使用MPI_Scatterv分散阵列的重叠区域 [英] Use MPI_Scatterv to Scatter Overlapping Regions of an Array
本文介绍了使用MPI_Scatterv分散阵列的重叠区域的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我有2D数组的1D数组表示形式:下面是一个6x6的示例:
[00000012300456700890100234500000] => [------]
[|0123|]
[|4567|]
[|8901|]
[|2345|]
[------]
典型的大小是514 * 514元素(512 + 2个晕圈).我必须在四个处理器之间分配数据:
Rank 0: Rank 1: Rank 2: Rank 3:
[----] [----] [|456] [567|]
[|012] [123|] [|890] [901|]
[|456] [567|] [|234] [345|]
[|890] [901|] [----] [----]
也就是说，以某种方式，到达第0位的数据的最右边部分也必须到达到达第1位的数据的左边部分，以此类推. >
我知道如何制作4x4大小的数据类型，但是不知道如何重新发送该数组的最后一个元素作为新的另一个元素的开始.
如何分发重叠的数据?
=== EDIT ===
使用Jonathon实现之后...
我目前正在尝试使用char数组(2D)进行此操作，但是将它们从处理器/等级中收集出来时会收到垃圾"消息.我更改了类型和所有内容，但无法确定当前问题出在哪里.
void distributeBySend_c(unsigned char **global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
MPI_Request reqs[dims[0]*dims[1]];
const int tag = 1;
if (rank == 0) {
MPI_Datatype block;
int starts[2] = {0,0};
int subsizes[2] = {localrows, localcols};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &block);
MPI_Type_commit(&block);
int reqno=0;
for (int i=0; i<dims[0]; i++) {
int startrow = i*datasize;
int destcoords[2];
destcoords[0] = i;
for (int j=0; j<dims[1]; j++) {
int startcol = j*datasize;
destcoords[1] = j;
int dest;
MPI_Cart_rank(cartcomm, destcoords, &dest);
MPI_Isend(&(global[startrow][startcol]), 1, block, dest, tag, cartcomm, &reqs[reqno++]);
}
}
}
unsigned char **local = alloc2dImage(localrows, localcols);
MPI_Recv(&(local[0][0]), localrows*localcols, MPI_CHAR, 0, tag, cartcomm, MPI_STATUS_IGNORE);
if (rank == 0)
MPI_Waitall(dims[0]*dims[1], reqs, MPI_STATUS_IGNORE);
eachprintarr_c(local, localrows, localcols, rank, size);
}
我得到的结果是:
---
Rank 0: ? ? ? ?
Rank 0: � ' V �
Rank 0: � ' V �
Rank 0: � ' V �
---
Rank 1: ? ? ? ?
Rank 1: � � � %
Rank 1: � � � %
Rank 1: � � � %
---
Rank 2: ? + + +
Rank 2: � � � �
Rank 2: � � � �
Rank 2: � � � �
---
Rank 3: + + + ?
Rank 3: � � �
Rank 3: � � �
Rank 3: � � �
解决方案
不幸的是，您不能使用MPI_Scatterv进行此操作，因为发送的数据重叠.
您最好的选择是要么通过Sends/Recvs手动执行此操作，这很容易，但伸缩性不佳；或仅分散内部"数据，并让处理器进行典型的保护单元/光晕交换，以获取所需的重叠数据.两种方式进行编码:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mpi.h"
char **alloc2d(const int n, const int m);
void free2d(char **p);
void printarr(const char **const arr, const int n, const int m, const char *pref);
void eachprintarr(const char **const arr, const int n, const int m, const int myrank, const int size);
const int datasize = 2;
const int halosize = 1;
void distributeBySend(const char **const global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
MPI_Request reqs[dims[0]*dims[1]];
const int tag = 1;
if (rank == 0) {
MPI_Datatype block;
int starts[2] = {0,0};
int subsizes[2] = {localrows, localcols};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &block);
MPI_Type_commit(&block);
int reqno=0;
for (int i=0; i<dims[0]; i++) {
int startrow = i*datasize;
int destcoords[2];
destcoords[0] = i;
for (int j=0; j<dims[1]; j++) {
int startcol = j*datasize;
destcoords[1] = j;
int dest;
MPI_Cart_rank(cartcomm, destcoords, &dest);
MPI_Isend(&(global[startrow][startcol]), 1, block, dest, tag, cartcomm, &reqs[reqno++]);
}
}
}
char **local = alloc2d(localrows, localcols);
MPI_Recv(&(local[0][0]), localrows*localcols, MPI_CHAR, 0, tag, cartcomm, MPI_STATUS_IGNORE);
if (rank == 0)
MPI_Waitall(dims[0]*dims[1], reqs, MPI_STATUS_IGNORE);
eachprintarr((const char **const)local, localrows, localcols, rank, size);
}
void scatterAndExchange(const char **const global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
const int lefttag=1, righttag=2, uptag=3, downtag=4;
char **local = alloc2d(localrows, localcols);
for (int i=0; i<localrows; i++)
for (int j=0; j<localcols; j++)
local[i][j] = '.';
MPI_Datatype tmp, globalblock;
MPI_Datatype localblock;
/* send just the interior data to the processors */
int starts[2] = {0,0};
int subsizes[2] = {datasize, datasize};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &tmp);
MPI_Type_create_resized(tmp, 0, sizeof(char), &globalblock);
MPI_Type_commit(&globalblock);
starts[0] = halosize; starts[1] = halosize;
sizes[0] = localrows; sizes[1] = localcols;
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &localblock);
MPI_Type_commit(&localblock);
int displs[size];
int counts[size];
for (int dest=0; dest<size; dest++) {
int destcoords[2];
MPI_Cart_coords(cartcomm, dest, 2, destcoords);
int row = halosize + destcoords[0]*datasize;
int col = halosize + destcoords[1]*datasize;
counts[dest] = 1;
displs[dest] = col + row*globalcols;
}
const char *ptr = (rank == 0 ? &(global[0][0]) : NULL ) ;
MPI_Scatterv( ptr, counts, displs, globalblock,
&(local[0][0]), 1, localblock,
0, cartcomm);
/* now send overlap data to neighbors above and below */
int left, right, up, down;
MPI_Cart_shift(cartcomm, 1, 1, &left, &right);
MPI_Cart_shift(cartcomm, 0, 1, &down, &up);
MPI_Sendrecv(&(local[localrows-2*halosize][0]), halosize*localcols, MPI_CHAR, up, uptag,
&(local[0][0]), halosize*localcols, MPI_CHAR, down, uptag,
cartcomm, MPI_STATUS_IGNORE);
MPI_Sendrecv(&(local[halosize][0]), halosize*localcols, MPI_CHAR, down, downtag,
&(local[localrows-halosize][0]), halosize*localcols, MPI_CHAR, up, downtag,
cartcomm, MPI_STATUS_IGNORE);
/* now send overlap data to neighbors left and right */
MPI_Datatype column;
sizes[0] = localrows; sizes[1] = localcols;
subsizes[0] = localrows; subsizes[1] = halosize;
starts[0] = 0; starts[1] = 0;
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &column);
MPI_Type_commit(&column);
MPI_Sendrecv(&(local[0][localcols-2*halosize]), 1, column, right, righttag,
&(local[0][0]), 1, column, left, righttag,
cartcomm, MPI_STATUS_IGNORE);
MPI_Sendrecv(&(local[0][halosize]), 1, column, left, lefttag,
&(local[0][localcols-halosize]), 1, column, right, lefttag,
cartcomm, MPI_STATUS_IGNORE);
eachprintarr((const char **const)local, localrows, localcols, rank, size);
}
int main(int argc, char **argv) {
int rank, size;
int dims[2] = {0,0};
int coords[2];
int periods[2] = {0, 0};
const int reorder = 1;
MPI_Comm cartcomm;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &size);
MPI_Dims_create(size, 2, dims);
MPI_Cart_create(MPI_COMM_WORLD, 2, dims, periods, reorder, &cartcomm);
MPI_Comm_rank(cartcomm, &rank);
MPI_Cart_coords(cartcomm, rank, 2, coords);
int globalcols = datasize*dims[0]+2*halosize;
int globalrows = datasize*dims[0]+2*halosize;
int localcols = datasize+2*halosize;
int localrows = datasize+2*halosize;
char **global = NULL;
if (rank == 0) {
global = alloc2d(globalrows, globalcols);
for (int i=0; i<globalrows; i++)
for (int j=0; j<globalcols; j++)
global[i][j] = '.';
char val = 'a';
for (int i=halosize; i<globalrows-halosize; i++)
for (int j=halosize; j<globalcols-halosize; j++) {
global[i][j] = val;
val++;
if (val > 'z') val = 'a';
}
printf("Global array: ---\n");
printarr((const char ** const)global, globalrows, globalcols, "");
}
if (argv[1] && !strcmp(argv[1],"sendrecv")) {
if (rank == 0)
printf("---\nDistributing with Send/Recv:---\n");
distributeBySend((const char **const) global, globalrows, globalcols,
localrows, localcols,
rank, size,
cartcomm, dims, coords);
} else {
if (rank == 0)
printf("---\nDistributing with Scatter/exchange:---\n");
scatterAndExchange((const char **const)global, globalrows, globalcols,
localrows, localcols,
rank, size,
cartcomm, dims, coords);
}
MPI_Finalize();
return 0;
}
char **alloc2d(const int n, const int m) {
char *data = malloc( n*m * sizeof(int) );
char **ptrs = malloc( n*sizeof(int *) );
for (int i=0; i<n; i++)
ptrs[i] = &(data[i*m]);
return ptrs;
}
void free2d(char **p) {
free(p[0]);
free(p);
}
void printarr(const char **const arr, const int n, const int m, const char *pref) {
for (int i=0; i<n; i++) {
printf("%s", pref);
for (int j=0; j<m; j++) printf("%c", arr[i][j]);
printf("\n");
}
}
void eachprintarr(const char **const arr, const int n, const int m, const int myrank, const int size) {
char line[12];
sprintf(line, "Rank %3d: ", myrank);
for (int rank=0; rank<size; rank++) {
if (rank == myrank) {
printf("---\n");
printarr(arr, n, m, line);
}
MPI_Barrier(MPI_COMM_WORLD);
}
}
跑步给予
$ mpirun -np 4 ./scatter sendrecv
Global array: ---
......
.abcd.
.efgh.
.ijkl.
.mnop.
......
---
Distributing with Send/Recv:---
---
Rank 0: ....
Rank 0: .abc
Rank 0: .efg
Rank 0: .ijk
---
Rank 1: ....
Rank 1: bcd.
Rank 1: fgh.
Rank 1: jkl.
---
Rank 2: .efg
Rank 2: .ijk
Rank 2: .mno
Rank 2: ....
---
Rank 3: fgh.
Rank 3: jkl.
Rank 3: nop.
Rank 3: ....
$ mpirun -np 4 ./scatter scatter
Global array: ---
......
.abcd.
.efgh.
.ijkl.
.mnop.
......
---
Distributing with Scatter/exchange:---
---
Rank 0: ....
Rank 0: .abc
Rank 0: .efg
Rank 0: .ijk
---
Rank 1: ....
Rank 1: bcd.
Rank 1: fgh.
Rank 1: jkl.
---
Rank 2: .efg
Rank 2: .ijk
Rank 2: .mno
Rank 2: ....
---
Rank 3: fgh.
Rank 3: jkl.
Rank 3: nop.
Rank 3: ....
I have a 1D-array representation of a 2D array: below is a 6x6 example:
[00000012300456700890100234500000] => [------]
[|0123|]
[|4567|]
[|8901|]
[|2345|]
[------]
A typical size will be 514*514 elements (512 + 2 halo cells). I have to distribute the data among, say, four processors:
Rank 0: Rank 1: Rank 2: Rank 3:
[----] [----] [|456] [567|]
[|012] [123|] [|890] [901|]
[|456] [567|] [|234] [345|]
[|890] [901|] [----] [----]
that is, in a way that the rightmost section of the data that goes to rank 0 also has to go to the left section of the data going to rank 1, and so on with all other pairs of neighbours.
I know how to make a datatype of 4x4 in size, but not how to re-send the last element of that array as the start of a new one to another rank.
How can I distribute the data with that overlap?
===EDIT===
After using your implementation of it Jonathon...
I'm trying to do this at the moment with a char array (2D), but I receive "garbage" when collecting them out of the processors/ranks. I changed the type and everything, but can't figure out where the problem is at the moment.
void distributeBySend_c(unsigned char **global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
MPI_Request reqs[dims[0]*dims[1]];
const int tag = 1;
if (rank == 0) {
MPI_Datatype block;
int starts[2] = {0,0};
int subsizes[2] = {localrows, localcols};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &block);
MPI_Type_commit(&block);
int reqno=0;
for (int i=0; i<dims[0]; i++) {
int startrow = i*datasize;
int destcoords[2];
destcoords[0] = i;
for (int j=0; j<dims[1]; j++) {
int startcol = j*datasize;
destcoords[1] = j;
int dest;
MPI_Cart_rank(cartcomm, destcoords, &dest);
MPI_Isend(&(global[startrow][startcol]), 1, block, dest, tag, cartcomm, &reqs[reqno++]);
}
}
}
unsigned char **local = alloc2dImage(localrows, localcols);
MPI_Recv(&(local[0][0]), localrows*localcols, MPI_CHAR, 0, tag, cartcomm, MPI_STATUS_IGNORE);
if (rank == 0)
MPI_Waitall(dims[0]*dims[1], reqs, MPI_STATUS_IGNORE);
eachprintarr_c(local, localrows, localcols, rank, size);
}
The result I get is:
---
Rank 0: ? ? ? ?
Rank 0: � ' V �
Rank 0: � ' V �
Rank 0: � ' V �
---
Rank 1: ? ? ? ?
Rank 1: � � � %
Rank 1: � � � %
Rank 1: � � � %
---
Rank 2: ? + + +
Rank 2: � � � �
Rank 2: � � � �
Rank 2: � � � �
---
Rank 3: + + + ?
Rank 3: � � �
Rank 3: � � �
Rank 3: � � �
解决方案
Unfortunately, you can't do this with MPI_Scatterv, because the data being sent overlaps.
Your best bet is to either manually do this with Sends/Recvs, which is easy enough but doesn't scale very well; or scatter the "interior" data only and have the processors do a typical guardcell/halo exchange to get the overlapping data they need. Coding it up both ways:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mpi.h"
char **alloc2d(const int n, const int m);
void free2d(char **p);
void printarr(const char **const arr, const int n, const int m, const char *pref);
void eachprintarr(const char **const arr, const int n, const int m, const int myrank, const int size);
const int datasize = 2;
const int halosize = 1;
void distributeBySend(const char **const global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
MPI_Request reqs[dims[0]*dims[1]];
const int tag = 1;
if (rank == 0) {
MPI_Datatype block;
int starts[2] = {0,0};
int subsizes[2] = {localrows, localcols};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &block);
MPI_Type_commit(&block);
int reqno=0;
for (int i=0; i<dims[0]; i++) {
int startrow = i*datasize;
int destcoords[2];
destcoords[0] = i;
for (int j=0; j<dims[1]; j++) {
int startcol = j*datasize;
destcoords[1] = j;
int dest;
MPI_Cart_rank(cartcomm, destcoords, &dest);
MPI_Isend(&(global[startrow][startcol]), 1, block, dest, tag, cartcomm, &reqs[reqno++]);
}
}
}
char **local = alloc2d(localrows, localcols);
MPI_Recv(&(local[0][0]), localrows*localcols, MPI_CHAR, 0, tag, cartcomm, MPI_STATUS_IGNORE);
if (rank == 0)
MPI_Waitall(dims[0]*dims[1], reqs, MPI_STATUS_IGNORE);
eachprintarr((const char **const)local, localrows, localcols, rank, size);
}
void scatterAndExchange(const char **const global, const int globalrows, const int globalcols,
const int localrows, const int localcols,
const int rank, const int size,
MPI_Comm cartcomm, const int dims[2], const int coords[2]) {
const int lefttag=1, righttag=2, uptag=3, downtag=4;
char **local = alloc2d(localrows, localcols);
for (int i=0; i<localrows; i++)
for (int j=0; j<localcols; j++)
local[i][j] = '.';
MPI_Datatype tmp, globalblock;
MPI_Datatype localblock;
/* send just the interior data to the processors */
int starts[2] = {0,0};
int subsizes[2] = {datasize, datasize};
int sizes[2] = {globalrows, globalcols};
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &tmp);
MPI_Type_create_resized(tmp, 0, sizeof(char), &globalblock);
MPI_Type_commit(&globalblock);
starts[0] = halosize; starts[1] = halosize;
sizes[0] = localrows; sizes[1] = localcols;
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &localblock);
MPI_Type_commit(&localblock);
int displs[size];
int counts[size];
for (int dest=0; dest<size; dest++) {
int destcoords[2];
MPI_Cart_coords(cartcomm, dest, 2, destcoords);
int row = halosize + destcoords[0]*datasize;
int col = halosize + destcoords[1]*datasize;
counts[dest] = 1;
displs[dest] = col + row*globalcols;
}
const char *ptr = (rank == 0 ? &(global[0][0]) : NULL ) ;
MPI_Scatterv( ptr, counts, displs, globalblock,
&(local[0][0]), 1, localblock,
0, cartcomm);
/* now send overlap data to neighbors above and below */
int left, right, up, down;
MPI_Cart_shift(cartcomm, 1, 1, &left, &right);
MPI_Cart_shift(cartcomm, 0, 1, &down, &up);
MPI_Sendrecv(&(local[localrows-2*halosize][0]), halosize*localcols, MPI_CHAR, up, uptag,
&(local[0][0]), halosize*localcols, MPI_CHAR, down, uptag,
cartcomm, MPI_STATUS_IGNORE);
MPI_Sendrecv(&(local[halosize][0]), halosize*localcols, MPI_CHAR, down, downtag,
&(local[localrows-halosize][0]), halosize*localcols, MPI_CHAR, up, downtag,
cartcomm, MPI_STATUS_IGNORE);
/* now send overlap data to neighbors left and right */
MPI_Datatype column;
sizes[0] = localrows; sizes[1] = localcols;
subsizes[0] = localrows; subsizes[1] = halosize;
starts[0] = 0; starts[1] = 0;
MPI_Type_create_subarray(2, sizes, subsizes, starts, MPI_ORDER_C, MPI_CHAR, &column);
MPI_Type_commit(&column);
MPI_Sendrecv(&(local[0][localcols-2*halosize]), 1, column, right, righttag,
&(local[0][0]), 1, column, left, righttag,
cartcomm, MPI_STATUS_IGNORE);
MPI_Sendrecv(&(local[0][halosize]), 1, column, left, lefttag,
&(local[0][localcols-halosize]), 1, column, right, lefttag,
cartcomm, MPI_STATUS_IGNORE);
eachprintarr((const char **const)local, localrows, localcols, rank, size);
}
int main(int argc, char **argv) {
int rank, size;
int dims[2] = {0,0};
int coords[2];
int periods[2] = {0, 0};
const int reorder = 1;
MPI_Comm cartcomm;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &size);
MPI_Dims_create(size, 2, dims);
MPI_Cart_create(MPI_COMM_WORLD, 2, dims, periods, reorder, &cartcomm);
MPI_Comm_rank(cartcomm, &rank);
MPI_Cart_coords(cartcomm, rank, 2, coords);
int globalcols = datasize*dims[0]+2*halosize;
int globalrows = datasize*dims[0]+2*halosize;
int localcols = datasize+2*halosize;
int localrows = datasize+2*halosize;
char **global = NULL;
if (rank == 0) {
global = alloc2d(globalrows, globalcols);
for (int i=0; i<globalrows; i++)
for (int j=0; j<globalcols; j++)
global[i][j] = '.';
char val = 'a';
for (int i=halosize; i<globalrows-halosize; i++)
for (int j=halosize; j<globalcols-halosize; j++) {
global[i][j] = val;
val++;
if (val > 'z') val = 'a';
}
printf("Global array: ---\n");
printarr((const char ** const)global, globalrows, globalcols, "");
}
if (argv[1] && !strcmp(argv[1],"sendrecv")) {
if (rank == 0)
printf("---\nDistributing with Send/Recv:---\n");
distributeBySend((const char **const) global, globalrows, globalcols,
localrows, localcols,
rank, size,
cartcomm, dims, coords);
} else {
if (rank == 0)
printf("---\nDistributing with Scatter/exchange:---\n");
scatterAndExchange((const char **const)global, globalrows, globalcols,
localrows, localcols,
rank, size,
cartcomm, dims, coords);
}
MPI_Finalize();
return 0;
}
char **alloc2d(const int n, const int m) {
char *data = malloc( n*m * sizeof(int) );
char **ptrs = malloc( n*sizeof(int *) );
for (int i=0; i<n; i++)
ptrs[i] = &(data[i*m]);
return ptrs;
}
void free2d(char **p) {
free(p[0]);
free(p);
}
void printarr(const char **const arr, const int n, const int m, const char *pref) {
for (int i=0; i<n; i++) {
printf("%s", pref);
for (int j=0; j<m; j++) printf("%c", arr[i][j]);
printf("\n");
}
}
void eachprintarr(const char **const arr, const int n, const int m, const int myrank, const int size) {
char line[12];
sprintf(line, "Rank %3d: ", myrank);
for (int rank=0; rank<size; rank++) {
if (rank == myrank) {
printf("---\n");
printarr(arr, n, m, line);
}
MPI_Barrier(MPI_COMM_WORLD);
}
}
Running gives
$ mpirun -np 4 ./scatter sendrecv
Global array: ---
......
.abcd.
.efgh.
.ijkl.
.mnop.
......
---
Distributing with Send/Recv:---
---
Rank 0: ....
Rank 0: .abc
Rank 0: .efg
Rank 0: .ijk
---
Rank 1: ....
Rank 1: bcd.
Rank 1: fgh.
Rank 1: jkl.
---
Rank 2: .efg
Rank 2: .ijk
Rank 2: .mno
Rank 2: ....
---
Rank 3: fgh.
Rank 3: jkl.
Rank 3: nop.
Rank 3: ....
$ mpirun -np 4 ./scatter scatter
Global array: ---
......
.abcd.
.efgh.
.ijkl.
.mnop.
......
---
Distributing with Scatter/exchange:---
---
Rank 0: ....
Rank 0: .abc
Rank 0: .efg
Rank 0: .ijk
---
Rank 1: ....
Rank 1: bcd.
Rank 1: fgh.
Rank 1: jkl.
---
Rank 2: .efg
Rank 2: .ijk
Rank 2: .mno
Rank 2: ....
---
Rank 3: fgh.
Rank 3: jkl.
Rank 3: nop.
Rank 3: ....
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