void LAV
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Matrix<Real>& x,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> xInd(0,n), uInd(n,n+m), vInd(n+m,n+2*m);
SparseMatrix<Real> AHat, G;
Matrix<Real> c, h;
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
auto cuv = c( IR(n,n+2*m), ALL );
Fill( cuv, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
const Int numEntriesA = A.NumEntries();
AHat.Reserve( numEntriesA + 2*m );
for( Int e=0; e<numEntriesA; ++e )
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
for( Int i=0; i<m; ++i )
{
AHat.QueueUpdate( i, i+n, Real( 1) );
AHat.QueueUpdate( i, i+n+m, Real(-1) );
}
AHat.ProcessQueues();
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
G.Reserve( G.Height() );
for( Int i=0; i<2*m; ++i )
G.QueueUpdate( i, i+n, Real(-1) );
G.ProcessQueues();
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine linear program
// ===============================
Matrix<Real> xHat, y, z, s;
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// =========
x = xHat( xInd, ALL );
}
Int ZeroNorm( const SparseMatrix<T>& A, Base<T> tol )
{
DEBUG_ONLY(CSE cse("ZeroNorm"))
Int numNonzeros = 0;
const Int numEntries = A.NumEntries();
for( Int k=0; k<numEntries; ++k )
if( Abs(A.Value(k)) > tol )
++numNonzeros;
return numNonzeros;
}
Base<F> EntrywiseNorm( const SparseMatrix<F>& A, Base<F> p )
{
DEBUG_CSE
// TODO: Make this more numerically stable
typedef Base<F> Real;
Real sum = 0;
const Int numEntries = A.NumEntries();
for( Int k=0; k<numEntries; ++k )
sum += Pow( Abs(A.Value(k)), p );
return Pow( sum, 1/p );
}
Base<Field>
MinAbsNonzero( const SparseMatrix<Field>& A, Base<Field> upperBound )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int numEntries = A.NumEntries();
Real minAbs = upperBound;
for( Int e=0; e<numEntries; ++e )
{
const Real absVal = Abs(A.Value(e));
if( absVal > Real(0) )
minAbs = Min(minAbs,absVal);
}
return minAbs;
}
void MatrixMarket( const SparseMatrix<T>& A, string basename="matrix" )
{
EL_DEBUG_CSE
string filename = basename + "." + FileExtension(MATRIX_MARKET);
ofstream file( filename.c_str(), std::ios::binary );
if( !file.is_open() )
RuntimeError("Could not open ",filename);
// Write the header
// ================
{
ostringstream os;
os << "%%MatrixMarket matrix coordinate ";
if( IsComplex<T>::value )
os << "complex ";
else
os << "real ";
os << "general\n";
file << os.str();
}
// Write the size line
// ===================
const Int m = A.Height();
const Int n = A.Width();
const Int numNonzeros = A.NumEntries();
file << BuildString(m," ",n," ",numNonzeros,"\n");
// Write the entries
// =================
for( Int e=0; e<numNonzeros; ++e )
{
const Int i = A.Row(e);
const Int j = A.Col(e);
const T value = A.Value(e);
if( IsComplex<T>::value )
{
file <<
BuildString(i," ",j," ",RealPart(value)," ",ImagPart(value),"\n");
}
else
{
file << BuildString(i," ",j," ",RealPart(value),"\n");
}
}
}
void IPM
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> uInd(0,n), vInd(n,2*n), rInd(2*n,2*n+m);
SparseMatrix<Real> Q, AHat, G;
Matrix<Real> c, h;
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
Q.Reserve( m );
for( Int e=0; e<m; ++e )
Q.QueueUpdate( 2*n+e, 2*n+e, Real(1) );
Q.ProcessQueues();
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto cuv = c( IR(0,2*n), ALL );
Fill( cuv, lambda );
// \hat A := [A, -A, I]
// ====================
const Int numEntriesA = A.NumEntries();
Zeros( AHat, m, 2*n+m );
AHat.Reserve( 2*numEntriesA+m );
for( Int e=0; e<numEntriesA; ++e )
{
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
AHat.QueueUpdate( A.Row(e), A.Col(e)+n, -A.Value(e) );
}
for( Int e=0; e<m; ++e )
AHat.QueueUpdate( e, e+2*n, Real(1) );
AHat.ProcessQueues();
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
G.Reserve( 2*m );
for( Int e=0; e<2*m; ++e )
G.QueueUpdate( e, e, Real(-1) );
G.ProcessQueues();
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
Matrix<Real> xHat, y, z, s;
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
x = xHat( uInd, ALL );
x -= xHat( vInd, ALL );
}
void IPM
( const SparseMatrix<Real>& A,
const Matrix<Real>& d,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> wInd(0,n), betaInd(n,n+1), zInd(n+1,n+m+1);
SparseMatrix<Real> Q, AHat, G;
Matrix<Real> c, b, h;
// Q := | I 0 0 |
// | 0 0 0 |
// | 0 0 0 |
// ==============
Zeros( Q, n+m+1, n+m+1 );
Q.Reserve( n );
for( Int e=0; e<n; ++e )
Q.QueueUpdate( e, e, Real(1) );
Q.ProcessQueues();
// c := [0;0;lambda]
// =================
Zeros( c, n+m+1, 1 );
auto cz = c( zInd, ALL );
Fill( cz, lambda );
// AHat = []
// =========
Zeros( AHat, 0, n+m+1 );
// b = []
// ======
Zeros( b, 0, 1 );
// G := |-diag(d) A, -d, -I|
// | 0, 0, -I|
// =========================
Zeros( G, 2*m, n+m+1 );
const Int numEntriesA = A.NumEntries();
G.Reserve( numEntriesA+3*m );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e), A.Col(e), -d(A.Row(e))*A.Value(e) );
for( Int e=0; e<m; ++e )
G.QueueUpdate( e, n, -d(e) );
for( Int e=0; e<m; ++e )
{
G.QueueUpdate( e, e+n+1, Real(-1) );
G.QueueUpdate( e+m, e+n+1, Real(-1) );
}
G.ProcessQueues();
// h := [-ones(m,1); zeros(m,1)]
// =============================
Zeros( h, 2*m, 1 );
auto h0 = h( IR(0,m), ALL );
Fill( h0, Real(-1) );
// Solve the affine QP
// ===================
Matrix<Real> y, z, s;
QP( Q, AHat, G, b, c, h, x, y, z, s, ctrl );
}
void RLS
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real rho,
Matrix<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Int> orders, firstInds;
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
for( Int i=0; i<m+1; ++i )
{
orders.Set( i, 0, m+1 );
firstInds.Set( i, 0, 0 );
}
for( Int i=0; i<n+2; ++i )
{
orders.Set( i+m+1, 0, n+2 );
firstInds.Set( i+m+1, 0, m+1 );
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
SparseMatrix<Real> G;
{
const Int numEntriesA = A.NumEntries();
Zeros( G, m+n+3, n+2 );
G.Reserve( numEntriesA+n+2 );
G.QueueUpdate( 0, 0, -1 );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.QueueUpdate( m+1, 1, -1 );
for( Int j=0; j<n; ++j )
G.QueueUpdate( j+m+2, j+2, -1 );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
Matrix<Real> h;
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]
Matrix<Real> c;
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
SparseMatrix<Real> AHat;
Zeros( AHat, 0, n+2 );
Matrix<Real> bHat;
Zeros( bHat, 0, 1 );
Matrix<Real> xHat, y, z, s;
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
