# 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
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.

Last revised: 2004-07-26