/**
* Specialized version of applyQ() that allows the zeros in an identity matrix
* to be taken advantage of depending on if isIdentity is true or not.
*
* @param B
* @param isIdentity If B is an identity matrix.
*/
public void applyQ(FMatrixRBlock B, bool isIdentity)
{
int minDimen = Math.Min(dataA.numCols, dataA.numRows);
FSubmatrixD1 subB = new FSubmatrixD1(B);
W.col0 = W.row0 = 0;
Y.row1 = W.row1 = dataA.numRows;
WTA.row0 = WTA.col0 = 0;
int start = minDimen - minDimen % blockLength;
if (start == minDimen)
{
start -= blockLength;
}
if (start < 0)
{
start = 0;
}
// (Q1^T * (Q2^T * (Q3^t * A)))
for (int i = start; i >= 0; i -= blockLength)
{
Y.col0 = i;
Y.col1 = Math.Min(Y.col0 + blockLength, dataA.numCols);
Y.row0 = i;
if (isIdentity)
{
subB.col0 = i;
}
subB.row0 = i;
setW();
WTA.row1 = Y.col1 - Y.col0;
WTA.col1 = subB.col1 - subB.col0;
WTA.original.reshape(WTA.row1, WTA.col1, false);
// Compute W matrix from reflectors stored in Y
if (!saveW)
{
BlockHouseHolder_FDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
// Apply the Qi to Q
BlockHouseHolder_FDRB.multTransA_vecCol(blockLength, Y, subB, WTA);
MatrixMult_FDRB.multPlus(blockLength, W, WTA, subB);
}
}
public virtual FMatrixRBlock getQ(FMatrixRBlock Q, bool transposed)
{
Q = QRDecompositionHouseholder_FDRB.initializeQ(Q, A.numRows, A.numCols, A.blockLength, false);
int height = Math.Min(A.blockLength, A.numRows);
V.reshape(height, A.numCols, false);
this.tmp.reshape(height, A.numCols, false);
FSubmatrixD1 subQ = new FSubmatrixD1(Q);
FSubmatrixD1 subU = new FSubmatrixD1(A);
FSubmatrixD1 subW = new FSubmatrixD1(V);
FSubmatrixD1 tmp = new FSubmatrixD1(this.tmp);
int N = A.numRows;
int start = N - N % A.blockLength;
if (start == N)
{
start -= A.blockLength;
}
if (start < 0)
{
start = 0;
}
// (Q1^T * (Q2^T * (Q3^t * A)))
for (int i = start; i >= 0; i -= A.blockLength)
{
int blockSize = Math.Min(A.blockLength, N - i);
subW.col0 = i;
subW.row1 = blockSize;
subW.original.reshape(subW.row1, subW.col1, false);
if (transposed)
{
tmp.row0 = i;
tmp.row1 = A.numCols;
tmp.col0 = 0;
tmp.col1 = blockSize;
}
else
{
tmp.col0 = i;
tmp.row1 = blockSize;
}
tmp.original.reshape(tmp.row1, tmp.col1, false);
subU.col0 = i;
subU.row0 = i;
subU.row1 = subU.row0 + blockSize;
// zeros and ones are saved and overwritten in U so that standard matrix multiplication can be used
copyZeros(subU);
// compute W for Q(i) = ( I + W*Y^T)
TridiagonalHelper_FDRB.computeW_row(A.blockLength, subU, subW, gammas, i);
subQ.col0 = i;
subQ.row0 = i;
// Apply the Qi to Q
// Qi = I + W*U^T
// Note that U and V are really row vectors. but standard notation assumed they are column vectors.
// which is why the functions called don't match the math above
// (I + W*U^T)*Q
// F=U^T*Q(i)
if (transposed)
{
MatrixMult_FDRB.multTransB(A.blockLength, subQ, subU, tmp);
}
else
{
MatrixMult_FDRB.mult(A.blockLength, subU, subQ, tmp);
}
// Q(i+1) = Q(i) + W*F
if (transposed)
{
MatrixMult_FDRB.multPlus(A.blockLength, tmp, subW, subQ);
}
else
{
MatrixMult_FDRB.multPlusTransA(A.blockLength, subW, tmp, subQ);
}
replaceZeros(subU);
}
return(Q);
}