comparison DEPENDENCIES/generic/include/boost/numeric/ublas/blas.hpp @ 16:2665513ce2d3

Add boost headers

+//  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