double EMD(Ap_FeatureVector1D *ap_fv1, FeatureVector1D *w1,
Ap_FeatureVector1D *ap_fv2, FeatureVector1D *w2,
Metric m)
{
signature_t *Signature1, *Signature2;
double distance;
Signature1 = (signature_t *)malloc(sizeof(signature_t));
if (Signature1 == NULL) {
Error(MSG1,"CreateSignature");
}
Signature2 = (signature_t *)malloc(sizeof(signature_t));
if (Signature2 == NULL) {
Error(MSG1,"CreateSignature");
}
Signature1->n = w1->n;
Signature1->Features = (feature_t *)ap_fv1;
Signature1->Weights = w1->X;
Signature2->n = w2->n;
Signature2->Features = (feature_t *)ap_fv2;
Signature2->Weights = w2->X;
distance = emd(Signature1, Signature2, m, NULL, NULL);
free(Signature1);
free(Signature2);
return(distance);
}
float pnm_labelmap_emd(pnm_labelmap_t *pgml1,
pnm_labelmap_t *pgml2,
int num)
{
int i,nb1,nb2,nb_min,size1,size2;
float fl,nb,scale1,scale2;
emd_signature_t s1,s2;
nb1 = pnm_labelmap_numOfPix(pgml1);
nb2 = pnm_labelmap_numOfPix(pgml2);
nb_min = (nb1<nb2) ? ((nb1<num) ? nb1 : num) : ((nb2<num) ? nb2 : num);
pnm_labelmap_signature(&s1,pgml1,nb_min);
/*fprintf(stderr, "Signature: n=%d, nb_min=%d, num=%d.\n",s1.n,nb_min,num);
*/
pnm_labelmap_signature(&s2,pgml2,nb_min);
/*fprintf(stderr, "Signature: n=%d, nb_min=%d, num=%d.\n",s2.n,nb_min,num);
*/
fl = emd(&s1, &s2, pnm_dist, 0, 0);
/*fl = emd_normalized(&s1, &s2, pnm_dist, 0, 0);*/
emd_signature_free(&s1);
emd_signature_free(&s2);
return fl;
}
//earth move distance
float PaletteIndex::histMatchDist(vector<int>& a, vector<int>& b)
{
//convert vector to signature
feature_t fa[512],fb[512];
float wa[512],wb[512];
int i = 0;
for (vector<int>::iterator it = a.begin(); it != a.end(); ++it)
{
fa[i].X=colors[i][0];
fa[i].Y=colors[i][1];
fa[i].Z=colors[i][2];
wa[i]=*it;
i++;
}
i = 0;
for (vector<int>::iterator it = b.begin(); it != b.end(); ++it)
{
fb[i].X=colors[i][0];
fb[i].Y=colors[i][1];
fb[i].Z=colors[i][2];
wb[i]=*it;
i++;
}
signature_t sa={512,fa,wa},sb={512,fb,wb};
float e = emd(&sa, &sb, dist, 0, 0);
return e;
}
float EmdSimilarity(GARG *garg1, GARG *garg2)
{
signature_t g1,g2;
int i;
float dist;
// load g1
g1.n = garg1->node_num;
g1.Features = (feature_t *)malloc(sizeof(feature_t)*g1.n);
g1.Weights = (float *)malloc(sizeof(float)*g1.n);
for(i=0;i<g1.n;i++)
{
garg1->GetNodeFeature(g1.Features[i],i);
g1.Features[i][0]/=320;
g1.Features[i][1]/=240;
g1.Features[i][2]/=256;
g1.Features[i][3]/=256;
g1.Features[i][4]/=256;
g1.Weights[i] = 1.0f/g1.n;
}
// load g2
g2.n = garg2->node_num;
g2.Features = (feature_t *)malloc(sizeof(feature_t)*g2.n);
g2.Weights = (float *)malloc(sizeof(float)*g2.n);
for(i=0;i<g2.n;i++)
{
garg2->GetNodeFeature(g2.Features[i],i);
g2.Features[i][0]/=320;
g2.Features[i][1]/=240;
g2.Features[i][2]/=256;
g2.Features[i][3]/=256;
g2.Features[i][4]/=256;
g2.Weights[i] = 1.0f/g2.n;
}
// Earth Mover's Distance
// download emd.c from http://ai.stanford.edu/~rubner/emd/default.htm
// then change emd.c to emd.cpp
#ifdef EMD_CODE_INCLUDED
dist = emd(&g1,&g2,_fdistance,NULL,NULL);
#else
dist = 0;
#endif
free(g1.Features);
free(g2.Features);
return 1-dist;
}
int compute_distance_matrix(EmdDB &db, double** mat)
{
// init diagonal to 0
for (int i=0; i<db.numEntries; i++)
{
mat[i][i] = 0;
}
cout << "Computing distance matrix. " << db.numEntries << " entries." << endl;
for (int i=0; i<db.numEntries; i++)
{
for (int j=i+1; j<db.numEntries; j++)
{
entry_t e1 = db.getEntry(i);
entry_t e2 = db.getEntry(j);
normalize_by_centroid(e1.signature);
normalize_by_centroid(e2.signature);
int64 emd_start = cvGetTickCount();
float e = emd(&e1.signature, &e2.signature, euclid_dist2, NULL, NULL);
int64 emd_end = cvGetTickCount();
double emd_time = ((double)emd_end - (double)emd_start) / cvGetTickFrequency();
mat[i][j] = e;
mat[j][i] = e;
//cout << i << ", " << j << " : " << e << endl;
*log_stream << db.getPath() << "," << e1.filename << "," << e2.filename << ","
<< e1.signature.n << "," << e2.signature.n << ","
<< signature_weight_sum(e1.signature) << "," << signature_weight_sum(e2.signature)
<< "," << emd_time << endl;
}
}
return 0;
}
double EarthMoversDistance(signatures *sample1, signatures *sample2, TrainingSet *ts)
{
double distance = 0.0, avg_weight = 0.0;
signature_t s1, s2;
long feature_index = 0, in_histogram = 0;
float *values1 = new float[ts->signature_count];
float *values2 = new float[ts->signature_count];
float *weights1 = new float[ts->signature_count];
flow_t *flow = new flow_t[ts->signature_count * 2 - 1]; /* the maximum possible size of the flow */
for (long sig_index = 0; sig_index < sample1->count; sig_index++)
{
// if (is_histogram_bin(ts->SignatureNames[sig_index]))
// {
if (feature_index>0 && is_same_hist(ts->SignatureNames[sig_index], ts->SignatureNames[sig_index - 1])==0) /* new histogram starts here */
{
if (avg_weight > 0) /* if the total weight is zero - no point computing the distance */
{
int flowsize;
s1.n = feature_index;
s2.n = feature_index;
s1.Features = values1;
s2.Features = values2;
s1.Weights = weights1;
s2.Weights = weights1;
/* compute the distance */
emd(&s1, &s2, dist, flow, &flowsize);
avg_weight /= feature_index;
for (long i = 0; i < flowsize; i++)
distance += avg_weight*flow[i].amount*fabs((float)(flow[i].to - flow[i].from));
}
feature_index = 0;
avg_weight = 0.0;
}
// else /* another histogram bin */
if (is_histogram_bin(ts->SignatureNames[sig_index]))
{
values1[feature_index] = (float)sample1->data[sig_index].value;
values2[feature_index] = (float)sample2->data[sig_index].value;
weights1[feature_index] = (float)ts->SignatureWeights[sig_index];
feature_index++;
avg_weight += ts->SignatureWeights[sig_index];
}
else distance += ts->SignatureWeights[sig_index] * fabs(sample1->data[sig_index].value - sample2->data[sig_index].value); /* independent value - no histogram */
}
/*
for (long sig_index = 0; sig_index < sample1->count; sig_index++)
if (ts->SignatureWeights[sig_index]>0)
{
values1[feature_index] = (float)sample1->data[sig_index].value;
values2[feature_index] = (float)sample2->data[sig_index].value;
weights1[feature_index] = (float)ts->SignatureWeights[sig_index];
feature_index++;
}
//feature_index = 300;
s1.n = feature_index;
s2.n = feature_index;
s1.Features = values1;
s2.Features = values2;
s1.Weights = weights1;
s2.Weights = weights1;
flow_t *flow = new flow_t[feature_index * 2 - 1];
int flowsize;
// distance = emd(&s1, &s2, dist, 0, 0);
distance=emd(&s1, &s2, dist, flow, &flowsize);
distance = 0;
for (long i = 0; i < flowsize; i++)
distance += flow[i].amount*fabs((float)(flow[i].to - flow[i].from));
*/
delete values1;
delete values2;
delete weights1;
delete flow;
return(distance);
}
static PyObject *compute_emd(PyObject *self, PyObject *args, PyObject *keywds)
{
static char *kwlist[] = {"feature1", "feature2", "weight1", "weight2",
NULL};
PyObject *feature1, *feature2, *weight1, *weight2;
double *f1, *f2;
float *w1, *w2;
int length1, length2;
signature_t signature1, signature2;
float distance;
PyObject *item;
int i;
if(!PyArg_ParseTupleAndKeywords(args, keywds, "OOOO", kwlist,
&feature1, &feature2, &weight1, &weight2))
return NULL;
if(!PySequence_Check(feature1)) {
PyErr_SetString(PyExc_TypeError, "feature1 must be a sequence");
return NULL;
}
if(!PySequence_Check(feature2)) {
PyErr_SetString(PyExc_TypeError, "feature2 must be a sequence");
return NULL;
}
if(!PySequence_Check(weight1)) {
PyErr_SetString(PyExc_TypeError, "weight1 must be a sequence");
return NULL;
}
if(!PySequence_Check(weight2)) {
PyErr_SetString(PyExc_TypeError, "weight2 must be a sequence");
return NULL;
}
length1 = PySequence_Size(feature1);
length2 = PySequence_Size(feature2);
if(PySequence_Size(weight1) != length1) {
PyErr_SetString(PyExc_TypeError, "feature1 and weight1 must be the same");
return NULL;
}
if(PySequence_Size(weight2) != length2) {
PyErr_SetString(PyExc_TypeError, "feature2 and weight2 must be the same");
return NULL;
}
f1 = alloca(length1 * sizeof(double));
f2 = alloca(length2 * sizeof(double));
w1 = alloca(length1 * sizeof(double));
w2 = alloca(length2 * sizeof(double));
for(i = 0; i < length1; i ++) {
item = PySequence_GetItem(feature1, i);
if(!PyFloat_Check(item) && !PyInt_Check(item)) {
Py_DECREF(item);
PyErr_SetString(PyExc_TypeError, "f1 should be a sequence of numbers");
return NULL;
}
f1[i] = PyFloat_AsDouble(item);
Py_DECREF(item);
item = PySequence_GetItem(weight1, i);
if(!PyFloat_Check(item) && !PyInt_Check(item)) {
Py_DECREF(item);
PyErr_SetString(PyExc_TypeError, "w1 should be a sequence of numbers");
return NULL;
}
w1[i] = PyFloat_AsDouble(item);
Py_DECREF(item);
}
for(i = 0; i < length2; i ++) {
item = PySequence_GetItem(feature2, i);
if(!PyFloat_Check(item) && !PyInt_Check(item)) {
Py_DECREF(item);
PyErr_SetString(PyExc_TypeError, "f2 should be a sequence of numbers");
return NULL;
}
f2[i] = PyFloat_AsDouble(item);
Py_DECREF(item);
item = PySequence_GetItem(weight2, i);
if(!PyFloat_Check(item) && !PyInt_Check(item)) {
Py_DECREF(item);
PyErr_SetString(PyExc_TypeError, "w2 should be a sequence of numbers");
return NULL;
}
w2[i] = PyFloat_AsDouble(item);
Py_DECREF(item);
}
signature1.n = length1;
signature1.Features = f1;
signature1.Weights = w1;
signature2.n = length2;
signature2.Features = f2;
signature2.Weights = w2;
distance = emd(&signature1, &signature2, double_dist, 0, 0);
return Py_BuildValue("d", distance);
}
/* The gateway routine */
void mexFunction(int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
{
double *c1, *w1, *c2, *w2, d, *pr;
int n1, n2, ndims, nflow;
feature_t *f1, *f2;
flow_t *pf;
if (nrhs < 4)
mexErrMsgTxt("Usage: [dist,flow] = emd(Centroid1, Weight1, Centroid2, weight2, <domain_size>, <distance_type>)\n Non-zero domain size in any dimension means that dimension is periodic.\n");
c1 = mxGetPr(prhs[0]);
w1 = mxGetPr(prhs[1]);
c2 = mxGetPr(prhs[2]);
w2 = mxGetPr(prhs[3]);
if (nrhs > 5) {
DISTANCE_TYPE_p = mxGetScalar(prhs[5]);
} else
DISTANCE_TYPE_p = 2; /* Default distance = L_2 (Euclidean) */
ndims = mxGetM(prhs[0]); /* Number of rows */
if (ndims != mxGetM(prhs[2]))
mexErrMsgTxt("Both signatures should have the same dimension\n");
if (nrhs > 4) {
if (ndims != mxGetM(prhs[4]))
mexErrMsgTxt("Signature max size vector has wrong dimension\n");
Fmax.x = mxGetPr(prhs[4]);
Fmax.size = ndims;
} else {
Fmax.allocate(ndims); /* Default non-periodic*/
for(int i=0; i<ndims; ++i)
Fmax.x[i] = 0;
}
/* Signature lengths */
n1 = mxGetN(prhs[0]);
n2 = mxGetN(prhs[2]);
if (mxGetNumberOfElements(prhs[1]) != n1 || mxGetNumberOfElements(prhs[3])
!= n2)
mexErrMsgTxt("Length of weight vector != Length of signature vector");
if( n1 > MAX_SIG_SIZE || n2 > MAX_SIG_SIZE )
{
char err[100] = "Signature size should be less than ";
mexErrMsgTxt(strcat(err, mxArrayToString(mxCreateDoubleScalar(
MAX_SIG_SIZE))));
}
f1 = new feature_t[n1];
f2 = new feature_t[n2];
for (int i=0; i<n1; ++i) {
f1[i].size = ndims;
f1[i].x = c1 + ndims*i;
// for (int j=0; j<ndims; ++j)
// std::cout << f1[i].x[j] << ' ';
// std::cout << std::endl << std::fflush;
}
for (int i=0; i<n2; ++i) {
f2[i].size = ndims;
f2[i].x = c2 + ndims*i;
// for (int j=0; j<ndims; ++j)
// std::cout << f1[i].x[j] << ' ';
// std::cout << std::endl << std::fflush;
}
// Make sure all points are inside the domain for periodic distances
for (int i=0; i<ndims; ++i)
{
if (Fmax.x[i]==0) continue;
for (int j=0; j<n1; ++j)
if(f1[j].x[i] < 0 || f1[j].x[i] > Fmax.x[i])
mexErrMsgTxt("Point outside domain in signature 1");
for (int j=0; j<n2; ++j)
if(f2[j].x[i] < 0 || f2[j].x[i] > Fmax.x[i])
mexErrMsgTxt("Point outside domain in signature 2");
}
signature_t s1 = {n1, f1, w1}, s2 = {n2, f2, w2};
if (nlhs>1) {
pf = new flow_t[n1+n2-1];
d = emd(&s1, &s2, dist_p, pf, &nflow);
plhs[1] = mxCreateDoubleMatrix(n1,n2,mxREAL);
pr = mxGetPr(plhs[1]);
for (int i=0; i<nflow; ++i)
pr[ pf[i].from + pf[i].to * n1 ] = pf[i].amount;
delete []pf;
} else {
d = emd(&s1, &s2, dist_p, NULL, NULL);
}
plhs[0] = mxCreateDoubleScalar(d);
}
int main(int argc, char **argv) {
#ifdef _OPENMP
printf("ERKALE - EMD from Hel, OpenMP version, running on %i cores.\n",omp_get_max_threads());
#else
printf("ERKALE - EMD from Hel, serial version.\n");
#endif
print_copyright();
print_license();
#ifdef SVNRELEASE
printf("At svn revision %s.\n\n",SVNREVISION);
#endif
print_hostname();
if(argc!=1 && argc!=2) {
printf("Usage: $ %s (runfile)\n",argv[0]);
return 0;
}
Timer t;
// Parse settings
Settings set;
set.add_string("LoadChk","Checkpoint file to load density from","erkale.chk");
set.add_bool("DoEMD", "Perform calculation of isotropic EMD (moments of EMD, Compton profile)", true);
set.add_double("EMDTol", "Tolerance for the numerical integration of the radial EMD",1e-8);
set.add_string("EMDlm", "Which projection of the radial EMD to compute","");
set.add_bool("EMDAdapt", "Use adaptive grid to compute EMD?", true);
set.add_string("EMDCube", "Calculate EMD on a cube? e.g. -10:.3:10 -5:.2:4 -2:.1:3", "");
set.add_string("EMDOrbitals", "Compute EMD of given orbitals, e.g. 1,2,4:6","");
set.add_string("Similarity", "Compute similarity measure to checkpoint","");
set.add_string("SimilarityGrid", "Grid to use for computing similarity integrals","500 77");
set.add_bool("SimilarityLM", "Seminumerical computation of similarity integrals?", false);
set.add_int("SimilarityLmax", "Maximum angular momentum for seminumerical computation", 6);
if(argc==2)
set.parse(argv[1]);
else
printf("Using default settings.\n");
set.print();
// Get the tolerance
double tol=set.get_double("EMDTol");
// Load checkpoint
Checkpoint chkpt(set.get_string("LoadChk"),false);
// Load basis set
BasisSet basis;
chkpt.read(basis);
// Load density matrix
arma::cx_mat P;
arma::mat Pr, Pi;
chkpt.read("P",Pr);
if(chkpt.exist("P_im")) {
chkpt.read("P_im",Pi);
P=Pr*COMPLEX1 + Pi*COMPLEXI;
} else
P=Pr*COMPLEX1;
// The projection to calculate
int l=0, m=0;
std::string lmstr=set.get_string("EMDlm");
if(lmstr.size()) {
// Get l and m values
std::vector<std::string> lmval=splitline(lmstr);
if(lmval.size()!=2)
throw std::runtime_error("Invalid specification of l and m values.\n");
l=readint(lmval[0]);
m=readint(lmval[1]);
}
bool adaptive=set.get_bool("EMDAdapt");
// Compute orbital EMDs?
if(set.get_string("EMDOrbitals")!="") {
// Get orbitals
std::vector<std::string> orbs=splitline(set.get_string("EMDOrbitals"));
// Polarized calculation?
bool restr;
chkpt.read("Restricted",restr);
if(restr!= (orbs.size()==1))
throw std::runtime_error("Invalid occupancies for spin alpha and beta!\n");
if(l!=0)
printf("\nComputing the (%i %+i) projection of the orbital EMD.\n",l,m);
for(size_t ispin=0;ispin<orbs.size();ispin++) {
// Indices of orbitals to include.
std::vector<size_t> idx=parse_range(orbs[ispin]);
// Change into C++ indexing
for(size_t i=0;i<idx.size();i++)
idx[i]--;
// Read orbitals
arma::mat C;
if(restr)
chkpt.read("C",C);
else {
if(ispin==0)
chkpt.read("Ca",C);
else
chkpt.read("Cb",C);
}
for(size_t i=0;i<idx.size();i++) {
// Names of output files
char emdname[80];
char momname[80];
char Jname[80];
char Jintname[80];
char suffix[80];
if(l==0)
sprintf(suffix,".txt");
else
sprintf(suffix,"_%i_%i.txt",l,m);
if(restr) {
sprintf(emdname,"emd-%i%s",(int) idx[i]+1,suffix);
sprintf(momname,"moments-%i%s",(int) idx[i]+1,suffix);
sprintf(Jname,"compton-%i%s",(int) idx[i]+1,suffix);
sprintf(Jintname,"compton-interp-%i%s",(int) idx[i]+1,suffix);
} else {
if(ispin==0) {
sprintf(emdname,"emd-a-%i%s",(int) idx[i]+1,suffix);
sprintf(momname,"moments-a-%i%s",(int) idx[i]+1,suffix);
sprintf(Jname,"compton-a-%i%s",(int) idx[i]+1,suffix);
sprintf(Jintname,"compton-interp-a-%i%s",(int) idx[i]+1,suffix);
} else {
sprintf(emdname,"emd-b-%i%s",(int) idx[i]+1,suffix);
sprintf(momname,"moments-b-%i%s",(int) idx[i]+1,suffix);
sprintf(Jname,"compton-b-%i%s",(int) idx[i]+1,suffix);
sprintf(Jintname,"compton-interp-b-%i%s",(int) idx[i]+1,suffix);
}
}
// Generate dummy density matrix
arma::cx_mat Pdum=C.col(idx[i])*arma::trans(C.col(idx[i]))*COMPLEX1;
Timer temd;
GaussianEMDEvaluator *poseval=new GaussianEMDEvaluator(basis,Pdum,l,std::abs(m));
GaussianEMDEvaluator *negeval;
if(m!=0)
negeval=new GaussianEMDEvaluator(basis,Pdum,l,-std::abs(m));
else
negeval=NULL;
EMD emd(poseval, negeval, 1, l, m);
if(adaptive) {
emd.initial_fill();
if(l==0 && m==0) emd.find_electrons();
emd.optimize_moments(true,tol);
} else
emd.fixed_fill();
emd.save(emdname);
emd.moments(momname);
if(l==0 && m==0) {
emd.compton_profile(Jname);
emd.compton_profile_interp(Jintname);
}
delete poseval;
if(m!=0) delete negeval;
}
}
}
if(set.get_bool("DoEMD")) {
t.print_time();
printf("\nCalculating EMD properties.\n");
printf("Please read and cite the reference:\n%s\n%s\n%s\n", \
"J. Lehtola, M. Hakala, J. Vaara and K. Hämäläinen", \
"Calculation of isotropic Compton profiles with Gaussian basis sets", \
"Phys. Chem. Chem. Phys. 13 (2011), pp. 5630 - 5641.");
if(l!=0)
printf("\nComputing the (%i %+i) projection of the EMD.\n",l,m);
else
printf("\nComputing the isotropic projection of the EMD.\n");
// Amount of electrons is
int Nel;
chkpt.read("Nel",Nel);
// Construct EMD evaluators
Timer temd;
GaussianEMDEvaluator *poseval=new GaussianEMDEvaluator(basis,P,l,std::abs(m));
GaussianEMDEvaluator *negeval;
if(m!=0)
negeval=new GaussianEMDEvaluator(basis,P,l,-std::abs(m));
else
negeval=NULL;
temd.set();
EMD emd(poseval, negeval, Nel, l, m);
if(adaptive) {
emd.initial_fill();
if(l==0 && m==0) emd.find_electrons();
emd.optimize_moments(true,tol);
} else
emd.fixed_fill();
if(l==0 && m==0) {
emd.save("emd.txt");
emd.moments("moments.txt");
emd.compton_profile("compton.txt");
emd.compton_profile_interp("compton-interp.txt");
} else {
char fname[80];
sprintf(fname,"emd_%i_%i.txt",l,m);
emd.save(fname);
sprintf(fname,"moments_%i_%i.txt",l,m);
emd.moments(fname);
}
if(l==0 && m==0)
printf("Calculating isotropic EMD properties took %s.\n",temd.elapsed().c_str());
else
printf("Calculating projected EMD properties took %s.\n",temd.elapsed().c_str());
delete poseval;
if(m!=0) delete negeval;
}
// Do EMD on a cube?
if(stricmp(set.get_string("EMDCube"),"")!=0) {
t.print_time();
Timer temd;
// Form grid in p space.
std::vector<double> px, py, pz;
parse_cube(set.get_string("EMDCube"),px,py,pz);
// Calculate EMD on cube
emd_cube(basis,P,px,py,pz);
printf("Calculating EMD on a cube took %s.\n",temd.elapsed().c_str());
}
// Compute similarity?
if(stricmp(set.get_string("Similarity"),"")!=0) {
// Load checkpoint
Checkpoint simchk(set.get_string("Similarity"),false);
// Get grid size
std::vector<std::string> gridsize=splitline(set.get_string("SimilarityGrid"));
if(gridsize.size()!=2) {
throw std::runtime_error("Invalid grid size!\n");
}
int nrad=readint(gridsize[0]);
int lmax=readint(gridsize[1]);
int radlmax=set.get_int("SimilarityLmax");
// Load basis set
BasisSet simbas;
simchk.read(simbas);
// Load density matrix
arma::mat simPr, simPi;
arma::cx_mat simP;
simchk.read("P",simPr);
if(simchk.exist("P_im")) {
simchk.read("P_im",simPi);
simP=simPr*COMPLEX1 + simPi*COMPLEXI;
} else
simP=simPr*COMPLEX1;
// Compute momentum density overlap
arma::cube ovl;
if(set.get_bool("SimilarityLM"))
ovl=emd_overlap_semi(basis,P,simbas,simP,nrad,radlmax);
else
ovl=emd_overlap(basis,P,simbas,simP,nrad,lmax);
// Amount of electrons
int Nela, Nelb;
chkpt.read("Nel", Nela);
simchk.read("Nel", Nelb);
// Shape function overlap
arma::cube sh=emd_similarity(ovl,Nela,Nelb);
sh.slice(0).save("similarity.dat",arma::raw_ascii);
sh.slice(1).save("similarity_avg.dat",arma::raw_ascii);
for(int s=0;s<2;s++) {
if(s) {
printf("%2s\t%9s\t%9s\t%9s\t%9s\t%9s\t%9s\t%9s\n","k","S0(AA)","S0(BB)","S0(AB)","I0(AA)","I0(BB)","I0(AB)","D0(AB)");
for(int k=-1;k<3;k++)
// Vandenbussche don't include p^2 in the spherical average
printf("%2i\t%e\t%e\t%e\t%e\t%e\t%e\t%e\n", k+1, sh(k+1,0,s), sh(k+1,1,s), sh(k+1,2,s), sh(k+1,3,s), sh(k+1,4,s), sh(k+1,5,s), sh(k+1,6,s));
} else {
printf("%2s\t%9s\t%9s\t%9s\t%9s\t%9s\t%9s\t%9s\n","k","S(AA)","S(BB)","S(AB)","I(AA)","I(BB)","I(AB)","D(AB)");
for(int k=-1;k<3;k++)
printf("%2i\t%e\t%e\t%e\t%e\t%e\t%e\t%e\n", k, sh(k+1,0,s), sh(k+1,1,s), sh(k+1,2,s), sh(k+1,3,s), sh(k+1,4,s), sh(k+1,5,s), sh(k+1,6,s));
}
printf("\n");
}
}
return 0;
}
int main(void) {
gslpp::complex zi = gslpp::complex::i();
std::vector<double> sd = {10., 5., 1.};
std::vector<gslpp::complex> sc = {30. + zi, 2. + 3. * zi, 1. + 4. * zi};
gslpp::matrix<double> md1(2, 2);
md1(0, 0) = 10.;
md1(1, 0) = 20.;
md1(0, 1) = 5.;
md1(1, 1) = 1.;
gslpp::matrix<double> md2(2, 2);
md2(0, 0) = -3.;
md2(1, 0) = 30.;
md2(0, 1) = -5.;
md2(1, 1) = 4.;
gslpp::matrix<gslpp::complex> mc1(2, 2);
mc1.assign(0, 0, 9. + 2 * zi);
mc1.assign(1, 0, 19. - 4 * zi);
mc1.assign(0, 1, 4. - 6 * zi);
mc1.assign(1, 1, 3. + 2 * zi);
gslpp::matrix<gslpp::complex> mc2(2, 2);
mc2.assign(0, 0, -8. + 3 * zi);
mc2.assign(1, 0, 11. - 5 * zi);
mc2.assign(0, 1, 2. + 5 * zi);
mc2.assign(1, 1, -3. + 4 * zi);
gslpp::vector<double> vd1(2);
gslpp::vector<double> vd2(2);
vd1(0) = 14.;
vd1(1) = -5;
vd2(0) = -9.;
vd2(1) = 3;
gslpp::vector<gslpp::complex> vc1(2);
gslpp::vector<gslpp::complex> vc2(2);
vc1.assign(0, 4. - 2. * zi);
vc1.assign(1, 6. - 8. * zi);
vc2.assign(0, 5. + 3. * zi);
vc2.assign(1, 4. - 12. * zi);
Expanded<double> esd(sd);
Expanded<gslpp::complex> esc(sc);
std::vector<gslpp::matrix<double> > mdv = {md1, md2};
Expanded<gslpp::matrix<double> > emd(mdv);
std::vector<gslpp::matrix<gslpp::complex> > mcv = {mc1, mc2};
Expanded<gslpp::matrix<gslpp::complex> > emc(mcv);
std::vector<gslpp::vector<double> > vdv = {vd1, vd2};
Expanded<gslpp::vector<double> > evd(vdv);
std::vector<gslpp::vector<gslpp::complex> > vcv = {vc1, vc2};
Expanded<gslpp::vector<gslpp::complex> > evc(vcv);
// Print Input
std::cout << std::endl;
std::cout << "esd " << esd << std::endl;
std::cout << "esc " << esc << std::endl;
std::cout << "evd " << evd << std::endl;
std::cout << "evc " << evc << std::endl;
std::cout << "emd " << emd << std::endl;
std::cout << "emc " << emc << std::endl;
std::cout << "-------------" << std::endl;
std::cout << "-sd " << -esd << std::endl;
std::cout << "-sc " << -esc << std::endl;
std::cout << "-vd " << -evd << std::endl;
std::cout << "-vc " << -evc << std::endl;
std::cout << "-md " << -emd << std::endl;
std::cout << "-mc " << -emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded * Expanded
std::cout << "sd*sd " << esd * esd << std::endl;
std::cout << "sd*sc " << esd * esc << std::endl;
std::cout << "sd*vd " << esd * evd << std::endl;
std::cout << "sd*vc " << esd * evc << std::endl;
std::cout << "sd*md " << esd * emd << std::endl;
std::cout << "sd*mc " << esd * emc << std::endl;
std::cout << "sc*sd " << esc * esd << std::endl;
std::cout << "sc*sc " << esc * esc << std::endl;
std::cout << "sc*vd " << esc * evd << std::endl;
std::cout << "sc*vc " << esc * evc << std::endl;
std::cout << "sc*md " << esc * emd << std::endl;
std::cout << "sc*mc " << esc * emc << std::endl;
std::cout << "vd*sd " << evd * esd << std::endl;
std::cout << "vd*sc " << evd * esc << std::endl;
std::cout << "vd*vd " << evd * evd << std::endl;
std::cout << "vd*vc " << evd * evc << std::endl;
std::cout << "vd*md " << evd * emd << std::endl;
std::cout << "vd*mc " << evd * emc << std::endl;
std::cout << "vc*sd " << evc * esd << std::endl;
std::cout << "vc*sc " << evc * esc << std::endl;
std::cout << "vc*vd " << evc * evd << std::endl;
std::cout << "vc*vc " << evc * evc << std::endl;
std::cout << "vc*md " << evc * emd << std::endl;
std::cout << "vc*mc " << evc * emc << std::endl;
std::cout << "md*sd " << emd * esd << std::endl;
std::cout << "md*sc " << emd * esc << std::endl;
std::cout << "md*vd " << emd * evd << std::endl;
std::cout << "md*vc " << emd * evc << std::endl;
std::cout << "md*md " << emd * emd << std::endl;
std::cout << "md*mc " << emd * emc << std::endl;
std::cout << "mc*sd " << emc * esd << std::endl;
std::cout << "mc*sc " << emc * esc << std::endl;
std::cout << "mc*vd " << emc * evd << std::endl;
std::cout << "mc*vc " << emc * evc << std::endl;
std::cout << "mc*md " << emc * emd << std::endl;
std::cout << "mc*mc " << emc * emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded + Expanded
std::cout << "sd + sd " << esd + esd << std::endl;
std::cout << "sd + sc " << esd + esc << std::endl;
std::cout << "sc + sd " << esc + esd << std::endl;
std::cout << "sc + sc " << esc + esc << std::endl;
std::cout << "vd + vd " << evd + evd << std::endl;
std::cout << "vd + vc " << evd + evc << std::endl;
std::cout << "vc + vd " << evc + evd << std::endl;
std::cout << "vc + vc " << evc + evc << std::endl;
std::cout << "md + md " << emd + emd << std::endl;
std::cout << "md + mc " << emd + emc << std::endl;
std::cout << "mc + md " << emc + emd << std::endl;
std::cout << "mc + mc " << emc + emc << std::endl;
//
std::cout << "-------------" << std::endl;
// Expanded - Expanded
std::cout << "sd - sd " << esd - esd << std::endl;
std::cout << "sd - sc " << esd - esc << std::endl;
std::cout << "sc - sd " << esc - esd << std::endl;
std::cout << "sc - sc " << esc - esc << std::endl;
std::cout << "vd - vd " << evd - evd << std::endl;
std::cout << "vd - vc " << evd - evc << std::endl;
std::cout << "vc - vd " << evc - evd << std::endl;
std::cout << "vc - vc " << evc - evc << std::endl;
std::cout << "md - md " << emd - emd << std::endl;
std::cout << "md - mc " << emd - emc << std::endl;
std::cout << "mc - md " << emc - emd << std::endl;
std::cout << "mc - mc " << emc - emc << std::endl;
std::cout << "-------------" << std::endl;
// Expanded * UnExpanded
std::cout << "esd*5 = " << esd * 5. << std::endl;
std::cout << "esd*(4-2I) = " << esd * (4. - 2. * zi) << std::endl;
std::cout << "esd*vd1 = " << esd * vd1 << std::endl;
std::cout << "esd*vc1 = " << esd * vc1 << std::endl;
std::cout << "esd*md1 = " << esd * md1 << std::endl;
std::cout << "esd*mc1 = " << esd * mc1 << std::endl;
//
std::cout << "esc*5 = " << esc * 5. << std::endl;
std::cout << "esc*(4-2I) = " << esc * (4. - 2. * zi) << std::endl;
std::cout << "esc*vd1 = " << esc * vd1 << std::endl;
std::cout << "esc*vc1 = " << esc * vc1 << std::endl;
std::cout << "esc*md1 = " << esc * md1 << std::endl;
std::cout << "esc*mc1 = " << esc * mc1 << std::endl;
//
std::cout << "evd*5 = " << evd * 5. << std::endl;
std::cout << "evd*(4-2I) = " << evd * (4. - 2. * zi) << std::endl;
std::cout << "evd*vd1 = " << evd * vd1 << std::endl;
std::cout << "evd*vc1 = " << evd * vc1 << std::endl;
std::cout << "evd*md1 = " << evd * md1 << std::endl;
std::cout << "evd*mc1 = " << evd * mc1 << std::endl;
//
std::cout << "evc*5 = " << evc * 5. << std::endl;
std::cout << "evc*(4-2I) = " << evc * (4. - 2. * zi) << std::endl;
std::cout << "evc*vd1 = " << evc * vd1 << std::endl;
std::cout << "evc*vc1 = " << evc * vc1 << std::endl;
std::cout << "evc*md1 = " << evc * md1 << std::endl;
std::cout << "evc*mc1 = " << evc * mc1 << std::endl;
//
std::cout << "emd*5 = " << emd * 5. << std::endl;
std::cout << "emd*(4-2I) = " << emd * (4. - 2. * zi) << std::endl;
std::cout << "emd*vd1 = " << emd * vd1 << std::endl;
std::cout << "emd*vc1 = " << emd * vc1 << std::endl;
std::cout << "emd*md1 = " << emd * md1 << std::endl;
std::cout << "emd*mc1 = " << emd * mc1 << std::endl;
//
std::cout << "emc*5 = " << emc * 5. << std::endl;
std::cout << "emc*(4-2I) = " << emc * (4. - 2. * zi) << std::endl;
std::cout << "emc*vd1 = " << emc * vd1 << std::endl;
std::cout << "emc*vc1 = " << emc * vc1 << std::endl;
std::cout << "emc*md1 = " << emc * md1 << std::endl;
std::cout << "emc*mc1 = " << emc * mc1 << std::endl;
std::cout << "-------------" << std::endl;
// // Expanded / UnExpanded-Scalar
std::cout << "esd/5 = " << esd / 5. << std::endl;
std::cout << "esd/(4-2I) = " << esd / (4. - 2. * zi) << std::endl;
std::cout << "esc/5 = " << esc / 5. << std::endl;
std::cout << "esc/(4-2I) = " << esc / (4. - 2. * zi) << std::endl;
std::cout << "evd/5 = " << evd / 5. << std::endl;
std::cout << "evd/(4-2I) = " << evd / (4. - 2. * zi) << std::endl;
std::cout << "evc/5 = " << evc / 5. << std::endl;
std::cout << "evc/(4-2I) = " << evc / (4. - 2. * zi) << std::endl;
std::cout << "emd/5 = " << emd / 5. << std::endl;
std::cout << "emd/(4-2I) = " << emd / (4. - 2. * zi) << std::endl;
std::cout << "emc/5 = " << emc / 5. << std::endl;
std::cout << "emc/(4-2I) = " << emc / (4. - 2. * zi) << std::endl;
std::cout << "-------------" << std::endl;
// UnExpanded * Expanded easy-check (must be 0)
std::cout << "zero1 = " << 5. * esd - esd * 5. << std::endl;
std::cout << "zero1 = " << 5. * esc - esc * 5. << std::endl;
std::cout << "zero1 = " << 5. * evd - evd * 5. << std::endl;
std::cout << "zero1 = " << 5. * evc - evc * 5. << std::endl;
std::cout << "zero1 = " << 5. * emd - emd * 5. << std::endl;
std::cout << "zero1 =" << 5. * emc - emc * 5. << std::endl;
//
std::cout << "zero2 = " << (4 - 2 * zi) * esd - esd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * esc - esc * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * evd - evd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * evc - evc * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * emd - emd * (4 - 2 * zi) << std::endl;
std::cout << "zero2 = " << (4 - 2 * zi) * emc - emc * (4 - 2 * zi) << std::endl;
std::cout << "zero3 = " << vd1 * esd - esd * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * esc - esc * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * evd - evd * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * evc - evc * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * emd - emd.transpose() * vd1 << std::endl;
std::cout << "zero3 = " << vd1 * emc - emc.transpose() * vd1 << std::endl;
//
std::cout << "zero4 = " << vc1 * esd - esd * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * esc - esc * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * evd - evd * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * evc - evc * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * emd - emd.transpose() * vc1 << std::endl;
std::cout << "zero4 = " << vc1 * emc - emc.transpose() * vc1 << std::endl;
//
std::cout << "zero5 = " << md1 * esd - esd * md1 << std::endl;
std::cout << "zero5 = " << md1 * esc - esc * md1 << std::endl;
std::cout << "zero5 = " << md1 * evd - evd * md1.transpose() << std::endl;
std::cout << "zero5 = " << md1 * evc - evc * md1.transpose() << std::endl;
std::cout << "zero5 = " << md1 * emd - (emd.transpose() * md1.transpose()).transpose() << std::endl;
std::cout << "zero5 = " << md1 * emc - (emc.transpose() * md1.transpose()).transpose() << std::endl;
//
std::cout << "zero6 = " << mc1 * esd - esd * mc1 << std::endl;
std::cout << "zero6 = " << mc1 * esc - esc * mc1 << std::endl;
std::cout << "zero6 = " << mc1 * evd - evd * mc1.transpose() << std::endl;
std::cout << "zero6 = " << mc1 * evc - evc * mc1.transpose() << std::endl;
std::cout << "zero6 = " << mc1 * emd - (emd.transpose() * mc1.transpose()).transpose() << std::endl;
std::cout << "zero6 = " << mc1 * emc - (emc.transpose() * mc1.transpose()).transpose() << std::endl;
std::cout << "true = " << (esd == esd) << std::endl;
std::cout << "true = " << (esc == esc) << std::endl;
std::cout << "true = " << (evd == evd) << std::endl;
std::cout << "true = " << (evc == evc) << std::endl;
std::cout << "true = " << (emd == emd) << std::endl;
std::cout << "true = " << (emc == emc) << std::endl;
std::cout << "false = " << (esd == esd * esd) << std::endl;
std::cout << "false = " << (esc == esc * esc) << std::endl;
std::cout << "false = " << (evd == 5 * evd) << std::endl;
std::cout << "false = " << (evc == 7 * evc) << std::endl;
std::cout << "false = " << (emd == emd * emd) << std::endl;
std::cout << "false = " << (emc == emc * emc) << std::endl;
Expanded<double> esd1(sd, 2);
std::vector<double> sdx = {10., 5., 1.,-7};
Expanded<double> esd2(sdx, 1);
std::cout << "esd1 * esd2 = " << esd1*esd2 << std::endl;
std::cout << "esd1 + esd2 = " << esd1+esd2 << std::endl;
std::cout << "esd1 - esd2 = " << esd1-esd2 << std::endl;
std::vector<double> q1={1.,0.};
std::vector<double> q2={5.,7.};
std::vector<std::vector<double> > v1 = {q1,q2};
std::vector<double> w1={3.,4.};
std::vector<double> w2={8.};
std::vector<std::vector<double> > v2 = {w1,w2};
Expanded<double> ev1(v1, 1, 0);
Expanded<double> ev2(v2);
std::cout << "ev1 = " << ev1 << std::endl;
std::cout << "ev2 = " << ev2 << std::endl;
std::cout << "ev1 * ev2 = " << ev1*ev2 << std::endl;
std::cout << "ev1 + ev2 = " << ev1+ev2 << std::endl;
std::cout << "1/ev1 = " << ev1.inverse() << std::endl;
std::cout << "1/ev2 = " << ev2.inverse() << std::endl;
complex ii(0, 1);
std::vector<complex> r1={1.+2.*ii, 3.+4.*ii};
std::vector<complex> r2={5. + 6.*ii, 7.+8.*ii, 9.+10.*ii};
std::vector<std::vector<complex> > vv1 = {r1,r2};
Expanded<complex> evv1(vv1, 1, 1);
std::cout << "evv1 = " << evv1 << std::endl;
std::cout << "1/evv1 = " << evv1.inverse() << std::endl;
std::cout << "ev1/evv1 = " << ev1/evv1 << std::endl;
std::cout << "evv1/ev1 = " << evv1/ev1 << std::endl;
Expanded<complex> tmp(evv1.truncate(std::vector<int>(2,2),2));
std::cout << "evv1 trunc at (std::vector<int>(2,2),2)" << tmp << std::endl;
std::cout << "evv1 series = " << evv1.Series(std::vector<int>(2,2),2) << std::endl;
Expanded<double> pp;
return (0);
}