1 // Copyright (c) 2000-2011 Joerg Walter, Mathias Koch, David Bellot
3 // Distributed under the Boost Software License, Version 1.0. (See
4 // accompanying file LICENSE_1_0.txt or copy at
5 // http://www.boost.org/LICENSE_1_0.txt)
7 // The authors gratefully acknowledge the support of
8 // GeNeSys mbH & Co. KG in producing this work.
10 #ifndef _BOOST_UBLAS_BLAS_
11 #define _BOOST_UBLAS_BLAS_
13 #include <boost/numeric/ublas/traits.hpp>
15 namespace boost { namespace numeric { namespace ublas {
18 /** Interface and implementation of BLAS level 1
19 * This includes functions which perform \b vector-vector operations.
20 * More information about BLAS can be found at
21 * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
25 /** 1-Norm: \f$\sum_i |x_i|\f$ (also called \f$\mathcal{L}_1\f$ or Manhattan norm)
27 * \param v a vector or vector expression
28 * \return the 1-Norm with type of the vector's type
30 * \tparam V type of the vector (not needed by default)
33 typename type_traits<typename V::value_type>::real_type
38 /** 2-Norm: \f$\sum_i |x_i|^2\f$ (also called \f$\mathcal{L}_2\f$ or Euclidean norm)
40 * \param v a vector or vector expression
41 * \return the 2-Norm with type of the vector's type
43 * \tparam V type of the vector (not needed by default)
46 typename type_traits<typename V::value_type>::real_type
51 /** Infinite-norm: \f$\max_i |x_i|\f$ (also called \f$\mathcal{L}_\infty\f$ norm)
53 * \param v a vector or vector expression
54 * \return the Infinite-Norm with type of the vector's type
56 * \tparam V type of the vector (not needed by default)
59 typename type_traits<typename V::value_type>::real_type
64 /** Inner product of vectors \f$v_1\f$ and \f$v_2\f$
66 * \param v1 first vector of the inner product
67 * \param v2 second vector of the inner product
68 * \return the inner product of the type of the most generic type of the 2 vectors
70 * \tparam V1 type of first vector (not needed by default)
71 * \tparam V2 type of second vector (not needed by default)
73 template<class V1, class V2>
74 typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type
75 dot (const V1 &v1, const V2 &v2) {
76 return inner_prod (v1, v2);
79 /** Copy vector \f$v_2\f$ to \f$v_1\f$
81 * \param v1 target vector
82 * \param v2 source vector
83 * \return a reference to the target vector
85 * \tparam V1 type of first vector (not needed by default)
86 * \tparam V2 type of second vector (not needed by default)
88 template<class V1, class V2>
89 V1 & copy (V1 &v1, const V2 &v2)
91 return v1.assign (v2);
94 /** Swap vectors \f$v_1\f$ and \f$v_2\f$
96 * \param v1 first vector
97 * \param v2 second vector
99 * \tparam V1 type of first vector (not needed by default)
100 * \tparam V2 type of second vector (not needed by default)
102 template<class V1, class V2>
103 void swap (V1 &v1, V2 &v2)
108 /** scale vector \f$v\f$ with scalar \f$t\f$
110 * \param v vector to be scaled
111 * \param t the scalar
114 * \tparam V type of the vector (not needed by default)
115 * \tparam T type of the scalar (not needed by default)
117 template<class V, class T>
118 V & scal (V &v, const T &t)
123 /** Compute \f$v_1= v_1 + t.v_2\f$
125 * \param v1 target and first vector
126 * \param t the scalar
127 * \param v2 second vector
128 * \return a reference to the first and target vector
130 * \tparam V1 type of the first vector (not needed by default)
131 * \tparam T type of the scalar (not needed by default)
132 * \tparam V2 type of the second vector (not needed by default)
134 template<class V1, class T, class V2>
135 V1 & axpy (V1 &v1, const T &t, const V2 &v2)
137 return v1.plus_assign (t * v2);
140 /** Performs rotation of points in the plane and assign the result to the first vector
142 * Each point is defined as a pair \c v1(i) and \c v2(i), being respectively
143 * the \f$x\f$ and \f$y\f$ coordinates. The parameters \c t1 and \t2 are respectively
144 * the cosine and sine of the angle of the rotation.
145 * Results are not returned but directly written into \c v1.
147 * \param t1 cosine of the rotation
148 * \param v1 vector of \f$x\f$ values
149 * \param t2 sine of the rotation
150 * \param v2 vector of \f$y\f$ values
152 * \tparam T1 type of the cosine value (not needed by default)
153 * \tparam V1 type of the \f$x\f$ vector (not needed by default)
154 * \tparam T2 type of the sine value (not needed by default)
155 * \tparam V2 type of the \f$y\f$ vector (not needed by default)
157 template<class T1, class V1, class T2, class V2>
158 void rot (const T1 &t1, V1 &v1, const T2 &t2, V2 &v2)
160 typedef typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type promote_type;
161 vector<promote_type> vt (t1 * v1 + t2 * v2);
162 v2.assign (- t2 * v1 + t1 * v2);
168 /** \brief Interface and implementation of BLAS level 2
169 * This includes functions which perform \b matrix-vector operations.
170 * More information about BLAS can be found at
171 * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
175 /** \brief multiply vector \c v with triangular matrix \c m
178 * \param m a triangular matrix
179 * \return the result of the product
181 * \tparam V type of the vector (not needed by default)
182 * \tparam M type of the matrix (not needed by default)
184 template<class V, class M>
185 V & tmv (V &v, const M &m)
187 return v = prod (m, v);
190 /** \brief solve \f$m.x = v\f$ in place, where \c m is a triangular matrix
194 * \param C (this parameter is not needed)
195 * \return a result vector from the above operation
197 * \tparam V type of the vector (not needed by default)
198 * \tparam M type of the matrix (not needed by default)
201 template<class V, class M, class C>
202 V & tsv (V &v, const M &m, C)
204 return v = solve (m, v, C ());
207 /** \brief compute \f$ v_1 = t_1.v_1 + t_2.(m.v_2)\f$, a general matrix-vector product
211 * \param t2 another scalar
213 * \param v2 another vector
214 * \return the vector \c v1 with the result from the above operation
216 * \tparam V1 type of first vector (not needed by default)
217 * \tparam T1 type of first scalar (not needed by default)
218 * \tparam T2 type of second scalar (not needed by default)
219 * \tparam M type of matrix (not needed by default)
220 * \tparam V2 type of second vector (not needed by default)
222 template<class V1, class T1, class T2, class M, class V2>
223 V1 & gmv (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2)
225 return v1 = t1 * v1 + t2 * prod (m, v2);
228 /** \brief Rank 1 update: \f$ m = m + t.(v_1.v_2^T)\f$
233 * \param v2 another vector
234 * \return a matrix with the result from the above operation
236 * \tparam M type of matrix (not needed by default)
237 * \tparam T type of scalar (not needed by default)
238 * \tparam V1 type of first vector (not needed by default)
239 * \tparam V2type of second vector (not needed by default)
241 template<class M, class T, class V1, class V2>
242 M & gr (M &m, const T &t, const V1 &v1, const V2 &v2)
244 #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
245 return m += t * outer_prod (v1, v2);
247 return m = m + t * outer_prod (v1, v2);
251 /** \brief symmetric rank 1 update: \f$m = m + t.(v.v^T)\f$
256 * \return a matrix with the result from the above operation
258 * \tparam M type of matrix (not needed by default)
259 * \tparam T type of scalar (not needed by default)
260 * \tparam V type of vector (not needed by default)
262 template<class M, class T, class V>
263 M & sr (M &m, const T &t, const V &v)
265 #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
266 return m += t * outer_prod (v, v);
268 return m = m + t * outer_prod (v, v);
272 /** \brief hermitian rank 1 update: \f$m = m + t.(v.v^H)\f$
277 * \return a matrix with the result from the above operation
279 * \tparam M type of matrix (not needed by default)
280 * \tparam T type of scalar (not needed by default)
281 * \tparam V type of vector (not needed by default)
283 template<class M, class T, class V>
284 M & hr (M &m, const T &t, const V &v)
286 #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
287 return m += t * outer_prod (v, conj (v));
289 return m = m + t * outer_prod (v, conj (v));
293 /** \brief symmetric rank 2 update: \f$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)\f$
298 * \param v2 another vector
299 * \return a matrix with the result from the above operation
301 * \tparam M type of matrix (not needed by default)
302 * \tparam T type of scalar (not needed by default)
303 * \tparam V1 type of first vector (not needed by default)
304 * \tparam V2type of second vector (not needed by default)
306 template<class M, class T, class V1, class V2>
307 M & sr2 (M &m, const T &t, const V1 &v1, const V2 &v2)
309 #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
310 return m += t * (outer_prod (v1, v2) + outer_prod (v2, v1));
312 return m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1));
316 /** \brief hermitian rank 2 update: \f$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)\f$
321 * \param v2 another vector
322 * \return a matrix with the result from the above operation
324 * \tparam M type of matrix (not needed by default)
325 * \tparam T type of scalar (not needed by default)
326 * \tparam V1 type of first vector (not needed by default)
327 * \tparam V2type of second vector (not needed by default)
329 template<class M, class T, class V1, class V2>
330 M & hr2 (M &m, const T &t, const V1 &v1, const V2 &v2)
332 #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
333 return m += t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
335 return m = m + t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
341 /** \brief Interface and implementation of BLAS level 3
342 * This includes functions which perform \b matrix-matrix operations.
343 * More information about BLAS can be found at
344 * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
348 /** \brief triangular matrix multiplication \f$m_1=t.m_2.m_3\f$ where \f$m_2\f$ and \f$m_3\f$ are triangular
350 * \param m1 a matrix for storing result
352 * \param m2 a triangular matrix
353 * \param m3 a triangular matrix
354 * \return the matrix \c m1
356 * \tparam M1 type of the result matrix (not needed by default)
357 * \tparam T type of the scalar (not needed by default)
358 * \tparam M2 type of the first triangular matrix (not needed by default)
359 * \tparam M3 type of the second triangular matrix (not needed by default)
362 template<class M1, class T, class M2, class M3>
363 M1 & tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3)
365 return m1 = t * prod (m2, m3);
368 /** \brief triangular solve \f$ m_2.x = t.m_1\f$ in place, \f$m_2\f$ is a triangular matrix
372 * \param m2 a triangular matrix
373 * \param C (not used)
374 * \return the \f$m_1\f$ matrix
376 * \tparam M1 type of the first matrix (not needed by default)
377 * \tparam T type of the scalar (not needed by default)
378 * \tparam M2 type of the triangular matrix (not needed by default)
381 template<class M1, class T, class M2, class C>
382 M1 & tsm (M1 &m1, const T &t, const M2 &m2, C)
384 return m1 = solve (m2, t * m1, C ());
387 /** \brief general matrix multiplication \f$m_1=t_1.m_1 + t_2.m_2.m_3\f$
389 * \param m1 first matrix
390 * \param t1 first scalar
391 * \param t2 second scalar
392 * \param m2 second matrix
393 * \param m3 third matrix
394 * \return the matrix \c m1
396 * \tparam M1 type of the first matrix (not needed by default)
397 * \tparam T1 type of the first scalar (not needed by default)
398 * \tparam T2 type of the second scalar (not needed by default)
399 * \tparam M2 type of the second matrix (not needed by default)
400 * \tparam M3 type of the third matrix (not needed by default)
402 template<class M1, class T1, class T2, class M2, class M3>
403 M1 & gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
405 return m1 = t1 * m1 + t2 * prod (m2, m3);
408 /** \brief symmetric rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m_2^T)\f$
410 * \param m1 first matrix
411 * \param t1 first scalar
412 * \param t2 second scalar
413 * \param m2 second matrix
414 * \return matrix \c m1
416 * \tparam M1 type of the first matrix (not needed by default)
417 * \tparam T1 type of the first scalar (not needed by default)
418 * \tparam T2 type of the second scalar (not needed by default)
419 * \tparam M2 type of the second matrix (not needed by default)
420 * \todo use opb_prod()
422 template<class M1, class T1, class T2, class M2>
423 M1 & srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
425 return m1 = t1 * m1 + t2 * prod (m2, trans (m2));
428 /** \brief hermitian rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m2^H)\f$
430 * \param m1 first matrix
431 * \param t1 first scalar
432 * \param t2 second scalar
433 * \param m2 second matrix
434 * \return matrix \c m1
436 * \tparam M1 type of the first matrix (not needed by default)
437 * \tparam T1 type of the first scalar (not needed by default)
438 * \tparam T2 type of the second scalar (not needed by default)
439 * \tparam M2 type of the second matrix (not needed by default)
440 * \todo use opb_prod()
442 template<class M1, class T1, class T2, class M2>
443 M1 & hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
445 return m1 = t1 * m1 + t2 * prod (m2, herm (m2));
448 /** \brief generalized symmetric rank \a k update: \f$m_1=t_1.m_1+t_2.(m_2.m3^T)+t_2.(m_3.m2^T)\f$
450 * \param m1 first matrix
451 * \param t1 first scalar
452 * \param t2 second scalar
453 * \param m2 second matrix
454 * \param m3 third matrix
455 * \return matrix \c m1
457 * \tparam M1 type of the first matrix (not needed by default)
458 * \tparam T1 type of the first scalar (not needed by default)
459 * \tparam T2 type of the second scalar (not needed by default)
460 * \tparam M2 type of the second matrix (not needed by default)
461 * \tparam M3 type of the third matrix (not needed by default)
462 * \todo use opb_prod()
464 template<class M1, class T1, class T2, class M2, class M3>
465 M1 & sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
467 return m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2)));
470 /** \brief generalized hermitian rank \a k update: * \f$m_1=t_1.m_1+t_2.(m_2.m_3^H)+(m_3.(t_2.m_2)^H)\f$
472 * \param m1 first matrix
473 * \param t1 first scalar
474 * \param t2 second scalar
475 * \param m2 second matrix
476 * \param m3 third matrix
477 * \return matrix \c m1
479 * \tparam M1 type of the first matrix (not needed by default)
480 * \tparam T1 type of the first scalar (not needed by default)
481 * \tparam T2 type of the second scalar (not needed by default)
482 * \tparam M2 type of the second matrix (not needed by default)
483 * \tparam M3 type of the third matrix (not needed by default)
484 * \todo use opb_prod()
486 template<class M1, class T1, class T2, class M2, class M3>
487 M1 & hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
491 + t2 * prod (m2, herm (m3))
492 + type_traits<T2>::conj (t2) * prod (m3, herm (m2));