void SymmetricGeomEquil( Matrix<F>& A, Matrix<Base<F>>& d, bool progress )
{
DEBUG_ONLY(CSE cse("SymmetricGeomEquil"))
// TODO: Ensure A is symmetric
typedef Base<F> Real;
const Int n = A.Height();
Ones( d, n, 1 );
// TODO: Expose these as control parameters
const Int minIter = 3;
const Int maxIter = 10;
const Real damp = Real(1)/Real(1000);
const Real relTol = Real(9)/Real(10);
// Compute the original ratio of the maximum to minimum nonzero
auto maxAbs = MaxAbsLoc( A );
const Real maxAbsVal = maxAbs.value;
if( maxAbsVal == Real(0) )
return;
const Real minAbsVal = MinAbsNonzero( A, maxAbsVal );
Real ratio = maxAbsVal / minAbsVal;
if( progress )
cout << " Original ratio is " << maxAbsVal << "/" << minAbsVal << "="
<< ratio << endl;
Matrix<Real> scales;
Zeros( scales, n, 1 );
const Real sqrtDamp = Sqrt(damp);
for( Int iter=0; iter<maxIter; ++iter )
{
// Geometrically equilibrate the columns
const Int n = A.Width();
Ones( dRowA, mA, 1 );
Ones( dRowB, mB, 1 );
Ones( dCol, n, 1 );
// TODO: Expose these as control parameters
const Int minIter = 3;
const Int maxIter = 6;
const Real relTol = Real(9)/Real(10);
// TODO: Incorporate damping
//const Real damp = Real(1)/Real(1000);
//const Real sqrtDamp = Sqrt(damp);
// Compute the original ratio of the maximum to minimum nonzero
auto maxAbsA = MaxAbsLoc( A );
auto maxAbsB = MaxAbsLoc( B );
const Real maxAbsVal = Max(maxAbsA.value,maxAbsB.value);
if( maxAbsVal == Real(0) )
return;
const Real minAbsValA = MinAbsNonzero( A, maxAbsVal );
const Real minAbsValB = MinAbsNonzero( B, maxAbsVal );
const Real minAbsVal = Min(minAbsValA,minAbsValB);
Real ratio = maxAbsVal / minAbsVal;
if( progress && A.Grid().Rank() == 0 )
Output("Original ratio is ",maxAbsVal,"/",minAbsVal,"=",ratio);
DistMatrix<Real,MC,STAR> rowScaleA(A.Grid()),
rowScaleB(A.Grid());
DistMatrix<Real,MR,STAR> colScale(A.Grid()), colScaleB(B.Grid());
const Int indent = PushIndent();
