public void Zero()
{
#if VECX_SIMD
SIMDProcessor.Zero16(p, size);
#else
Array.Clear(p, 0, size);
#endif
}
public void Zero(int length)
{
SetSize(length);
#if VECX_SIMD
SIMDProcessor.Zero16(p, length);
#else
Array.Clear(p, 0, size);
#endif
}
bool padded; // set to true if the rows of the initial matrix are 16 byte padded
bool FactorClamped()
{
clampedChangeStart = 0;
for (int i = 0; i < numClamped; i++)
{
Array.Copy(clamped[i], rowPtrs[i], numClamped);
}
return(SIMDProcessor.MatX_LDLTFactor(clamped, diagonal, numClamped));
}
void SolveClamped(ref idVecX x, float[] b)
{
// solve L
SIMDProcessor.MatX_LowerTriangularSolve(clamped, solveCache1.ToArray(), b, numClamped, clampedChangeStart);
// solve D
SIMDProcessor.Mul(solveCache2.ToArray(), solveCache1.ToArray(), diagonal.ToArray(), numClamped);
// solve Lt
SIMDProcessor.MatX_LowerTriangularSolveTranspose(clamped, x.ToArray(), solveCache2.ToArray(), numClamped);
clampedChangeStart = numClamped;
}
// modifies this->delta_a and uses this->delta_f
void CalcAccelDelta(int d)
{
// only the not clamped variables, including the current variable, can have a change in acceleration
for (int j = numClamped; j <= d; j++)
{
// only the clamped variables and the current variable have a force delta unequal zero
float dot;
SIMDProcessor.Dot(out dot, rowPtrs[j], delta_f.ToArray(), numClamped);
delta_a[j] = dot + rowPtrs[j][d] * delta_f[d];
}
}
public void Negate()
{
#if VECX_SIMD
SIMDProcessor.Negate16(p, size);
#else
for (int i = 0; i < size; i++)
{
p[i] = -p[i];
}
#endif
}
public idVecX opMul(float a)
{
#if VECX_SIMD
SIMDProcessor.MulAssign16(p, a, size);
#else
for (int i = 0; i < size; i++)
{
p[i] *= a;
}
#endif
return(this);
}
public idVecX opAdd(idVecX a)
{
Debug.Assert(size == a.size);
#if VECX_SIMD
SIMDProcessor.AddAssign16(p, a.p, size);
#else
for (int i = 0; i < size; i++)
{
p[i] += a.p[i];
}
#endif
tempIndex = 0;
return(this);
}
public static idVecX operator *(idVecX a, float b)
{
idVecX m = new idVecX();
m.SetTempSize(a.size);
#if VECX_SIMD
SIMDProcessor.Mul16(m.p, p, a, size);
#else
for (int i = 0; i < a.size; i++)
{
m.p[i] = a.p[i] * b;
}
#endif
return(m);
}
public static idVecX operator +(idVecX a, idVecX b)
{
Debug.Assert(a.size == b.size);
idVecX m = new idVecX();
m.SetTempSize(a.size);
#if VECX_SIMD
SIMDProcessor.Add16(m.p, a.p, b.p, a.size);
#else
for (int i = 0; i < a.size; i++)
{
m.p[i] = a.p[i] + b.p[i];
}
#endif
return(m);
}
void AddClamped(int r, bool useSolveCache)
{
Debug.Assert(r >= numClamped);
if (numClamped < clampedChangeStart)
{
clampedChangeStart = numClamped;
}
// add a row at the bottom and a column at the right of the factored matrix for the clamped variables
Swap(numClamped, r);
// solve for v in L * v = rowPtr[numClamped]
float dot = 0;
if (useSolveCache)
{
// the lower triangular solve was cached in SolveClamped called by CalcForceDelta
Array.Copy(clamped[numClamped], solveCache2.ToArray(), numClamped);
// calculate row dot product
SIMDProcessor.Dot(out dot, solveCache2.ToArray(), solveCache1.ToArray(), numClamped);
}
else
{
float[] v = new float[numClamped];
SIMDProcessor.MatX_LowerTriangularSolve(clamped, v, rowPtrs[numClamped], numClamped);
// add bottom row to L
SIMDProcessor.Mul(clamped[numClamped], v, diagonal.ToArray(), numClamped);
// calculate row dot product
SIMDProcessor.Dot(out dot, clamped[numClamped], v, numClamped);
}
// update diagonal[numClamped]
float d = rowPtrs[numClamped][numClamped] - dot;
if (d == 0.0f)
{
idLib.common.Printf("AddClamped: updating factorization failed\n"); numClamped++; return;
}
clamped[numClamped][numClamped] = d;
diagonal[numClamped] = 1.0f / d;
numClamped++;
}
public override bool Solve(ref idMatX o_m, ref idVecX o_x, ref idVecX o_b, ref idVecX o_lo, ref idVecX o_hi, int[] o_boxIndex)
{
// true when the matrix rows are 16 byte padded
padded = (((o_m.GetNumRows() + 3) & ~3) == o_m.GetNumColumns());
Debug.Assert(padded || o_m.GetNumRows() == o_m.GetNumColumns());
Debug.Assert(o_x.GetSize() == o_m.GetNumRows());
Debug.Assert(o_b.GetSize() == o_m.GetNumRows());
Debug.Assert(o_lo.GetSize() == o_m.GetNumRows());
Debug.Assert(o_hi.GetSize() == o_m.GetNumRows());
// allocate memory for permuted input
f.SetData(o_m.GetNumRows(), VECX_ALLOCA(o_m.GetNumRows()));
a.SetData(o_b.GetSize(), VECX_ALLOCA(o_b.GetSize()));
b.SetData(o_b.GetSize(), VECX_ALLOCA(o_b.GetSize()));
lo.SetData(o_lo.GetSize(), VECX_ALLOCA(o_lo.GetSize()));
hi.SetData(o_hi.GetSize(), VECX_ALLOCA(o_hi.GetSize()));
if (o_boxIndex != null)
{
boxIndex = new int[o_x.GetSize()];
Array.Copy(boxIndex, o_boxIndex, o_x.GetSize());
}
else
{
boxIndex = null;
}
// we override the const on o_m here but on exit the matrix is unchanged
m.SetData(o_m.GetNumRows(), o_m.GetNumColumns(), (float[])o_m[0]);
f.Zero();
a.Zero();
b = o_b;
lo = o_lo;
hi = o_hi;
// pointers to the rows of m
rowPtrs = new float[m.GetNumRows()][];
for (int i = 0; i < m.GetNumRows(); i++)
{
rowPtrs[i] = m[i];
}
// tells if a variable is at the low boundary, high boundary or inbetween
side = new int[m.GetNumRows()];
// index to keep track of the permutation
permuted = new int[m.GetNumRows()];
for (int i = 0; i < m.GetNumRows(); i++)
{
permuted[i] = i;
}
// permute input so all unbounded variables come first
numUnbounded = 0;
for (int i = 0; i < m.GetNumRows(); i++)
{
if (lo[i] == -float.NegativeInfinity && hi[i] == float.PositiveInfinity)
{
if (numUnbounded != i)
{
Swap(numUnbounded, i);
}
numUnbounded++;
}
}
// permute input so all variables using the boxIndex come last
int boxStartIndex = m.GetNumRows();
if (boxIndex != null)
{
for (int i = m.GetNumRows() - 1; i >= numUnbounded; i--)
{
if (boxIndex[i] >= 0 && (lo[i] != float.NegativeInfinity || hi[i] != float.PositiveInfinity))
{
boxStartIndex--;
if (boxStartIndex != i)
{
Swap(boxStartIndex, i);
}
}
}
}
// sub matrix for factorization
clamped.SetData(m.GetNumRows(), m.GetNumColumns(), MATX_ALLOCA(m.GetNumRows() * m.GetNumColumns()));
diagonal.SetData(m.GetNumRows(), VECX_ALLOCA(m.GetNumRows()));
// all unbounded variables are clamped
numClamped = numUnbounded;
// if there are unbounded variables
if (numUnbounded != 0)
{
// factor and solve for unbounded variables
if (!FactorClamped())
{
idLib.common.Printf("idLCP_Square::Solve: unbounded factorization failed\n");
return(false);
}
SolveClamped(f, b.ToArray());
// if there are no bounded variables we are done
if (numUnbounded == m.GetNumRows())
{
o_x = f; // the vector is not permuted
return(true);
}
}
#if IGNORE_UNSATISFIABLE_VARIABLES
int numIgnored = 0;
#endif
// allocate for delta force and delta acceleration
delta_f.SetData(m.GetNumRows(), VECX_ALLOCA(m.GetNumRows()));
delta_a.SetData(m.GetNumRows(), VECX_ALLOCA(m.GetNumRows()));
// // solve for bounded variables
string failed = null;
float dot;
for (int i = numUnbounded; i < m.GetNumRows(); i++)
{
// once we hit the box start index we can initialize the low and high boundaries of the variables using the box index
if (i == boxStartIndex)
{
for (int j = 0; j < boxStartIndex; j++)
{
o_x[permuted[j]] = f[j];
}
for (int j = boxStartIndex; j < m.GetNumRows(); j++)
{
float s = o_x[boxIndex[j]];
if (lo[j] != float.NegativeInfinity)
{
lo[j] = -idMath.Fabs(lo[j] * s);
}
if (hi[j] != float.PositiveInfinity)
{
hi[j] = idMath.Fabs(hi[j] * s);
}
}
}
// calculate acceleration for current variable
SIMDProcessor.Dot(out dot, rowPtrs[i], f.ToArray(), i);
a[i] = dot - b[i];
// if already at the low boundary
if (lo[i] >= -LCP_BOUND_EPSILON && a[i] >= -LCP_ACCEL_EPSILON)
{
side[i] = -1; continue;
}
// if already at the high boundary
if (hi[i] <= LCP_BOUND_EPSILON && a[i] <= LCP_ACCEL_EPSILON)
{
side[i] = 1; continue;
}
// if inside the clamped region
if (idMath.Fabs(a[i]) <= LCP_ACCEL_EPSILON)
{
side[i] = 0; AddClamped(i); continue;
}
// drive the current variable into a valid region
int n;
for (n = 0; n < maxIterations; n++)
{
// direction to move
float dir = (a[i] <= 0.0f ? 1.0f : -1.0f);
// calculate force delta
CalcForceDelta(i, dir);
// calculate acceleration delta: delta_a = m * delta_f;
CalcAccelDelta(i);
// maximum step we can take
float maxStep;
int limit;
int limitSide;
GetMaxStep(i, dir, out maxStep, out limit, out limitSide);
if (maxStep <= 0.0f)
{
#if IGNORE_UNSATISFIABLE_VARIABLES
// ignore the current variable completely
lo[i] = hi[i] = 0.0f;
f[i] = 0.0f;
side[i] = -1;
numIgnored++;
#else
failed = string.Format("invalid step size %.4f", maxStep);
#endif
break;
}
// change force
ChangeForce(i, maxStep);
// change acceleration
ChangeAccel(i, maxStep);
// clamp/unclamp the variable that limited this step
side[limit] = limitSide;
switch (limitSide)
{
case 0:
a[limit] = 0.0f;
AddClamped(limit);
break;
case -1:
f[limit] = lo[limit];
if (limit != i)
{
RemoveClamped(limit);
}
break;
case 1:
f[limit] = hi[limit];
if (limit != i)
{
RemoveClamped(limit);
}
break;
}
// if the current variable limited the step we can continue with the next variable
if (limit == i)
{
break;
}
}
if (n >= maxIterations)
{
failed = string.Format("max iterations %d", maxIterations);
break;
}
if (failed != null)
{
break;
}
}
#if IGNORE_UNSATISFIABLE_VARIABLES
if (numIgnored > 0)
{
if (lcp_showFailures.GetBool())
{
idLib.common.Printf("idLCP_Symmetric::Solve: %d of %d bounded variables ignored\n", numIgnored, m.GetNumRows() - numUnbounded);
}
}
#endif
// if failed clear remaining forces
if (failed != null)
{
if (lcp_showFailures.GetBool())
{
idLib.common.Printf("idLCP_Square::Solve: %s (%d of %d bounded variables ignored)\n", failed, m.GetNumRows() - i, m.GetNumRows() - numUnbounded);
}
for (int j = i; j < m.GetNumRows(); j++)
{
f[j] = 0.0f;
}
}
#if _DEBUG && false
if (failed == null)
{
// test whether or not the solution satisfies the complementarity conditions
for (int i = 0; i < m.GetNumRows(); i++)
{
a[i] = -b[i];
for (int j = 0; j < m.GetNumRows(); j++)
{
a[i] += rowPtrs[i][j] * f[j];
}
if (f[i] == lo[i])
{
if (lo[i] != hi[i] && a[i] < -LCP_ACCEL_EPSILON)
{
int bah1 = 1;
}
}
else if (f[i] == hi[i])
{
if (lo[i] != hi[i] && a[i] > LCP_ACCEL_EPSILON)
{
int bah2 = 1;
}
}
else if (f[i] < lo[i] || f[i] > hi[i] || idMath.Fabs(a[i]) > 1.0f)
{
int bah3 = 1;
}
}
}
#endif
// unpermute result
for (int i = 0; i < f.GetSize(); i++)
{
o_x[permuted[i]] = f[i];
}
// unpermute original matrix
for (int i = 0; i < m.GetNumRows(); i++)
{
for (int j = 0; j < m.GetNumRows(); j++)
{
if (permuted[j] == i)
{
break;
}
}
if (i != j)
{
m.SwapColumns(i, j);
idSwap(permuted[i], permuted[j]);
}
}
return(true);
}
// modifies this->a and uses this->delta_a
void ChangeAccel(int d, float step)
{
// only the not clamped variables, including the current variable, can have an acceleration unequal zero
SIMDProcessor.MulAdd(a.ToArray() + numClamped, step, delta_a.ToArray() + numClamped, d - numClamped + 1);
}
// modifies this->f and uses this->delta_f
void ChangeForce(int d, float step)
{
// only the clamped variables and current variable have a force delta unequal zero
SIMDProcessor.MulAdd(f.ToArray(), step, delta_f.ToArray(), numClamped);
f[d] += step * delta_f[d];
}
void RemoveClamped(int r)
{
double diag;
Debug.Assert(r < numClamped);
if (r < clampedChangeStart)
{
clampedChangeStart = r;
}
numClamped--;
// no need to swap and update the factored matrix when the last row and column are removed
if (r == numClamped)
{
return;
}
// swap the to be removed row/column with the last row/column
Swap(r, numClamped);
// update the factored matrix
float[] addSub = new float[numClamped];
if (r == 0)
{
if (numClamped == 1)
{
diag = rowPtrs[0][0];
if (diag == 0.0f)
{
idLib.common.Printf("RemoveClamped: updating factorization failed\n"); return;
}
clamped[0][0] = diag;
diagonal[0] = (float)(1.0f / diag);
return;
}
// calculate the row/column to be added to the lower right sub matrix starting at (r, r)
float[] original = rowPtrs[numClamped];
float[] ptr = rowPtrs[r];
addSub[0] = ptr[0] - original[numClamped];
for (int i = 1; i < numClamped; i++)
{
addSub[i] = ptr[i] - original[i];
}
}
else
{
float[] v = new float[numClamped];
// solve for v in L * v = rowPtr[r]
SIMDProcessor.MatX_LowerTriangularSolve(clamped, v, rowPtrs[r], r);
// update removed row
SIMDProcessor.Mul(clamped[r], v, diagonal.ToArray(), r);
// if the last row/column of the matrix is updated
if (r == numClamped - 1)
{
// only calculate new diagonal
float dot;
SIMDProcessor.Dot(out dot, clamped[r], v, r);
diag = rowPtrs[r][r] - dot;
if (diag == 0.0f)
{
idLib.common.Printf("RemoveClamped: updating factorization failed\n"); return;
}
clamped[r][r] = diag;
diagonal[r] = (float)(1.0f / diag);
return;
}
// calculate the row/column to be added to the lower right sub matrix starting at (r, r)
for (int i = 0; i < r; i++)
{
v[i] = clamped[r][i] * clamped[i][i];
}
for (int i = r; i < numClamped; i++)
{
double sum = (i == r ? clamped[r][r] : clamped[r][r] * clamped[i][r]);
float[] ptr = clamped[i];
for (int j = 0; j < r; j++)
{
sum += ptr[j] * v[j];
}
addSub[i] = (float)(rowPtrs[r][i] - sum);
}
}
// add row/column to the lower right sub matrix starting at (r, r)
float[] v1 = new float[numClamped];
float[] v2 = new float[numClamped];
diag = idMath.SQRT_1OVER2;
v1[r] = (float)((0.5f * addSub[r] + 1.0f) * diag);
v2[r] = (float)((0.5f * addSub[r] - 1.0f) * diag);
for (int i = r + 1; i < numClamped; i++)
{
v1[i] = v2[i] = (float)(addSub[i] * diag);
}
double alpha1 = 1.0f;
double alpha2 = -1.0f;
// simultaneous update/downdate of the sub matrix starting at (r, r)
int n = clamped.GetNumColumns();
for (int i = r; i < numClamped; i++)
{
diag = clamped[i][i];
double p1 = v1[i];
double newDiag = diag + alpha1 * p1 * p1;
if (newDiag == 0.0f)
{
idLib.Common.Printf("RemoveClamped: updating factorization failed\n"); return;
}
alpha1 /= newDiag;
double beta1 = p1 * alpha1;
alpha1 *= diag;
diag = newDiag;
double p2 = v2[i];
newDiag = diag + alpha2 * p2 * p2;
if (newDiag == 0.0f)
{
idLib.common.Printf("RemoveClamped: updating factorization failed\n"); return;
}
clamped[i][i] = newDiag;
double invNewDiag;
diagonal[i] = (float)(invNewDiag = 1.0f / newDiag);
alpha2 *= invNewDiag;
double beta2 = p2 * alpha2;
alpha2 *= diag;
// update column below diagonal (i,i)
float[] ptr = clamped.ToArray() + i;
for (int j = i + 1; j < numClamped - 1; j += 2)
{
float sum0 = ptr[(j + 0) * n];
float sum1 = ptr[(j + 1) * n];
v1[j + 0] -= (float)(p1 * sum0);
v1[j + 1] -= (float)(p1 * sum1);
sum0 += (float)(beta1 * v1[j + 0]);
sum1 += (float)(beta1 * v1[j + 1]);
v2[j + 0] -= (float)(p2 * sum0);
v2[j + 1] -= (float)(p2 * sum1);
sum0 += (float)(beta2 * v2[j + 0]);
sum1 += (float)(beta2 * v2[j + 1]);
ptr[(j + 0) * n] = sum0;
ptr[(j + 1) * n] = sum1;
}
for (int j; j < numClamped; j++)
{
double sum = ptr[j * n];
v1[j] -= (float)(p1 * sum);
sum += beta1 * v1[j];
v2[j] -= (float)(p2 * sum);
sum += beta2 * v2[j];
ptr[j * n] = (float)sum;
}
}
}