diff --git a/README.rst b/README.rst index 68d96b4..981b0a2 100644 --- a/README.rst +++ b/README.rst @@ -206,8 +206,8 @@ you can use the weighted inner product formulation (refer to `examples/ex_05_non Computational Cost Estimates ---------------------------- -To guide the user in choosing the appropriate setting for the specific dataset at hand, we provide a rough estimate of the computational -cost of the MODULO decompositions, with and without the memory-saving option. +We here provide a rough estimate of the amoung of RAM required to decompose a test case with and without the memory saving option. +This option reduces the memory usage at the cost of increasing the computational time (see https://www.youtube.com/watch?v=LclxO1WTuao) Given a dataset $D \\in \\mathbb{R}^{n_s \\times n_t}$, we consider the computation of $n_r$ modes. When using the memory saving option, we refer to $n_t' = n_t / n_p$ as the number of time steps in each partition, and to $n_s' = n_s / n_p$ as the number of spatial points in each partition. @@ -231,9 +231,31 @@ $n_t' = n_t / n_p$ as the number of time steps in each partition, and to $n_s' = - $n_t^2 + n_t \\times n_r$ - $n_s \\times n_t' + n_s' \\times n_t + n_s \\times n_r$ -As shown in the table, the computational cost of the decomposition is dominated by the computation of the correlation matrix $K$ in Phase 2. The -memory-saving option significantly reduces the computational cost of this phase, as the correlation matrix is computed for each partition, rather than -for the entire dataset. +If the memory saving option is active, the memory requirements are mostly linked to the storage of the correlation matrix $K$ in Phase 2. +This table can be used to estimate if a dataset is too large for the available RAM, recalling that data in single precision requires 4 bytes (or 32 bits). + +For example, for a dataset with n_s=100 000 and n_t = 5000 the following table estimates the RAM required in the two cases: + +.. list-table:: + :header-rows: 1 + + * - + - Phase 1: $D$ + - Phase 2: $K$ + - Phase 3: $\\Psi$ + - Phase 4: $\\Phi$ + * - No Memory Saving + - 1.86 GB + - 96 MB + - ≈96 MB + - ≈1.95 GB + * - Memory Saving + - / + - 190 MB + 0.95 MB + - ≈96 MB + - 1.86 GB + 190 MB + 3.81 MB + + Community guidelines ---------------------