/**
* <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,
FSubmatrixD1 A,
FSubmatrixD1 V,
int row)
{
int height = Math.Min(blockLength, A.row1 - A.row0);
float[] dataA = A.original.data;
float[] 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;
float u_row = (i + 1 == row) ? 1.0f : dataA[indexU];
float v_row = dataV[indexV];
// take in account the leading one
float 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_FDRB.add_row(blockLength, A, row, 1, V, i, u_row, A, row, row, A.col1 - A.col0);
VectorOps_FDRB.add_row(blockLength, A, row, 1, A, i, v_row, A, row, row, A.col1 - A.col0);
A.set(i, i + 1, before);
}
}
public virtual bool decompose(FMatrixRBlock orig)
{
if (orig.numCols != orig.numRows)
{
throw new ArgumentException("Input matrix must be square.");
}
init(orig);
FSubmatrixD1 subA = new FSubmatrixD1(A);
FSubmatrixD1 subV = new FSubmatrixD1(V);
FSubmatrixD1 subU = new FSubmatrixD1(A);
int N = orig.numCols;
for (int i = 0; i < N; i += A.blockLength)
{
// Console.WriteLine("-------- triag i "+i);
int height = Math.Min(A.blockLength, A.numRows - i);
subA.col0 = subU.col0 = i;
subA.row0 = subU.row0 = i;
subU.row1 = subU.row0 + height;
subV.col0 = i;
subV.row1 = height;
subV.original.reshape(subV.row1, subV.col1, false);
// bidiagonalize the top row
TridiagonalHelper_FDRB.tridiagUpperRow(A.blockLength, subA, gammas, subV);
// apply Householder reflectors to the lower portion using block multiplication
if (subU.row1 < orig.numCols)
{
// take in account the 1 in the last row. The others are skipped over.
float before = subU.get(A.blockLength - 1, A.blockLength);
subU.set(A.blockLength - 1, A.blockLength, 1);
// A = A + U*V^T + V*U^T
multPlusTransA(A.blockLength, subU, subV, subA);
multPlusTransA(A.blockLength, subV, subU, subA);
subU.set(A.blockLength - 1, A.blockLength, before);
}
}
return(true);
}
private bool decomposeLower()
{
int blockLength = T.blockLength;
subA.set(T);
subB.set(T);
subC.set(T);
for (int i = 0; i < T.numCols; i += blockLength)
{
int widthA = Math.Min(blockLength, T.numCols - i);
subA.col0 = i;
subA.col1 = i + widthA;
subA.row0 = subA.col0;
subA.row1 = subA.col1;
subB.col0 = i;
subB.col1 = i + widthA;
subB.row0 = i + widthA;
subB.row1 = T.numRows;
subC.col0 = i + widthA;
subC.col1 = T.numRows;
subC.row0 = i + widthA;
subC.row1 = T.numRows;
// cholesky on inner block A
if (!InnerCholesky_FDRB.lower(subA))
{
return(false);
}
// on the last block these operations are not needed.
if (widthA == blockLength)
{
// B = L^-1 B
TriangularSolver_FDRB.solveBlock(blockLength, false, subA, subB, false, true);
// C = C - B * B^T
InnerRankUpdate_FDRB.symmRankNMinus_L(blockLength, subC, subB);
}
}
MatrixOps_FDRB.zeroTriangle(true, T);
return(true);
}
/**
* <p>
* Computes the householder vector that is used to create reflector for the column.
* The results are stored in the original matrix.
* </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 computeHouseHolderCol(int blockLength, FSubmatrixD1 Y,
float[] gamma, int i)
{
float max = BlockHouseHolder_FDRB.findMaxCol(blockLength, Y, i);
if (max == 0.0f)
{
return(false);
}
else
{
// computes tau and normalizes u by max
float tau = computeTauAndDivideCol(blockLength, Y, i, max);
// divide u by u_0
float u_0 = Y.get(i, i) + tau;
divideElementsCol(blockLength, Y, i, u_0);
gamma[Y.col0 + i] = u_0 / tau;
tau *= max;
// after the reflector is applied the column would be all zeros but be -tau in the first element
Y.set(i, i, -tau);
}
return(true);
}
/**
* <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, FSubmatrixD1 Y,
float[] gamma, int i)
{
float max = BlockHouseHolder_FDRB.findMaxRow(blockLength, Y, i, i + 1);
if (max == 0.0f)
{
return(false);
}
else
{
// computes tau and normalizes u by max
float tau = computeTauAndDivideRow(blockLength, Y, i, i + 1, max);
// divide u by u_0
float u_0 = Y.get(i, i + 1) + tau;
VectorOps_FDRB.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);
}
private void replaceZeros(FSubmatrixD1 subU)
{
int N = Math.Min(A.blockLength, subU.col1 - subU.col0);
for (int i = 0; i < N; i++)
{
// save the zeros
for (int j = 0; j <= i; j++)
{
subU.set(i, j, zerosM.get(i, j));
}
// save the one
if (subU.col0 + i + 1 < subU.original.numCols)
{
subU.set(i, i + 1, zerosM.get(i, i + 1));
}
}
}
/**
* <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,
FSubmatrixD1 A,
FSubmatrixD1 V,
int row,
float gamma)
{
// val=(y^T*u)
float val = BlockHouseHolder_FDRB.innerProdRow(blockLength, A, row, V, row, 1);
// take in account the one
float before = A.get(row, row + 1);
A.set(row, row + 1, 1);
// v = y - (1/2)gamma*val * u
VectorOps_FDRB.add_row(blockLength, V, row, 1, A, row, -0.5f * gamma * val, V, row, row + 1,
A.col1 - A.col0);
A.set(row, row + 1, before);
}
/**
* <p>
* Multiples the appropriate submatrix of A by the specified reflector and stores
* the result ('y') in V.<br>
* <br>
* y = A*u<br>
* </p>
*
* @param blockLength
* @param A Contains the 'A' matrix and 'u' vector.
* @param V Where resulting 'y' row vectors are stored.
* @param row row in matrix 'A' that 'u' vector and the row in 'V' that 'y' is stored in.
*/
public static void multA_u(int blockLength,
FSubmatrixD1 A,
FSubmatrixD1 V,
int row)
{
int heightMatA = A.row1 - A.row0;
for (int i = row + 1; i < heightMatA; i++)
{
float val = innerProdRowSymm(blockLength, A, row, A, i, 1);
V.set(row, i, val);
}
}
public static void add_row(int blockLength,
FSubmatrixD1 A, int rowA, float alpha,
FSubmatrixD1 B, int rowB, float beta,
FSubmatrixD1 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_FDRB.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,
FSubmatrixD1 Y,
FSubmatrixD1 W,
int row,
int zeroOffset,
float 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_FDRB.scale_row(blockLength, Y, row, val, W, row, offset + 1, Y.col1 - Y.col0);
}