/**
* <p>
* A = (I + W Y<sup>T</sup>)<sup>T</sup>A<BR>
* A = A + Y (W<sup>T</sup>A)<BR>
* <br>
* where A is a submatrix of the input matrix.
* </p>
*/
protected void updateA(DSubmatrixD1 A)
{
setW();
A.row0 = Y.row0;
A.row1 = Y.row1;
A.col0 = Y.col1;
A.col1 = Y.original.numCols;
WTA.row0 = 0;
WTA.col0 = 0;
WTA.row1 = W.col1 - W.col0;
WTA.col1 = A.col1 - A.col0;
WTA.original.reshape(WTA.row1, WTA.col1, false);
if (A.col1 > A.col0)
{
BlockHouseHolder_DDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
MatrixMult_DDRB.multTransA(blockLength, W, A, WTA);
BlockHouseHolder_DDRB.multAdd_zeros(blockLength, Y, WTA, A);
}
else if (saveW)
{
BlockHouseHolder_DDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
}
/**
* 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(DMatrixRBlock B, bool isIdentity)
{
int minDimen = Math.Min(dataA.numCols, dataA.numRows);
DSubmatrixD1 subB = new DSubmatrixD1(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_DDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
// Apply the Qi to Q
BlockHouseHolder_DDRB.multTransA_vecCol(blockLength, Y, subB, WTA);
MatrixMult_DDRB.multPlus(blockLength, W, WTA, subB);
}
}
/**
* <p>
* Multiplies the provided matrix by Q<sup>T</sup> using householder reflectors. This is more
* efficient that computing Q then applying it to the matrix.
* </p>
*
* <p>
* Q = Q*(I - γ W*Y^T)<br>
* QR = A ≥ R = Q^T*A = (Q3^T * (Q2^T * (Q1^t * A)))
* </p>
*
* @param B Matrix which Q is applied to. Modified.
*/
public void applyQTran(DMatrixRBlock B)
{
int minDimen = Math.Min(dataA.numCols, dataA.numRows);
DSubmatrixD1 subB = new DSubmatrixD1(B);
W.col0 = W.row0 = 0;
Y.row1 = W.row1 = dataA.numRows;
WTA.row0 = WTA.col0 = 0;
// (Q3^T * (Q2^T * (Q1^t * A)))
for (int i = 0; i < minDimen; i += blockLength)
{
Y.col0 = i;
Y.col1 = Math.Min(Y.col0 + blockLength, dataA.numCols);
Y.row0 = i;
subB.row0 = i;
// subB.row1 = B.numRows;
// subB.col0 = 0;
// subB.col1 = B.numCols;
setW();
// W.original.reshape(W.row1,W.col1,false);
WTA.row0 = 0;
WTA.col0 = 0;
WTA.row1 = W.col1 - W.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_DDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
// Apply the Qi to Q
MatrixMult_DDRB.multTransA(blockLength, W, subB, WTA);
BlockHouseHolder_DDRB.multAdd_zeros(blockLength, Y, WTA, subB);
}
}
public virtual DMatrixRBlock getQ(DMatrixRBlock Q, bool transposed)
{
Q = QRDecompositionHouseholder_DDRB.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);
DSubmatrixD1 subQ = new DSubmatrixD1(Q);
DSubmatrixD1 subU = new DSubmatrixD1(A);
DSubmatrixD1 subW = new DSubmatrixD1(V);
DSubmatrixD1 temp = new DSubmatrixD1(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)
{
temp.row0 = i;
temp.row1 = A.numCols;
temp.col0 = 0;
temp.col1 = blockSize;
}
else
{
temp.col0 = i;
temp.row1 = blockSize;
}
temp.original.reshape(temp.row1, temp.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_DDRB.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_DDRB.multTransB(A.blockLength, subQ, subU, temp);
}
else
{
MatrixMult_DDRB.mult(A.blockLength, subU, subQ, temp);
}
// Q(i+1) = Q(i) + W*F
if (transposed)
{
MatrixMult_DDRB.multPlus(A.blockLength, temp, subW, subQ);
}
else
{
MatrixMult_DDRB.multPlusTransA(A.blockLength, subW, temp, subQ);
}
replaceZeros(subU);
}
return(Q);
}
