Skip to main content

Table 2 Number of reads and writes at each step (in bytes)

From: A MapReduce-based Adjoint method for preventing brain disease

  Cholesky (Bytes) Indirect TSQR (bytes) Direct TSQR (bytes) Householder QR (bytes) MR-AM (bytes)
\(R_{1}^{m}\) 8mn + Km 8mn + Km 8mn + Km 8mn + Km Kmn + (m − 1)(n − 1)
\(W_{1}^{m}\) 8m1n2 + 8m1n 8m1n2 + 8m1n \(8mn + 8m_{1} n^{2} + Km + 64m_{1}\) 8mn + Km Kmn + 8mn
\(R_{1}^{r}\) 8m1n2 + 8m1n 8m1n2 + 8m1n 0 0 kmn + 8mn
\(W_{1}^{r}\) 8n2 + 8n 8r1n2 + 8r1n 0 0 k + 8 k
\(R_{2}^{m}\) 8n2 + 8n 8r1n2 + 8r1n 8m1n2 + Km1 8mn + Km
\(W_{2}^{m}\) 8n2 + 8n 8r1n2 + 8r1n 8m1n2 + Km1 16m1
\(R_{2}^{r}\) 8n2 + 8n 8r1n2 + 8r1n 8m1n2 + Km1 0
\(W_{2}^{r}\) 8n2 + 8n 8n2 + 8n \(8m_{1} n^{2} + 32m_{1} + 8n^{2} + 8n\) 0
\(R_{3}^{m}\) \(8mn + Km + m_{3} \left( {8n^{2} + 8n} \right)\) \(8mn + Km + m_{3} \left( {8n^{2} + 8n} \right)\) \(8mn + Km + m_{3} \left( {8m_{1} n^{2} + 64m_{1} }\right)\)
\(W_{3}^{m}\) 8mn + Km 8mn + Km 8mn + Km
\(R_{3}^{r}\) 0 0 0
\(W_{3}^{r}\) 0 0 0
  1. We assume a double is 8 bytes and is the number of bytes for a key. The amount of key data is separated from the amount of value data