The two scaling parameters α and β measure interprocessor communication overhead required by the algorithm. The computational power r ( p 0, q 0 ) on a set of processors decomposed into a ( p 0, q 0 ) grid determines the computational power r ( p, q ) on a set of processors decomposed into a ( p, q ) grid by the formula r ( p, q ) = ( p / p 0 ) α ( q / q 0 ) β r ( p 0, q 0 ). You should also have a look at the original High Performance LINPACK.Dimensional analysis yields a new scaling formula for the Linpack benchmark.

One can prove that when k goes to infinity || X ||_k goes towards max(|x1|.,|xk|). There || X ||_1 denotes the sum of absolute values of the components of X, || X ||_1 = |x1| +.

The notation || X ||_oo comes from analysis. That is || Ax - b ||_oo is the residual, || A ||_oo is the maximum of the absolute values of the elements of the matrix AĪnd || b ||_oo is the maximum absolute value of the right hand side vector. The funny looking subscript _oo represents the infinity symbol. Here || X ||_oo denotes the maximum norm. Linpack documentation gives the following formula for normalized residual. To have a measure that is independent of the machine architecture the normalized residual is computed. For 64-bit floating point numbers eps is about 1e-15. the smallest number such that 1 + eps > eps.

It should be on the order of machine epsilon eps, i.e. The maximum norm of the vector r is the maximum of the absolute values of its elements max(|r_1|.,|r_N|). To check the solution the Linpack benchmark computes the residiual vector r = Ax - b. With larger pages it might make sense to set this value to a large number, e.g. Once again to use the cache efficiently it is advised to have all arrays start at the boundary of memory pages. Often n is selected to be the smallest integer divisible by 8 that is greater than N. Do avoid this it is advised to set n>N inserting some padding between the column data. The reason is that when n=N the algorithm running in several parallel threads may run into a phenomenon known as cache thrashing. Note that we use a different symbol n instead of N. This is equivalent to solving a vector equation Ax=b where x and b are N-dimensional vectors and A is an N*N matrix.Īn N*N matrix is represented in the memory as an N*N array where individual columns are stored at offsets 0, n, 2*n etc. Linpack benchmark solves a system of N simultaneous linear equations. The parameters that you seem to be confused are all related to the way matrices are represented and accessed. This is the setup for Intel optimized Linpack benchmark.

Note 4 linpack benchmark