559 typedef typename BaseType::reference reference;
560 typedef typename BaseType::const_reference const_reference;
561 typedef typename BaseType::difference_type difference_type;
562 typedef typename BaseType::difference_type_1 difference_type_1;
563 typedef ALLOC allocator_type;
564
565 TemporaryMatrix(difference_type const & shape)
566 : BaseType(shape, ALLOC())
567 {}
568
569 TemporaryMatrix(difference_type const & shape, const_reference init)
570 : BaseType(shape, init, ALLOC())
571 {}
572
573 TemporaryMatrix(difference_type_1 rows, difference_type_1 columns)
574 : BaseType(rows, columns, ALLOC())
575 {}
576
577 TemporaryMatrix(difference_type_1 rows, difference_type_1 columns, const_reference init)
578 : BaseType(rows, columns, init, ALLOC())
579 {}
580
581 template<class U, class C>
582 TemporaryMatrix(const MultiArrayView<2, U, C> &rhs)
583 : BaseType(rhs)
584 {}
585
586 TemporaryMatrix(const TemporaryMatrix &rhs)
587 : BaseType()
588 {
589 this->swap(const_cast<TemporaryMatrix &>(rhs));
590 }
591
592 template <class U>
593 TemporaryMatrix & init(const U & init)
594 {
595 BaseType::init(init);
596 return *this;
597 }
598
599 template <class U, class C>
600 TemporaryMatrix & operator+=(MultiArrayView<2, U, C> const & other)
601 {
602 BaseType::operator+=(other);
603 return *this;
604 }
605
606 template <class U, class C>
607 TemporaryMatrix & operator-=(MultiArrayView<2, U, C> const & other)
608 {
609 BaseType::operator-=(other);
610 return *this;
611 }
612
613 template <class U, class C>
614 TemporaryMatrix & operator*=(MultiArrayView<2, U, C> const & other)
615 {
616 BaseType::operator*=(other);
617 return *this;
618 }
619
620 template <class U, class C>
621 TemporaryMatrix & operator/=(MultiArrayView<2, U, C> const & other)
622 {
623 BaseType::operator/=(other);
624 return *this;
625 }
626
627 TemporaryMatrix & operator+=(T other)
628 {
629 BaseType::operator+=(other);
630 return *this;
631 }
632
633 TemporaryMatrix & operator-=(T other)
634 {
635 BaseType::operator-=(other);
636 return *this;
637 }
638
639 TemporaryMatrix & operator*=(T other)
640 {
641 BaseType::operator*=(other);
642 return *this;
643 }
644
645 TemporaryMatrix & operator/=(T other)
646 {
647 BaseType::operator/=(other);
648 return *this;
649 }
650 private:
651
652 TemporaryMatrix &operator=(const TemporaryMatrix &rhs); // intentionally not implemented
653 };
654
655 /** \defgroup LinearAlgebraFunctions Matrix Functions
656
657 \brief Basic matrix algebra, element-wise mathematical functions, row and columns statistics, data normalization etc.
658
659 \ingroup LinearAlgebraModule
660 */
661 //@{
662
663 /** Number of rows of a matrix represented as a <tt>MultiArrayView<2, ...></tt>
664
665 <b>\#include</b> <vigra/matrix.hxx> or<br>
666 <b>\#include</b> <vigra/linear_algebra.hxx><br>
667 Namespaces: vigra and vigra::linalg
668 */
669 template <class T, class C>
670 inline MultiArrayIndex
671 rowCount(const MultiArrayView<2, T, C> &x)
672 {
673 return x.shape(0);
674 }
675
676 /** Number of columns of a matrix represented as a <tt>MultiArrayView<2, ...></tt>
677
678 <b>\#include</b> <vigra/matrix.hxx> or<br>
679 <b>\#include</b> <vigra/linear_algebra.hxx><br>
680 Namespaces: vigra and vigra::linalg
681 */
682 template <class T, class C>
683 inline MultiArrayIndex
684 columnCount(const MultiArrayView<2, T, C> &x)
685 {
686 return x.shape(1);
687 }
688
689 /** Create a row vector view for row \a d of the matrix \a m
690
691 <b>\#include</b> <vigra/matrix.hxx> or<br>
692 <b>\#include</b> <vigra/linear_algebra.hxx><br>
693 Namespaces: vigra and vigra::linalg
694 */
695 template <class T, class C>
696 inline MultiArrayView <2, T, C>
697 rowVector(MultiArrayView <2, T, C> const & m, MultiArrayIndex d)
698 {
699 typedef typename MultiArrayView <2, T, C>::difference_type Shape;
700 return m.subarray(Shape(d, 0), Shape(d+1, columnCount(m)));
701 }
702
703
704 /** Create a row vector view of the matrix \a m starting at element \a first and ranging
705 to column \a end (non-inclusive).
706
707 <b>\#include</b> <vigra/matrix.hxx> or<br>
708 <b>\#include</b> <vigra/linear_algebra.hxx><br>
709 Namespaces: vigra and vigra::linalg
710 */
711 template <class T, class C>
712 inline MultiArrayView <2, T, C>
713 rowVector(MultiArrayView <2, T, C> const & m, MultiArrayShape<2>::type first, MultiArrayIndex end)
714 {
715 typedef typename MultiArrayView <2, T, C>::difference_type Shape;
716 return m.subarray(first, Shape(first[0]+1, end));
717 }
718
719 /** Create a column vector view for column \a d of the matrix \a m
720
721 <b>\#include</b> <vigra/matrix.hxx> or<br>
722 <b>\#include</b> <vigra/linear_algebra.hxx><br>
723 Namespaces: vigra and vigra::linalg
724 */
725 template <class T, class C>
726 inline MultiArrayView <2, T, C>
727 columnVector(MultiArrayView<2, T, C> const & m, MultiArrayIndex d)
728 {
729 typedef typename MultiArrayView <2, T, C>::difference_type Shape;
730 return m.subarray(Shape(0, d), Shape(rowCount(m), d+1));
731 }
732
733 /** Create a column vector view of the matrix \a m starting at element \a first and
734 ranging to row \a end (non-inclusive).
735
736 <b>\#include</b> <vigra/matrix.hxx> or<br>
737 <b>\#include</b> <vigra/linear_algebra.hxx><br>
738 Namespaces: vigra and vigra::linalg
739 **/
740 template <class T, class C>
741 inline MultiArrayView <2, T, C>
742 columnVector(MultiArrayView<2, T, C> const & m, MultiArrayShape<2>::type first, int end)
743 {
744 typedef typename MultiArrayView <2, T, C>::difference_type Shape;
745 return m.subarray(first, Shape(end, first[1]+1));
746 }
747
748 /** Create a sub vector view of the vector \a m starting at element \a first and
749 ranging to row \a end (non-inclusive).
750
751 Note: This function may only be called when either <tt>rowCount(m) == 1</tt> or
752 <tt>columnCount(m) == 1</tt>, i.e. when \a m really represents a vector.
753 Otherwise, a PreconditionViolation exception is raised.
754
755 <b>\#include</b> <vigra/matrix.hxx> or<br>
756 <b>\#include</b> <vigra/linear_algebra.hxx><br>
757 Namespaces: vigra and vigra::linalg
758 **/
759 template <class T, class C>
760 inline MultiArrayView <2, T, C>
761 subVector(MultiArrayView<2, T, C> const & m, int first, int end)
762 {
763 typedef typename MultiArrayView <2, T, C>::difference_type Shape;
764 if(columnCount(m) == 1)
765 return m.subarray(Shape(first, 0), Shape(end, 1));
766 vigra_precondition(rowCount(m) == 1,
767 "linalg::subVector(): Input must be a vector (1xN or Nx1).");
768 return m.subarray(Shape(0, first), Shape(1, end));
769 }
770
771 /** Check whether matrix \a m is symmetric.
772
773 <b>\#include</b> <vigra/matrix.hxx> or<br>
774 <b>\#include</b> <vigra/linear_algebra.hxx><br>
775 Namespaces: vigra and vigra::linalg
776 */
777 template <class T, class C>
778 bool
779 isSymmetric(MultiArrayView<2, T, C> const & m)
780 {
781 const MultiArrayIndex size = rowCount(m);
782 if(size != columnCount(m))
783 return false;
784
785 for(MultiArrayIndex i = 0; i < size; ++i)
786 for(MultiArrayIndex j = i+1; j < size; ++j)
787 if(m(j, i) != m(i, j))
788 return false;
789 return true;
790 }
791
792
793 /** Compute the trace of a square matrix.
794
795 <b>\#include</b> <vigra/matrix.hxx> or<br>
796 <b>\#include</b> <vigra/linear_algebra.hxx><br>
797 Namespaces: vigra and vigra::linalg
798 */
799 template <class T, class C>
800 typename NumericTraits<T>::Promote
801 trace(MultiArrayView<2, T, C> const & m)
802 {
803 typedef typename NumericTraits<T>::Promote SumType;
804
805 const MultiArrayIndex size = rowCount(m);
806 vigra_precondition(size == columnCount(m), "linalg::trace(): Matrix must be square.");
807
808 SumType sum = NumericTraits<SumType>::zero();
809 for(MultiArrayIndex i = 0; i < size; ++i)
810 sum += m(i, i);
811 return sum;
812 }
813
814 #ifdef DOXYGEN // documentation only -- function is already defined in vigra/multi_array.hxx
815
816 /** calculate the squared Frobenius norm of a matrix.
817 Equal to the sum of squares of the matrix elements.
818
819 <b>\#include</b> <vigra/matrix.hxx>
820 Namespace: vigra
821 */
822 template <class T, class ALLOC>
823 typename Matrix<T, ALLLOC>::SquaredNormType
824 squaredNorm(const Matrix<T, ALLLOC> &a);
825
826 /** calculate the Frobenius norm of a matrix.
827 Equal to the root of the sum of squares of the matrix elements.
828
829 <b>\#include</b> <vigra/matrix.hxx>
830 Namespace: vigra
831 */
832 template <class T, class ALLOC>
833 typename Matrix<T, ALLLOC>::NormType
834 norm(const Matrix<T, ALLLOC> &a);
835
836 #endif // DOXYGEN
837
838 /** initialize the given square matrix as an identity matrix.
839
840 <b>\#include</b> <vigra/matrix.hxx> or<br>
841 <b>\#include</b> <vigra/linear_algebra.hxx><br>
842 Namespaces: vigra and vigra::linalg
843 */
844 template <class T, class C>
845 void identityMatrix(MultiArrayView<2, T, C> &r)
846 {
847 const MultiArrayIndex rows = rowCount(r);
848 vigra_precondition(rows == columnCount(r),
849 "identityMatrix(): Matrix must be square.");
850 for(MultiArrayIndex i = 0; i < rows; ++i) {
851 for(MultiArrayIndex j = 0; j < rows; ++j)
852 r(j, i) = NumericTraits<T>::zero();
853 r(i, i) = NumericTraits<T>::one();
854 }
855 }
856
857 /** create an identity matrix of the given size.
858 Usage:
859
860 \code
861 vigra::Matrix<double> m = vigra::identityMatrix<double>(size);
862 \endcode
863
864 <b>\#include</b> <vigra/matrix.hxx> or<br>
865 <b>\#include</b> <vigra/linear_algebra.hxx><br>
866 Namespaces: vigra and vigra::linalg
867 */
868 template <class T>
869 TemporaryMatrix<T> identityMatrix(MultiArrayIndex size)
870 {
871 TemporaryMatrix<T> ret(size, size, NumericTraits<T>::zero());
872 for(MultiArrayIndex i = 0; i < size; ++i)
873 ret(i, i) = NumericTraits<T>::one();
874 return ret;
875 }
876
877 /** create matrix of ones of the given size.
878 Usage:
879
880 \code
881 vigra::Matrix<double> m = vigra::ones<double>(rows, cols);
882 \endcode
883
884 <b>\#include</b> <vigra/matrix.hxx> or<br>
885 <b>\#include</b> <vigra/linear_algebra.hxx><br>
886 Namespaces: vigra and vigra::linalg
887 */
888 template <class T>
889 TemporaryMatrix<T> ones(MultiArrayIndex rows, MultiArrayIndex cols)
890 {
891 return TemporaryMatrix<T>(rows, cols, NumericTraits<T>::one());
892 }
893
894
895
896 template <class T, class C1, class C2>
897 void diagonalMatrixImpl(MultiArrayView<1, T, C1> const & v, MultiArrayView<2, T, C2> &r)
898 {
899 const MultiArrayIndex size = v.elementCount();
900 vigra_precondition(rowCount(r) == size && columnCount(r) == size,
901 "diagonalMatrix(): result must be a square matrix.");
902 for(MultiArrayIndex i = 0; i < size; ++i)
903 r(i, i) = v(i);
904 }
905
906 /** make a diagonal matrix from a vector.
907 The vector is given as matrix \a v, which must either have a single
908 row or column. The result is written into the square matrix \a r.
909
910 <b>\#include</b> <vigra/matrix.hxx> or<br>
911 <b>\#include</b> <vigra/linear_algebra.hxx><br>
912 Namespaces: vigra and vigra::linalg
913 */
914 template <class T, class C1, class C2>
915 void diagonalMatrix(MultiArrayView<2, T, C1> const & v, MultiArrayView<2, T, C2> &r)
916 {
917 vigra_precondition(rowCount(v) == 1 || columnCount(v) == 1,
918 "diagonalMatrix(): input must be a vector.");
919 r.init(NumericTraits<T>::zero());
920 if(rowCount(v) == 1)
921 diagonalMatrixImpl(v.bindInner(0), r);
922 else
923 diagonalMatrixImpl(v.bindOuter(0), r);
924 }
925
926 /** create a diagonal matrix from a vector.
927 The vector is given as matrix \a v, which must either have a single
928 row or column. The result is returned as a temporary matrix.
929 Usage:
930
931 \code
932 vigra::Matrix<double> v(1, len);
933 v = ...;
934
935 vigra::Matrix<double> m = diagonalMatrix(v);
936 \endcode
937
938 <b>\#include</b> <vigra/matrix.hxx> or<br>
939 <b>\#include</b> <vigra/linear_algebra.hxx><br>
940 Namespaces: vigra and vigra::linalg
941 */
942 template <class T, class C>
943 TemporaryMatrix<T> diagonalMatrix(MultiArrayView<2, T, C> const & v)
944 {
945 vigra_precondition(rowCount(v) == 1 || columnCount(v) == 1,
946 "diagonalMatrix(): input must be a vector.");
947 MultiArrayIndex size = v.elementCount();
948 TemporaryMatrix<T> ret(size, size, NumericTraits<T>::zero());
949 if(rowCount(v) == 1)
950 diagonalMatrixImpl(v.bindInner(0), ret);
951 else
952 diagonalMatrixImpl(v.bindOuter(0), ret);
953 return ret;
954 }
955
956 /** transpose matrix \a v.
957 The result is written into \a r which must have the correct (i.e.
958 transposed) shape.
959
960 <b>\#include</b> <vigra/matrix.hxx> or<br>
961 <b>\#include</b> <vigra/linear_algebra.hxx><br>
962 Namespaces: vigra and vigra::linalg
963 */
964 template <class T, class C1, class C2>
965 void transpose(const MultiArrayView<2, T, C1> &v, MultiArrayView<2, T, C2> &r)
966 {
967 const MultiArrayIndex rows = rowCount(r);
968 const MultiArrayIndex cols = columnCount(r);
969 vigra_precondition(rows == columnCount(v) && cols == rowCount(v),
970 "transpose(): arrays must have transposed shapes.");
971 for(MultiArrayIndex i = 0; i < cols; ++i)
972 for(MultiArrayIndex j = 0; j < rows; ++j)
973 r(j, i) = v(i, j);
974 }
975
976 /** create the transpose of matrix \a v.
977 This does not copy any data, but only creates a transposed view
978 to the original matrix. A copy is only made when the transposed view
979 is assigned to another matrix.
980 Usage:
981
982 \code
983 vigra::Matrix<double> v(rows, cols);
984 v = ...;
985
986 vigra::Matrix<double> m = transpose(v);
987 \endcode
988
989 <b>\#include</b> <vigra/matrix.hxx> or<br>
990 <b>\#include</b> <vigra/linear_algebra.hxx><br>
991 Namespaces: vigra and vigra::linalg
992 */
993 template <class T, class C>
994 inline MultiArrayView<2, T, StridedArrayTag>
995 transpose(MultiArrayView<2, T, C> const & v)
996 {
997 return v.transpose();
998 }
999
1000 /** Create new matrix by concatenating two matrices \a a and \a b vertically, i.e. on top of each other.
1001 The two matrices must have the same number of columns.
1002 The result is returned as a temporary matrix.
1003
1004 <b>\#include</b> <vigra/matrix.hxx> or<br>
1005 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1006 Namespace: vigra::linalg
1007 */
1008 template <class T, class C1, class C2>
1009 inline TemporaryMatrix<T>
1010 joinVertically(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1011 {
1012 typedef typename TemporaryMatrix<T>::difference_type Shape;
1013
1014 MultiArrayIndex n = columnCount(a);
1015 vigra_precondition(n == columnCount(b),
1016 "joinVertically(): shape mismatch.");
1017
1018 MultiArrayIndex ma = rowCount(a);
1019 MultiArrayIndex mb = rowCount(b);
1020 TemporaryMatrix<T> t(ma + mb, n, T());
1021 t.subarray(Shape(0,0), Shape(ma, n)) = a;
1022 t.subarray(Shape(ma,0), Shape(ma+mb, n)) = b;
1023 return t;
1024 }
1025
1026 /** Create new matrix by concatenating two matrices \a a and \a b horizontally, i.e. side by side.
1027 The two matrices must have the same number of rows.
1028 The result is returned as a temporary matrix.
1029
1030 <b>\#include</b> <vigra/matrix.hxx> or<br>
1031 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1032 Namespace: vigra::linalg
1033 */
1034 template <class T, class C1, class C2>
1035 inline TemporaryMatrix<T>
1036 joinHorizontally(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1037 {
1038 typedef typename TemporaryMatrix<T>::difference_type Shape;
1039
1040 MultiArrayIndex m = rowCount(a);
1041 vigra_precondition(m == rowCount(b),
1042 "joinHorizontally(): shape mismatch.");
1043
1044 MultiArrayIndex na = columnCount(a);
1045 MultiArrayIndex nb = columnCount(b);
1046 TemporaryMatrix<T> t(m, na + nb, T());
1047 t.subarray(Shape(0,0), Shape(m, na)) = a;
1048 t.subarray(Shape(0, na), Shape(m, na + nb)) = b;
1049 return t;
1050 }
1051
1052 /** Initialize a matrix with repeated copies of a given matrix.
1053
1054 Matrix \a r will consist of \a verticalCount downward repetitions of \a v,
1055 and \a horizontalCount side-by-side repetitions. When \a v has size <tt>m</tt> by <tt>n</tt>,
1056 \a r must have size <tt>(m*verticalCount)</tt> by <tt>(n*horizontalCount)</tt>.
1057
1058 <b>\#include</b> <vigra/matrix.hxx> or<br>
1059 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1060 Namespace: vigra::linalg
1061 */
1062 template <class T, class C1, class C2>
1063 void repeatMatrix(MultiArrayView<2, T, C1> const & v, MultiArrayView<2, T, C2> &r,
1064 unsigned int verticalCount, unsigned int horizontalCount)
1065 {
1066 typedef typename Matrix<T>::difference_type Shape;
1067
1068 MultiArrayIndex m = rowCount(v), n = columnCount(v);
1069 vigra_precondition(m*verticalCount == rowCount(r) && n*horizontalCount == columnCount(r),
1070 "repeatMatrix(): Shape mismatch.");
1071
1072 for(MultiArrayIndex l=0; l<static_cast<MultiArrayIndex>(horizontalCount); ++l)
1073 {
1074 for(MultiArrayIndex k=0; k<static_cast<MultiArrayIndex>(verticalCount); ++k)
1075 {
1076 r.subarray(Shape(k*m, l*n), Shape((k+1)*m, (l+1)*n)) = v;
1077 }
1078 }
1079 }
1080
1081 /** Create a new matrix by repeating a given matrix.
1082
1083 The resulting matrix \a r will consist of \a verticalCount downward repetitions of \a v,
1084 and \a horizontalCount side-by-side repetitions, i.e. it will be of size
1085 <tt>(m*verticalCount)</tt> by <tt>(n*horizontalCount)</tt> when \a v has size <tt>m</tt> by <tt>n</tt>.
1086 The result is returned as a temporary matrix.
1087
1088 <b>\#include</b> <vigra/matrix.hxx> or<br>
1089 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1090 Namespace: vigra::linalg
1091 */
1092 template <class T, class C>
1093 TemporaryMatrix<T>
1094 repeatMatrix(MultiArrayView<2, T, C> const & v, unsigned int verticalCount, unsigned int horizontalCount)
1095 {
1096 MultiArrayIndex m = rowCount(v), n = columnCount(v);
1097 TemporaryMatrix<T> ret(verticalCount*m, horizontalCount*n);
1098 repeatMatrix(v, ret, verticalCount, horizontalCount);
1099 return ret;
1100 }
1101
1102 /** add matrices \a a and \a b.
1103 The result is written into \a r. All three matrices must have the same shape.
1104
1105 <b>\#include</b> <vigra/matrix.hxx> or<br>
1106 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1107 Namespace: vigra::linalg
1108 */
1109 template <class T, class C1, class C2, class C3>
1110 void add(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b,
1111 MultiArrayView<2, T, C3> &r)
1112 {
1113 const MultiArrayIndex rrows = rowCount(r);
1114 const MultiArrayIndex rcols = columnCount(r);
1115 vigra_precondition(rrows == rowCount(a) && rcols == columnCount(a) &&
1116 rrows == rowCount(b) && rcols == columnCount(b),
1117 "add(): Matrix shapes must agree.");
1118
1119 for(MultiArrayIndex i = 0; i < rcols; ++i) {
1120 for(MultiArrayIndex j = 0; j < rrows; ++j) {
1121 r(j, i) = a(j, i) + b(j, i);
1122 }
1123 }
1124 }
1125
1126 /** add matrices \a a and \a b.
1127 The two matrices must have the same shape.
1128 The result is returned as a temporary matrix.
1129
1130 <b>\#include</b> <vigra/matrix.hxx> or<br>
1131 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1132 Namespace: vigra::linalg
1133 */
1134 template <class T, class C1, class C2>
1135 inline TemporaryMatrix<T>
1136 operator+(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1137 {
1138 return TemporaryMatrix<T>(a) += b;
1139 }
1140
1141 template <class T, class C>
1142 inline TemporaryMatrix<T>
1143 operator+(const TemporaryMatrix<T> &a, const MultiArrayView<2, T, C> &b)
1144 {
1145 return const_cast<TemporaryMatrix<T> &>(a) += b;
1146 }
1147
1148 template <class T, class C>
1149 inline TemporaryMatrix<T>
1150 operator+(const MultiArrayView<2, T, C> &a, const TemporaryMatrix<T> &b)
1151 {
1152 return const_cast<TemporaryMatrix<T> &>(b) += a;
1153 }
1154
1155 template <class T>
1156 inline TemporaryMatrix<T>
1157 operator+(const TemporaryMatrix<T> &a, const TemporaryMatrix<T> &b)
1158 {
1159 return const_cast<TemporaryMatrix<T> &>(a) += b;
1160 }
1161
1162 /** add scalar \a b to every element of the matrix \a a.
1163 The result is returned as a temporary matrix.
1164
1165 <b>\#include</b> <vigra/matrix.hxx> or<br>
1166 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1167 Namespace: vigra::linalg
1168 */
1169 template <class T, class C>
1170 inline TemporaryMatrix<T>
1171 operator+(const MultiArrayView<2, T, C> &a, T b)
1172 {
1173 return TemporaryMatrix<T>(a) += b;
1174 }
1175
1176 template <class T>
1177 inline TemporaryMatrix<T>
1178 operator+(const TemporaryMatrix<T> &a, T b)
1179 {
1180 return const_cast<TemporaryMatrix<T> &>(a) += b;
1181 }
1182
1183 /** add scalar \a a to every element of the matrix \a b.
1184 The result is returned as a temporary matrix.
1185
1186 <b>\#include</b> <vigra/matrix.hxx> or<br>
1187 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1188 Namespace: vigra::linalg
1189 */
1190 template <class T, class C>
1191 inline TemporaryMatrix<T>
1192 operator+(T a, const MultiArrayView<2, T, C> &b)
1193 {
1194 return TemporaryMatrix<T>(b) += a;
1195 }
1196
1197 template <class T>
1198 inline TemporaryMatrix<T>
1199 operator+(T a, const TemporaryMatrix<T> &b)
1200 {
1201 return const_cast<TemporaryMatrix<T> &>(b) += a;
1202 }
1203
1204 /** subtract matrix \a b from \a a.
1205 The result is written into \a r. All three matrices must have the same shape.
1206
1207 <b>\#include</b> <vigra/matrix.hxx> or<br>
1208 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1209 Namespace: vigra::linalg
1210 */
1211 template <class T, class C1, class C2, class C3>
1212 void sub(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b,
1213 MultiArrayView<2, T, C3> &r)
1214 {
1215 const MultiArrayIndex rrows = rowCount(r);
1216 const MultiArrayIndex rcols = columnCount(r);
1217 vigra_precondition(rrows == rowCount(a) && rcols == columnCount(a) &&
1218 rrows == rowCount(b) && rcols == columnCount(b),
1219 "subtract(): Matrix shapes must agree.");
1220
1221 for(MultiArrayIndex i = 0; i < rcols; ++i) {
1222 for(MultiArrayIndex j = 0; j < rrows; ++j) {
1223 r(j, i) = a(j, i) - b(j, i);
1224 }
1225 }
1226 }
1227
1228 /** subtract matrix \a b from \a a.
1229 The two matrices must have the same shape.
1230 The result is returned as a temporary matrix.
1231
1232 <b>\#include</b> <vigra/matrix.hxx> or<br>
1233 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1234 Namespace: vigra::linalg
1235 */
1236 template <class T, class C1, class C2>
1237 inline TemporaryMatrix<T>
1238 operator-(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1239 {
1240 return TemporaryMatrix<T>(a) -= b;
1241 }
1242
1243 template <class T, class C>
1244 inline TemporaryMatrix<T>
1245 operator-(const TemporaryMatrix<T> &a, const MultiArrayView<2, T, C> &b)
1246 {
1247 return const_cast<TemporaryMatrix<T> &>(a) -= b;
1248 }
1249
1250 template <class T, class C>
1251 TemporaryMatrix<T>
1252 operator-(const MultiArrayView<2, T, C> &a, const TemporaryMatrix<T> &b)
1253 {
1254 const MultiArrayIndex rows = rowCount(a);
1255 const MultiArrayIndex cols = columnCount(a);
1256 vigra_precondition(rows == b.rowCount() && cols == b.columnCount(),
1257 "Matrix::operator-(): Shape mismatch.");
1258
1259 for(MultiArrayIndex i = 0; i < cols; ++i)
1260 for(MultiArrayIndex j = 0; j < rows; ++j)
1261 const_cast<TemporaryMatrix<T> &>(b)(j, i) = a(j, i) - b(j, i);
1262 return b;
1263 }
1264
1265 template <class T>
1266 inline TemporaryMatrix<T>
1267 operator-(const TemporaryMatrix<T> &a, const TemporaryMatrix<T> &b)
1268 {
1269 return const_cast<TemporaryMatrix<T> &>(a) -= b;
1270 }
1271
1272 /** negate matrix \a a.
1273 The result is returned as a temporary matrix.
1274
1275 <b>\#include</b> <vigra/matrix.hxx> or<br>
1276 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1277 Namespace: vigra::linalg
1278 */
1279 template <class T, class C>
1280 inline TemporaryMatrix<T>
1281 operator-(const MultiArrayView<2, T, C> &a)
1282 {
1283 return TemporaryMatrix<T>(a) *= -NumericTraits<T>::one();
1284 }
1285
1286 template <class T>
1287 inline TemporaryMatrix<T>
1288 operator-(const TemporaryMatrix<T> &a)
1289 {
1290 return const_cast<TemporaryMatrix<T> &>(a) *= -NumericTraits<T>::one();
1291 }
1292
1293 /** subtract scalar \a b from every element of the matrix \a a.
1294 The result is returned as a temporary matrix.
1295
1296 <b>\#include</b> <vigra/matrix.hxx> or<br>
1297 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1298 Namespace: vigra::linalg
1299 */
1300 template <class T, class C>
1301 inline TemporaryMatrix<T>
1302 operator-(const MultiArrayView<2, T, C> &a, T b)
1303 {
1304 return TemporaryMatrix<T>(a) -= b;
1305 }
1306
1307 template <class T>
1308 inline TemporaryMatrix<T>
1309 operator-(const TemporaryMatrix<T> &a, T b)
1310 {
1311 return const_cast<TemporaryMatrix<T> &>(a) -= b;
1312 }
1313
1314 /** subtract every element of the matrix \a b from scalar \a a.
1315 The result is returned as a temporary matrix.
1316
1317 <b>\#include</b> <vigra/matrix.hxx> or<br>
1318 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1319 Namespace: vigra::linalg
1320 */
1321 template <class T, class C>
1322 inline TemporaryMatrix<T>
1323 operator-(T a, const MultiArrayView<2, T, C> &b)
1324 {
1325 return TemporaryMatrix<T>(b.shape(), a) -= b;
1326 }
1327
1328 /** calculate the inner product of two matrices representing vectors.
1329 Typically, matrix \a x has a single row, and matrix \a y has
1330 a single column, and the other dimensions match. In addition, this
1331 function handles the cases when either or both of the two inputs are
1332 transposed (e.g. it can compute the dot product of two column vectors).
1333 A <tt>PreconditionViolation</tt> exception is thrown when
1334 the shape conditions are violated.
1335
1336 <b>\#include</b> <vigra/matrix.hxx> or<br>
1337 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1338 Namespaces: vigra and vigra::linalg
1339 */
1340 template <class T, class C1, class C2>
1341 typename NormTraits<T>::SquaredNormType
1342 dot(const MultiArrayView<2, T, C1> &x, const MultiArrayView<2, T, C2> &y)
1343 {
1344 typename NormTraits<T>::SquaredNormType ret =
1345 NumericTraits<typename NormTraits<T>::SquaredNormType>::zero();
1346 if(y.shape(1) == 1)
1347 {
1348 std::ptrdiff_t size = y.shape(0);
1349 if(x.shape(0) == 1 && x.shape(1) == size) // proper scalar product
1350 for(std::ptrdiff_t i = 0; i < size; ++i)
1351 ret += x(0, i) * y(i, 0);
1352 else if(x.shape(1) == 1u && x.shape(0) == size) // two column vectors
1353 for(std::ptrdiff_t i = 0; i < size; ++i)
1354 ret += x(i, 0) * y(i, 0);
1355 else
1356 vigra_precondition(false, "dot(): wrong matrix shapes.");
1357 }
1358 else if(y.shape(0) == 1)
1359 {
1360 std::ptrdiff_t size = y.shape(1);
1361 if(x.shape(0) == 1u && x.shape(1) == size) // two row vectors
1362 for(std::ptrdiff_t i = 0; i < size; ++i)
1363 ret += x(0, i) * y(0, i);
1364 else if(x.shape(1) == 1u && x.shape(0) == size) // column dot row
1365 for(std::ptrdiff_t i = 0; i < size; ++i)
1366 ret += x(i, 0) * y(0, i);
1367 else
1368 vigra_precondition(false, "dot(): wrong matrix shapes.");
1369 }
1370 else
1371 vigra_precondition(false, "dot(): wrong matrix shapes.");
1372 return ret;
1373 }
1374
1375 /** calculate the inner product of two vectors. The vector
1376 lengths must match.
1377
1378 <b>\#include</b> <vigra/matrix.hxx> or<br>
1379 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1380 Namespaces: vigra and vigra::linalg
1381 */
1382 template <class T, class C1, class C2>
1383 typename NormTraits<T>::SquaredNormType
1384 dot(const MultiArrayView<1, T, C1> &x, const MultiArrayView<1, T, C2> &y)
1385 {
1386 const MultiArrayIndex n = x.elementCount();
1387 vigra_precondition(n == y.elementCount(),
1388 "dot(): shape mismatch.");
1389 typename NormTraits<T>::SquaredNormType ret =
1390 NumericTraits<typename NormTraits<T>::SquaredNormType>::zero();
1391 for(MultiArrayIndex i = 0; i < n; ++i)
1392 ret += x(i) * y(i);
1393 return ret;
1394 }
1395
1396 /** calculate the cross product of two vectors of length 3.
1397 The result is written into \a r.
1398
1399 <b>\#include</b> <vigra/matrix.hxx> or<br>
1400 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1401 Namespaces: vigra and vigra::linalg
1402 */
1403 template <class T, class C1, class C2, class C3>
1404 void cross(const MultiArrayView<1, T, C1> &x, const MultiArrayView<1, T, C2> &y,
1405 MultiArrayView<1, T, C3> &r)
1406 {
1407 vigra_precondition(3 == x.elementCount() && 3 == y.elementCount() && 3 == r.elementCount(),
1408 "cross(): vectors must have length 3.");
1409 r(0) = x(1)*y(2) - x(2)*y(1);
1410 r(1) = x(2)*y(0) - x(0)*y(2);
1411 r(2) = x(0)*y(1) - x(1)*y(0);
1412 }
1413
1414 /** calculate the cross product of two matrices representing vectors.
1415 That is, \a x, \a y, and \a r must have a single column of length 3. The result
1416 is written into \a r.
1417
1418 <b>\#include</b> <vigra/matrix.hxx> or<br>
1419 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1420 Namespaces: vigra and vigra::linalg
1421 */
1422 template <class T, class C1, class C2, class C3>
1423 void cross(const MultiArrayView<2, T, C1> &x, const MultiArrayView<2, T, C2> &y,
1424 MultiArrayView<2, T, C3> &r)
1425 {
1426 vigra_precondition(3 == rowCount(x) && 3 == rowCount(y) && 3 == rowCount(r) ,
1427 "cross(): vectors must have length 3.");
1428 r(0,0) = x(1,0)*y(2,0) - x(2,0)*y(1,0);
1429 r(1,0) = x(2,0)*y(0,0) - x(0,0)*y(2,0);
1430 r(2,0) = x(0,0)*y(1,0) - x(1,0)*y(0,0);
1431 }
1432
1433 /** calculate the cross product of two matrices representing vectors.
1434 That is, \a x, and \a y must have a single column of length 3. The result
1435 is returned as a temporary matrix.
1436
1437 <b>\#include</b> <vigra/matrix.hxx> or<br>
1438 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1439 Namespaces: vigra and vigra::linalg
1440 */
1441 template <class T, class C1, class C2>
1442 TemporaryMatrix<T>
1443 cross(const MultiArrayView<2, T, C1> &x, const MultiArrayView<2, T, C2> &y)
1444 {
1445 TemporaryMatrix<T> ret(3, 1);
1446 cross(x, y, ret);
1447 return ret;
1448 }
1449 /** calculate the outer product of two matrices representing vectors.
1450 That is, matrix \a x must have a single column, and matrix \a y must
1451 have a single row, and the other dimensions must match. The result
1452 is written into \a r.
1453
1454 <b>\#include</b> <vigra/matrix.hxx> or<br>
1455 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1456 Namespaces: vigra and vigra::linalg
1457 */
1458 template <class T, class C1, class C2, class C3>
1459 void outer(const MultiArrayView<2, T, C1> &x, const MultiArrayView<2, T, C2> &y,
1460 MultiArrayView<2, T, C3> &r)
1461 {
1462 const MultiArrayIndex rows = rowCount(r);
1463 const MultiArrayIndex cols = columnCount(r);
1464 vigra_precondition(rows == rowCount(x) && cols == columnCount(y) &&
1465 1 == columnCount(x) && 1 == rowCount(y),
1466 "outer(): shape mismatch.");
1467 for(MultiArrayIndex i = 0; i < cols; ++i)
1468 for(MultiArrayIndex j = 0; j < rows; ++j)
1469 r(j, i) = x(j, 0) * y(0, i);
1470 }
1471
1472 /** calculate the outer product of two matrices representing vectors.
1473 That is, matrix \a x must have a single column, and matrix \a y must
1474 have a single row, and the other dimensions must match. The result
1475 is returned as a temporary matrix.
1476
1477 <b>\#include</b> <vigra/matrix.hxx> or<br>
1478 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1479 Namespaces: vigra and vigra::linalg
1480 */
1481 template <class T, class C1, class C2>
1482 TemporaryMatrix<T>
1483 outer(const MultiArrayView<2, T, C1> &x, const MultiArrayView<2, T, C2> &y)
1484 {
1485 const MultiArrayIndex rows = rowCount(x);
1486 const MultiArrayIndex cols = columnCount(y);
1487 vigra_precondition(1 == columnCount(x) && 1 == rowCount(y),
1488 "outer(): shape mismatch.");
1489 TemporaryMatrix<T> ret(rows, cols);
1490 outer(x, y, ret);
1491 return ret;
1492 }
1493
1494 /** calculate the outer product of a matrix (representing a vector) with itself.
1495 The result is returned as a temporary matrix.
1496
1497 <b>\#include</b> <vigra/matrix.hxx> or<br>
1498 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1499 Namespaces: vigra and vigra::linalg
1500 */
1501 template <class T, class C>
1502 TemporaryMatrix<T>
1503 outer(const MultiArrayView<2, T, C> &x)
1504 {
1505 const MultiArrayIndex rows = rowCount(x);
1506 const MultiArrayIndex cols = columnCount(x);
1507 vigra_precondition(rows == 1 || cols == 1,
1508 "outer(): matrix does not represent a vector.");
1509 const MultiArrayIndex size = std::max(rows, cols);
1510 TemporaryMatrix<T> ret(size, size);
1511
1512 if(rows == 1)
1513 {
1514 for(MultiArrayIndex i = 0; i < size; ++i)
1515 for(MultiArrayIndex j = 0; j < size; ++j)
1516 ret(j, i) = x(0, j) * x(0, i);
1517 }
1518 else
1519 {
1520 for(MultiArrayIndex i = 0; i < size; ++i)
1521 for(MultiArrayIndex j = 0; j < size; ++j)
1522 ret(j, i) = x(j, 0) * x(i, 0);
1523 }
1524 return ret;
1525 }
1526
1527 /** calculate the outer product of a TinyVector with itself.
1528 The result is returned as a temporary matrix.
1529
1530 <b>\#include</b> <vigra/matrix.hxx> or<br>
1531 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1532 Namespaces: vigra and vigra::linalg
1533 */
1534 template <class T, int N>
1535 TemporaryMatrix<T>
1536 outer(const TinyVector<T, N> &x)
1537 {
1538 TemporaryMatrix<T> ret(N, N);
1539
1540 for(MultiArrayIndex i = 0; i < N; ++i)
1541 for(MultiArrayIndex j = 0; j < N; ++j)
1542 ret(j, i) = x[j] * x[i];
1543 return ret;
1544 }
1545
1546 template <class T>
1547 class PointWise
1548 {
1549 public:
1550 T const & t;
1551
1552 PointWise(T const & it)
1553 : t(it)
1554 {}
1555 };
1556
1557 template <class T>
1558 PointWise<T> pointWise(T const & t)
1559 {
1560 return PointWise<T>(t);
1561 }
1562
1563
1564 /** multiply matrix \a a with scalar \a b.
1565 The result is written into \a r. \a a and \a r must have the same shape.
1566
1567 <b>\#include</b> <vigra/matrix.hxx> or<br>
1568 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1569 Namespace: vigra::linalg
1570 */
1571 template <class T, class C1, class C2>
1572 void smul(const MultiArrayView<2, T, C1> &a, T b, MultiArrayView<2, T, C2> &r)
1573 {
1574 const MultiArrayIndex rows = rowCount(a);
1575 const MultiArrayIndex cols = columnCount(a);
1576 vigra_precondition(rows == rowCount(r) && cols == columnCount(r),
1577 "smul(): Matrix sizes must agree.");
1578
1579 for(MultiArrayIndex i = 0; i < cols; ++i)
1580 for(MultiArrayIndex j = 0; j < rows; ++j)
1581 r(j, i) = a(j, i) * b;
1582 }
1583
1584 /** multiply scalar \a a with matrix \a b.
1585 The result is written into \a r. \a b and \a r must have the same shape.
1586
1587 <b>\#include</b> <vigra/matrix.hxx> or<br>
1588 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1589 Namespace: vigra::linalg
1590 */
1591 template <class T, class C2, class C3>
1592 void smul(T a, const MultiArrayView<2, T, C2> &b, MultiArrayView<2, T, C3> &r)
1593 {
1594 smul(b, a, r);
1595 }
1596
1597 /** perform matrix multiplication of matrices \a a and \a b.
1598 The result is written into \a r. The three matrices must have matching shapes.
1599
1600 <b>\#include</b> <vigra/matrix.hxx> or<br>
1601 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1602 Namespace: vigra::linalg
1603 */
1604 template <class T, class C1, class C2, class C3>
1605 void mmul(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b,
1606 MultiArrayView<2, T, C3> &r)
1607 {
1608 const MultiArrayIndex rrows = rowCount(r);
1609 const MultiArrayIndex rcols = columnCount(r);
1610 const MultiArrayIndex acols = columnCount(a);
1611 vigra_precondition(rrows == rowCount(a) && rcols == columnCount(b) && acols == rowCount(b),
1612 "mmul(): Matrix shapes must agree.");
1613
1614 // order of loops ensures that inner loop goes down columns
1615 for(MultiArrayIndex i = 0; i < rcols; ++i)
1616 {
1617 for(MultiArrayIndex j = 0; j < rrows; ++j)
1618 r(j, i) = a(j, 0) * b(0, i);
1619 for(MultiArrayIndex k = 1; k < acols; ++k)
1620 for(MultiArrayIndex j = 0; j < rrows; ++j)
1621 r(j, i) += a(j, k) * b(k, i);
1622 }
1623 }
1624
1625 /** perform matrix multiplication of matrices \a a and \a b.
1626 \a a and \a b must have matching shapes.
1627 The result is returned as a temporary matrix.
1628
1629 <b>\#include</b> <vigra/matrix.hxx> or<br>
1630 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1631 Namespace: vigra::linalg
1632 */
1633 template <class T, class C1, class C2>
1634 inline TemporaryMatrix<T>
1635 mmul(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1636 {
1637 TemporaryMatrix<T> ret(rowCount(a), columnCount(b));
1638 mmul(a, b, ret);
1639 return ret;
1640 }
1641
1642 /** multiply two matrices \a a and \a b pointwise.
1643 The result is written into \a r. All three matrices must have the same shape.
1644
1645 <b>\#include</b> <vigra/matrix.hxx> or<br>
1646 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1647 Namespace: vigra::linalg
1648 */
1649 template <class T, class C1, class C2, class C3>
1650 void pmul(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b,
1651 MultiArrayView<2, T, C3> &r)
1652 {
1653 const MultiArrayIndex rrows = rowCount(r);
1654 const MultiArrayIndex rcols = columnCount(r);
1655 vigra_precondition(rrows == rowCount(a) && rcols == columnCount(a) &&
1656 rrows == rowCount(b) && rcols == columnCount(b),
1657 "pmul(): Matrix shapes must agree.");
1658
1659 for(MultiArrayIndex i = 0; i < rcols; ++i) {
1660 for(MultiArrayIndex j = 0; j < rrows; ++j) {
1661 r(j, i) = a(j, i) * b(j, i);
1662 }
1663 }
1664 }
1665
1666 /** multiply matrices \a a and \a b pointwise.
1667 \a a and \a b must have matching shapes.
1668 The result is returned as a temporary matrix.
1669
1670 <b>\#include</b> <vigra/matrix.hxx> or<br>
1671 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1672 Namespace: vigra::linalg
1673 */
1674 template <class T, class C1, class C2>
1675 inline TemporaryMatrix<T>
1676 pmul(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1677 {
1678 TemporaryMatrix<T> ret(a.shape());
1679 pmul(a, b, ret);
1680 return ret;
1681 }
1682
1683 /** multiply matrices \a a and \a b pointwise.
1684 \a a and \a b must have matching shapes.
1685 The result is returned as a temporary matrix.
1686
1687 Usage:
1688
1689 \code
1690 Matrix<double> a(m,n), b(m,n);
1691
1692 Matrix<double> c = a * pointWise(b);
1693 // is equivalent to
1694 // Matrix<double> c = pmul(a, b);
1695 \endcode
1696
1697 <b>\#include</b> <vigra/matrix.hxx> or<br>
1698 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1699 Namespace: vigra::linalg
1700 */
1701 template <class T, class C, class U>
1702 inline TemporaryMatrix<T>
1703 operator*(const MultiArrayView<2, T, C> &a, PointWise<U> b)
1704 {
1705 return pmul(a, b.t);
1706 }
1707
1708 /** multiply matrix \a a with scalar \a b.
1709 The result is returned as a temporary matrix.
1710
1711 <b>\#include</b> <vigra/matrix.hxx> or<br>
1712 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1713 Namespace: vigra::linalg
1714 */
1715 template <class T, class C>
1716 inline TemporaryMatrix<T>
1717 operator*(const MultiArrayView<2, T, C> &a, T b)
1718 {
1719 return TemporaryMatrix<T>(a) *= b;
1720 }
1721
1722 template <class T>
1723 inline TemporaryMatrix<T>
1724 operator*(const TemporaryMatrix<T> &a, T b)
1725 {
1726 return const_cast<TemporaryMatrix<T> &>(a) *= b;
1727 }
1728
1729 /** multiply scalar \a a with matrix \a b.
1730 The result is returned as a temporary matrix.
1731
1732 <b>\#include</b> <vigra/matrix.hxx> or<br>
1733 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1734 Namespace: vigra::linalg
1735 */
1736 template <class T, class C>
1737 inline TemporaryMatrix<T>
1738 operator*(T a, const MultiArrayView<2, T, C> &b)
1739 {
1740 return TemporaryMatrix<T>(b) *= a;
1741 }
1742
1743 template <class T>
1744 inline TemporaryMatrix<T>
1745 operator*(T a, const TemporaryMatrix<T> &b)
1746 {
1747 return const_cast<TemporaryMatrix<T> &>(b) *= a;
1748 }
1749
1750 /** multiply matrix \a a with TinyVector \a b.
1751 \a a must be of size <tt>N x N</tt>. Vector \a b and the result
1752 vector are interpreted as column vectors.
1753
1754 <b>\#include</b> <vigra/matrix.hxx> or<br>
1755 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1756 Namespace: vigra::linalg
1757 */
1758 template <class T, class A, int N, class DATA, class DERIVED>
1759 TinyVector<T, N>
1760 operator*(const Matrix<T, A> &a, const TinyVectorBase<T, N, DATA, DERIVED> &b)
1761 {
1762 vigra_precondition(N == rowCount(a) && N == columnCount(a),
1763 "operator*(Matrix, TinyVector): Shape mismatch.");
1764
1765 TinyVector<T, N> res = TinyVectorView<T, N>(&a(0,0)) * b[0];
1766 for(MultiArrayIndex i = 1; i < N; ++i)
1767 res += TinyVectorView<T, N>(&a(0,i)) * b[i];
1768 return res;
1769 }
1770
1771 /** multiply TinyVector \a a with matrix \a b.
1772 \a b must be of size <tt>N x N</tt>. Vector \a a and the result
1773 vector are interpreted as row vectors.
1774
1775 <b>\#include</b> <vigra/matrix.hxx> or<br>
1776 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1777 Namespace: vigra::linalg
1778 */
1779 template <class T, int N, class DATA, class DERIVED, class A>
1780 TinyVector<T, N>
1781 operator*(const TinyVectorBase<T, N, DATA, DERIVED> &a, const Matrix<T, A> &b)
1782 {
1783 vigra_precondition(N == rowCount(b) && N == columnCount(b),
1784 "operator*(TinyVector, Matrix): Shape mismatch.");
1785
1786 TinyVector<T, N> res;
1787 for(MultiArrayIndex i = 0; i < N; ++i)
1788 res[i] = dot(a, TinyVectorView<T, N>(&b(0,i)));
1789 return res;
1790 }
1791
1792 /** perform matrix multiplication of matrices \a a and \a b.
1793 \a a and \a b must have matching shapes.
1794 The result is returned as a temporary matrix.
1795
1796 <b>\#include</b> <vigra/matrix.hxx> or<br>
1797 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1798 Namespace: vigra::linalg
1799 */
1800 template <class T, class C1, class C2>
1801 inline TemporaryMatrix<T>
1802 operator*(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1803 {
1804 TemporaryMatrix<T> ret(rowCount(a), columnCount(b));
1805 mmul(a, b, ret);
1806 return ret;
1807 }
1808
1809 /** divide matrix \a a by scalar \a b.
1810 The result is written into \a r. \a a and \a r must have the same shape.
1811
1812 <b>\#include</b> <vigra/matrix.hxx> or<br>
1813 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1814 Namespace: vigra::linalg
1815 */
1816 template <class T, class C1, class C2>
1817 void sdiv(const MultiArrayView<2, T, C1> &a, T b, MultiArrayView<2, T, C2> &r)
1818 {
1819 const MultiArrayIndex rows = rowCount(a);
1820 const MultiArrayIndex cols = columnCount(a);
1821 vigra_precondition(rows == rowCount(r) && cols == columnCount(r),
1822 "sdiv(): Matrix sizes must agree.");
1823
1824 for(MultiArrayIndex i = 0; i < cols; ++i)
1825 for(MultiArrayIndex j = 0; j < rows; ++j)
1826 r(j, i) = a(j, i) / b;
1827 }
1828
1829 /** divide two matrices \a a and \a b pointwise.
1830 The result is written into \a r. All three matrices must have the same shape.
1831
1832 <b>\#include</b> <vigra/matrix.hxx> or<br>
1833 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1834 Namespace: vigra::linalg
1835 */
1836 template <class T, class C1, class C2, class C3>
1837 void pdiv(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b,
1838 MultiArrayView<2, T, C3> &r)
1839 {
1840 const MultiArrayIndex rrows = rowCount(r);
1841 const MultiArrayIndex rcols = columnCount(r);
1842 vigra_precondition(rrows == rowCount(a) && rcols == columnCount(a) &&
1843 rrows == rowCount(b) && rcols == columnCount(b),
1844 "pdiv(): Matrix shapes must agree.");
1845
1846 for(MultiArrayIndex i = 0; i < rcols; ++i) {
1847 for(MultiArrayIndex j = 0; j < rrows; ++j) {
1848 r(j, i) = a(j, i) / b(j, i);
1849 }
1850 }
1851 }
1852
1853 /** divide matrices \a a and \a b pointwise.
1854 \a a and \a b must have matching shapes.
1855 The result is returned as a temporary matrix.
1856
1857 <b>\#include</b> <vigra/matrix.hxx> or<br>
1858 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1859 Namespace: vigra::linalg
1860 */
1861 template <class T, class C1, class C2>
1862 inline TemporaryMatrix<T>
1863 pdiv(const MultiArrayView<2, T, C1> &a, const MultiArrayView<2, T, C2> &b)
1864 {
1865 TemporaryMatrix<T> ret(a.shape());
1866 pdiv(a, b, ret);
1867 return ret;
1868 }
1869
1870 /** divide matrices \a a and \a b pointwise.
1871 \a a and \a b must have matching shapes.
1872 The result is returned as a temporary matrix.
1873
1874 Usage:
1875
1876 \code
1877 Matrix<double> a(m,n), b(m,n);
1878
1879 Matrix<double> c = a / pointWise(b);
1880 // is equivalent to
1881 // Matrix<double> c = pdiv(a, b);
1882 \endcode
1883
1884 <b>\#include</b> <vigra/matrix.hxx> or<br>
1885 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1886 Namespace: vigra::linalg
1887 */
1888 template <class T, class C, class U>
1889 inline TemporaryMatrix<T>
1890 operator/(const MultiArrayView<2, T, C> &a, PointWise<U> b)
1891 {
1892 return pdiv(a, b.t);
1893 }
1894
1895 /** divide matrix \a a by scalar \a b.
1896 The result is returned as a temporary matrix.
1897
1898 <b>\#include</b> <vigra/matrix.hxx> or<br>
1899 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1900 Namespace: vigra::linalg
1901 */
1902 template <class T, class C>
1903 inline TemporaryMatrix<T>
1904 operator/(const MultiArrayView<2, T, C> &a, T b)
1905 {
1906 return TemporaryMatrix<T>(a) /= b;
1907 }
1908
1909 template <class T>
1910 inline TemporaryMatrix<T>
1911 operator/(const TemporaryMatrix<T> &a, T b)
1912 {
1913 return const_cast<TemporaryMatrix<T> &>(a) /= b;
1914 }
1915
1916 /** Create a matrix whose elements are the quotients between scalar \a a and
1917 matrix \a b. The result is returned as a temporary matrix.
1918
1919 <b>\#include</b> <vigra/matrix.hxx> or<br>
1920 <b>\#include</b> <vigra/linear_algebra.hxx><br>
1921 Namespace: vigra::linalg
1922 */
1923 template <class T, class C>
1924 inline TemporaryMatrix<T>
1925 operator/(T a, const MultiArrayView<2, T, C> &b)
1926 {
1927 return TemporaryMatrix<T>(b.shape(), a) / pointWise(b);
1928 }
1929
1930 using vigra::argMin;
1931 using vigra::argMinIf;
1932 using vigra::argMax;
1933 using vigra::argMaxIf;
1934
1935 /** \brief Find the index of the minimum element in a matrix.
1936
1937 The function returns the index in column-major scan-order sense,
1938 i.e. according to the order used by <tt>MultiArrayView::operator[]</tt>.
1939 If the matrix is actually a vector, this is just the row or columns index.
1940 In case of a truly 2-dimensional matrix, the index can be converted to an
1941 index pair by calling <tt>MultiArrayView::scanOrderIndexToCoordinate()</tt>
1942
1943 <b>Required Interface:</b>
1944
1945 \code
1946 bool f = a[0] < NumericTraits<T>::max();
1947 \endcode
1948
1949 <b>\#include</b> <vigra/matrix.hxx><br>
1950 Namespace: vigra
1951 */
1952 template <class T, class C>
1953 int argMin(MultiArrayView<2, T, C> const & a)
1954 {
1955 T vopt = NumericTraits<T>::max();
1956 int best = -1;
1957 for(int k=0; k < a.size(); ++k)
1958 {
1959 if(a[k] < vopt)
1960 {
1961 vopt = a[k];
1962 best = k;
1963 }
1964 }
1965 return best;
1966 }
1967
1968 /** \brief Find the index of the maximum element in a matrix.
1969
1970 The function returns the index in column-major scan-order sense,
1971 i.e. according to the order used by <tt>MultiArrayView::operator[]</tt>.
1972 If the matrix is actually a vector, this is just the row or columns index.
1973 In case of a truly 2-dimensional matrix, the index can be converted to an
1974 index pair by calling <tt>MultiArrayView::scanOrderIndexToCoordinate()</tt>
1975
1976 <b>Required Interface:</b>
1977
1978 \code
1979 bool f = NumericTraits<T>::min() < a[0];
1980 \endcode
1981
1982 <b>\#include</b> <vigra/matrix.hxx><br>
1983 Namespace: vigra
1984 */
1985 template <class T, class C>
1986 int argMax(MultiArrayView<2, T, C> const & a)
1987 {
1988 T vopt = NumericTraits<T>::min();
1989 int best = -1;
1990 for(int k=0; k < a.size(); ++k)
1991 {
1992 if(vopt < a[k])
1993 {
1994 vopt = a[k];
1995 best = k;
1996 }
1997 }
1998 return best;
1999 }
2000
2001 /** \brief Find the index of the minimum element in a matrix subject to a condition.
2002
2003 The function returns <tt>-1</tt> if no element conforms to \a condition.
2004 Otherwise, the index of the maximum element is returned in column-major scan-order sense,
2005 i.e. according to the order used by <tt>MultiArrayView::operator[]</tt>.
2006 If the matrix is actually a vector, this is just the row or columns index.
2007 In case of a truly 2-dimensional matrix, the index can be converted to an
2008 index pair by calling <tt>MultiArrayView::scanOrderIndexToCoordinate()</tt>
2009
2010 <b>Required Interface:</b>
2011
2012 \code
2013 bool c = condition(a[0]);
2014 bool f = a[0] < NumericTraits<T>::max();
2015 \endcode
2016
2017 <b>\#include</b> <vigra/matrix.hxx><br>
2018 Namespace: vigra
2019 */
2020 template <class T, class C, class UnaryFunctor>
2021 int argMinIf(MultiArrayView<2, T, C> const & a, UnaryFunctor condition)
2022 {
2023 T vopt = NumericTraits<T>::max();
2024 int best = -1;
2025 for(int k=0; k < a.size(); ++k)
2026 {
2027 if(condition(a[k]) && a[k] < vopt)
2028 {
2029 vopt = a[k];
2030 best = k;
2031 }
2032 }
2033 return best;
2034 }
2035
2036 /** \brief Find the index of the maximum element in a matrix subject to a condition.
2037
2038 The function returns <tt>-1</tt> if no element conforms to \a condition.
2039 Otherwise, the index of the maximum element is returned in column-major scan-order sense,
2040 i.e. according to the order used by <tt>MultiArrayView::operator[]</tt>.
2041 If the matrix is actually a vector, this is just the row or columns index.
2042 In case of a truly 2-dimensional matrix, the index can be converted to an
2043 index pair by calling <tt>MultiArrayView::scanOrderIndexToCoordinate()</tt>
2044
2045 <b>Required Interface:</b>
2046
2047 \code
2048 bool c = condition(a[0]);
2049 bool f = NumericTraits<T>::min() < a[0];
2050 \endcode
2051
2052 <b>\#include</b> <vigra/matrix.hxx><br>
2053 Namespace: vigra
2054 */
2055 template <class T, class C, class UnaryFunctor>
2056 int argMaxIf(MultiArrayView<2, T, C> const & a, UnaryFunctor condition)
2057 {
2058 T vopt = NumericTraits<T>::min();
2059 int best = -1;
2060 for(int k=0; k < a.size(); ++k)
2061 {
2062 if(condition(a[k]) && vopt < a[k])
2063 {
2064 vopt = a[k];
2065 best = k;
2066 }
2067 }
2068 return best;
2069 }
2070
2071 /** Matrix point-wise power.
2072 */
2073 template <class T, class C>
2074 linalg::TemporaryMatrix<T> pow(MultiArrayView<2, T, C> const & v, T exponent)
2075 {
2076 linalg::TemporaryMatrix<T> t(v.shape());
2077 MultiArrayIndex m = rowCount(v), n = columnCount(v);
2078
2079 for(MultiArrayIndex i = 0; i < n; ++i)
2080 for(MultiArrayIndex j = 0; j < m; ++j)
2081 t(j, i) = vigra::pow(v(j, i), exponent);
2082 return t;
2083 }
2084
2085 template <class T>
2086 linalg::TemporaryMatrix<T> pow(linalg::TemporaryMatrix<T> const & v, T exponent)
2087 {
2088 linalg::TemporaryMatrix<T> & t = const_cast<linalg::TemporaryMatrix<T> &>(v);
2089 MultiArrayIndex m = rowCount(t), n = columnCount(t);
2090
2091 for(MultiArrayIndex i = 0; i < n; ++i)
2092 for(MultiArrayIndex j = 0; j < m; ++j)
2093 t(j, i) = vigra::pow(t(j, i), exponent);
2094 return t;
2095 }
2096
2097 template <class T, class C>
2098 linalg::TemporaryMatrix<T> pow(MultiArrayView<2, T, C> const & v, int exponent)
2099 {
2100 linalg::TemporaryMatrix<T> t(v.shape());
2101 MultiArrayIndex m = rowCount(v), n = columnCount(v);
2102
2103 for(MultiArrayIndex i = 0; i < n; ++i)
2104 for(MultiArrayIndex j = 0; j < m; ++j)
2105 t(j, i) = vigra::pow(v(j, i), exponent);
2106 return t;
2107 }
2108
2109 template <class T>
2110 linalg::TemporaryMatrix<T> pow(linalg::TemporaryMatrix<T> const & v, int exponent)
2111 {
2112 linalg::TemporaryMatrix<T> & t = const_cast<linalg::TemporaryMatrix<T> &>(v);
2113 MultiArrayIndex m = rowCount(t), n = columnCount(t);
2114
2115 for(MultiArrayIndex i = 0; i < n; ++i)
2116 for(MultiArrayIndex j = 0; j < m; ++j)
2117 t(j, i) = vigra::pow(t(j, i), exponent);
2118 return t;
2119 }
2120
2121 template <class C>
2122 linalg::TemporaryMatrix<int> pow(MultiArrayView<2, int, C> const & v, int exponent)
2123 {
2124 linalg::TemporaryMatrix<int> t(v.shape());
2125 MultiArrayIndex m = rowCount(v), n = columnCount(v);
2126
2127 for(MultiArrayIndex i = 0; i < n; ++i)
2128 for(MultiArrayIndex j = 0; j < m; ++j)
2129 t(j, i) = static_cast<int>(vigra::pow(static_cast<double>(v(j, i)), exponent));
2130 return t;
2131 }
2132
2133 inline
2134 linalg::TemporaryMatrix<int> pow(linalg::TemporaryMatrix<int> const & v, int exponent)
2135 {
2136 linalg::TemporaryMatrix<int> & t = const_cast<linalg::TemporaryMatrix<int> &>(v);
2137 MultiArrayIndex m = rowCount(t), n = columnCount(t);
2138
2139 for(MultiArrayIndex i = 0; i < n; ++i)
2140 for(MultiArrayIndex j = 0; j < m; ++j)
2141 t(j, i) = static_cast<int>(vigra::pow(static_cast<double>(t(j, i)), exponent));
2142 return t;
2143 }
2144
2145 /** Matrix point-wise sqrt. */
2146 template <class T, class C>
2147 linalg::TemporaryMatrix<T> sqrt(MultiArrayView<2, T, C> const & v);
2148 /** Matrix point-wise exp. */
2149 template <class T, class C>
2150 linalg::TemporaryMatrix<T> exp(MultiArrayView<2, T, C> const & v);
2151 /** Matrix point-wise log. */
2152 template <class T, class C>
2153 linalg::TemporaryMatrix<T> log(MultiArrayView<2, T, C> const & v);
2154 /** Matrix point-wise log10. */
2155 template <class T, class C>
2156 linalg::TemporaryMatrix<T> log10(MultiArrayView<2, T, C> const & v);
2157 /** Matrix point-wise sin. */
2158 template <class T, class C>
2159 linalg::TemporaryMatrix<T> sin(MultiArrayView<2, T, C> const & v);
2160 /** Matrix point-wise asin. */
2161 template <class T, class C>
2162 linalg::TemporaryMatrix<T> asin(MultiArrayView<2, T, C> const & v);
2163 /** Matrix point-wise cos. */
2164 template <class T, class C>
2165 linalg::TemporaryMatrix<T> cos(MultiArrayView<2, T, C> const & v);
2166 /** Matrix point-wise acos. */
2167 template <class T, class C>
2168 linalg::TemporaryMatrix<T> acos(MultiArrayView<2, T, C> const & v);
2169 /** Matrix point-wise tan. */
2170 template <class T, class C>
2171 linalg::TemporaryMatrix<T> tan(MultiArrayView<2, T, C> const & v);
2172 /** Matrix point-wise atan. */
2173 template <class T, class C>
2174 linalg::TemporaryMatrix<T> atan(MultiArrayView<2, T, C> const & v);
2175 /** Matrix point-wise round. */
2176 template <class T, class C>
2177 linalg::TemporaryMatrix<T> round(MultiArrayView<2, T, C> const & v);
2178 /** Matrix point-wise floor. */
2179 template <class T, class C>
2180 linalg::TemporaryMatrix<T> floor(MultiArrayView<2, T, C> const & v);
2181 /** Matrix point-wise ceil. */
2182 template <class T, class C>
2183 linalg::TemporaryMatrix<T> ceil(MultiArrayView<2, T, C> const & v);
2184 /** Matrix point-wise abs. */
2185 template <class T, class C>
2186 linalg::TemporaryMatrix<T> abs(MultiArrayView<2, T, C> const & v);
2187 /** Matrix point-wise square. */
2188 template <class T, class C>
2189 linalg::TemporaryMatrix<T> sq(MultiArrayView<2, T, C> const & v);
2190 /** Matrix point-wise sign. */
2191 template <class T, class C>
2192 linalg::TemporaryMatrix<T> sign(MultiArrayView<2, T, C> const & v);
2193
2194 #define VIGRA_MATRIX_UNARY_FUNCTION(FUNCTION, NAMESPACE) \
2195 using NAMESPACE::FUNCTION; \
2196 template <class T, class C> \
2197 linalg::TemporaryMatrix<T> FUNCTION(MultiArrayView<2, T, C> const & v) \
2198 { \
2199 linalg::TemporaryMatrix<T> t(v.shape()); \
2200 MultiArrayIndex m = rowCount(v), n = columnCount(v); \
2201 \
2202 for(MultiArrayIndex i = 0; i < n; ++i) \
2203 for(MultiArrayIndex j = 0; j < m; ++j) \
2204 t(j, i) = NAMESPACE::FUNCTION(v(j, i)); \
2205 return t; \
2206 } \
2207 \
2208 template <class T> \
2209 linalg::TemporaryMatrix<T> FUNCTION(linalg::Matrix<T> const & v) \
2210 { \
2211 linalg::TemporaryMatrix<T> t(v.shape()); \
2212 MultiArrayIndex m = rowCount(v), n = columnCount(v); \
2213 \
2214 for(MultiArrayIndex i = 0; i < n; ++i) \
2215 for(MultiArrayIndex j = 0; j < m; ++j) \
2216 t(j, i) = NAMESPACE::FUNCTION(v(j, i)); \
2217 return t; \
2218 } \
2219 \
2220 template <class T> \
2221 linalg::TemporaryMatrix<T> FUNCTION(linalg::TemporaryMatrix<T> const & v) \
2222 { \
2223 linalg::TemporaryMatrix<T> & t = const_cast<linalg::TemporaryMatrix<T> &>(v); \
2224 MultiArrayIndex m = rowCount(t), n = columnCount(t); \
2225 \
2226 for(MultiArrayIndex i = 0; i < n; ++i) \
2227 for(MultiArrayIndex j = 0; j < m; ++j) \
2228 t(j, i) = NAMESPACE::FUNCTION(t(j, i)); \
2229 return v; \
2230 }\
2231 }\
2232 using linalg::FUNCTION;\
2233 namespace linalg {
2234
2235 VIGRA_MATRIX_UNARY_FUNCTION(sqrt, std)
2236 VIGRA_MATRIX_UNARY_FUNCTION(exp, std)
2237 VIGRA_MATRIX_UNARY_FUNCTION(log, std)
2238 VIGRA_MATRIX_UNARY_FUNCTION(log10, std)
2239 VIGRA_MATRIX_UNARY_FUNCTION(sin, std)
2240 VIGRA_MATRIX_UNARY_FUNCTION(asin, std)
2241 VIGRA_MATRIX_UNARY_FUNCTION(cos, std)
2242 VIGRA_MATRIX_UNARY_FUNCTION(acos, std)
2243 VIGRA_MATRIX_UNARY_FUNCTION(tan, std)
2244 VIGRA_MATRIX_UNARY_FUNCTION(atan, std)
2245 VIGRA_MATRIX_UNARY_FUNCTION(round, vigra)
2246 VIGRA_MATRIX_UNARY_FUNCTION(floor, vigra)
2247 VIGRA_MATRIX_UNARY_FUNCTION(ceil, vigra)
2248 VIGRA_MATRIX_UNARY_FUNCTION(abs, vigra)
2249 VIGRA_MATRIX_UNARY_FUNCTION(sq, vigra)
2250 VIGRA_MATRIX_UNARY_FUNCTION(sign, vigra)
2251
2252 #undef VIGRA_MATRIX_UNARY_FUNCTION
2253
2254 //@}
2255
2256 } // namespace linalg
2257
2258 using linalg::RowMajor;
2259 using linalg::ColumnMajor;
2260 using linalg::Matrix;
2261 using linalg::identityMatrix;
2262 using linalg::diagonalMatrix;
2263 using linalg::transpose;
2264 using linalg::pointWise;
2265 using linalg::trace;
2266 using linalg::dot;
2267 using linalg::cross;
2268 using linalg::outer;
2269 using linalg::rowCount;
2270 using linalg::columnCount;
2271 using linalg::rowVector;
2272 using linalg::columnVector;
2273 using linalg::subVector;
2274 using linalg::isSymmetric;
2275 using linalg::joinHorizontally;
2276 using linalg::joinVertically;
2277 using linalg::argMin;
2278 using linalg::argMinIf;
2279 using linalg::argMax;
2280 using linalg::argMaxIf;
2281
2282 /********************************************************/
2283 /* */
2284 /* NormTraits */
2285 /* */
2286 /********************************************************/
2287
2288 template <class T, class ALLOC>
2289 struct NormTraits<Matrix<T, ALLOC> >
2290 : public NormTraits<MultiArray<2, T, ALLOC> >
2291 {
2292 typedef NormTraits<MultiArray<2, T, ALLOC> > BaseType;
2293 typedef Matrix<T, ALLOC> Type;
2294 typedef typename BaseType::SquaredNormType SquaredNormType;
2295 typedef typename BaseType::NormType NormType;
2296 };
2297
2298 template <class T, class ALLOC>
2299 struct NormTraits<linalg::TemporaryMatrix<T, ALLOC> >
2300 : public NormTraits<Matrix<T, ALLOC> >
2301 {
2302 typedef NormTraits<Matrix<T, ALLOC> > BaseType;
2303 typedef linalg::TemporaryMatrix<T, ALLOC> Type;
2304 typedef typename BaseType::SquaredNormType SquaredNormType;
2305 typedef typename BaseType::NormType NormType;
2306 };
2307
2308 } // namespace vigra
2309
2310 namespace std {
2311
2312 /** \addtogroup LinearAlgebraFunctions
2313 */
2314 //@{
2315
2316 /** print a matrix \a m to the stream \a s.
2317
2318 <b>\#include</b> <vigra/matrix.hxx> or<br>
2319 <b>\#include</b> <vigra/linear_algebra.hxx><br>
2320 Namespace: std
2321 */
2322 template <class T, class C>
2323 ostream &
2324 operator<<(ostream & s, const vigra::MultiArrayView<2, T, C> &m)
2325 {
2326 const vigra::MultiArrayIndex rows = vigra::linalg::rowCount(m);
2327 const vigra::MultiArrayIndex cols = vigra::linalg::columnCount(m);
2328 ios::fmtflags flags = s.setf(ios::right | ios::fixed, ios::adjustfield | ios::floatfield);
2329 for(vigra::MultiArrayIndex j = 0; j < rows; ++j)
2330 {
2331 for(vigra::MultiArrayIndex i = 0; i < cols; ++i)
2332 {
2333 s << m(j, i) << " ";
2334 }
2335 s << endl;
2336 }
2337 s.setf(flags);
2338 return s;
2339 }
2340
2341 //@}
2342
2343 } // namespace std
2344
2345 namespace vigra {
2346
2347 namespace linalg {
2348
2349 namespace detail {
2350
2351 template <class T1, class C1, class T2, class C2, class T3, class C3>
2352 void
2353 columnStatisticsImpl(MultiArrayView<2, T1, C1> const & A,
2354 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & sumOfSquaredDifferences)
2355 {
2356 MultiArrayIndex m = rowCount(A);
2357 MultiArrayIndex n = columnCount(A);
2358 vigra_precondition(1 == rowCount(mean) && n == columnCount(mean) &&
2359 1 == rowCount(sumOfSquaredDifferences) && n == columnCount(sumOfSquaredDifferences),
2360 "columnStatistics(): Shape mismatch between input and output.");
2361
2362 // West's algorithm for incremental variance computation
2363 mean.init(NumericTraits<T2>::zero());
2364 sumOfSquaredDifferences.init(NumericTraits<T3>::zero());
2365
2366 for(MultiArrayIndex k=0; k<m; ++k)
2367 {
2368 typedef typename NumericTraits<T2>::RealPromote TmpType;
2369 Matrix<T2> t = rowVector(A, k) - mean;
2370 TmpType f = TmpType(1.0 / (k + 1.0)),
2371 f1 = TmpType(1.0 - f);
2372 mean += f*t;
2373 sumOfSquaredDifferences += f1*sq(t);
2374 }
2375 }
2376
2377 template <class T1, class C1, class T2, class C2, class T3, class C3>
2378 void
2379 columnStatistics2PassImpl(MultiArrayView<2, T1, C1> const & A,
2380 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & sumOfSquaredDifferences)
2381 {
2382 MultiArrayIndex m = rowCount(A);
2383 MultiArrayIndex n = columnCount(A);
2384 vigra_precondition(1 == rowCount(mean) && n == columnCount(mean) &&
2385 1 == rowCount(sumOfSquaredDifferences) && n == columnCount(sumOfSquaredDifferences),
2386 "columnStatistics(): Shape mismatch between input and output.");
2387
2388 // two-pass algorithm for incremental variance computation
2389 mean.init(NumericTraits<T2>::zero());
2390 for(MultiArrayIndex k=0; k<m; ++k)
2391 {
2392 mean += rowVector(A, k);
2393 }
2394 mean /= static_cast<double>(m);
2395
2396 sumOfSquaredDifferences.init(NumericTraits<T3>::zero());
2397 for(MultiArrayIndex k=0; k<m; ++k)
2398 {
2399 sumOfSquaredDifferences += sq(rowVector(A, k) - mean);
2400 }
2401 }
2402
2403 } // namespace detail
2404
2405 /** \addtogroup LinearAlgebraFunctions
2406 */
2407 //@{
2408 /** Compute statistics of every column of matrix \a A.
2409
2410 The result matrices must be row vectors with as many columns as \a A.
2411
2412 <b> Declarations:</b>
2413
2414 compute only the mean:
2415 \code
2416 namespace vigra { namespace linalg {
2417 template <class T1, class C1, class T2, class C2>
2418 void
2419 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2420 MultiArrayView<2, T2, C2> & mean);
2421 } }
2422 \endcode
2423
2424 compute mean and standard deviation:
2425 \code
2426 namespace vigra { namespace linalg {
2427 template <class T1, class C1, class T2, class C2, class T3, class C3>
2428 void
2429 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2430 MultiArrayView<2, T2, C2> & mean,
2431 MultiArrayView<2, T3, C3> & stdDev);
2432 } }
2433 \endcode
2434
2435 compute mean, standard deviation, and norm:
2436 \code
2437 namespace vigra { namespace linalg {
2438 template <class T1, class C1, class T2, class C2, class T3, class C3, class T4, class C4>
2439 void
2440 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2441 MultiArrayView<2, T2, C2> & mean,
2442 MultiArrayView<2, T3, C3> & stdDev,
2443 MultiArrayView<2, T4, C4> & norm);
2444 } }
2445 \endcode
2446
2447 <b> Usage:</b>
2448
2449 <b>\#include</b> <vigra/matrix.hxx> or<br>
2450 <b>\#include</b> <vigra/linear_algebra.hxx><br>
2451 Namespaces: vigra and vigra::linalg
2452
2453 \code
2454 Matrix A(rows, columns);
2455 .. // fill A
2456 Matrix columnMean(1, columns), columnStdDev(1, columns), columnNorm(1, columns);
2457
2458 columnStatistics(A, columnMean, columnStdDev, columnNorm);
2459
2460 \endcode
2461 */
2462 doxygen_overloaded_function(template <...> void columnStatistics)
2463
2464 template <class T1, class C1, class T2, class C2>
2465 void
2466 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2467 MultiArrayView<2, T2, C2> & mean)
2468 {
2469 MultiArrayIndex m = rowCount(A);
2470 MultiArrayIndex n = columnCount(A);
2471 vigra_precondition(1 == rowCount(mean) && n == columnCount(mean),
2472 "columnStatistics(): Shape mismatch between input and output.");
2473
2474 mean.init(NumericTraits<T2>::zero());
2475
2476 for(MultiArrayIndex k=0; k<m; ++k)
2477 {
2478 mean += rowVector(A, k);
2479 }
2480 mean /= T2(m);
2481 }
2482
2483 template <class T1, class C1, class T2, class C2, class T3, class C3>
2484 void
2485 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2486 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & stdDev)
2487 {
2488 detail::columnStatisticsImpl(A, mean, stdDev);
2489
2490 if(rowCount(A) > 1)
2491 stdDev = sqrt(stdDev / T3(rowCount(A) - 1.0));
2492 }
2493
2494 template <class T1, class C1, class T2, class C2, class T3, class C3, class T4, class C4>
2495 void
2496 columnStatistics(MultiArrayView<2, T1, C1> const & A,
2497 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & stdDev, MultiArrayView<2, T4, C4> & norm)
2498 {
2499 MultiArrayIndex m = rowCount(A);
2500 MultiArrayIndex n = columnCount(A);
2501 vigra_precondition(1 == rowCount(mean) && n == columnCount(mean) &&
2502 1 == rowCount(stdDev) && n == columnCount(stdDev) &&
2503 1 == rowCount(norm) && n == columnCount(norm),
2504 "columnStatistics(): Shape mismatch between input and output.");
2505
2506 detail::columnStatisticsImpl(A, mean, stdDev);
2507 norm = sqrt(stdDev + T2(m) * sq(mean));
2508 stdDev = sqrt(stdDev / T3(m - 1.0));
2509 }
2510
2511 /** Compute statistics of every row of matrix \a A.
2512
2513 The result matrices must be column vectors with as many rows as \a A.
2514
2515 <b> Declarations:</b>
2516
2517 compute only the mean:
2518 \code
2519 namespace vigra { namespace linalg {
2520 template <class T1, class C1, class T2, class C2>
2521 void
2522 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2523 MultiArrayView<2, T2, C2> & mean);
2524 } }
2525 \endcode
2526
2527 compute mean and standard deviation:
2528 \code
2529 namespace vigra { namespace linalg {
2530 template <class T1, class C1, class T2, class C2, class T3, class C3>
2531 void
2532 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2533 MultiArrayView<2, T2, C2> & mean,
2534 MultiArrayView<2, T3, C3> & stdDev);
2535 } }
2536 \endcode
2537
2538 compute mean, standard deviation, and norm:
2539 \code
2540 namespace vigra { namespace linalg {
2541 template <class T1, class C1, class T2, class C2, class T3, class C3, class T4, class C4>
2542 void
2543 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2544 MultiArrayView<2, T2, C2> & mean,
2545 MultiArrayView<2, T3, C3> & stdDev,
2546 MultiArrayView<2, T4, C4> & norm);
2547 } }
2548 \endcode
2549
2550 <b> Usage:</b>
2551
2552 <b>\#include</b> <vigra/matrix.hxx> or<br>
2553 <b>\#include</b> <vigra/linear_algebra.hxx><br>
2554 Namespaces: vigra and vigra::linalg
2555
2556 \code
2557 Matrix A(rows, columns);
2558 .. // fill A
2559 Matrix rowMean(rows, 1), rowStdDev(rows, 1), rowNorm(rows, 1);
2560
2561 rowStatistics(a, rowMean, rowStdDev, rowNorm);
2562
2563 \endcode
2564 */
2565 doxygen_overloaded_function(template <...> void rowStatistics)
2566
2567 template <class T1, class C1, class T2, class C2>
2568 void
2569 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2570 MultiArrayView<2, T2, C2> & mean)
2571 {
2572 vigra_precondition(1 == columnCount(mean) && rowCount(A) == rowCount(mean),
2573 "rowStatistics(): Shape mismatch between input and output.");
2574 MultiArrayView<2, T2, StridedArrayTag> tm = transpose(mean);
2575 columnStatistics(transpose(A), tm);
2576 }
2577
2578 template <class T1, class C1, class T2, class C2, class T3, class C3>
2579 void
2580 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2581 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & stdDev)
2582 {
2583 vigra_precondition(1 == columnCount(mean) && rowCount(A) == rowCount(mean) &&
2584 1 == columnCount(stdDev) && rowCount(A) == rowCount(stdDev),
2585 "rowStatistics(): Shape mismatch between input and output.");
2586 MultiArrayView<2, T2, StridedArrayTag> tm = transpose(mean);
2587 MultiArrayView<2, T3, StridedArrayTag> ts = transpose(stdDev);
2588 columnStatistics(transpose(A), tm, ts);
2589 }
2590
2591 template <class T1, class C1, class T2, class C2, class T3, class C3, class T4, class C4>
2592 void
2593 rowStatistics(MultiArrayView<2, T1, C1> const & A,
2594 MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & stdDev, MultiArrayView<2, T4, C4> & norm)
2595 {
2596 vigra_precondition(1 == columnCount(mean) && rowCount(A) == rowCount(mean) &&
2597 1 == columnCount(stdDev) && rowCount(A) == rowCount(stdDev) &&
2598 1 == columnCount(norm) && rowCount(A) == rowCount(norm),
2599 "rowStatistics(): Shape mismatch between input and output.");
2600 MultiArrayView<2, T2, StridedArrayTag> tm = transpose(mean);
2601 MultiArrayView<2, T3, StridedArrayTag> ts = transpose(stdDev);
2602 MultiArrayView<2, T4, StridedArrayTag> tn = transpose(norm);
2603 columnStatistics(transpose(A), tm, ts, tn);
2604 }
2605
2606 namespace detail {
2607
2608 template <class T1, class C1, class U, class T2, class C2, class T3, class C3>
2609 void updateCovarianceMatrix(MultiArrayView<2, T1, C1> const & features,
2610 U & count, MultiArrayView<2, T2, C2> & mean, MultiArrayView<2, T3, C3> & covariance)
2611 {
2612 MultiArrayIndex n = std::max(rowCount(features), columnCount(features));
2613 vigra_precondition(std::min(rowCount(features), columnCount(features)) == 1,
2614 "updateCovarianceMatrix(): Features must be a row or column vector.");
2615 vigra_precondition(mean.shape() == features.shape(),
2616 "updateCovarianceMatrix(): Shape mismatch between feature vector and mean vector.");
2617 vigra_precondition(n == rowCount(covariance) && n == columnCount(covariance),
2618 "updateCovarianceMatrix(): Shape mismatch between feature vector and covariance matrix.");
2619
2620 // West's algorithm for incremental covariance matrix computation
2621 Matrix<T2> t = features - mean;
2622 ++count;
2623 T2 f = T2(1.0) / count,
2624 f1 = T2(1.0) - f;
2625 mean += f*t;
2626
2627 if(rowCount(features) == 1) // update column covariance from current row
2628 {
2629 for(MultiArrayIndex k=0; k<n; ++k)
2630 {
2631 covariance(k, k) += f1*sq(t(0, k));
2632 for(MultiArrayIndex l=k+1; l<n; ++l)
2633 {
2634 covariance(k, l) += f1*t(0, k)*t(0, l);
2635 covariance(l, k) = covariance(k, l);
2636 }
2637 }
2638 }
2639 else // update row covariance from current column
2640 {
2641 for(MultiArrayIndex k=0; k<n; ++k)
2642 {
2643 covariance(k, k) += f1*sq(t(k, 0));
2644 for(MultiArrayIndex l=k+1; l<n; ++l)
2645 {
2646 covariance(k, l) += f1*t(k, 0)*t(l, 0);
2647 covariance(l, k) = covariance(k, l);
2648 }
2649 }
2650 }
2651 }
2652
2653 } // namespace detail
2654
2655 /** \brief Compute the covariance matrix between the columns of a matrix \a features.
2656
2657 The result matrix \a covariance must by a square matrix with as many rows and
2658 columns as the number of columns in matrix \a features.
2659
2660 <b>\#include</b> <vigra/matrix.hxx><br>
2661 Namespace: vigra
2662 */
2663 template <class T1, class C1, class T2, class C2>
2664 void covarianceMatrixOfColumns(MultiArrayView<2, T1, C1> const & features,
2665 MultiArrayView<2, T2, C2> & covariance)
2666 {
2667 MultiArrayIndex m = rowCount(features), n = columnCount(features);
2668 vigra_precondition(n == rowCount(covariance) && n == columnCount(covariance),
2669 "covarianceMatrixOfColumns(): Shape mismatch between feature matrix and covariance matrix.");
2670 MultiArrayIndex count = 0;
2671 Matrix<T2> means(1, n);
2672 covariance.init(NumericTraits<T2>::zero());
2673 for(MultiArrayIndex k=0; k<m; ++k)
2674 detail::updateCovarianceMatrix(rowVector(features, k), count, means, covariance);
2675 covariance /= T2(m - 1);
2676 }
2677
2678 /** \brief Compute the covariance matrix between the columns of a matrix \a features.
2679
2680 The result is returned as a square temporary matrix with as many rows and
2681 columns as the number of columns in matrix \a features.
2682
2683 <b>\#include</b> <vigra/matrix.hxx><br>
2684 Namespace: vigra
2685 */
2686 template <class T, class C>
2687 TemporaryMatrix<T>
2688 covarianceMatrixOfColumns(MultiArrayView<2, T, C> const & features)
2689 {
2690 TemporaryMatrix<T> res(columnCount(features), columnCount(features));
2691 covarianceMatrixOfColumns(features, res);
2692 return res;
2693 }
2694
2695 /** \brief Compute the covariance matrix between the rows of a matrix \a features.
2696
2697 The result matrix \a covariance must by a square matrix with as many rows and
2698 columns as the number of rows in matrix \a features.
2699
2700 <b>\#include</b> <vigra/matrix.hxx><br>
2701 Namespace: vigra
2702 */
2703 template <class T1, class C1, class T2, class C2>
2704 void covarianceMatrixOfRows(MultiArrayView<2, T1, C1> const & features,
2705 MultiArrayView<2, T2, C2> & covariance)
2706 {
2707 MultiArrayIndex m = rowCount(features), n = columnCount(features);
2708 vigra_precondition(m == rowCount(covariance) && m == columnCount(covariance),
2709 "covarianceMatrixOfRows(): Shape mismatch between feature matrix and covariance matrix.");
2710 MultiArrayIndex count = 0;
2711 Matrix<T2> means(m, 1);
2712 covariance.init(NumericTraits<T2>::zero());
2713 for(MultiArrayIndex k=0; k<n; ++k)
2714 detail::updateCovarianceMatrix(columnVector(features, k), count, means, covariance);
2715 covariance /= T2(n - 1);
2716 }
2717
2718 /** \brief Compute the covariance matrix between the rows of a matrix \a features.
2719
2720 The result is returned as a square temporary matrix with as many rows and
2721 columns as the number of rows in matrix \a features.
2722
2723 <b>\#include</b> <vigra/matrix.hxx><br>
2724 Namespace: vigra
2725 */
2726 template <class T, class C>
2727 TemporaryMatrix<T>
2728 covarianceMatrixOfRows(MultiArrayView<2, T, C> const & features)
2729 {
2730 TemporaryMatrix<T> res(rowCount(features), rowCount(features));
2731 covarianceMatrixOfRows(features, res);
2732 return res;
2733 }
2734
2735 enum DataPreparationGoals { ZeroMean = 1, UnitVariance = 2, UnitNorm = 4, UnitSum = 8 };
2736
2737 inline DataPreparationGoals operator|(DataPreparationGoals l, DataPreparationGoals r)
2738 {
2739 return DataPreparationGoals(int(l) | int(r));
2740 }
2741
2742 namespace detail {
2743
2744 template <class T, class C1, class C2, class C3, class C4>
2745 void
2746 prepareDataImpl(const MultiArrayView<2, T, C1> & A,
2747 MultiArrayView<2, T, C2> & res, MultiArrayView<2, T, C3> & offset, MultiArrayView<2, T, C4> & scaling,
2748 DataPreparationGoals goals)
2749 {
2750 MultiArrayIndex m = rowCount(A);
2751 MultiArrayIndex n = columnCount(A);
2752 vigra_precondition(A.shape() == res.shape() &&
2753 n == columnCount(offset) && 1 == rowCount(offset) &&
2754 n == columnCount(scaling) && 1 == rowCount(scaling),
2755 "prepareDataImpl(): Shape mismatch between input and output.");
2756
2757 if(!goals)
2758 {
2759 res = A;
2760 offset.init(NumericTraits<T>::zero());
2761 scaling.init(NumericTraits<T>::one());
2762 return;
2763 }
2764
2765 bool zeroMean = (goals & ZeroMean) != 0;
2766 bool unitVariance = (goals & UnitVariance) != 0;
2767 bool unitNorm = (goals & UnitNorm) != 0;
2768 bool unitSum = (goals & UnitSum) != 0;
2769
2770 if(unitSum)
2771 {
2772 vigra_precondition(goals == UnitSum,
2773 "prepareData(): Unit sum is not compatible with any other data preparation goal.");
2774
2775 transformMultiArray(srcMultiArrayRange(A), destMultiArrayRange(scaling), FindSum<T>());
2776
2777 offset.init(NumericTraits<T>::zero());
2778
2779 for(MultiArrayIndex k=0; k<n; ++k)
2780 {
2781 if(scaling(0, k) != NumericTraits<T>::zero())
2782 {
2783 scaling(0, k) = NumericTraits<T>::one() / scaling(0, k);
2784 columnVector(res, k) = columnVector(A, k) * scaling(0, k);
2785 }
2786 else
2787 {
2788 scaling(0, k) = NumericTraits<T>::one();
2789 }
2790 }
2791
2792 return;
2793 }
2794
2795 vigra_precondition(!(unitVariance && unitNorm),
2796 "prepareData(): Unit variance and unit norm cannot be achieved at the same time.");
2797
2798 Matrix<T> mean(1, n), sumOfSquaredDifferences(1, n);
2799 detail::columnStatisticsImpl(A, mean, sumOfSquaredDifferences);
2800
2801 for(MultiArrayIndex k=0; k<n; ++k)
2802 {
2803 T stdDev = std::sqrt(sumOfSquaredDifferences(0, k) / T(m-1));
2804 if(closeAtTolerance(stdDev / mean(0,k), NumericTraits<T>::zero()))
2805 stdDev = NumericTraits<T>::zero();
2806 if(zeroMean && stdDev > NumericTraits<T>::zero())
2807 {
2808 columnVector(res, k) = columnVector(A, k) - mean(0,k);
2809 offset(0, k) = mean(0, k);
2810 mean(0, k) = NumericTraits<T>::zero();
2811 }
2812 else
2813 {
2814 columnVector(res, k) = columnVector(A, k);
2815 offset(0, k) = NumericTraits<T>::zero();
2816 }
2817
2818 T norm = mean(0,k) == NumericTraits<T>::zero()
2819 ? std::sqrt(sumOfSquaredDifferences(0, k))
2820 : std::sqrt(sumOfSquaredDifferences(0, k) + T(m) * sq(mean(0,k)));
2821 if(unitNorm && norm > NumericTraits<T>::zero())
2822 {
2823 columnVector(res, k) /= norm;
2824 scaling(0, k) = NumericTraits<T>::one() / norm;
2825 }
2826 else if(unitVariance && stdDev > NumericTraits<T>::zero())
2827 {
2828 columnVector(res, k) /= stdDev;
2829 scaling(0, k) = NumericTraits<T>::one() / stdDev;
2830 }
2831 else
2832 {
2833 scaling(0, k) = NumericTraits<T>::one();
2834 }
2835 }
2836 }
2837
2838 } // namespace detail
2839
2840 /** \brief Standardize the columns of a matrix according to given <tt>DataPreparationGoals</tt>.
2841
2842 For every column of the matrix \a A, this function computes mean,
2843 standard deviation, and norm. It then applies a linear transformation to the values of
2844 the column according to these statistics and the given <tt>DataPreparationGoals</tt>.
2845 The result is returned in matrix \a res which must have the same size as \a A.
2846 Optionally, the transformation applied can also be returned in the matrices \a offset
2847 and \a scaling (see below for an example how these matrices can be used to standardize
2848 more data according to the same transformation).
2849
2850 The following <tt>DataPreparationGoals</tt> are supported:
2851
2852 <DL>
2853 <DT><tt>ZeroMean</tt><DD> Subtract the column mean form every column if the values in the column are not constant.
2854 Do nothing in a constant column.
2855 <DT><tt>UnitSum</tt><DD> Scale the columns so that the their sum is one if the sum was initially non-zero.
2856 Do nothing in a zero-sum column.
2857 <DT><tt>UnitVariance</tt><DD> Divide by the column standard deviation if the values in the column are not constant.
2858 Do nothing in a constant column.
2859 <DT><tt>UnitNorm</tt><DD> Divide by the column norm if it is non-zero.
2860 <DT><tt>ZeroMean | UnitVariance</tt><DD> First subtract the mean and then divide by the standard deviation, unless the
2861 column is constant (in which case the column remains unchanged).
2862 <DT><tt>ZeroMean | UnitNorm</tt><DD> If the column is non-constant, subtract the mean. Then divide by the norm
2863 of the result if the norm is non-zero.
2864 </DL>
2865
2866 <b> Declarations:</b>
2867
2868 Standardize the matrix and return the parameters of the linear transformation.
2869 The matrices \a offset and \a scaling must be row vectors with as many columns as \a A.
2870 \code
2871 namespace vigra { namespace linalg {
2872 template <class T, class C1, class C2, class C3, class C4>
2873 void
2874 prepareColumns(MultiArrayView<2, T, C1> const & A,
2875 MultiArrayView<2, T, C2> & res,
2876 MultiArrayView<2, T, C3> & offset,
2877 MultiArrayView<2, T, C4> & scaling,
2878 DataPreparationGoals goals = ZeroMean | UnitVariance);
2879 } }
2880 \endcode
2881
2882 Only standardize the matrix.
2883 \code
2884 namespace vigra { namespace linalg {
2885 template <class T, class C1, class C2>
2886 void
2887 prepareColumns(MultiArrayView<2, T, C1> const & A,
2888 MultiArrayView<2, T, C2> & res,
2889 DataPreparationGoals goals = ZeroMean | UnitVariance);
2890 } }
2891 \endcode
2892
2893 <b> Usage:</b>
2894
2895 <b>\#include</b> <vigra/matrix.hxx> or<br>
2896 <b>\#include</b> <vigra/linear_algebra.hxx><br>
2897 Namespaces: vigra and vigra::linalg
2898
2899 \code
2900 Matrix A(rows, columns);
2901 .. // fill A
2902 Matrix standardizedA(rows, columns), offset(1, columns), scaling(1, columns);
2903
2904 prepareColumns(A, standardizedA, offset, scaling, ZeroMean | UnitNorm);
2905
2906 // use offset and scaling to prepare additional data according to the same transformation
2907 Matrix newData(nrows, columns);
2908
2909 Matrix standardizedNewData = (newData - repeatMatrix(offset, nrows, 1)) * pointWise(repeatMatrix(scaling, nrows, 1));
2910
2911 \endcode
2912 */
2913 doxygen_overloaded_function(template <...> void prepareColumns)
2914
2915 template <class T, class C1, class C2, class C3, class C4>
2916 inline void
2917 prepareColumns(MultiArrayView<2, T, C1> const & A,
2918 MultiArrayView<2, T, C2> & res, MultiArrayView<2, T, C3> & offset, MultiArrayView<2, T, C4> & scaling,
2919 DataPreparationGoals goals = ZeroMean | UnitVariance)
2920 {
2921 detail::prepareDataImpl(A, res, offset, scaling, goals);
2922 }
2923
2924 template <class T, class C1, class C2>
2925 inline void
2926 prepareColumns(MultiArrayView<2, T, C1> const & A, MultiArrayView<2, T, C2> & res,
2927 DataPreparationGoals goals = ZeroMean | UnitVariance)
2928 {
2929 Matrix<T> offset(1, columnCount(A)), scaling(1, columnCount(A));
2930 detail::prepareDataImpl(A, res, offset, scaling, goals);
2931 }
2932
2933 /** \brief Standardize the rows of a matrix according to given <tt>DataPreparationGoals</tt>.
2934
2935 This algorithm works in the same way as \ref prepareColumns() (see there for detailed
2936 documentation), but is applied to the rows of the matrix \a A instead. Accordingly, the
2937 matrices holding the parameters of the linear transformation must be column vectors
2938 with as many rows as \a A.
2939
2940 <b> Declarations:</b>
2941
2942 Standardize the matrix and return the parameters of the linear transformation.
2943 The matrices \a offset and \a scaling must be column vectors
2944 with as many rows as \a A.
2945
2946 \code
2947 namespace vigra { namespace linalg {
2948 template <class T, class C1, class C2, class C3, class C4>
2949 void
2950 prepareRows(MultiArrayView<2, T, C1> const & A,
2951 MultiArrayView<2, T, C2> & res,
2952 MultiArrayView<2, T, C3> & offset,
2953 MultiArrayView<2, T, C4> & scaling,
2954 DataPreparationGoals goals = ZeroMean | UnitVariance)´;
2955 } }
2956 \endcode
2957
2958 Only standardize the matrix.
2959 \code
2960 namespace vigra { namespace linalg {
2961 template <class T, class C1, class C2>
2962 void
2963 prepareRows(MultiArrayView<2, T, C1> const & A,
2964 MultiArrayView<2, T, C2> & res,
2965 DataPreparationGoals goals = ZeroMean | UnitVariance);
2966 } }
2967 \endcode
2968
2969 <b> Usage:</b>
2970
2971 <b>\#include</b> <vigra/matrix.hxx> or<br>
2972 <b>\#include</b> <vigra/linear_algebra.hxx><br>
2973 Namespaces: vigra and vigra::linalg
2974
2975 \code
2976 Matrix A(rows, columns);
2977 .. // fill A
2978 Matrix standardizedA(rows, columns), offset(rows, 1), scaling(rows, 1);
2979
2980 prepareRows(A, standardizedA, offset, scaling, ZeroMean | UnitNorm);
2981
2982 // use offset and scaling to prepare additional data according to the same transformation
2983 Matrix newData(rows, ncolumns);
2984
2985 Matrix standardizedNewData = (newData - repeatMatrix(offset, 1, ncolumns)) * pointWise(repeatMatrix(scaling, 1, ncolumns));
2986
2987 \endcode
2988 */
2989 doxygen_overloaded_function(template <...> void prepareRows)
2990
2991 template <class T, class C1, class C2, class C3, class C4>
2992 inline void
2993 prepareRows(MultiArrayView<2, T, C1> const & A,
2994 MultiArrayView<2, T, C2> & res, MultiArrayView<2, T, C3> & offset, MultiArrayView<2, T, C4> & scaling,
2995 DataPreparationGoals goals = ZeroMean | UnitVariance)
2996 {
2997 MultiArrayView<2, T, StridedArrayTag> tr = transpose(res), to = transpose(offset), ts = transpose(scaling);
2998 detail::prepareDataImpl(transpose(A), tr, to, ts, goals);
2999 }
3000
3001 template <class T, class C1, class C2>
3002 inline void
3003 prepareRows(MultiArrayView<2, T, C1> const & A, MultiArrayView<2, T, C2> & res,
3004 DataPreparationGoals goals = ZeroMean | UnitVariance)
3005 {
3006 MultiArrayView<2, T, StridedArrayTag> tr = transpose(res);
3007 Matrix<T> offset(1, rowCount(A)), scaling(1, rowCount(A));
3008 detail::prepareDataImpl(transpose(A), tr, offset, scaling, goals);
3009 }
3010
3011 //@}
3012
3013 } // namespace linalg
3014
3015 using linalg::columnStatistics;
3016 using linalg::prepareColumns;
3017 using linalg::rowStatistics;
3018 using linalg::prepareRows;
3019 using linalg::ZeroMean;
3020 using linalg::UnitVariance;
3021 using linalg::UnitNorm;
3022 using linalg::UnitSum;
3023
3024 } // namespace vigra
3025
3026
3027
3028 #endif // VIGRA_MATRIX_HXX
vigra::linalg::Matrix::Matrix
Matrix(difference_type_1 rows, difference_type_1 columns, const_reference init, allocator_type const &alloc=allocator_type())
Definition: matrix.hxx:187
vigra::linalg::Matrix::operator-=
Matrix & operator-=(MultiArrayView< 2, U, C > const &other)
Definition: matrix.hxx:486
vigra::linalg::Matrix::operator+=
Matrix & operator+=(T other)
Definition: matrix.hxx:512
vigra::linalg::Matrix::operator-=
Matrix & operator-=(T other)
Definition: matrix.hxx:520
vigra::linalg::acos
linalg::TemporaryMatrix< T > acos(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::rowCount
difference_type_1 rowCount() const
Definition: matrix.hxx:367
vigra::linalg::Matrix::squaredNorm
NormTraits< Matrix >::SquaredNormType squaredNorm() const
vigra::linalg::covarianceMatrixOfColumns
void covarianceMatrixOfColumns(MultiArrayView< 2, T1, C1 > const &features, MultiArrayView< 2, T2, C2 > &covariance)
Compute the covariance matrix between the columns of a matrix features.
Definition: matrix.hxx:2664
vigra::linalg::columnVector
MultiArrayView< 2, T, C > columnVector(MultiArrayView< 2, T, C > const &m, MultiArrayIndex d)
Definition: matrix.hxx:727
vigra::linalg::Matrix::Matrix
Matrix(const difference_type &aShape, ALLOC const &alloc=allocator_type())
Definition: matrix.hxx:157
vigra::argMinIf
Iterator argMinIf(Iterator first, Iterator last, UnaryFunctor condition)
Find the minimum element in a sequence conforming to a condition.
Definition: algorithm.hxx:129
vigra::linalg::ceil
linalg::TemporaryMatrix< T > ceil(MultiArrayView< 2, T, C > const &v)
vigra::MultiArray< 2, T, ALLOC >::pointer
view_type::pointer pointer
Definition: multi_array.hxx:2502
vigra::MultiArrayView::difference_type
MultiArrayShape< actual_dimension >::type difference_type
Definition: multi_array.hxx:739
vigra::linalg::Matrix::Matrix
Matrix(difference_type_1 rows, difference_type_1 columns, const_pointer init, RawArrayMemoryLayout layout=RowMajor, allocator_type const &alloc=allocator_type())
Definition: matrix.hxx:221
vigra::linalg::rowCount
MultiArrayIndex rowCount(const MultiArrayView< 2, T, C > &x)
Definition: matrix.hxx:671
vigra::linalg::transpose
void transpose(const MultiArrayView< 2, T, C1 > &v, MultiArrayView< 2, T, C2 > &r)
Definition: matrix.hxx:965
vigra::MultiArray< 2, T, ALLOC >::operator/=
MultiArray & operator/=(const MultiArrayView< N, U, StrideTag > &rhs)
Definition: multi_array.hxx:2750
vigra::linalg::sqrt
linalg::TemporaryMatrix< T > sqrt(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::operator=
Matrix & operator=(const Matrix &rhs)
Definition: matrix.hxx:272
vigra::linalg::cross
void cross(const MultiArrayView< 1, T, C1 > &x, const MultiArrayView< 1, T, C2 > &y, MultiArrayView< 1, T, C3 > &r)
Definition: matrix.hxx:1404
vigra::linalg::sin
linalg::TemporaryMatrix< T > sin(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::columnCount
difference_type_1 columnCount() const
Definition: matrix.hxx:374
vigra::linalg::argMin
int argMin(MultiArrayView< 2, T, C > const &a)
Find the index of the minimum element in a matrix.
Definition: matrix.hxx:1953
vigra::MultiArrayView< N, vigra::detail::ResolveMultiband< T >::type, vigra::detail::ResolveMultiband< T >::Stride >::shape
const difference_type & shape() const
Definition: multi_array.hxx:1648
vigra::MultiArrayView< N, vigra::detail::ResolveMultiband< T >::type, vigra::detail::ResolveMultiband< T >::Stride >::m_shape
difference_type m_shape
Definition: multi_array.hxx:795
vigra::linalg::Matrix
Definition: matrix.hxx:123
vigra::linalg::exp
linalg::TemporaryMatrix< T > exp(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::elementCount
difference_type_1 elementCount() const
Definition: matrix.hxx:381
vigra::linalg::sign
linalg::TemporaryMatrix< T > sign(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::init
Matrix & init(const U &init)
Definition: matrix.hxx:317
vigra::MultiArrayView< N, vigra::detail::ResolveMultiband< T >::type, vigra::detail::ResolveMultiband< T >::Stride >::data
pointer data() const
Definition: multi_array.hxx:1898
vigra::linalg::operator+
TemporaryMatrix< T > operator+(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
Definition: matrix.hxx:1136
vigra::linalg::Matrix::operator/=
Matrix & operator/=(T other)
Definition: matrix.hxx:536
vigra::MultiArrayView::elementCount
difference_type_1 elementCount() const
Definition: multi_array.hxx:1630
vigra::linalg::round
linalg::TemporaryMatrix< T > round(MultiArrayView< 2, T, C > const &v)
vigra::linalg::argMinIf
int argMinIf(MultiArrayView< 2, T, C > const &a, UnaryFunctor condition)
Find the index of the minimum element in a matrix subject to a condition.
Definition: matrix.hxx:2021
vigra::linalg::joinVertically
TemporaryMatrix< T > joinVertically(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
Definition: matrix.hxx:1010
vigra::MultiArray
Main MultiArray class containing the memory management.
Definition: multi_array.hxx:2474
vigra::linalg::repeatMatrix
void repeatMatrix(MultiArrayView< 2, T, C1 > const &v, MultiArrayView< 2, T, C2 > &r, unsigned int verticalCount, unsigned int horizontalCount)
Definition: matrix.hxx:1063
vigra::linalg::ones
TemporaryMatrix< T > ones(MultiArrayIndex rows, MultiArrayIndex cols)
Definition: matrix.hxx:889
vigra::MultiArray< 2, T, ALLOC >::reshape
void reshape(const difference_type &shape)
Definition: multi_array.hxx:2861
vigra::linalg::asin
linalg::TemporaryMatrix< T > asin(MultiArrayView< 2, T, C > const &v)
vigra::linalg::isSymmetric
bool isSymmetric(const MultiArrayView< 2, T, C > &v)
Definition: matrix.hxx:779
vigra::linalg::Matrix::operator*=
Matrix & operator*=(MultiArrayView< 2, U, C > const &other)
Definition: matrix.hxx:495
vigra::FindAverage
Find the average pixel value in an image or ROI.
Definition: inspectimage.hxx:1248
vigra::linalg::operator/
TemporaryMatrix< T > operator/(const MultiArrayView< 2, T, C > &a, PointWise< U > b)
Definition: matrix.hxx:1890
vigra::linalg::Matrix::isSymmetric
bool isSymmetric() const
Definition: matrix.hxx:388
vigra::linalg::covarianceMatrixOfRows
void covarianceMatrixOfRows(MultiArrayView< 2, T1, C1 > const &features, MultiArrayView< 2, T2, C2 > &covariance)
Compute the covariance matrix between the rows of a matrix features.
Definition: matrix.hxx:2704
vigra::linalg::argMaxIf
int argMaxIf(MultiArrayView< 2, T, C > const &a, UnaryFunctor condition)
Find the index of the maximum element in a matrix subject to a condition.
Definition: matrix.hxx:2056
vigra::linalg::add
void add(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1110
vigra::MultiArray< 2, T, ALLOC >::operator+=
MultiArray & operator+=(const MultiArrayView< N, U, StrideTag > &rhs)
Definition: multi_array.hxx:2703
vigra::MultiArrayIndex
std::ptrdiff_t MultiArrayIndex
Definition: multi_fwd.hxx:60
vigra::FindSum
Find the sum of the pixel values in an image or ROI.
Definition: inspectimage.hxx:1143
vigra::linalg::mmul
void mmul(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1605
vigra::linalg::Matrix::Matrix
Matrix(difference_type_1 rows, difference_type_1 columns, ALLOC const &alloc=allocator_type())
Definition: matrix.hxx:167
vigra::linalg::Matrix::operator/=
Matrix & operator/=(MultiArrayView< 2, U, C > const &other)
Definition: matrix.hxx:504
vigra::MultiArrayView::transpose
MultiArrayView< N, T, StridedArrayTag > transpose() const
Definition: multi_array.hxx:1567
vigra::MultiArray< 2, T, ALLOC >::difference_type
view_type::difference_type difference_type
Definition: multi_array.hxx:2522
vigra::operator-=
FFTWComplex< R > & operator-=(FFTWComplex< R > &a, const FFTWComplex< R > &b)
subtract-assignment
Definition: fftw3.hxx:867
vigra::MultiArray< 2, T, ALLOC >::operator-=
MultiArray & operator-=(const MultiArrayView< N, U, StrideTag > &rhs)
Definition: multi_array.hxx:2719
vigra::linalg::Matrix::Matrix
Matrix(ALLOC const &alloc)
Definition: matrix.hxx:148
vigra::linalg::trace
NumericTraits< T >::Promote trace(MultiArrayView< 2, T, C > const &m)
Definition: matrix.hxx:801
vigra::linalg::prepareRows
void prepareRows(...)
Standardize the rows of a matrix according to given DataPreparationGoals.
vigra::MultiArray< 2, T, ALLOC >::operator=
MultiArray & operator=(const MultiArray &rhs)
Definition: multi_array.hxx:2669
vigra::MultiArrayView::bindInner
MultiArrayView< N-M, T, StridedArrayTag > bindInner(const TinyVector< Index, M > &d) const
Definition: multi_array.hxx:2207
vigra::linalg::sdiv
void sdiv(const MultiArrayView< 2, T, C1 > &a, T b, MultiArrayView< 2, T, C2 > &r)
Definition: matrix.hxx:1817
vigra::linalg::Matrix::rowVector
view_type rowVector(difference_type_1 d) const
Definition: matrix.hxx:353
vigra::MultiArrayView::size
difference_type_1 size() const
Definition: multi_array.hxx:1641
vigra::linalg::Matrix::mean
TemporaryMatrix< T > mean() const
Definition: matrix.hxx:418
vigra::linalg::columnStatistics
void columnStatistics(...)
vigra::operator+=
FFTWComplex< R > & operator+=(FFTWComplex< R > &a, const FFTWComplex< R > &b)
add-assignment
Definition: fftw3.hxx:859
vigra::MultiArrayShape
Definition: multi_fwd.hxx:63
vigra::MultiArray< 2, T, ALLOC >::reference
view_type::reference reference
Definition: multi_array.hxx:2510
vigra::linalg::operator-
TemporaryMatrix< T > operator-(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
Definition: matrix.hxx:1238
vigra::linalg::log10
linalg::TemporaryMatrix< T > log10(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::reshape
void reshape(difference_type const &newShape, const_reference init)
Definition: matrix.hxx:346
vigra::linalg::sub
void sub(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1212
vigra::linalg::Matrix::reshape
void reshape(difference_type const &newShape)
Definition: matrix.hxx:339
vigra::linalg::pow
linalg::TemporaryMatrix< T > pow(MultiArrayView< 2, T, C > const &v, T exponent)
Definition: matrix.hxx:2074
vigra::sum
NumericTraits< V >::Promote sum(TinyVectorBase< V, SIZE, D1, D2 > const &l)
sum of the vector's elements
Definition: tinyvector.hxx:2073
vigra::linalg::joinHorizontally
TemporaryMatrix< T > joinHorizontally(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b)
Definition: matrix.hxx:1036
vigra::MultiArray< 2, T, ALLOC >::init
MultiArray & init(const U &init)
Definition: multi_array.hxx:2851
vigra::pow
TinyVector< V, SIZE > pow(TinyVectorBase< V, SIZE, D1, D2 > const &v, E exponent)
Definition: tinyvector.hxx:2036
vigra::argMax
Iterator argMax(Iterator first, Iterator last)
Find the maximum element in a sequence.
Definition: algorithm.hxx:96
vigra::linalg::sq
linalg::TemporaryMatrix< T > sq(MultiArrayView< 2, T, C > const &v)
vigra::linalg::norm
Matrix< T, ALLLOC >::NormType norm(const Matrix< T, ALLLOC > &a)
vigra::linalg::Matrix::Matrix
Matrix(const MultiArrayView< 2, U, C > &rhs)
Definition: matrix.hxx:263
vigra::doxygen_overloaded_function
doxygen_overloaded_function(template<...> void separableConvolveBlockwise) template< unsigned int N
Separated convolution on ChunkedArrays.
vigra::MultiArrayView< N, vigra::detail::ResolveMultiband< T >::type, vigra::detail::ResolveMultiband< T >::Stride >::copy
void copy(const MultiArrayView &rhs)
Definition: multi_array.hxx:1216
vigra::linalg::squaredNorm
Matrix< T, ALLLOC >::SquaredNormType squaredNorm(const Matrix< T, ALLLOC > &a)
vigra::MultiArray< 2, T, ALLOC >::allocator
allocator_type const & allocator() const
Definition: multi_array.hxx:2910
vigra::linalg::Matrix::operator=
Matrix & operator=(const MultiArrayView< 2, U, C > &rhs)
Definition: matrix.hxx:300
vigra::linalg::subVector
MultiArrayView< 2, T, C > subVector(MultiArrayView< 2, T, C > const &m, int first, int end)
Definition: matrix.hxx:761
vigra::operator*=
FFTWComplex< R > & operator*=(FFTWComplex< R > &a, const FFTWComplex< R > &b)
multiply-assignment
Definition: fftw3.hxx:875
vigra::TinyVectorView
Wrapper for fixed size vectors.
Definition: tinyvector.hxx:621
vigra::linalg::Matrix::reshape
void reshape(difference_type_1 rows, difference_type_1 columns)
Definition: matrix.hxx:325
vigra::MultiArray< 2, T, ALLOC >::const_pointer
view_type::const_pointer const_pointer
Definition: multi_array.hxx:2506
vigra::MultiArray< 2, T, ALLOC >::value_type
view_type::value_type value_type
Definition: multi_array.hxx:2498
vigra::linalg::Matrix::operator=
Matrix & operator=(const TemporaryMatrix< T, ALLOC > &rhs)
Definition: matrix.hxx:284
vigra::linalg::Matrix::operator*=
Matrix & operator*=(T other)
Definition: matrix.hxx:528
vigra::TinyVector< T, N >
vigra::linalg::diagonalMatrix
void diagonalMatrix(MultiArrayView< 2, T, C1 > const &v, MultiArrayView< 2, T, C2 > &r)
Definition: matrix.hxx:915
vigra::linalg::argMax
int argMax(MultiArrayView< 2, T, C > const &a)
Find the index of the maximum element in a matrix.
Definition: matrix.hxx:1986
vigra::linalg::dot
NormTraits< T >::SquaredNormType dot(const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y)
Definition: matrix.hxx:1342
vigra::linalg::outer
void outer(const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1459
vigra::linalg::Matrix::transpose
MultiArrayView< 2, vluae_type, StridedArrayTag > transpose() const
vigra::linalg::Matrix::reshape
void reshape(difference_type_1 rows, difference_type_1 columns, const_reference init)
Definition: matrix.hxx:332
vigra::closeAtTolerance
bool closeAtTolerance(T1 l, T2 r, typename PromoteTraits< T1, T2 >::Promote epsilon)
Tolerance based floating-point equality.
Definition: mathutil.hxx:1638
vigra::linalg::log
linalg::TemporaryMatrix< T > log(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::mean
TemporaryMatrix< T > mean(difference_type_1 d) const
Definition: matrix.hxx:429
vigra::argMaxIf
Iterator argMaxIf(Iterator first, Iterator last, UnaryFunctor condition)
Find the maximum element in a sequence conforming to a condition.
Definition: algorithm.hxx:165
vigra::linalg::identityMatrix
void identityMatrix(MultiArrayView< 2, T, C > &r)
Definition: matrix.hxx:845
vigra::linalg::Matrix::Matrix
Matrix(const difference_type &aShape, const_reference init, allocator_type const &alloc=allocator_type())
Definition: matrix.hxx:177
vigra::linalg::Matrix::sum
TemporaryMatrix< T > sum(difference_type_1 d) const
Definition: matrix.hxx:406
vigra::linalg::rowVector
MultiArrayView< 2, T, C > rowVector(MultiArrayView< 2, T, C > const &m, MultiArrayIndex d)
Definition: matrix.hxx:697
vigra::linalg::prepareColumns
void prepareColumns(...)
Standardize the columns of a matrix according to given DataPreparationGoals.
vigra::MultiArray< 2, T, ALLOC >::difference_type_1
view_type::difference_type_1 difference_type_1
Definition: multi_array.hxx:2526
vigra::linalg::columnCount
MultiArrayIndex columnCount(const MultiArrayView< 2, T, C > &x)
Definition: matrix.hxx:684
vigra::linalg::pmul
void pmul(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1650
vigra::TinyVectorBase
Base class for fixed size vectors.
Definition: tinyvector.hxx:82
vigra::linalg::Matrix::Matrix
Matrix(const difference_type &shape, const_pointer init, RawArrayMemoryLayout layout=RowMajor, allocator_type const &alloc=allocator_type())
Definition: matrix.hxx:199
vigra::MultiArrayView
Base class for, and view to, vigra::MultiArray.
Definition: multi_array.hxx:704
vigra::transformMultiArray
void transformMultiArray(...)
Transform a multi-dimensional array with a unary function or functor.
vigra::linalg::atan
linalg::TemporaryMatrix< T > atan(MultiArrayView< 2, T, C > const &v)
vigra::linalg::smul
void smul(const MultiArrayView< 2, T, C1 > &a, T b, MultiArrayView< 2, T, C2 > &r)
Definition: matrix.hxx:1572
vigra::linalg::tan
linalg::TemporaryMatrix< T > tan(MultiArrayView< 2, T, C > const &v)
vigra::MultiArrayView::init
MultiArrayView & init(const U &init)
Definition: multi_array.hxx:1206
vigra::argMin
Iterator argMin(Iterator first, Iterator last)
Find the minimum element in a sequence.
Definition: algorithm.hxx:68
vigra::operator/=
FFTWComplex< R > & operator/=(FFTWComplex< R > &a, const FFTWComplex< R > &b)
divide-assignment
Definition: fftw3.hxx:884
vigra::MultiArrayView::subarray
MultiArrayView subarray(difference_type p, difference_type q) const
Definition: multi_array.hxx:1528
vigra::linalg::abs
linalg::TemporaryMatrix< T > abs(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::Matrix
Matrix(const Matrix &rhs)
Definition: matrix.hxx:239
vigra::linalg::cos
linalg::TemporaryMatrix< T > cos(MultiArrayView< 2, T, C > const &v)
vigra::linalg::Matrix::Matrix
Matrix(const TemporaryMatrix< T, ALLOC > &rhs)
Definition: matrix.hxx:253
vigra::MultiArray< 2, T, ALLOC >::swap
void swap(MultiArray &other)
vigra::linalg::Matrix::Matrix
Matrix()
Definition: matrix.hxx:143
vigra::linalg::Matrix::columnVector
view_type columnVector(difference_type_1 d) const
Definition: matrix.hxx:360
vigra::linalg::Matrix::norm
NormTraits< Matrix >::NormType norm() const
vigra::linalg::Matrix::sum
TemporaryMatrix< T > sum() const
Definition: matrix.hxx:395
vigra::linalg::rowStatistics
void rowStatistics(...)
vigra::linalg::Matrix::operator()
value_type & operator()(difference_type_1 row, difference_type_1 column)
vigra::MultiArrayView::bindOuter
MultiArrayView< N-M, T, StrideTag > bindOuter(const TinyVector< Index, M > &d) const
Definition: multi_array.hxx:2184
vigra::linalg::pdiv
void pdiv(const MultiArrayView< 2, T, C1 > &a, const MultiArrayView< 2, T, C2 > &b, MultiArrayView< 2, T, C3 > &r)
Definition: matrix.hxx:1837
vigra::linalg::Matrix::operator+=
Matrix & operator+=(MultiArrayView< 2, U, C > const &other)
Definition: matrix.hxx:477
vigra::linalg::floor
linalg::TemporaryMatrix< T > floor(MultiArrayView< 2, T, C > const &v)
vigra::MultiArray< 2, T, ALLOC >::const_reference
view_type::const_reference const_reference
Definition: multi_array.hxx:2514
vigra::linalg::Matrix::operator=
Matrix & operator=(value_type const &v)
Definition: matrix.hxx:309
vigra::linalg::operator*
TemporaryMatrix< T > operator*(const MultiArrayView< 2, T, C > &a, PointWise< U > b)
Definition: matrix.hxx:1703
vigra::MultiArray< 2, T, ALLOC >::operator*=
MultiArray & operator*=(const MultiArrayView< N, U, StrideTag > &rhs)
Definition: multi_array.hxx:2734

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.11.1 (Fri May 19 2017)