Tuning matvec library.
        ======================

      I. Introduction

  Modern computers supports a hierarchy of memory. We can consider three
level model of memory: registers (fastest), cache memory (medium), RAM
memory (slow). Modern processor can make several tens of multiplications for
time of getting operands from main memory. So efficient implementation of
elemantary vector/matrix operations: dor product, product of a mastrix and
a vector, matrix product, matrix inversion is far from elementary. If an 
operand is not found in cache, this event is called cache miss, data will
be requested rom main memory and processor will wait for completeion of 
this operation. The purpose of optimization is to minimize the number of cache
misses. It can be achived by immplementing such a modificaion of alogrithm
which performs operations under block of vectors and matrix. At the same
time such algoritms will have low performance at low dimensionns due to
overheads for groupping operands in blocks. An effricient procedure matches
several algorithms which have the optimal perfomance at a range of dimensions.

  Some operations, f.e. multiplication of rectangular matrixes, is done
in highly optimized BLAS library. However, this library does not support
operations under symmetric matrixes in upper triangular representation.
Matvec library provides a set of highly optimized routines for these 
operations whcih in turn call BLAS routines.

      II. How to tune.

  Matvec supports a set of parameters which describes dimensions for
block algorithms. Optiomal value of these parameters depends on an 
architecture of the specific processor. There is a program matvec_test
which execute specific routine under consideration and measures its 
performance. A user can change values of the matvec parameters, compile
the routien under consideration, link matvec_test with new version of matvec
linrary and run a test. Parameters are located in file 
$MK5_ROOT/include/matvec.i . Upon completion tuning these paramters should be 
copied to $Mk5_ROOT/local/solve.i file since matvec.i is a temporary file.
Then Calc/Solve should be re-compiled and re-linked with use of command
$MK5_ROOT/support/make_all_mk5


     III. Parameters to be tuned.

1) MUL_MM_IT_S ( C_s = A_r * B_r(T) ) where is A_r, B_r are rectangular 
               matrices, C_s is a square symmetric matric un upper triangular 
               representation.

   DB2__MUL_MM_IT_S -- maximal dimension when result C_s is first held in memory
                       as a rectangular matrix and them isx transform to
                       a sym. matrix.
   DB3__MUL_MM_IT_S -- Block size.

2) MUL_MM_TI_S ( C_s = A_r(T) * B_ ) where is A_r, B_r are rectangular 
               matrices, C_s is a square symmetric matric un upper triangular 
               representation.

   DB2__MUL_MM_T_S -- maximal dimension when result C_s is first held in memory
                       as a rectangular matrix and them isx transform to
                       a sym. matrix.
   DB3__MUL_MM_TI_S -- Block size.


...  document will be completed later ...

Leonid Petrov
20-MAY-2003 18:12:45