int main(int argc, char*argv[])
{
MatrixXd a(3, 4) ,b(3,4);
vector<MatrixXd> ZE;
a << 1,2,3,4,5,6,7,8,9,10,11,12;
b << 13,14,15,16,17,18,19,20,21,22,23,24;
double lambda=0.02;
LowRankRepresentation lrr(a, b, lambda);
ZE = lrr.result(a, b, lambda);
cout << "Z = " << endl << ZE[0] <<endl;
cout << "E = " << endl << ZE[1] <<endl;
return 0;
}
/* Always include this */
void mexFunction(int nlhs, mxArray *plhs[], /* Output variables */
int nrhs, const mxArray *prhs[]) /* Input variables */
{
if(nrhs < 1 || nrhs > 3) /* Check the number of arguments */
mexErrMsgTxt("Wrong number of input arguments.");
else if(nlhs > 2)
mexErrMsgTxt("Too many output arguments.");
/* if (nrhs == 2)
lambda = 0.02;
else
lambda = prhs[2];
*/
double *X, *D,*Z,*E,lambda;
int XM, XN,DM,DN, ZM,ZN,m, n;
lambda = mxGetScalar(lambda_IN); /* Get lambda */
X = mxGetPr(X_IN); /* Get the pointer to the data of X */
XM = mxGetM(X_IN); /* Get the dimensions of X */
XN = mxGetN(X_IN);
D = mxGetPr(D_IN);
DM = mxGetM(D_IN);
DN = mxGetN(D_IN);
ZM = DN;
ZN = XN;
m=0,n=0;
//X[m + M*n]
MatrixXd x(XM, XN) ,d(DM,DN),z(ZM,ZN);
vector<MatrixXd> ze;
Z_OUT = mxCreateDoubleMatrix(DN, XN, mxREAL);
Z = mxGetPr(Z_OUT); /* Get the pointer to the data of Z */
E_OUT = mxCreateDoubleMatrix(DN, XN, mxREAL);
E = mxGetPr(E_OUT);
//cout << "ZM" << ZM << "ZN" << ZN << endl;;
for (n=0;n<XN;n++)
for(m=0;m<XM;m++)
x(m,n) = X[m+ZM*n];
for (n=0;n<DN;n++)
for(m=0;m<DM;m++)
d(m,n) = D[m+ZM*n];
LowRankRepresentation lrr(x, d, lambda);
ze = lrr.result(x, d, lambda);
for (n=0;n<ZN;n++)
for(m=0;m<ZM;m++)
Z[m+ZM*n] = ze[0](m,n);
for (n=0;n<ZN;n++)
for(m=0;m<ZM;m++)
E[m+ZM*n] = ze[1](m,n);
//Z = ZE[0];
//E = ZE[1];
//mexPrintf("Hello, world!\n"); /* Do something interesting */
return;
}
void Tri2dFCBlockSolver::gradSetupQuadratic()
{
// form quadratic sub elements
int nElemQ = 3*nElem;
int nneQ = 6; //quadratic elements
int nngQ = 4; //quadratic elements
Array2D<int> elemQ(nElemQ,nneQ),gNode(nElemQ,nngQ);
int m=0;
for (int n=0; n<nElem; n++){
elemQ(m ,0) = elem(n,0);
elemQ(m ,1) = elem(n,4);
elemQ(m ,2) = elem(n,7);
elemQ(m ,3) = elem(n,3);
elemQ(m ,4) = elem(n,9);
elemQ(m ,5) = elem(n,8);
gNode(m ,0) = 0;
gNode(m ,1) = 3;
gNode(m ,2) = 4;
gNode(m++,3) = 5;
elemQ(m ,0) = elem(n,3);
elemQ(m ,1) = elem(n,1);
elemQ(m ,2) = elem(n,6);
elemQ(m ,3) = elem(n,4);
elemQ(m ,4) = elem(n,5);
elemQ(m ,5) = elem(n,9);
gNode(m ,0) = 1;
gNode(m ,1) = 4;
gNode(m ,2) = 5;
gNode(m++,3) = 3;
elemQ(m ,0) = elem(n,8);
elemQ(m ,1) = elem(n,5);
elemQ(m ,2) = elem(n,2);
elemQ(m ,3) = elem(n,9);
elemQ(m ,4) = elem(n,6);
elemQ(m ,5) = elem(n,7);
gNode(m ,0) = 2;
gNode(m ,1) = 5;
gNode(m ,2) = 3;
gNode(m++,3) = 4;
}
/*
for (int n=0; n<nElemQ; n++){
cout << n << " ";
for (int j=0; j<nneQ; j++) cout << elemQ(n,j) << " ";
cout << endl;
}
exit(0);
*/
// Jacobian terms
Array2D <double> xr(nElemQ,nngQ),yr(nElemQ,nngQ),xs(nElemQ,nngQ),
ys(nElemQ,nngQ),jac(nElemQ,nngQ),rs(nneQ,3),lc(nneQ,nneQ);
xr.set(0.);
yr.set(0.);
xs.set(0.);
ys.set(0.);
jac.set(0.);
int orderE=2; //quadratic elements
solutionPoints(orderE,
spacing,
&rs(0,0));
bool test=true;
lagrangePoly(test,
orderE,
&rs(0,0),
&lc(0,0));
int j,km,lm;
double lrm,lsm,ri,si;
for (int n=0; n<nElemQ; n++){
// evaluate the Jacobian terms at the mesh points
for (int i=0; i<nngQ; i++){ //ith mesh point
ri = rs(gNode(n,i),0);
si = rs(gNode(n,i),1);
for (int m=0; m<nneQ; m++){ //mth Lagrange polynomial
j = 0;
lrm = 0.;
lsm = 0.;
for (int k=0; k<=orderE; k++)
for (int l=0; l<=orderE-k; l++){
km = max(0,k-1);
lm = max(0,l-1);
lrm +=((double)k)*pow(ri,km)*pow(si,l )*lc(m,j );
lsm +=((double)l)*pow(ri,k )*pow(si,lm)*lc(m,j++);
}
xr(n,i) += lrm*x(elemQ(n,m),0);
yr(n,i) += lrm*x(elemQ(n,m),1);
xs(n,i) += lsm*x(elemQ(n,m),0);
ys(n,i) += lsm*x(elemQ(n,m),1);
}
jac(n,i) = xr(n,i)*ys(n,i)-yr(n,i)*xs(n,i);
}}
// lr(i,j) = (dl_j/dr)_i (a row is all Lagrange polynomials (derivatives)
// evaluated at a single mesh point i, same with the other derivatives)
Array2D<double> lr(nneQ,nneQ),ls(nneQ,nneQ),lrr(nneQ,nneQ),
lss(nneQ,nneQ),lrs(nneQ,nneQ);
lr.set(0.);
ls.set(0.);
lrr.set(0.);
lss.set(0.);
lrs.set(0.);
int kmm,lmm;
for (int n=0; n<nneQ; n++) // nth Lagrange polynomial
for (int i=0; i<nneQ; i++){ // ith mesh point
j = 0;
ri = rs(i,0);
si = rs(i,1);
for (int k=0; k<=orderE; k++)
for (int l=0; l<=orderE-k; l++){
km = max(0,k-1);
lm = max(0,l-1);
kmm = max(0,k-2);
lmm = max(0,l-2);
lr (i,n) +=((double)k)*pow(ri,km)*pow(si,l )*lc(n,j);
ls (i,n) +=((double)l)*pow(ri,k )*pow(si,lm)*lc(n,j);
lrr(i,n) +=((double)(k*km))*pow(ri,kmm)*pow(si,l )*lc(n,j );
lss(i,n) +=((double)(l*lm))*pow(ri,k )*pow(si,lmm)*lc(n,j );
lrs(i,n) +=((double)(k*l ))*pow(ri,km )*pow(si,lm )*lc(n,j++);
}}
// compute averaged quadratic FEM gradient coefficients
Array1D<double> sumj(nNode);
sumj.set(0.);
for (int n=0; n<nElemQ; n++)
for (int i=0; i<nngQ; i++){
m = gNode(n,i);
sumj(elemQ(n,m)) += jac(n,i);
}
for (int n=0; n<nNode; n++) sumj(n) = 1./sumj(n);
int k1,k2;
double xri,yri,xsi,ysi;
Array2D<double> ax(nNode,2);
ax.set(0.);
gxQ.set(0.);
for (int n=0; n<nElemQ; n++)
for (int i=0; i<nngQ; i++){
m = gNode(n,i);
k1 = elemQ(n,m);
xri = xr(n,i);
yri = yr(n,i);
xsi = xs(n,i);
ysi = ys(n,i);
for (int j=0; j<nneQ; j++){
k2 = elemQ(n,j);
ax(k2,0) = lr(m,j)*ysi-ls(m,j)*yri;
ax(k2,1) =-lr(m,j)*xsi+ls(m,j)*xri;
}
for(int j=psp2(k1); j<psp2(k1+1); j++){
k2 = psp1(j);
gxQ(j,0) += ax(k2,0);
gxQ(j,1) += ax(k2,1);
}
for (int j=0; j<nneQ; j++){
k2 = elemQ(n,j);
ax(k2,0) = 0.;
ax(k2,1) = 0.;
}}
for (int n=0; n<nNode; n++)
for (int i=psp2(n); i<psp2(n+1); i++){
gxQ(i,0) *= sumj(n);
gxQ(i,1) *= sumj(n);
}
// deallocate work arrays
elemQ.deallocate();
gNode.deallocate();
xr.deallocate();
yr.deallocate();
xs.deallocate();
ys.deallocate();
jac.deallocate();
rs.deallocate();
lc.deallocate();
lr.deallocate();
ls.deallocate();
lrr.deallocate();
lss.deallocate();
lrs.deallocate();
sumj.deallocate();
ax.deallocate();
}
