// form H = (1/h) W (x) I - I (x) J
// get the L, U, p factors of H
int _formIRKmatrixZ(RKOCP r, Vector y, Vector u, Vector p, double t, double h, Matrix L, Matrix U, int *P) {
int n = r->n_states+1;
int s = r->rk_stages;
double **W = r->rk_w->e;
int err = 0;
int i, j, k, l;
Matrix H = MatrixNew(n*s, n*s);
Matrix J = MatrixNew(n, n);
// get Fy, Fu, Fp, Ly, Lu, Lp
if (r->ocp->Ddifferential_equations == NULL) {
OCPFDfL(r->ocp, y, u, p, t, r->Fy, r->Fu, r->Fp, r->Ly, r->Lu, r->Lp);
} else {
r->ocp->Ddifferential_equations(y, u, p, t, r->Fy, r->Fu, r->Fp, r->Ly, r->Lu, r->Lp);
}
for (i = 0; i < r->n_states; i ++) {
for (j = 0; j < r->n_states; j++) {
J->e[i][j] = r->Fy->e[i][j];
}
J->e[r->n_states][i] = r->Ly->e[i];
}
// H = (1/h) W (x) I - I (x) J
for (i = 0; i < s; i++) {
for (j = 0; j < s; j++) {
double wij_h = W[i][j] / h;
for (k = 0; k < n; k++) {
H->e[i*n + k][j*n + k] += wij_h;
}
}
for (k = 0; k < n; k++) {
for (l = 0; l < n; l++) {
H->e[i*n + k][i*n + l] -= J->e[k][l];
}
}
}
err = LUFactor(H, L, U, P);
MatrixDelete(J);
MatrixDelete(H);
return err;
}
void FixedEndPointsGVI::InitializeContractionMatrix(){
int i, j, k; i = 0; j = 0; k = 0;
double Pauser; Pauser = 0.0;
for(i = 0; i < myMethodOrder; i++){
for(j = 0; j < myMethodOrder; j++){
ContractionMatrix[i][j] = 0.0;
for(k = 0; k < myQuadratureOrder; k++){
ContractionMatrix[i][j] += QuadratureWeights[k]*DerivativePointValuesAtQuadraturePoints[i][k]*DerivativePointValuesAtQuadraturePoints[j][k];
}
}
}
for(i = 0; i < myMethodOrder; i++){
DerivativeInnerProducts[i] = ContractionMatrix[myMethodOrder - 1][i];
ContractionMatrix[myMethodOrder - 1][i] = 0.0;
ContractionMatrix[0][i] = 0.0;
}
ContractionMatrix[myMethodOrder - 1][myMethodOrder - 1] = 1.0;
ContractionMatrix[0][0] = 1.0;
LUFactor(ContractionMatrix, myMethodOrder);
}
int main(int argc, char **argv[])
{
/* <reference> */
float inSubMat[M][M], outSubMat[M][M], LU[M][M], L[M][M], U[M][M];
int subdist, rowdist, coldist;
int i, j, dist, k1, k2, p1, p2, q1, q2, q3;
/* </reference> */
double t0, t1;
t0 = wall_clock();
for (i = 0; i < N; i++)
{
for (j = 0; j < N; j++)
{
if (i == j)
{
outMat[i][j] = N;
}
else
{
outMat[i][j] = 1;
}
}
}
/* <master id="234567"> */
_distributor = _open_space("distributor", 0, "234567");
_constructor = _open_space("constructor", 0, "234567");
i = 0;
while (i < N)
{
j = i + M - 1;
dist = M;
if (j > N-1)
{
j = N-1;
dist = N - i;
}
/* LU factors for submatrix */
for (k1 = 0; k1 < dist; k1++)
{
for (k2 = 0; k2 < dist; k2++)
{
inSubMat[k1][k2] = outMat[i+k1][i+k2];
}
}
LUFactor(inSubMat, outSubMat, dist);
/* update */
for (k1 = 0; k1 < dist; k1++)
{
for (k2 = 0; k2 < dist; k2++)
{
outMat[i+k1][i+k2] = outSubMat[k1][k2];
LU[k1][k2] = outSubMat[k1][k2];
}
}
/* Solve triangles, LZ and WU */
for (k1 = j+1; k1 < N; k1 = k1+M)
{
k2 = k1 + M - 1;
subdist = M;
if (k2 > N-1)
{
k2 = N - 1;
subdist = N - k1;
}
/* Solve LZ */
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
inSubMat[p1-i][p2-k1] = outMat[p1][p2];
}
}
TriangleSolver(LU, inSubMat, outSubMat, subdist, 1);
/* update */
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
outMat[p1][p2] = outSubMat[p1-i][p2-k1];
}
}
/* Solve WU */
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
inSubMat[p2-k1][p1-i] = outMat[p2][p1];
}
}
TriangleSolver(LU, inSubMat, outSubMat, subdist, 2);
/* update */
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
outMat[p2][p1] = outSubMat[p2-k1][p1-i];
}
}
}
_cleanup_space(_distributor, "234567");
_cleanup_space(_constructor, "234567");
/* <token action="SET" idxset="(k1)"/> */
sprintf(_tp_name, "token#%s", "234567");
sprintf(_tp_token, "=(k1:%d~%d,%d:#%d)", j+1, N, 1, M);
_tp_size = sizeof(_tp_token);
_tokens = _set_token(_distributor, _tp_name, (char *)_tp_token, _tp_size);
if (_tokens < 0) exit(-1);
/* <send var="i" type="int"/> */
sprintf(_tp_name, "int:i#%s", "234567");
_tp_size = sizeof(int);
_tp_i_234567 = &i;
_status = _send_data(_distributor, _tp_name, (char *)_tp_i_234567, _tp_size);
if (_status < 0) exit(-1);
/* <send var="j" type="int"/> */
sprintf(_tp_name, "int:j#%s", "234567");
_tp_size = sizeof(int);
_tp_j_234567 = &j;
_status = _send_data(_distributor, _tp_name, (char *)_tp_j_234567, _tp_size);
if (_status < 0) exit(-1);
/* <send var="outMat" type="float[N(i~N)][N(i~N)]"/> */
sprintf(_tp_name, "float(%d)(%d):outMat#%s[%d~%d,%d][%d~%d,%d]@%d", (N), (N), "234567", (i), (N), 1, (i), (N), 1, sizeof(float));
_tp_size = (((N) - (i)) * ((N) - (i))) * sizeof(float);
_tp_outMat_234567 = (float *)malloc(_tp_size);
for (_x0_234567 = (i), _y0_234567 =0; _x0_234567 < (N); _x0_234567 +=1, _y0_234567 ++) {
for (_x1_234567 = (i), _y1_234567 =0; _x1_234567 < (N); _x1_234567 +=1, _y1_234567 ++) {
_tp_outMat_234567[_y0_234567 * ((N) - (i)) + _y1_234567] = outMat[_x0_234567][_x1_234567];
}
}
_status = _send_data(_distributor, _tp_name, (char *)_tp_outMat_234567, _tp_size);
if (_status < 0) exit(-1);
free(_tp_outMat_234567);
/* <read var="outMat" type="float[N(j+1~N)][N(j+1~N)]"/> */
sprintf(_tp_name, "float(%d)(%d):outMat#%s[%d~%d,%d][%d~%d,%d]@%d", (N), (N), "234567", (j+1), (N), 1, (j+1), (N), 1, sizeof(float));
_tp_size = (((N) - (j+1)) * ((N) - (j+1))) * sizeof(float);
_tp_outMat_234567 = (float *)malloc(_tp_size);
_tp_size = _read_data(_constructor, _tp_name, (char *)_tp_outMat_234567, _tp_size);
if (_tp_size < 0) exit(-1);
for (_x0_234567 = (j+1), _y0_234567 =0; _x0_234567 < (N); _x0_234567 +=1, _y0_234567 ++) {
for (_x1_234567 = (j+1), _y1_234567 =0; _x1_234567 < (N); _x1_234567 +=1, _y1_234567 ++) {
outMat[_x0_234567][_x1_234567] = _tp_outMat_234567[_y0_234567 * ((N) - (j+1)) + _y1_234567];
}
}
free(_tp_outMat_234567);
i = i + M;
}
_close_space(_constructor, "234567", 1);
_close_space(_distributor, "234567", 1);
/* </master> */
/*
for (i = 0; i < N; i++)
{
for (j = 0; j < N; j++)
{
printf("%6.3f ", outMat[i][j]);
}
printf("\n");
}
*/
t1 = wall_clock() - t0;
if (t1>0) printf(" (%f) MFLOPS.\n", (float) 2*N*N*N/3/t1);
else printf(" MFLOPS: Not measured.\n");
printf("elapse time = %10.6f\n", t1/1000000);
return 0;
}
int main()
{
/* <reference> */
int i, j, dist, k1, k2, p1, p2, q1, q2, q3;
int subdist, rowdist, coldist;
float inSubMat[M][M], outSubMat[M][M], LU[M][M], L[M][M], U[M][M];
/* </reference> */
double t0, t1;
t0 = wall_clock();
for (i=0; i<N; i++)
{
for (j=0; j<N; j++)
{
if (i==j)
{
outMat[i][j] = N;
}
else
{
outMat[i][j] = 1;
}
}
}
/* <master id="123456"> */
for (i = 0; i < N; i = i + M)
{
j = i + M - 1;
dist = M;
if (j > N-1)
{
j = N-1;
dist = N - i;
}
// LU factors for submatrix
for (k1 = 0; k1 < dist; k1++)
{
for (k2 = 0; k2 < dist; k2++)
{
inSubMat[k1][k2] = outMat[i+k1][i+k2];
}
}
LUFactor(inSubMat, outSubMat, dist);
//update
for (k1 = 0; k1 < dist; k1++)
{
for (k2 = 0; k2 < dist; k2++)
{
outMat[i+k1][i+k2] = outSubMat[k1][k2];
LU[k1][k2] = outSubMat[k1][k2];
}
}
for (k1 = j + 1; k1 < N; k1 = k1 + M)
{
k2 = k1 + M - 1;
subdist = M;
if (k2 > N-1)
{
k2 = N - 1;
subdist = N - k1;
}
//Solve LZ
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
inSubMat[p1-i][p2-k1] = outMat[p1][p2];
}
}
TriangleSolver(LU, inSubMat, outSubMat, subdist, 1);
//update
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
outMat[p1][p2] = outSubMat[p1-i][p2-k1];
}
}
//Solve WU
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
inSubMat[p2-k1][p1-i] = outMat[p2][p1];
}
}
TriangleSolver(LU, inSubMat, outSubMat, subdist, 2);
//update
for (p1 = i; p1 < i+M; p1++)
{
for (p2 = k1; p2 <= k2; p2++)
{
outMat[p2][p1] = outSubMat[p2-k1][p1-i];
}
}
}
/* <send var="i" type="int"/> */
/* <send var="outMat" type="float[N(i~N) ][N(i~N) ]"/> */
/* <worker> */
/* <read var="i" type="int"/> */
/* <read var="outMat" type="float[N(i~i+M)][N(i~N) ]"/> */
/* <read var="outMat" type="float[N(k1) ][N(i~N) ]"/> */
//A = A - WZ
/* <target index="k1" limits="(i+M,N,M)" chunk="M" order="1"> */
for (k1 = i + M; k1 < N; k1 = k1 + M)
/* </target> */
{
k2 = k1 + M - 1;
rowdist = M;
if (k2 > N-1)
{
k2 = N - 1;
rowdist = N - k1;
}
for (p1 = i + M; p1 < N; p1 = p1 + M)
{
p2 = p1 + M - 1;
coldist = M;
if (p2 > N-1)
{
p2 = N - 1;
coldist = N - p1;
}
/*
* matrix multiplication
* outMat[k1:k2][p1:p2] = outMat[k1:k2][p1:p2] -
outMat[k1:k2][i:i+M-1] * outMat[i:i+M-1][k1:k2];
*/
for (q1 = k1; q1 <= k2; q1++)
{
for (q2 = p1; q2 <= p2; q2++)
{
for (q3 = 0; q3 < M; q3++)
{
outMat[q1][q2] = outMat[q1][q2] -
outMat[q1][i+q3]*outMat[i+q3][q2];
}
}
}
}
}
/* <send var="outMat" type="float[N(k1) ][N(i+M~N)]"/> */
/* </worker> */
/* <read var="outMat" type="float[N(i+M~N) ][N(i+M~N)]"/> */
}
/* </master> */
/*
for (i=0; i<N; i++)
{
for (j=0; j<N; j++)
{
printf("%6.3f ", outMat[i][j]);
}
printf("\n");
}
*/
t1 = wall_clock() - t0;
if (t1>0) printf(" (%f) MFLOPS.\n", (float) 2*N*N*N/3/t1);
else printf(" MFLOPS: Not measured.\n");
printf("elapse time = %10.6f\n", t1/1000000);
return 0;
}
