/**
* <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);
}
}
/**
* <p>
* Performs a tridiagonal decomposition on the upper row only.
* </p>
*
* <p>
* For each row 'a' in 'A':
* Compute 'u' the householder reflector.
* y(:) = A*u
* v(i) = y - (1/2)*(y^T*u)*u
* a(i+1) = a(i) - u*γ*v^T - v*u^t
* </p>
*
* @param blockLength Size of a block
* @param A is the row block being decomposed. Modified.
* @param gammas Householder gammas.
* @param V Where computed 'v' are stored in a row block. Modified.
*/
public static void tridiagUpperRow(int blockLength,
DSubmatrixD1 A,
double[] gammas,
DSubmatrixD1 V)
{
int blockHeight = Math.Min(blockLength, A.row1 - A.row0);
if (blockHeight <= 1)
{
return;
}
int width = A.col1 - A.col0;
int num = Math.Min(width - 1, blockHeight);
int applyIndex = Math.Min(width, blockHeight);
// step through rows in the block
for (int i = 0; i < num; i++)
{
// compute the new reflector and save it in a row in 'A'
BlockHouseHolder_DDRB.computeHouseHolderRow(blockLength, A, gammas, i);
double gamma = gammas[A.row0 + i];
// compute y
computeY(blockLength, A, V, i, gamma);
// compute v from y
computeRowOfV(blockLength, A, V, i, gamma);
// Apply the reflectors to the next row in 'A' only
if (i + 1 < applyIndex)
{
applyReflectorsToRow(blockLength, A, V, i + 1);
}
}
}
/**
* <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);
}
/**
* Performs a standard bidiagonal decomposition just on the outer blocks of the provided matrix
*
* @param blockLength
* @param A
* @param gammasU
*/
public static bool bidiagOuterBlocks(int blockLength,
DSubmatrixD1 A,
double[] gammasU,
double[] gammasV)
{
// Console.WriteLine("---------- Orig");
// A.original.print();
int width = Math.Min(blockLength, A.col1 - A.col0);
int height = Math.Min(blockLength, A.row1 - A.row0);
int min = Math.Min(width, height);
for (int i = 0; i < min; i++)
{
//--- Apply reflector to the column
// compute the householder vector
if (!BlockHouseHolder_DDRB.computeHouseHolderCol(blockLength, A, gammasU, i))
{
return(false);
}
// apply to rest of the columns in the column block
BlockHouseHolder_DDRB.rank1UpdateMultR_Col(blockLength, A, i, gammasU[A.col0 + i]);
// apply to the top row block
BlockHouseHolder_DDRB.rank1UpdateMultR_TopRow(blockLength, A, i, gammasU[A.col0 + i]);
Console.WriteLine("After column stuff");
A.original.print();
//-- Apply reflector to the row
if (!BlockHouseHolder_DDRB.computeHouseHolderRow(blockLength, A, gammasV, i))
{
return(false);
}
// apply to rest of the rows in the row block
BlockHouseHolder_DDRB.rank1UpdateMultL_Row(blockLength, A, i, i + 1, gammasV[A.row0 + i]);
Console.WriteLine("After update row");
A.original.print();
// apply to the left column block
// TODO THIS WON'T WORK!!!!!!!!!!!!!
// Needs the whole matrix to have been updated by the left reflector to compute the correct solution
// rank1UpdateMultL_LeftCol(blockLength,A,i,i+1,gammasV[A.row0+i]);
Console.WriteLine("After row stuff");
A.original.print();
}
return(true);
}
/**
* <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);
}