Vector

The other MPI type constructor we have already seen used is MPI_Type_vector. We used this constructor in the program that exchanged columns of a matrix between processes using MPI_Sendrecv. In C columns are not laid out contiguously (rows are), so we had to call MPI_Type_vector in order to tell the program how to pick data from the matrix so that we would end up transferring the whole column in one go.

In Fortran we would have to do this for matrix rows, because in Fortran columns are laid contiguously and rows are not.

The synopsis of this function in C is:

MPI_Type_vector(int count, int blocklength, int stride,
                MPI_Datatype oldtype, MPI_Datatype *newtype)

and in Fortran:

mpi_type_vector(count, blocklength, stride, oldtype, newtype, ierror)
integer count, blocklength, stride, oldtype, newtype, ierror

The function picks up count blocks of data of type MPI_Datatype. Each block is blocklength data items long. The separation between the beginning of one block and the beginning of the next one is stride. The newly constructed data type is now associated with the memory location pointed to by newtype, which has been structured to store all information about this datatype. Within each block data items of type oldtype are laid out contiguously.

For example, if the old type is:

oldtype = {(double, 0), (char, 8)}

then the call to

MPI_Type_vector(2, 3, 4, named_double, &six_named_doubles)

will create a new MPI data type, which is going to have the following map:

newtype = 
{(double,  0), (char,  8), (double, 16), (char, 24), (double, 32), (char,  40),
 (double, 64), (char, 72), (double, 80), (char, 88), (double, 96), (char, 104)}

In plain language: we are taking two blocks of data. Each block comprises 3 structures of type named_double (the map of which is {(double, 0), (char, 8)}) concatenated contiguously. The stride is set to the extent of 4 objects of the same type, i.e., since the extent of named_double is 16, the stride is 64 bytes because $4\times16=64$.

Function MPI_Type_contiguous can be thought of as a special case of MPI_Type_vector:

MPI_Type_contiguous(count, oldtype, &newtype)
   = MPI_Type_vector(count, 1, 1, oldtype, &newtype)

This means that if you ever have to write your own MPI, you can begin by definining MPI_Type_vector and then write MPI_Type_contiguous as a simple wrapper around the former. But then it may be also the case that you can capitalize on some hardware features and write a faster implementation of MPI_Type_contiguous directly.

In MPI_Type_vector the stride is defined in terms of an extent of the basic data type used in the operation. There is a special variant of this function that lets you define stride simply in bytes, if you know what they are. This function is called MPI_Type_hvector and its synopsis in C is:

MPI_Type_hvector(int count, int blocklength, MPI_Aint stride,
                 MPI_Datatype oldtype, MPI_Datatype *newtype)

The Fortran synopsis of this function is:

mpi_type_hvector(count, blocklength, stride, oldtype, newtype, ierror)
integer count, blocklength, stride, oldtype, newtype, ierror

In term of MPI_Type_hvector the previous example

MPI_Type_vector(2, 3, 4, named_double, &six_named_doubles)

would be written as follows:

MPI_Type_hvector(2, 3, 64, named_double, &six_named_doubles)