Example of message passing mechanism

A very simple master program using pvm may be found in the ALIAS distribution under the name
MasterGeneralSolve.C while the corresponding slave program is SlaveGeneralSolve.C: these programs are used by Maple for creating the parallel implementation of the GeneralSolve procedure. Here we use text message passing:

• the master program send a box with $n$ unknowns by writing in a text buffer the keyword B followed by $2n$ reals which are the extremity of the box ranges for each unknown.
• then it append to this message the value N of ALIAS_Parallel_Max_Bisection with the keyword SP (hence SP N is appended to the buffer. If N is negative then the value M of ALIAS_Parallel_Max_Box is appended to the buffer by appending the text P I M (the value of ALIAS_Parallel_Max_Bisection is computed by the master program: if the box is large a positive value is chosen while for small box a negative value is given).

This buffer is then sent to a slave computer with the pvm_pkstr procedure. As soon as a buffer is received by the slave computer the value of the box to be processed is extracted from the message using the ALIAS procedure ALIAS_Read_Buffer (which also update the value of ALIAS_Parallel_Max_Bisection and ALIAS_Parallel_Max_Box. As soon as the slave computer has terminated its computation it send back to the master in a text buffer:

• the boxes still to be processed (using the keywords B for each box or N is no box remain to be processed)
• the solution that have been eventually found (using the keyword S followed by the $2n$ reals)
• a failure code if the slave has not been able to process the box (using the keyword F followed by the error code)

For the algorithms using the derivatives the jacobian matrix is also transferred to the slaves. For large system this may slow down considerably the communication between the slaves and the master. Hence it may be a good policy to inhibit the transfer of the jacobian by setting the variable `ALIAS/transmit_gradient` to 0.