/**
* <p>
* Computes the householder vector from the specified row
* </p>
*
* <p>
* The householder vector 'u' is computed as follows:<br>
* <br>
* u(1) = 1 <br>
* u(i) = x(i)/(τ + x(1))<br>
* </p>
*
* The first element is implicitly assumed to be one and not written.
*
* @return If there was any problems or not. true = no problem.
*/
public static bool computeHouseHolderRow(int blockLength, DSubmatrixD1 Y,
double[] gamma, int i)
{
double max = BlockHouseHolder_DDRB.findMaxRow(blockLength, Y, i, i + 1);
if (max == 0.0)
{
return(false);
}
else
{
// computes tau and normalizes u by max
double tau = computeTauAndDivideRow(blockLength, Y, i, i + 1, max);
// divide u by u_0
double u_0 = Y.get(i, i + 1) + tau;
VectorOps_DDRB.div_row(blockLength, Y, i, u_0, Y, i, i + 1, Y.col1 - Y.col0);
gamma[Y.row0 + i] = u_0 / tau;
// after the reflector is applied the column would be all zeros but be -tau in the first element
Y.set(i, i + 1, -tau * max);
}
return(true);
}
/**
* <p>
* Computes W from the householder reflectors stored in the columns of the row block
* submatrix Y.
* </p>
*
* <p>
* Y = v<sup>(1)</sup><br>
* W = -β<sub>1</sub>v<sup>(1)</sup><br>
* for j=2:r<br>
* z = -β(I +WY<sup>T</sup>)v<sup>(j)</sup> <br>
* W = [W z]<br>
* Y = [Y v<sup>(j)</sup>]<br>
* end<br>
* <br>
* where v<sup>(.)</sup> are the house holder vectors, and r is the block length. Note that
* Y already contains the householder vectors so it does not need to be modified.
* </p>
*
* <p>
* Y and W are assumed to have the same number of rows and columns.
* </p>
*/
public static void computeW_row(int blockLength,
DSubmatrixD1 Y, DSubmatrixD1 W,
double[] beta, int betaIndex)
{
int heightY = Y.row1 - Y.row0;
CommonOps_DDRM.fill(W.original, 0);
// W = -beta*v(1)
BlockHouseHolder_DDRB.scale_row(blockLength, Y, W, 0, 1, -beta[betaIndex++]);
int min = Math.Min(heightY, W.col1 - W.col0);
// set up rest of the rows
for (int i = 1; i < min; i++)
{
// w=-beta*(I + W*Y^T)*u
double b = -beta[betaIndex++];
// w = w -beta*W*(Y^T*u)
for (int j = 0; j < i; j++)
{
double yv = BlockHouseHolder_DDRB.innerProdRow(blockLength, Y, i, Y, j, 1);
VectorOps_DDRB.add_row(blockLength, W, i, 1, W, j, b * yv, W, i, 1, Y.col1 - Y.col0);
}
//w=w -beta*u + stuff above
BlockHouseHolder_DDRB.add_row(blockLength, Y, i, b, W, i, 1, W, i, 1, Y.col1 - Y.col0);
}
}
public static double innerProdRowSymm(int blockLength,
DSubmatrixD1 A,
int rowA,
DSubmatrixD1 B,
int rowB, int zeroOffset)
{
int offset = rowA + zeroOffset;
if (offset + B.col0 >= B.col1)
{
return(0);
}
if (offset < rowB)
{
// take in account the one in 'A'
double total = B.get(offset, rowB);
total += VectorOps_DDRB.dot_row_col(blockLength, A, rowA, B, rowB, offset + 1, rowB);
total += VectorOps_DDRB.dot_row(blockLength, A, rowA, B, rowB, rowB, A.col1 - A.col0);
return(total);
}
else
{
// take in account the one in 'A'
double total = B.get(rowB, offset);
total += VectorOps_DDRB.dot_row(blockLength, A, rowA, B, rowB, offset + 1, A.col1 - A.col0);
return(total);
}
}
/**
* <p>
* Computes the 'y' vector and stores the result in 'v'<br>
* <br>
* y = -γ(A + U*V^T + V*U^T)u
* </p>
*
* @param blockLength
* @param A Contains the reflectors and the row being updated.
* @param V Contains previously computed 'v' vectors.
* @param row The row of 'A' that is to be updated.
*/
public static void computeY(int blockLength,
DSubmatrixD1 A,
DSubmatrixD1 V,
int row,
double gamma)
{
// Elements in 'y' before 'row' are known to be zero and the element at 'row'
// is not used. Thus only elements after row and after are computed.
// y = A*u
multA_u(blockLength, A, V, row);
for (int i = 0; i < row; i++)
{
// y = y + u_i*v_i^t*u + v_i*u_i^t*u
// v_i^t*u
double dot_v_u = BlockHouseHolder_DDRB.innerProdRow(blockLength, A, row, V, i, 1);
// u_i^t*u
double dot_u_u = BlockHouseHolder_DDRB.innerProdRow(blockLength, A, row, A, i, 1);
// y = y + u_i*(v_i^t*u)
// the ones in these 'u' are skipped over since the next submatrix of A
// is only updated
VectorOps_DDRB.add_row(blockLength, V, row, 1, A, i, dot_v_u, V, row, row + 1, A.col1 - A.col0);
// y = y + v_i*(u_i^t*u)
// the 1 in U is taken account above
VectorOps_DDRB.add_row(blockLength, V, row, 1, V, i, dot_u_u, V, row, row + 1, A.col1 - A.col0);
}
// y = -gamma*y
VectorOps_DDRB.scale_row(blockLength, V, row, -gamma, V, row, row + 1, V.col1 - V.col0);
}
/**
* <p>
* Applies the reflectors that have been computed previously to the specified row.
* <br>
* A = A + u*v^T + v*u^T only along the specified row in A.
* </p>
*
* @param blockLength
* @param A Contains the reflectors and the row being updated.
* @param V Contains previously computed 'v' vectors.
* @param row The row of 'A' that is to be updated.
*/
public static void applyReflectorsToRow(int blockLength,
DSubmatrixD1 A,
DSubmatrixD1 V,
int row)
{
int height = Math.Min(blockLength, A.row1 - A.row0);
double[] dataA = A.original.data;
double[] dataV = V.original.data;
int indexU, indexV;
// for each previously computed reflector
for (int i = 0; i < row; i++)
{
int width = Math.Min(blockLength, A.col1 - A.col0);
indexU = A.original.numCols * A.row0 + height * A.col0 + i * width + row;
indexV = V.original.numCols * V.row0 + height * V.col0 + i * width + row;
double u_row = (i + 1 == row) ? 1.0 : dataA[indexU];
double v_row = dataV[indexV];
// take in account the leading one
double before = A.get(i, i + 1);
A.set(i, i + 1, 1);
// grab only the relevant row from A = A + u*v^T + v*u^T
VectorOps_DDRB.add_row(blockLength, A, row, 1, V, i, u_row, A, row, row, A.col1 - A.col0);
VectorOps_DDRB.add_row(blockLength, A, row, 1, A, i, v_row, A, row, row, A.col1 - A.col0);
A.set(i, i + 1, before);
}
}
public static void add_row(int blockLength,
DSubmatrixD1 A, int rowA, double alpha,
DSubmatrixD1 B, int rowB, double beta,
DSubmatrixD1 C, int rowC,
int zeroOffset, int end)
{
int offset = rowA + zeroOffset;
if (C.col0 + offset >= C.col1)
{
return;
}
// handle leading one
C.set(rowC, offset, alpha + B.get(rowB, offset) * beta);
VectorOps_DDRB.add_row(blockLength, A, rowA, alpha, B, rowB, beta, C, rowC, offset + 1, end);
}
/**
* Scales the elements in the specified row starting at element colStart by 'val'.<br>
* W = val*Y
*
* Takes in account zeros and leading one automatically.
*
* @param zeroOffset How far off the diagonal is the first element in the vector.
*/
public static void scale_row(int blockLength,
DSubmatrixD1 Y,
DSubmatrixD1 W,
int row,
int zeroOffset,
double val)
{
int offset = row + zeroOffset;
if (offset >= W.col1 - W.col0)
{
return;
}
// handle the one
W.set(row, offset, val);
// scale rest of the vector
VectorOps_DDRB.scale_row(blockLength, Y, row, val, W, row, offset + 1, Y.col1 - Y.col0);
}
/**
* <p>
* Final computation for a single row of 'v':<br>
* <br>
* v = y -(1/2)γ(y^T*u)*u
* </p>
*
* @param blockLength
* @param A
* @param V
* @param row
* @param gamma
*/
public static void computeRowOfV(int blockLength,
DSubmatrixD1 A,
DSubmatrixD1 V,
int row,
double gamma)
{
// val=(y^T*u)
double val = BlockHouseHolder_DDRB.innerProdRow(blockLength, A, row, V, row, 1);
// take in account the one
double before = A.get(row, row + 1);
A.set(row, row + 1, 1);
// v = y - (1/2)gamma*val * u
VectorOps_DDRB.add_row(blockLength, V, row, 1, A, row, -0.5 * gamma * val, V, row, row + 1,
A.col1 - A.col0);
A.set(row, row + 1, before);
}