/**
* <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);
}
}
}
/**
* 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);
}