# Level 3 BLAS

## Functions

template<class M1, class T, class M2, class M3> M1 & | boost::numeric::ublas::blas_3::tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3)
| triangular matrix multiplication
template<class M1, class T, class M2, class C> M1 & | boost::numeric::ublas::blas_3::tsm (M1 &m1, const T &t, const M2 &m2, C)
| triangular solve m2 * x = t * m1 in place, m2 is a triangular matrix
template<class M1, class T1, class T2, class M2, class M3> M1 & | boost::numeric::ublas::blas_3::gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
| general matrix multiplication
template<class M1, class T1, class T2, class M2> M1 & | boost::numeric::ublas::blas_3::srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
| symmetric rank k update: m1 = t * m1 + t2 * (m2 * m2T)
template<class M1, class T1, class T2, class M2> M1 & | boost::numeric::ublas::blas_3::hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2)
| hermitian rank k update: m1 = t * m1 + t2 * (m2 * m2H)
template<class M1, class T1, class T2, class M2, class M3> M1 & | boost::numeric::ublas::blas_3::sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
| generalized symmetric rank k update: m1 = t1 * m1 + t2 * (m2 * m3T) + t2 * (m3 * m2T)
template<class M1, class T1, class T2, class M2, class M3> M1 & | boost::numeric::ublas::blas_3::hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3)
| generalized hermitian rank k update: m1 = t1 * m1 + t2 * (m2 * m3H) + (m3 * (t2 * m2)H)
template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & | boost::numeric::ublas::axpy_prod (const matrix_expression< E1 > &e1, const matrix_expression< E2 > &e2, M &m, bool init=true)
| computes `M += A X` or `M = A X` in an optimized fashion.
template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & | boost::numeric::ublas::opb_prod (const matrix_expression< E1 > &e1, const matrix_expression< E2 > &e2, M &m, bool init=true)
| computes `M += A X` or `M = A X` in an optimized fashion.

## Function Documentation

M1& tmm | ( | M1 & | m1,
|  | const T & | t,
|  | const M2 & | m2,
|  | const M3 & | m3
| ) |

| triangular matrix multiplication

M1& tsm | ( | M1 & | m1,
|  | const T & | t,
|  | const M2 & | m2,
|  | C |
| ) |

| triangular solve m2 * x = t * m1 in place, m2 is a triangular matrix

M1& gmm | ( | M1 & | m1,
|  | const T1 & | t1,
|  | const T2 & | t2,
|  | const M2 & | m2,
|  | const M3 & | m3
| ) |

| general matrix multiplication

M1& srk | ( | M1 & | m1,
|  | const T1 & | t1,
|  | const T2 & | t2,
|  | const M2 & | m2
| ) |

symmetric rank k update: m1 = t * m1 + t2 * (m2 * m2T)

Todo:
  use opb_prod()

M1& hrk | ( | M1 & | m1,
|  | const T1 & | t1,
|  | const T2 & | t2,
|  | const M2 & | m2
| ) |

hermitian rank k update: m1 = t * m1 + t2 * (m2 * m2H)

Todo:
  use opb_prod()

M1& sr2k | ( | M1 & | m1,
|  | const T1 & | t1,
|  | const T2 & | t2,
|  | const M2 & | m2,
|  | const M3 & | m3
| ) |

generalized symmetric rank k update: m1 = t1 * m1 + t2 * (m2 * m3T) + t2 * (m3 * m2T)

Todo:
  use opb_prod()

M1& hr2k | ( | M1 & | m1,
|  | const T1 & | t1,
|  | const T2 & | t2,
|  | const M2 & | m2,
|  | const M3 & | m3
| ) |

generalized hermitian rank k update: m1 = t1 * m1 + t2 * (m2 * m3H) + (m3 * (t2 * m2)H)

Todo:
  use opb_prod()

Copyright (©) 2000-2004 Michael Stevens, Mathias Koch, Joerg Walter, Gunter Winkler
Use, modification and distribution are subject to 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).