500 lines
18 KiB
C++
500 lines
18 KiB
C++
// Copyright (c) 2000-2011 Joerg Walter, Mathias Koch, David Bellot
|
|
//
|
|
// Distributed under the Boost Software License, Version 1.0. (See
|
|
// accompanying file LICENSE_1_0.txt or copy at
|
|
// http://www.boost.org/LICENSE_1_0.txt)
|
|
//
|
|
// The authors gratefully acknowledge the support of
|
|
// GeNeSys mbH & Co. KG in producing this work.
|
|
|
|
#ifndef _BOOST_UBLAS_BLAS_
|
|
#define _BOOST_UBLAS_BLAS_
|
|
|
|
#include <boost/numeric/ublas/traits.hpp>
|
|
|
|
namespace boost { namespace numeric { namespace ublas {
|
|
|
|
|
|
/** Interface and implementation of BLAS level 1
|
|
* This includes functions which perform \b vector-vector operations.
|
|
* More information about BLAS can be found at
|
|
* <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
|
|
*/
|
|
namespace blas_1 {
|
|
|
|
/** 1-Norm: \f$\sum_i |x_i|\f$ (also called \f$\mathcal{L}_1\f$ or Manhattan norm)
|
|
*
|
|
* \param v a vector or vector expression
|
|
* \return the 1-Norm with type of the vector's type
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
*/
|
|
template<class V>
|
|
typename type_traits<typename V::value_type>::real_type
|
|
asum (const V &v) {
|
|
return norm_1 (v);
|
|
}
|
|
|
|
/** 2-Norm: \f$\sum_i |x_i|^2\f$ (also called \f$\mathcal{L}_2\f$ or Euclidean norm)
|
|
*
|
|
* \param v a vector or vector expression
|
|
* \return the 2-Norm with type of the vector's type
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
*/
|
|
template<class V>
|
|
typename type_traits<typename V::value_type>::real_type
|
|
nrm2 (const V &v) {
|
|
return norm_2 (v);
|
|
}
|
|
|
|
/** Infinite-norm: \f$\max_i |x_i|\f$ (also called \f$\mathcal{L}_\infty\f$ norm)
|
|
*
|
|
* \param v a vector or vector expression
|
|
* \return the Infinite-Norm with type of the vector's type
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
*/
|
|
template<class V>
|
|
typename type_traits<typename V::value_type>::real_type
|
|
amax (const V &v) {
|
|
return norm_inf (v);
|
|
}
|
|
|
|
/** Inner product of vectors \f$v_1\f$ and \f$v_2\f$
|
|
*
|
|
* \param v1 first vector of the inner product
|
|
* \param v2 second vector of the inner product
|
|
* \return the inner product of the type of the most generic type of the 2 vectors
|
|
*
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2 type of second vector (not needed by default)
|
|
*/
|
|
template<class V1, class V2>
|
|
typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type
|
|
dot (const V1 &v1, const V2 &v2) {
|
|
return inner_prod (v1, v2);
|
|
}
|
|
|
|
/** Copy vector \f$v_2\f$ to \f$v_1\f$
|
|
*
|
|
* \param v1 target vector
|
|
* \param v2 source vector
|
|
* \return a reference to the target vector
|
|
*
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2 type of second vector (not needed by default)
|
|
*/
|
|
template<class V1, class V2>
|
|
V1 & copy (V1 &v1, const V2 &v2)
|
|
{
|
|
return v1.assign (v2);
|
|
}
|
|
|
|
/** Swap vectors \f$v_1\f$ and \f$v_2\f$
|
|
*
|
|
* \param v1 first vector
|
|
* \param v2 second vector
|
|
*
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2 type of second vector (not needed by default)
|
|
*/
|
|
template<class V1, class V2>
|
|
void swap (V1 &v1, V2 &v2)
|
|
{
|
|
v1.swap (v2);
|
|
}
|
|
|
|
/** scale vector \f$v\f$ with scalar \f$t\f$
|
|
*
|
|
* \param v vector to be scaled
|
|
* \param t the scalar
|
|
* \return \c t*v
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
* \tparam T type of the scalar (not needed by default)
|
|
*/
|
|
template<class V, class T>
|
|
V & scal (V &v, const T &t)
|
|
{
|
|
return v *= t;
|
|
}
|
|
|
|
/** Compute \f$v_1= v_1 + t.v_2\f$
|
|
*
|
|
* \param v1 target and first vector
|
|
* \param t the scalar
|
|
* \param v2 second vector
|
|
* \return a reference to the first and target vector
|
|
*
|
|
* \tparam V1 type of the first vector (not needed by default)
|
|
* \tparam T type of the scalar (not needed by default)
|
|
* \tparam V2 type of the second vector (not needed by default)
|
|
*/
|
|
template<class V1, class T, class V2>
|
|
V1 & axpy (V1 &v1, const T &t, const V2 &v2)
|
|
{
|
|
return v1.plus_assign (t * v2);
|
|
}
|
|
|
|
/** Performs rotation of points in the plane and assign the result to the first vector
|
|
*
|
|
* Each point is defined as a pair \c v1(i) and \c v2(i), being respectively
|
|
* the \f$x\f$ and \f$y\f$ coordinates. The parameters \c t1 and \t2 are respectively
|
|
* the cosine and sine of the angle of the rotation.
|
|
* Results are not returned but directly written into \c v1.
|
|
*
|
|
* \param t1 cosine of the rotation
|
|
* \param v1 vector of \f$x\f$ values
|
|
* \param t2 sine of the rotation
|
|
* \param v2 vector of \f$y\f$ values
|
|
*
|
|
* \tparam T1 type of the cosine value (not needed by default)
|
|
* \tparam V1 type of the \f$x\f$ vector (not needed by default)
|
|
* \tparam T2 type of the sine value (not needed by default)
|
|
* \tparam V2 type of the \f$y\f$ vector (not needed by default)
|
|
*/
|
|
template<class T1, class V1, class T2, class V2>
|
|
void rot (const T1 &t1, V1 &v1, const T2 &t2, V2 &v2)
|
|
{
|
|
typedef typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type promote_type;
|
|
vector<promote_type> vt (t1 * v1 + t2 * v2);
|
|
v2.assign (- t2 * v1 + t1 * v2);
|
|
v1.assign (vt);
|
|
}
|
|
|
|
}
|
|
|
|
/** \brief Interface and implementation of BLAS level 2
|
|
* This includes functions which perform \b matrix-vector operations.
|
|
* More information about BLAS can be found at
|
|
* <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
|
|
*/
|
|
namespace blas_2 {
|
|
|
|
/** \brief multiply vector \c v with triangular matrix \c m
|
|
*
|
|
* \param v a vector
|
|
* \param m a triangular matrix
|
|
* \return the result of the product
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
* \tparam M type of the matrix (not needed by default)
|
|
*/
|
|
template<class V, class M>
|
|
V & tmv (V &v, const M &m)
|
|
{
|
|
return v = prod (m, v);
|
|
}
|
|
|
|
/** \brief solve \f$m.x = v\f$ in place, where \c m is a triangular matrix
|
|
*
|
|
* \param v a vector
|
|
* \param m a matrix
|
|
* \param C (this parameter is not needed)
|
|
* \return a result vector from the above operation
|
|
*
|
|
* \tparam V type of the vector (not needed by default)
|
|
* \tparam M type of the matrix (not needed by default)
|
|
* \tparam C n/a
|
|
*/
|
|
template<class V, class M, class C>
|
|
V & tsv (V &v, const M &m, C)
|
|
{
|
|
return v = solve (m, v, C ());
|
|
}
|
|
|
|
/** \brief compute \f$ v_1 = t_1.v_1 + t_2.(m.v_2)\f$, a general matrix-vector product
|
|
*
|
|
* \param v1 a vector
|
|
* \param t1 a scalar
|
|
* \param t2 another scalar
|
|
* \param m a matrix
|
|
* \param v2 another vector
|
|
* \return the vector \c v1 with the result from the above operation
|
|
*
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam T1 type of first scalar (not needed by default)
|
|
* \tparam T2 type of second scalar (not needed by default)
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam V2 type of second vector (not needed by default)
|
|
*/
|
|
template<class V1, class T1, class T2, class M, class V2>
|
|
V1 & gmv (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2)
|
|
{
|
|
return v1 = t1 * v1 + t2 * prod (m, v2);
|
|
}
|
|
|
|
/** \brief Rank 1 update: \f$ m = m + t.(v_1.v_2^T)\f$
|
|
*
|
|
* \param m a matrix
|
|
* \param t a scalar
|
|
* \param v1 a vector
|
|
* \param v2 another vector
|
|
* \return a matrix with the result from the above operation
|
|
*
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam T type of scalar (not needed by default)
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2type of second vector (not needed by default)
|
|
*/
|
|
template<class M, class T, class V1, class V2>
|
|
M & gr (M &m, const T &t, const V1 &v1, const V2 &v2)
|
|
{
|
|
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
|
|
return m += t * outer_prod (v1, v2);
|
|
#else
|
|
return m = m + t * outer_prod (v1, v2);
|
|
#endif
|
|
}
|
|
|
|
/** \brief symmetric rank 1 update: \f$m = m + t.(v.v^T)\f$
|
|
*
|
|
* \param m a matrix
|
|
* \param t a scalar
|
|
* \param v a vector
|
|
* \return a matrix with the result from the above operation
|
|
*
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam T type of scalar (not needed by default)
|
|
* \tparam V type of vector (not needed by default)
|
|
*/
|
|
template<class M, class T, class V>
|
|
M & sr (M &m, const T &t, const V &v)
|
|
{
|
|
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
|
|
return m += t * outer_prod (v, v);
|
|
#else
|
|
return m = m + t * outer_prod (v, v);
|
|
#endif
|
|
}
|
|
|
|
/** \brief hermitian rank 1 update: \f$m = m + t.(v.v^H)\f$
|
|
*
|
|
* \param m a matrix
|
|
* \param t a scalar
|
|
* \param v a vector
|
|
* \return a matrix with the result from the above operation
|
|
*
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam T type of scalar (not needed by default)
|
|
* \tparam V type of vector (not needed by default)
|
|
*/
|
|
template<class M, class T, class V>
|
|
M & hr (M &m, const T &t, const V &v)
|
|
{
|
|
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
|
|
return m += t * outer_prod (v, conj (v));
|
|
#else
|
|
return m = m + t * outer_prod (v, conj (v));
|
|
#endif
|
|
}
|
|
|
|
/** \brief symmetric rank 2 update: \f$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)\f$
|
|
*
|
|
* \param m a matrix
|
|
* \param t a scalar
|
|
* \param v1 a vector
|
|
* \param v2 another vector
|
|
* \return a matrix with the result from the above operation
|
|
*
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam T type of scalar (not needed by default)
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2type of second vector (not needed by default)
|
|
*/
|
|
template<class M, class T, class V1, class V2>
|
|
M & sr2 (M &m, const T &t, const V1 &v1, const V2 &v2)
|
|
{
|
|
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
|
|
return m += t * (outer_prod (v1, v2) + outer_prod (v2, v1));
|
|
#else
|
|
return m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1));
|
|
#endif
|
|
}
|
|
|
|
/** \brief hermitian rank 2 update: \f$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)\f$
|
|
*
|
|
* \param m a matrix
|
|
* \param t a scalar
|
|
* \param v1 a vector
|
|
* \param v2 another vector
|
|
* \return a matrix with the result from the above operation
|
|
*
|
|
* \tparam M type of matrix (not needed by default)
|
|
* \tparam T type of scalar (not needed by default)
|
|
* \tparam V1 type of first vector (not needed by default)
|
|
* \tparam V2type of second vector (not needed by default)
|
|
*/
|
|
template<class M, class T, class V1, class V2>
|
|
M & hr2 (M &m, const T &t, const V1 &v1, const V2 &v2)
|
|
{
|
|
#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
|
|
return m += t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
|
|
#else
|
|
return m = m + t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
|
|
#endif
|
|
}
|
|
|
|
}
|
|
|
|
/** \brief Interface and implementation of BLAS level 3
|
|
* This includes functions which perform \b matrix-matrix operations.
|
|
* More information about BLAS can be found at
|
|
* <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a>
|
|
*/
|
|
namespace blas_3 {
|
|
|
|
/** \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
|
|
*
|
|
* \param m1 a matrix for storing result
|
|
* \param t a scalar
|
|
* \param m2 a triangular matrix
|
|
* \param m3 a triangular matrix
|
|
* \return the matrix \c m1
|
|
*
|
|
* \tparam M1 type of the result matrix (not needed by default)
|
|
* \tparam T type of the scalar (not needed by default)
|
|
* \tparam M2 type of the first triangular matrix (not needed by default)
|
|
* \tparam M3 type of the second triangular matrix (not needed by default)
|
|
*
|
|
*/
|
|
template<class M1, class T, class M2, class M3>
|
|
M1 & tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3)
|
|
{
|
|
return m1 = t * prod (m2, m3);
|
|
}
|
|
|
|
/** \brief triangular solve \f$ m_2.x = t.m_1\f$ in place, \f$m_2\f$ is a triangular matrix
|
|
*
|
|
* \param m1 a matrix
|
|
* \param t a scalar
|
|
* \param m2 a triangular matrix
|
|
* \param C (not used)
|
|
* \return the \f$m_1\f$ matrix
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T type of the scalar (not needed by default)
|
|
* \tparam M2 type of the triangular matrix (not needed by default)
|
|
* \tparam C (n/a)
|
|
*/
|
|
template<class M1, class T, class M2, class C>
|
|
M1 & tsm (M1 &m1, const T &t, const M2 &m2, C)
|
|
{
|
|
return m1 = solve (m2, t * m1, C ());
|
|
}
|
|
|
|
/** \brief general matrix multiplication \f$m_1=t_1.m_1 + t_2.m_2.m_3\f$
|
|
*
|
|
* \param m1 first matrix
|
|
* \param t1 first scalar
|
|
* \param t2 second scalar
|
|
* \param m2 second matrix
|
|
* \param m3 third matrix
|
|
* \return the matrix \c m1
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T1 type of the first scalar (not needed by default)
|
|
* \tparam T2 type of the second scalar (not needed by default)
|
|
* \tparam M2 type of the second matrix (not needed by default)
|
|
* \tparam M3 type of the third matrix (not needed by default)
|
|
*/
|
|
template<class M1, class T1, class T2, class M2, class M3>
|
|
M1 & gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
|
|
{
|
|
return m1 = t1 * m1 + t2 * prod (m2, m3);
|
|
}
|
|
|
|
/** \brief symmetric rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m_2^T)\f$
|
|
*
|
|
* \param m1 first matrix
|
|
* \param t1 first scalar
|
|
* \param t2 second scalar
|
|
* \param m2 second matrix
|
|
* \return matrix \c m1
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T1 type of the first scalar (not needed by default)
|
|
* \tparam T2 type of the second scalar (not needed by default)
|
|
* \tparam M2 type of the second matrix (not needed by default)
|
|
* \todo use opb_prod()
|
|
*/
|
|
template<class M1, class T1, class T2, class M2>
|
|
M1 & srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
|
|
{
|
|
return m1 = t1 * m1 + t2 * prod (m2, trans (m2));
|
|
}
|
|
|
|
/** \brief hermitian rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m2^H)\f$
|
|
*
|
|
* \param m1 first matrix
|
|
* \param t1 first scalar
|
|
* \param t2 second scalar
|
|
* \param m2 second matrix
|
|
* \return matrix \c m1
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T1 type of the first scalar (not needed by default)
|
|
* \tparam T2 type of the second scalar (not needed by default)
|
|
* \tparam M2 type of the second matrix (not needed by default)
|
|
* \todo use opb_prod()
|
|
*/
|
|
template<class M1, class T1, class T2, class M2>
|
|
M1 & hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
|
|
{
|
|
return m1 = t1 * m1 + t2 * prod (m2, herm (m2));
|
|
}
|
|
|
|
/** \brief generalized symmetric rank \a k update: \f$m_1=t_1.m_1+t_2.(m_2.m3^T)+t_2.(m_3.m2^T)\f$
|
|
*
|
|
* \param m1 first matrix
|
|
* \param t1 first scalar
|
|
* \param t2 second scalar
|
|
* \param m2 second matrix
|
|
* \param m3 third matrix
|
|
* \return matrix \c m1
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T1 type of the first scalar (not needed by default)
|
|
* \tparam T2 type of the second scalar (not needed by default)
|
|
* \tparam M2 type of the second matrix (not needed by default)
|
|
* \tparam M3 type of the third matrix (not needed by default)
|
|
* \todo use opb_prod()
|
|
*/
|
|
template<class M1, class T1, class T2, class M2, class M3>
|
|
M1 & sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
|
|
{
|
|
return m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2)));
|
|
}
|
|
|
|
/** \brief generalized hermitian rank \a k update: * \f$m_1=t_1.m_1+t_2.(m_2.m_3^H)+(m_3.(t_2.m_2)^H)\f$
|
|
*
|
|
* \param m1 first matrix
|
|
* \param t1 first scalar
|
|
* \param t2 second scalar
|
|
* \param m2 second matrix
|
|
* \param m3 third matrix
|
|
* \return matrix \c m1
|
|
*
|
|
* \tparam M1 type of the first matrix (not needed by default)
|
|
* \tparam T1 type of the first scalar (not needed by default)
|
|
* \tparam T2 type of the second scalar (not needed by default)
|
|
* \tparam M2 type of the second matrix (not needed by default)
|
|
* \tparam M3 type of the third matrix (not needed by default)
|
|
* \todo use opb_prod()
|
|
*/
|
|
template<class M1, class T1, class T2, class M2, class M3>
|
|
M1 & hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
|
|
{
|
|
return m1 =
|
|
t1 * m1
|
|
+ t2 * prod (m2, herm (m3))
|
|
+ type_traits<T2>::conj (t2) * prod (m3, herm (m2));
|
|
}
|
|
|
|
}
|
|
|
|
}}}
|
|
|
|
#endif
|