void QP
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& B,
DistMultiVec<Real>& X,
const qp::direct::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Int k = B.Width();
mpi::Comm comm = A.Comm();
DistSparseMatrix<Real> Q(comm), AHat(comm);
DistMultiVec<Real> bHat(comm), c(comm);
Herk( LOWER, ADJOINT, Real(1), A, Q );
MakeHermitian( LOWER, Q );
Zeros( AHat, 0, n );
Zeros( bHat, 0, 1 );
Zeros( X, n, k );
DistMultiVec<Real> q(comm), y(comm), z(comm);
auto& qLoc = q.Matrix();
auto& XLoc = X.Matrix();
auto& BLoc = B.LockedMatrix();
for( Int j=0; j<k; ++j )
{
auto xLoc = XLoc( ALL, IR(j) );
auto bLoc = BLoc( ALL, IR(j) );
Zeros( c, n, 1 );
Zeros( q, m, 1 );
qLoc = bLoc;
Multiply( ADJOINT, Real(-1), A, q, Real(0), c );
Zeros( q, n, 1 );
qLoc = xLoc;
El::QP( Q, AHat, bHat, c, q, y, z, ctrl );
xLoc = qLoc;
}
}
void QP
( const ElementalMatrix<Real>& APre,
const ElementalMatrix<Real>& BPre,
ElementalMatrix<Real>& XPre,
const qp::direct::Ctrl<Real>& ctrl )
{
DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR>
AProx( APre ),
BProx( BPre );
DistMatrixWriteProxy<Real,Real,MC,MR>
XProx( XPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& X = XProx.Get();
const Int n = A.Width();
const Int k = B.Width();
const Grid& g = A.Grid();
DistMatrix<Real> Q(g), AHat(g), bHat(g), c(g);
Herk( LOWER, ADJOINT, Real(1), A, Q );
Zeros( AHat, 0, n );
Zeros( bHat, 0, 1 );
Zeros( X, n, k );
DistMatrix<Real> y(g), z(g);
for( Int j=0; j<k; ++j )
{
auto x = X( ALL, IR(j) );
auto b = B( ALL, IR(j) );
Zeros( c, n, 1 );
Gemv( ADJOINT, Real(-1), A, b, Real(0), c );
El::QP( Q, AHat, bHat, c, x, y, z, ctrl );
}
}
double AnalyticIntegral(
SpkModel &model ,
const std::valarray<int> &N ,
const std::valarray<double> &y ,
const std::valarray<double> &alpha ,
const std::valarray<double> &L ,
const std::valarray<double> &U ,
size_t individual )
{
double Pi = 4. * atan(1.);
// set the fixed effects
model.setPopPar(alpha);
// set the individual
model.selectIndividual(individual);
// index in y where measurements for this individual starts
size_t start = 0;
size_t i;
for(i = 0; i < individual; i++)
{ assert( N[i] >= 0 );
start += N[i];
}
// number of measurements for this individual
assert( N[individual] >= 0 );
size_t Ni = N[individual];
// data for this individual
std::valarray<double> yi = y[ std::slice( start, Ni, 1 ) ];
// set the random effects = 0
std::valarray<double> b(1);
b[0] = 0.;
model.setIndPar(b);
std::valarray<double> Fi(Ni);
model.dataMean(Fi);
// model for the variance of random effects
std::valarray<double> D(1);
model.indParVariance(D);
// model for variance of the measurements given random effects
std::valarray<double> Ri( Ni * Ni );
model.dataVariance(Ri);
// determine bHat
double residual = 0;
size_t j;
for(j = 0; j < Ni; j++)
{ assert( Ri[j * Ni + j] == Ri[0] );
residual += (yi[j] - Fi[j]);
}
std::valarray<double> bHat(1);
bHat[0] = residual * D[0] / (Ni * D[0] + Ri[0]);
// now evaluate the Map Bayesian objective at its optimal value
model.setIndPar(bHat);
model.dataMean(Fi);
double sum = bHat[0] * bHat[0] / D[0] + log( 2. * Pi * D[0] );
for(j = 0; j < Ni; j++)
{ sum += (yi[j] - Fi[j]) * (yi[j] - Fi[j]) / Ri[0];
sum += log( 2. * Pi * Ri[0] );
}
double GHat = .5 * sum;
// square root of Hessian of the Map Bayesian objective
double rootHessian = sqrt( 1. / D[0] + Ni / Ri[0]);
// determine the values of beta that correspond to the limits
double Gamma_L = (L[0] - bHat[0]) * rootHessian;
double Gamma_U = (U[0] - bHat[0]) * rootHessian;
// compute the upper tails corresponding to the standard normal
double Q_L = gsl_sf_erf_Q(Gamma_L);
double Q_U = gsl_sf_erf_Q(Gamma_U);
// analytic value of the integral
double factor = exp(-GHat) * sqrt(2. * Pi) / rootHessian;
return factor * (Q_L - Q_U);
}
void RLS
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
Real rho,
DistMultiVec<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
DistMultiVec<Int> orders(comm), firstInds(comm);
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
{
const Int localHeight = orders.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = orders.GlobalRow(iLoc);
if( i < m+1 )
{
orders.SetLocal( iLoc, 0, m+1 );
firstInds.SetLocal( iLoc, 0, 0 );
}
else
{
orders.SetLocal( iLoc, 0, n+2 );
firstInds.SetLocal( iLoc, 0, m+1 );
}
}
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
DistSparseMatrix<Real> G(comm);
{
Zeros( G, m+n+3, n+2 );
// Count the number of entries of G to reserve
// -------------------------------------------
Int numLocalUpdates = 0;
const Int localHeight = G.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 || i == m+1 || (i>m+1 && i<m+n+2) )
++numLocalUpdates;
}
const Int numEntriesA = A.NumLocalEntries();
G.Reserve( numLocalUpdates+numEntriesA, numEntriesA );
// Queue the local updates
// -----------------------
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 )
G.QueueLocalUpdate( iLoc, 0, -1 );
else if( i == m+1 )
G.QueueLocalUpdate( iLoc, 1, -1 );
else if( i > m+1 && i < m+n+2 )
G.QueueLocalUpdate( iLoc, i-m, -1 );
}
// Queue the remote updates
// ------------------------
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
DistMultiVec<Real> h(comm);
Zeros( h, m+n+3, 1 );
auto& bLoc = b.LockedMatrix();
{
const Int bLocalHeight = b.LocalHeight();
h.Reserve( bLocalHeight );
for( Int iLoc=0; iLoc<bLocalHeight; ++iLoc )
h.QueueUpdate( b.GlobalRow(iLoc)+1, 0, bLoc(iLoc) );
h.ProcessQueues();
}
h.Set( END, 0, 1 );
// c := [1; rho; 0]
DistMultiVec<Real> c(comm);
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
DistSparseMatrix<Real> AHat(comm);
Zeros( AHat, 0, n+2 );
DistMultiVec<Real> bHat(comm);
Zeros( bHat, 0, 1 );
DistMultiVec<Real> xHat(comm), y(comm), z(comm), s(comm);
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
void RLS
( const ElementalMatrix<Real>& APre,
const ElementalMatrix<Real>& bPre,
Real rho,
ElementalMatrix<Real>& xPre,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR>
AProx( APre ),
bProx( bPre );
DistMatrixWriteProxy<Real,Real,MC,MR>
xProx( xPre );
auto& A = AProx.GetLocked();
auto& b = bProx.GetLocked();
auto& x = xProx.Get();
const Int m = A.Height();
const Int n = A.Width();
const Grid& g = A.Grid();
DistMatrix<Int,VC,STAR> orders(g), firstInds(g);
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
{
const Int localHeight = orders.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = orders.GlobalRow(iLoc);
if( i < m+1 )
{
orders.SetLocal( iLoc, 0, m+1 );
firstInds.SetLocal( iLoc, 0, 0 );
}
else
{
orders.SetLocal( iLoc, 0, n+2 );
firstInds.SetLocal( iLoc, 0, m+1 );
}
}
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
DistMatrix<Real> G(g);
{
Zeros( G, m+n+3, n+2 );
G.Set( 0, 0, -1 );
auto GA = G( IR(1,m+1), IR(2,n+2) );
GA = A;
G.Set( m+1, 1, -1 );
auto GI = G( IR(m+2,m+n+2), IR(2,n+2) );
Identity( GI, n, n );
GI *= -1;
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
DistMatrix<Real> h(g);
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
DistMatrix<Real> c(g);
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
DistMatrix<Real> AHat(g), bHat(g);
Zeros( AHat, 0, n+2 );
Zeros( bHat, 0, 1 );
DistMatrix<Real> xHat(g), y(g), z(g), s(g);
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
