void Sylvester
( Int m,
ElementalMatrix<F>& WPre,
ElementalMatrix<F>& X,
SignCtrl<Base<F>> ctrl )
{
EL_DEBUG_CSE
DistMatrixReadProxy<F,F,MC,MR> WProx( WPre );
auto& W = WProx.Get();
const Grid& g = W.Grid();
Sign( W, ctrl );
DistMatrix<F> WTL(g), WTR(g),
WBL(g), WBR(g);
PartitionDownDiagonal
( W, WTL, WTR,
WBL, WBR, m );
// WTL and WBR should be the positive and negative identity, WBL should be
// zero, and WTR should be -2 X
Copy( WTR, X );
X *= -F(1)/F(2);
// TODO: Think of how to probe for checks on other quadrants.
// Add UpdateDiagonal routine to avoid explicit identity Axpy?
/*
typedef Base<F> Real;
UpdateDiagonal( WTL, F(-1) );
const Real errorWTL = FrobeniusNorm( WTL );
const Int n = W.Height() - m;
UpdateDiagonal( WBR, F(1) );
const Real errorWBR = FrobeniusNorm( WBR );
const Real errorWBL = FrobeniusNorm( WBL );
*/
}
void Riccati
( ElementalMatrix<F>& WPre,
ElementalMatrix<F>& X,
SignCtrl<Base<F>> ctrl )
{
DEBUG_CSE
DistMatrixReadProxy<F,F,MC,MR> WProx( WPre );
auto& W = WProx.Get();
const Grid& g = W.Grid();
Sign( W, ctrl );
const Int n = W.Height()/2;
DistMatrix<F> WTL(g), WTR(g),
WBL(g), WBR(g);
PartitionDownDiagonal
( W, WTL, WTR,
WBL, WBR, n );
// (ML, MR) = sgn(W) - I
ShiftDiagonal( W, F(-1) );
// Solve for X in ML X = -MR
DistMatrix<F> ML(g), MR(g);
PartitionRight( W, ML, MR, n );
MR *= -1;
ls::Overwrite( NORMAL, ML, MR, X );
}
inline int
Lyapunov( const DistMatrix<F>& A, const DistMatrix<F>& C, DistMatrix<F>& X )
{
#ifndef RELEASE
CallStackEntry cse("Sylvester");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( C.Height() != A.Height() || C.Width() != A.Height() )
LogicError("C must conform with A");
if( A.Grid() != C.Grid() )
LogicError("A and C must have the same grid");
#endif
const Grid& g = A.Grid();
const Int m = A.Height();
DistMatrix<F> W(g), WTL(g), WTR(g),
WBL(g), WBR(g);
Zeros( W, 2*m, 2*m );
PartitionDownDiagonal
( W, WTL, WTR,
WBL, WBR, m );
WTL = A;
Adjoint( A, WBR ); Scale( F(-1), WBR );
WTR = C; Scale( F(-1), WTR );
return Sylvester( m, W, X );
}
void flow_rain(t_env *env)
{
int add;
int flowest[4];
int lower;
int lowest;
int x;
int y;
water_bck(env);
x = 0;
while (x < MAP_SIZE)
{
y = 0;
while (y < MAP_SIZE)
{
flowest[0] = WTR(x, y);
if (x > 0)
flowest[0] = WTR(x - 1, y);
flowest[1] = WTR(x, y);
if (x < MAP_SIZE - 1)
flowest[1] = WTR(x + 1, y);
flowest[2] = WTR(x, y);
if (y > 0)
flowest[2] = WTR(x, y - 1);
flowest[3] = WTR(x, y);
if (y < MAP_SIZE - 1)
flowest[3] = WTR(x, y + 1);
if ((flowest[0] <= WTR(x, y))
&& (flowest[1] <= WTR(x, y))
&& (flowest[2] <= WTR(x, y))
&& (flowest[3] <= WTR(x, y)))
add = -1;
else
add = 0;
lower = 0;
lowest = WTR(x, y) + add;
if (x > 0 && WTR(x - 1, y) < lowest && env->water_tmp[x][y] > 0 && env->water[x][y] > 0)
{
lower = 1;
lowest = WTR(x - 1, y);
}
else if (x < MAP_SIZE - 1 && WTR(x + 1, y) < lowest && env->water_tmp[x][y] > 0 && env->water[x][y] > 0)
{
lower = 2;
lowest = WTR(x + 1, y);
}
else if (y > 0 && WTR(x, y - 1) < lowest && env->water_tmp[x][y] > 0 && env->water[x][y] > 0)
{
lower = 3;
lowest = WTR(x, y - 1);
}
else if (y < MAP_SIZE - 1 && WTR(x, y + 1) < lowest && env->water_tmp[x][y] > 0 && env->water[x][y] > 0)
{
lower = 4;
lowest = WTR(x, y + 1);
}
if (lower == 1)
{
env->water[x - 1][y]++;
env->water[x][y]--;
}
if (lower == 2)
{
env->water[x + 1][y]++;
env->water[x][y]--;
}
if (lower == 3)
{
env->water[x][y - 1]++;
env->water[x][y]--;
}
if (lower == 4)
{
env->water[x][y + 1]++;
env->water[x][y]--;
}
y++;
}
x++;
}
}
