void setup (int N, const Parameter ¶m, Array<double, 1> &WR, Array<double,2> &ev, Array<double,2> &evInv)
{
int Nm1 = N;
int i;
Array<double, 1> x;
Array<double, 2> D;
Array<double, 1> r;
Array<double, 2> Dsec;
Array<double, 1> XX;
Array<double, 1> YY;
Array<double, 2> A(N,N);
Array<double, 2> B(N,N);
Array<int, 1> IPIV(Nm1);
char BALANC[1];
char JOBVL[1];
char JOBVR[1];
char SENSE[1];
int LDA;
int LDVL;
int LDVR;
int NRHS;
int LDB;
int INFO;
//resize output arrays
WR.resize(N);
ev.resize(N, N);
evInv.resize(N, N);
// parameters for DGEEVX
Array<double, 1> WI(Nm1); // WR(Nm1),
// The real and imaginary part of the eig.values
Array<double, 2> VL(N, N);
Array<double, 2> VR(Nm1,Nm1); //VR(Nm1,Nm1);
// The left and rigth eigenvectors
int ILO, IHI; // Info on the balanced output matrix
Array<double, 1> SCALE(Nm1); // Scaling factors applied for balancing
double ABNRM; // 1-Norm of the balanced matrix
Array<double, 1> RCONDE(Nm1);
// the reciprocal cond. numb of the respective eig.val
Array<double, 1> RCONDV(Nm1);
// the reciprocal cond. numb of the respective eig.vec
int LWORK = (N+1)*(N+7); // Depending on SENSE
Array<double, 1> WORK(LWORK);
Array<int, 1> IWORK(2*(N+1)-2);
// Compute the Chebyshev differensiation matrix and D*D
// cheb(N, x, D);
cheb(N, x, D);
Dsec.resize(D.shape());
MatrixMatrixMultiply(D, D, Dsec);
// Compute the 1. and 2. derivatives of the transformations
XYmat(N, param, XX, YY, r);
// Set up the full timepropagation matrix A
// dy/dt = - i A y
Range range(1, N); //Dsec and D have range 0, N+1.
//We don't want the edge points in A
A = XX(tensor::i) * Dsec(range, range) + YY(tensor::i) * D(range, range);
//Transpose A
for (int i=0; i<A.extent(0); i++)
{
for (int j=0; j<i; j++)
{
double t = A(i,j);
A(i,j) = A(j, i);
A(j,i) = t;
}
}
// Add radialpart of non-time dependent potential here
/* 2D radial
for (int i=0; i<A.extent(0); i++)
{
A(i, i) += 0.25 / (r(i)*r(i));
}
*/
// Compute eigen decomposition
BALANC[0] ='B';
JOBVL[0] ='V';
JOBVR[0] ='V';
SENSE[0] ='B';
LDA = Nm1;
LDVL = Nm1;
LDVR = Nm1;
FORTRAN_NAME(dgeevx)(BALANC, JOBVL, JOBVR, SENSE, &Nm1,
A.data(), &LDA, WR.data(), WI.data(),
VL.data(), &LDVL, VR.data(), &LDVR, &ILO, &IHI,
SCALE.data(), &ABNRM,
RCONDE.data(), RCONDV.data(), WORK.data(), &LWORK,
IWORK.data(), &INFO);
// Compute the inverse of the eigen vector matrix
NRHS = Nm1;
evInv = VR ;// VL;
LDB = LDA;
B = 0.0;
for (i=0; i<Nm1; i++) B(i,i) = 1.0;
FORTRAN_NAME(dgesv)(&Nm1, &NRHS, evInv.data(), &LDA, IPIV.data(), B.data(), &LDB, &INFO);
ev = VR(tensor::j, tensor::i); //Transpose
evInv = B(tensor::j, tensor::i); //Transpose
//cout << "Eigenvectors (right): " << ev << endl;
//cout << "Eigenvectors (inv): " << evInv << endl;
//printf(" Done inverse, INFO = %d \n", INFO);
} // done
int main(int argc, char *argv[])
{
//Declaration of variables
int my_rank, num_procs;
int num_rows, num_cols;
double **A, **B, **C;
int nrA, ncA, nrB, ncB;
double **a, **b, **c;
int nra, nca, nrb, ncb;
int sqrt_p;
int *rsA, *csA, *rsB, *csB;
int mrA, mcA, mrB, mcB;
//Declare MPI-suff
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
char *Mat_A, *Mat_B, *Mat_C;
Mat_A = argv[1];
Mat_B = argv[2];
Mat_C = argv[3];
sqrt_p = sqrt(num_procs);
if(my_rank == 0){
//read_matrix_binaryformat(Mat_A, &A, &nrA, &ncA );
//read_matrix_binaryformat(Mat_B, &B, &nrB, &ncB );
nrA = 100;
ncA = 50;
nrB = 50;
ncB = 100;
allocate_matrix(&A, nrA, ncA);
allocate_matrix(&B, nrB, ncB);
fill_matrix(&A, nrA, ncA);
fill_matrix(&B, nrB, ncB);
char A_id = 'A', B_id = 'B';
print_matrix(nrA, ncA, A, my_rank, A_id);
print_matrix(nrB, ncB, B, my_rank, B_id);
}
MPI_Bcast(&nrA, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&ncA, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&nrB, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&ncB, 1, MPI_INT, 0, MPI_COMM_WORLD);
find_size(nrA, ncA, &nra, &nca, my_rank, sqrt_p);
find_size(nrB, ncB, &nrb, &ncb, my_rank, sqrt_p);
rsA = (int*)malloc(num_procs*sizeof(int));
csA = (int*)malloc(num_procs*sizeof(int));
rsB = (int*)malloc(num_procs*sizeof(int));
csB = (int*)malloc(num_procs*sizeof(int));
for(int i=0; i<num_procs; ++i) {
if(i == my_rank) {
rsA[i] = nra;
csA[i] = nca;
rsB[i] = nrb;
csB[i] = ncb;
} else {
MPI_Sendrecv(&nra, 1, MPI_INT, i, 1, &(rsA[i]), 1, MPI_INT, i, 1,
MPI_COMM_WORLD, MPI_STATUS_IGNORE);
MPI_Sendrecv(&nca, 1, MPI_INT, i, 1, &(csA[i]), 1, MPI_INT, i, 1,
MPI_COMM_WORLD, MPI_STATUS_IGNORE);
MPI_Sendrecv(&nrb, 1, MPI_INT, i, 1, &(rsB[i]), 1, MPI_INT, i, 1,
MPI_COMM_WORLD, MPI_STATUS_IGNORE);
MPI_Sendrecv(&ncb, 1, MPI_INT, i, 1, &(csB[i]), 1, MPI_INT, i, 1,
MPI_COMM_WORLD, MPI_STATUS_IGNORE);
}
//printf("nra[%i] = %i, my_rank:%i\n", i, rsA[i], my_rank);
}
// root finds large enough sizes
if(my_rank == 0) {
find_max(rsA, &mrA, num_procs);
find_max(csA, &mcA, num_procs);
find_max(rsB, &mrB, num_procs);
find_max(csB, &mcB, num_procs);
}
// send bigbuffs to all
MPI_Bcast(&mrA, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&mcA, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&mrB, 1, MPI_INT, 0, MPI_COMM_WORLD);
MPI_Bcast(&mcB, 1, MPI_INT, 0, MPI_COMM_WORLD);
// allocate sub matrices
allocate_matrix(&a, mrA, mcA);
allocate_matrix(&b, mrB, mcB);
allocate_matrix(&c, mrA, mcB);
if(my_rank == 0) {
// root sets its own matrices
for(int i=0; i<nra; ++i) {
for(int j=0; j<nca; ++j) {
a[i][j] = A[i][j];
}
}
for(int i=0; i<nrb; ++i) {
for(int j=0; j<ncb; ++j) {
b[i][j] = B[i][j];
}
}
MPI_Datatype btA;
MPI_Datatype btB;
// initialize row and column index variables
int riA = 0;
int riB = 0;
int ciA = csA[0];
int ciB = csB[0];
int tmpk = 1;
for(int k=1; k<num_procs; ++k) {
//send to slaves
// create strided types (blocks/chunks/blarg)
MPI_Type_vector(rsA[k], csA[k], ncA, MPI_DOUBLE, &btA);
MPI_Type_create_resized(btA, 0, sizeof(double), &btA);
MPI_Type_commit(&btA);
MPI_Type_vector(rsB[k], csB[k], ncB, MPI_DOUBLE, &btB);
MPI_Type_create_resized(btB, 0, sizeof(double), &btB);
MPI_Type_commit(&btB);
// send to slaves
MPI_Send(&((*A)[ncA*riA + ciA]), 1, btA, k, 1, MPI_COMM_WORLD);
MPI_Send(&((*B)[ncB*riB + ciB]), 1, btB, k, 2, MPI_COMM_WORLD);
// free types for next iteration
MPI_Type_free(&btA);
MPI_Type_free(&btB);
ciA += csA[k];
ciB += csB[k];
tmpk++;
if(tmpk == sqrt_p) {
// jump down to next chunk row
riA += rsA[k-1];
riB += rsB[k-1];
ciA = 0;
ciB = 0;
tmpk = 0;
}
}
// deallocate A and B
//deallocate(&A);
//deallocate(&B);
} else {
// slaves recv from root a chunk/block/somethgin
// create data types
MPI_Datatype btA;
MPI_Datatype btB;
// create strided data types
MPI_Type_vector(nra, nca, mcA, MPI_DOUBLE, &btA);
MPI_Type_create_resized(btA, 0, sizeof(double), &btA);
MPI_Type_commit(&btA);
MPI_Type_vector(nrb, ncb, mcB, MPI_DOUBLE, &btB);
MPI_Type_create_resized(btB, 0, sizeof(double), &btB);
MPI_Type_commit(&btB);
// recv from root a chunk
MPI_Recv(&((*a)[0]), 1, btA, 0, 1, MPI_COMM_WORLD,
MPI_STATUS_IGNORE);
MPI_Recv(&((*b)[0]), 1, btB, 0, 2, MPI_COMM_WORLD,
MPI_STATUS_IGNORE);
// free types
MPI_Type_free(&btA);
MPI_Type_free(&btB);
//char a_id = 'a', b_id = 'b';
//print_matrix(nra, nca, a, my_rank, a_id);
}
char a_id = 'a', b_id = 'b';
//print_matrix(nra, nca, a, my_rank, a_id);
//print_matrix(nrb, ncb, b, my_rank, b_id);
MatrixMatrixMultiply(&a, &b, &c, mrA, mcA, mrB, mcB, rsA, csA, rsB, csB,
MPI_COMM_WORLD);
if(my_rank == 0) {
// allocate result
allocate_matrix(&C, nrA, ncB);
// root sets its own matrices
for(int i=0; i<nra; ++i) {
for(int j=0; j<ncb; ++j) {
C[i][j] = c[i][j];
}
}
MPI_Datatype btC;
int riC = 0;
int ciC = csB[0];
int tmpk = 1;
for(int k=1; k<num_procs; ++k) {
MPI_Type_vector(rsA[k], csB[k], ncB, MPI_DOUBLE, &btC);
MPI_Type_create_resized(btC, 0, sizeof(double), &btC);
MPI_Type_commit(&btC);
printf("%i\n", ncB*riC+ciC);
MPI_Recv(&((*C)[ncB*riC+ciC]), 1, btC, k, k, MPI_COMM_WORLD,
MPI_STATUS_IGNORE);
MPI_Type_free(&btC);
ciC += csB[k];
if(tmpk == sqrt_p) {
riC += rsA[k-1];
ciC = 0;
tmpk = 0;
}
}
//read_matrix_binaryformat(Mat_A, &A, &nrA, &ncA );
//read_matrix_binaryformat(Mat_B, &B, &nrB, &ncB );
test_result(nrA, ncA, nrB, ncB, A, B, C);
//test_result(nrA, ncA, nrB, ncB, A, B, C);
deallocate(&A);
deallocate(&B);
deallocate(&C);
} else {
MPI_Datatype btC;
MPI_Type_vector(nra, ncb, mcB, MPI_DOUBLE, &btC);
MPI_Type_create_resized(btC, 0, sizeof(double), &btC);
MPI_Type_commit(&btC);
MPI_Send(&((*c)[0]), 1, btC, 0, my_rank, MPI_COMM_WORLD);
MPI_Type_free(&btC);
}
// deallocate sub matrices
deallocate(&a);
deallocate(&b);
deallocate(&c);
free(rsA);
free(csA);
free(rsB);
free(csB);
MPI_Finalize();
return 0;
}