static void gradCov(omxFitFunction *oo, FitContext *fc)
{
const double Scale = Global->llScale;
omxExpectation *expectation = oo->expectation;
BA81FitState *state = (BA81FitState*) oo->argStruct;
BA81Expect *estate = (BA81Expect*) expectation->argStruct;
if (estate->verbose >= 1) mxLog("%s: cross product approximation", oo->name());
estate->grp.ba81OutcomeProb(estate->itemParam->data, FALSE);
const int numThreads = Global->numThreads;
const int numUnique = estate->getNumUnique();
ba81NormalQuad &quad = estate->getQuad();
const int numSpecific = quad.numSpecific;
const int maxDims = quad.maxDims;
const int pDims = numSpecific? maxDims-1 : maxDims;
const int maxAbilities = quad.maxAbilities;
Eigen::MatrixXd icovMat(pDims, pDims);
if (maxAbilities) {
Eigen::VectorXd mean;
Eigen::MatrixXd srcMat;
estate->getLatentDistribution(fc, mean, srcMat);
icovMat = srcMat.topLeftCorner(pDims, pDims);
Matrix tmp(icovMat.data(), pDims, pDims);
int info = InvertSymmetricPosDef(tmp, 'U');
if (info) {
omxRaiseErrorf("%s: latent covariance matrix is not positive definite", oo->name());
return;
}
icovMat.triangularView<Eigen::Lower>() = icovMat.transpose().triangularView<Eigen::Lower>();
}
std::vector<int> &rowMap = estate->grp.rowMap;
double *rowWeight = estate->grp.rowWeight;
std::vector<bool> &rowSkip = estate->grp.rowSkip;
const int totalQuadPoints = quad.totalQuadPoints;
omxMatrix *itemParam = estate->itemParam;
omxBuffer<double> patternLik(numUnique);
const int priDerivCoef = pDims + triangleLoc1(pDims);
const int numLatents = maxAbilities + triangleLoc1(maxAbilities);
const int thrDerivSize = itemParam->cols * state->itemDerivPadSize;
const int totalOutcomes = estate->totalOutcomes();
const int numItems = state->freeItemParams? estate->numItems() : 0;
const size_t numParam = fc->varGroup->vars.size();
std::vector<double> thrGrad(numThreads * numParam);
std::vector<double> thrMeat(numThreads * numParam * numParam);
const double *wherePrep = quad.wherePrep.data();
if (numSpecific == 0) {
omxBuffer<double> thrLxk(totalQuadPoints * numThreads);
omxBuffer<double> derivCoef(totalQuadPoints * priDerivCoef);
if (state->freeLatents) {
#pragma omp parallel for num_threads(numThreads)
for (int qx=0; qx < totalQuadPoints; qx++) {
const double *where = wherePrep + qx * maxDims;
calcDerivCoef(fc, state, estate, icovMat.data(), where,
derivCoef.data() + qx * priDerivCoef);
}
}
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
double *lxk = thrLxk.data() + thrId * totalQuadPoints;
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
std::vector<double> deriv0(thrDerivSize);
std::vector<double> latentGrad(numLatents);
std::vector<double> patGrad(numParam);
double *grad = thrGrad.data() + thrId * numParam;
double *meat = thrMeat.data() + thrId * numParam * numParam;
estate->grp.ba81LikelihoodSlow2(px, lxk);
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalQuadPoints; qx++) {
patternLik1 += lxk[qx];
}
patternLik[px] = patternLik1;
// if (!validPatternLik(state, patternLik1)) complain, TODO
for (int qx=0; qx < totalQuadPoints; qx++) {
double tmp = lxk[qx];
mapLatentDeriv(state, estate, tmp, derivCoef.data() + qx * priDerivCoef,
latentGrad.data());
for (int ix=0; ix < numItems; ++ix) {
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
OMXZERO(expected.data(), estate->itemOutcomes(ix));
expected[pick-1] = tmp;
const double *spec = estate->itemSpec(ix);
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
double *myDeriv = deriv0.data() + ix * state->itemDerivPadSize;
(*Glibrpf_model[id].dLL1)(spec, iparam, wherePrep + qx * maxDims,
expected.data(), myDeriv);
}
}
gradCov_finish_1pat(1 / patternLik1, rowWeight[px], numItems, numLatents, numParam,
state, estate, itemParam, deriv0, latentGrad, Scale, patGrad, grad, meat);
}
} else {
const int totalPrimaryPoints = quad.totalPrimaryPoints;
const int specificPoints = quad.quadGridSize;
omxBuffer<double> thrLxk(totalQuadPoints * numSpecific * numThreads);
omxBuffer<double> thrEi(totalPrimaryPoints * numThreads);
omxBuffer<double> thrEis(totalPrimaryPoints * numSpecific * numThreads);
const int derivPerPoint = priDerivCoef + 2 * numSpecific;
omxBuffer<double> derivCoef(totalQuadPoints * derivPerPoint);
if (state->freeLatents) {
#pragma omp parallel for num_threads(numThreads)
for (int qx=0; qx < totalQuadPoints; qx++) {
const double *where = wherePrep + qx * maxDims;
calcDerivCoef(fc, state, estate, icovMat.data(), where,
derivCoef.data() + qx * derivPerPoint);
for (int Sgroup=0; Sgroup < numSpecific; ++Sgroup) {
calcDerivCoef1(fc, state, estate, where, Sgroup,
derivCoef.data() + qx * derivPerPoint + priDerivCoef + 2 * Sgroup);
}
}
}
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
double *lxk = thrLxk.data() + totalQuadPoints * numSpecific * thrId;
double *Ei = thrEi.data() + totalPrimaryPoints * thrId;
double *Eis = thrEis.data() + totalPrimaryPoints * numSpecific * thrId;
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
std::vector<double> deriv0(thrDerivSize);
std::vector<double> latentGrad(numLatents);
std::vector<double> patGrad(numParam);
double *grad = thrGrad.data() + thrId * numParam;
double *meat = thrMeat.data() + thrId * numParam * numParam;
estate->grp.cai2010EiEis(px, lxk, Eis, Ei);
for (int qx=0, qloc = 0; qx < totalPrimaryPoints; qx++) {
for (int sgroup=0; sgroup < numSpecific; ++sgroup) {
Eis[qloc] = Ei[qx] / Eis[qloc];
++qloc;
}
}
for (int qloc=0, eisloc=0, qx=0; eisloc < totalPrimaryPoints * numSpecific; eisloc += numSpecific) {
for (int sx=0; sx < specificPoints; sx++) {
mapLatentDeriv(state, estate, Eis[eisloc] * lxk[qloc],
derivCoef.data() + qx * derivPerPoint,
latentGrad.data());
for (int Sgroup=0; Sgroup < numSpecific; Sgroup++) {
double lxk1 = lxk[qloc];
double Eis1 = Eis[eisloc + Sgroup];
double tmp = Eis1 * lxk1;
mapLatentDerivS(state, estate, Sgroup, tmp,
derivCoef.data() + qx * derivPerPoint + priDerivCoef + 2 * Sgroup,
latentGrad.data());
for (int ix=0; ix < numItems; ++ix) {
if (estate->grp.Sgroup[ix] != Sgroup) continue;
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
OMXZERO(expected.data(), estate->itemOutcomes(ix));
expected[pick-1] = tmp;
const double *spec = estate->itemSpec(ix);
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
const int dims = spec[RPF_ISpecDims];
double *myDeriv = deriv0.data() + ix * state->itemDerivPadSize;
const double *where = wherePrep + qx * maxDims;
Eigen::VectorXd ptheta(dims);
for (int dx=0; dx < dims; dx++) {
ptheta[dx] = where[std::min(dx, maxDims-1)];
}
(*Glibrpf_model[id].dLL1)(spec, iparam, ptheta.data(),
expected.data(), myDeriv);
}
++qloc;
}
++qx;
}
}
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalPrimaryPoints; ++qx) {
patternLik1 += Ei[qx];
}
patternLik[px] = patternLik1;
gradCov_finish_1pat(1 / patternLik1, rowWeight[px], numItems, numLatents, numParam,
state, estate, itemParam, deriv0, latentGrad, Scale, patGrad, grad, meat);
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrGrad.data() + tx * numParam;
for (size_t en=0; en < numParam; ++en) {
thrGrad[en] += th[en];
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrMeat.data() + tx * numParam * numParam;
for (size_t en=0; en < numParam * numParam; ++en) {
thrMeat[en] += th[en];
}
}
for (size_t d1=0; d1 < numParam; ++d1) {
fc->grad(d1) += thrGrad[d1];
}
if (fc->infoB) {
for (size_t d1=0; d1 < numParam; ++d1) {
for (size_t d2=0; d2 < numParam; ++d2) {
int cell = d1 * numParam + d2;
fc->infoB[cell] += thrMeat[cell];
}
}
}
}
static void sandwich(omxFitFunction *oo, FitContext *fc)
{
const double abScale = fabs(Global->llScale);
omxExpectation *expectation = oo->expectation;
BA81FitState *state = (BA81FitState*) oo->argStruct;
BA81Expect *estate = (BA81Expect*) expectation->argStruct;
if (estate->verbose >= 1) mxLog("%s: sandwich", oo->name());
estate->grp.ba81OutcomeProb(estate->itemParam->data, FALSE);
const int numThreads = Global->numThreads;
const int numUnique = estate->getNumUnique();
ba81NormalQuad &quad = estate->getQuad();
const int numSpecific = quad.numSpecific;
const int maxDims = quad.maxDims;
std::vector<int> &rowMap = estate->grp.rowMap;
double *rowWeight = estate->grp.rowWeight;
std::vector<bool> &rowSkip = estate->grp.rowSkip;
const int totalQuadPoints = quad.totalQuadPoints;
omxMatrix *itemParam = estate->itemParam;
omxBuffer<double> patternLik(numUnique);
std::vector<const double*> &itemSpec = estate->grp.spec;
const int totalOutcomes = estate->totalOutcomes();
const int numItems = estate->grp.numItems();
const size_t numParam = fc->varGroup->vars.size();
const double *wherePrep = quad.wherePrep.data();
std::vector<double> thrBreadG(numThreads * numParam * numParam);
std::vector<double> thrBreadH(numThreads * numParam * numParam);
std::vector<double> thrMeat(numThreads * numParam * numParam);
if (numSpecific == 0) {
omxBuffer<double> thrLxk(totalQuadPoints * numThreads);
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
double *lxk = thrLxk.data() + thrId * totalQuadPoints;
omxBuffer<double> itemDeriv(state->itemDerivPadSize);
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
double *breadG = thrBreadG.data() + thrId * numParam * numParam; //a
double *breadH = thrBreadH.data() + thrId * numParam * numParam; //a
double *meat = thrMeat.data() + thrId * numParam * numParam; //b
std::vector<double> patGrad(numParam);
estate->grp.ba81LikelihoodSlow2(px, lxk);
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalQuadPoints; qx++) {
patternLik1 += lxk[qx];
}
patternLik[px] = patternLik1;
// if (!validPatternLik(state, patternLik1)) complain
double weight = 1 / patternLik[px];
for (int qx=0; qx < totalQuadPoints; qx++) {
double tmp = lxk[qx] * weight;
double sqrtTmp = sqrt(tmp);
std::vector<double> gradBuf(numParam);
int gradOffset = 0;
for (int ix=0; ix < numItems; ++ix) {
if (ix) gradOffset += state->paramPerItem[ix-1];
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
pick -= 1;
const int iOutcomes = estate->itemOutcomes(ix);
OMXZERO(expected.data(), iOutcomes);
expected[pick] = 1;
const double *spec = itemSpec[ix];
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
OMXZERO(itemDeriv.data(), state->itemDerivPadSize);
(*Glibrpf_model[id].dLL1)(spec, iparam, wherePrep + qx * maxDims,
expected.data(), itemDeriv.data());
(*Glibrpf_model[id].dLL2)(spec, iparam, itemDeriv.data());
for (int par = 0; par < state->paramPerItem[ix]; ++par) {
int to = state->itemGradMap[gradOffset + par];
if (to >= 0) {
gradBuf[to] -= itemDeriv[par] * sqrtTmp;
patGrad[to] -= itemDeriv[par] * tmp;
}
}
int derivBase = ix * state->itemDerivPadSize;
for (int ox=0; ox < state->itemDerivPadSize; ox++) {
int to = state->paramMap[derivBase + ox];
if (to >= int(numParam)) {
int Hto = to - numParam;
breadH[Hto] += abScale * itemDeriv[ox] * tmp * rowWeight[px];
}
}
}
addSymOuterProd(abScale * rowWeight[px], gradBuf.data(), numParam, breadG);
}
addSymOuterProd(abScale * rowWeight[px], patGrad.data(), numParam, meat);
}
} else {
Rf_error("Sandwich information matrix method is not implemented for bifactor models");
const int totalPrimaryPoints = quad.totalPrimaryPoints;
const int specificPoints = quad.quadGridSize;
omxBuffer<double> thrLxk(totalQuadPoints * numSpecific * numThreads);
omxBuffer<double> thrEi(totalPrimaryPoints * numThreads);
omxBuffer<double> thrEis(totalPrimaryPoints * numSpecific * numThreads);
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
omxBuffer<double> itemDeriv(state->itemDerivPadSize);
double *breadG = thrBreadG.data() + thrId * numParam * numParam; //a
double *breadH = thrBreadH.data() + thrId * numParam * numParam; //a
double *meat = thrMeat.data() + thrId * numParam * numParam; //b
std::vector<double> patGrad(numParam);
double *lxk = thrLxk.data() + totalQuadPoints * numSpecific * thrId;
double *Ei = thrEi.data() + totalPrimaryPoints * thrId;
double *Eis = thrEis.data() + totalPrimaryPoints * numSpecific * thrId;
estate->grp.cai2010EiEis(px, lxk, Eis, Ei);
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalPrimaryPoints; ++qx) {
patternLik1 += Ei[qx];
}
patternLik[px] = patternLik1;
for (int qx=0, qloc = 0; qx < totalPrimaryPoints; qx++) {
for (int sgroup=0; sgroup < numSpecific; ++sgroup) {
Eis[qloc] = Ei[qx] / Eis[qloc];
++qloc;
}
}
// WARNING: I didn't work out the math. I just coded this the way
// it seems to make sense.
for (int qloc=0, eisloc=0, qx=0; eisloc < totalPrimaryPoints * numSpecific; eisloc += numSpecific) {
for (int sx=0; sx < specificPoints; sx++) {
for (int Sgroup=0; Sgroup < numSpecific; Sgroup++) {
std::vector<double> gradBuf(numParam);
int gradOffset = 0;
double lxk1 = lxk[qloc + Sgroup];
double Eis1 = Eis[eisloc + Sgroup];
double tmp = Eis1 * lxk1 / patternLik1;
double sqrtTmp = sqrt(tmp);
for (int ix=0; ix < numItems; ++ix) {
if (ix) gradOffset += state->paramPerItem[ix-1];
if (estate->grp.Sgroup[ix] != Sgroup) continue;
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
OMXZERO(expected.data(), estate->itemOutcomes(ix));
expected[pick-1] = 1;
const double *spec = itemSpec[ix];
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
const int dims = spec[RPF_ISpecDims];
OMXZERO(itemDeriv.data(), state->itemDerivPadSize);
const double *where = wherePrep + qx * maxDims;
Eigen::VectorXd ptheta(dims);
for (int dx=0; dx < dims; dx++) {
ptheta[dx] = where[std::min(dx, maxDims-1)];
}
(*Glibrpf_model[id].dLL1)(spec, iparam, ptheta.data(),
expected.data(), itemDeriv.data());
(*Glibrpf_model[id].dLL2)(spec, iparam, itemDeriv.data());
for (int par = 0; par < state->paramPerItem[ix]; ++par) {
int to = state->itemGradMap[gradOffset + par];
if (to >= 0) {
gradBuf[to] -= itemDeriv[par] * sqrtTmp;
patGrad[to] -= itemDeriv[par] * tmp;
}
}
int derivBase = ix * state->itemDerivPadSize;
for (int ox=0; ox < state->itemDerivPadSize; ox++) {
int to = state->paramMap[derivBase + ox];
if (to >= int(numParam)) {
int Hto = to - numParam;
breadH[Hto] += (abScale * itemDeriv[ox] *
tmp * rowWeight[px]);
}
}
}
addSymOuterProd(abScale * rowWeight[px], gradBuf.data(), numParam, breadG);
}
qloc += numSpecific;
++qx;
}
}
addSymOuterProd(abScale * rowWeight[px], patGrad.data(), numParam, meat);
}
}
// only need upper triangle TODO
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrBreadG.data() + tx * numParam * numParam;
for (size_t en=0; en < numParam * numParam; ++en) {
thrBreadG[en] += th[en];
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrBreadH.data() + tx * numParam * numParam;
for (size_t en=0; en < numParam * numParam; ++en) {
thrBreadH[en] += th[en];
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrMeat.data() + tx * numParam * numParam;
for (size_t en=0; en < numParam * numParam; ++en) {
thrMeat[en] += th[en];
}
}
//pda(thrBreadG.data(), numParam, numParam);
//pda(thrBreadH.data(), numParam, numParam);
//pda(thrMeat.data(), numParam, numParam);
if (fc->infoA) {
for (size_t d1=0; d1 < numParam; ++d1) {
for (size_t d2=0; d2 < numParam; ++d2) {
int cell = d1 * numParam + d2;
fc->infoA[cell] += thrBreadH[cell] - thrBreadG[cell] + thrMeat[cell];
}
}
}
if (fc->infoB) {
for (size_t d1=0; d1 < numParam; ++d1) {
for (size_t d2=0; d2 < numParam; ++d2) {
int cell = d1 * numParam + d2;
fc->infoB[cell] += thrMeat[cell];
}
}
}
}