: : Chapter $3\mathrm{.}9,$ Problem $12$E

Problem

$[11]($sects$.7\mathrm{.}2\mathrm{.}1$ and $7\mathrm{.}2\mathrm{.}2),[230]($sect$.5\mathrm{.}2)$ Matrix transpose in a two$-$dimensional mesh. Given a matrix $A=\{a_{i,j}\}$ for $1i,jn$ design a parallel algorithm to evaluate the transpose $A^{TT}$ of matrix A for a two$-$dimensional mesh of $n^2$ processors $P_{i,j}$ where $1i,jn($see Exercise $4).$ Assume that initially each processor $P_{i,j}$ stores an element $a_{i,j}$ of matrix $A.$ After completion of computation processors $P_{i,j}$ should store elements $a_{j,i}$ of the transposed matrix $A^T.$ To transfer data use the statements send and receive.