/**
* <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);
}
}
/**
* <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,
FSubmatrixD1 A,
FSubmatrixD1 V,
int row,
float 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
float dot_v_u = BlockHouseHolder_FDRB.innerProdRow(blockLength, A, row, V, i, 1);
// u_i^t*u
float dot_u_u = BlockHouseHolder_FDRB.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_FDRB.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_FDRB.add_row(blockLength, V, row, 1, V, i, dot_u_u, V, row, row + 1, A.col1 - A.col0);
}
// y = -gamma*y
VectorOps_FDRB.scale_row(blockLength, V, row, -gamma, V, row, row + 1, V.col1 - V.col0);
}
/**
* <p>
* Given an already computed tridiagonal decomposition, compute the V row block vector.<br>
* <br>
* y(:) = A*u<br>
* v(i) = y - (1/2)*γ*(y^T*u)*u
* </p>
*/
public static void computeV_blockVector(int blockLength,
FSubmatrixD1 A,
float[] gammas,
FSubmatrixD1 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);
for (int i = 0; i < num; i++)
{
float gamma = gammas[A.row0 + i];
// compute y
computeY(blockLength, A, V, i, gamma);
// compute v from y
computeRowOfV(blockLength, A, V, i, gamma);
}
}
/**
* <p>
* Performs a matrix multiplication on {@link FMatrixRBlock} submatrices.<br>
* <br>
* c = c + a * b <br>
* <br>
* </p>
*
* <p>
* It is assumed that all submatrices start at the beginning of a block and end at the end of a block.
* </p>
*
* @param blockLength Size of the blocks in the submatrix.
* @param A A submatrix. Not modified.
* @param B A submatrix. Not modified.
* @param C Result of the operation. Modified,
*/
public static void multPlus(int blockLength,
FSubmatrixD1 A, FSubmatrixD1 B,
FSubmatrixD1 C)
{
// checkInput( blockLength,A,B,C);
for (int i = A.row0; i < A.row1; i += blockLength)
{
int heightA = Math.Min(blockLength, A.row1 - i);
for (int j = B.col0; j < B.col1; j += blockLength)
{
int widthB = Math.Min(blockLength, B.col1 - j);
int indexC = (i - A.row0 + C.row0) * C.original.numCols + (j - B.col0 + C.col0) * heightA;
for (int k = A.col0; k < A.col1; k += blockLength)
{
int widthA = Math.Min(blockLength, A.col1 - k);
int indexA = i * A.original.numCols + k * heightA;
int indexB = (k - A.col0 + B.row0) * B.original.numCols + j * widthA;
InnerMultiplication_FDRB.blockMultPlus(A.original.data, B.original.data, C.original.data,
indexA, indexB, indexC, heightA, widthA, widthB);
}
}
}
}
public static bool lower(FSubmatrixD1 T)
{
int n = T.row1 - T.row0;
int indexT = T.row0 * T.original.numCols + T.col0 * n;
return(lower(T.original.data, indexT, n));
}
/**
* <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,
FSubmatrixD1 Y, FSubmatrixD1 W,
float[] beta, int betaIndex)
{
int heightY = Y.row1 - Y.row0;
CommonOps_FDRM.fill(W.original, 0);
// W = -beta*v(1)
BlockHouseHolder_FDRB.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
float b = -beta[betaIndex++];
// w = w -beta*W*(Y^T*u)
for (int j = 0; j < i; j++)
{
float yv = BlockHouseHolder_FDRB.innerProdRow(blockLength, Y, i, Y, j, 1);
VectorOps_FDRB.add_row(blockLength, W, i, 1, W, j, b * yv, W, i, 1, Y.col1 - Y.col0);
}
//w=w -beta*u + stuff above
BlockHouseHolder_FDRB.add_row(blockLength, Y, i, b, W, i, 1, W, i, 1, Y.col1 - Y.col0);
}
}
public static void multTransB(FMatrixRBlock A, FMatrixRBlock B, FMatrixRBlock C)
{
if (A.numCols != B.numCols)
{
throw new ArgumentException("Columns in A are incompatible with columns in B");
}
if (A.numRows != C.numRows)
{
throw new ArgumentException("Rows in A are incompatible with rows in C");
}
if (B.numRows != C.numCols)
{
throw new ArgumentException("Rows in B are incompatible with columns in C");
}
if (A.blockLength != B.blockLength || A.blockLength != C.blockLength)
{
throw new ArgumentException("Block lengths are not all the same.");
}
int blockLength = A.blockLength;
FSubmatrixD1 Asub = new FSubmatrixD1(A, 0, A.numRows, 0, A.numCols);
FSubmatrixD1 Bsub = new FSubmatrixD1(B, 0, B.numRows, 0, B.numCols);
FSubmatrixD1 Csub = new FSubmatrixD1(C, 0, C.numRows, 0, C.numCols);
MatrixMult_FDRB.multTransB(blockLength, Asub, Bsub, Csub);
}
/**
* <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,
FSubmatrixD1 A,
float[] gammas,
FSubmatrixD1 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_FDRB.computeHouseHolderRow(blockLength, A, gammas, i);
float 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);
}
}
}
public virtual void invert(FMatrixRBlock A_inv)
{
FMatrixRBlock T = decomposer.getT(null);
if (A_inv.numRows != T.numRows || A_inv.numCols != T.numCols)
{
throw new ArgumentException("Unexpected number or rows and/or columns");
}
if (temp == null || temp.Length < blockLength * blockLength)
{
temp = new float[blockLength * blockLength];
}
// zero the upper triangular portion of A_inv
MatrixOps_FDRB.zeroTriangle(true, A_inv);
FSubmatrixD1 L = new FSubmatrixD1(T);
FSubmatrixD1 B = new FSubmatrixD1(A_inv);
// invert L from cholesky decomposition and write the solution into the lower
// triangular portion of A_inv
// B = inv(L)
TriangularSolver_FDRB.invert(blockLength, false, L, B, temp);
// B = L^-T * B
// todo could speed up by taking advantage of B being lower triangular
// todo take advantage of symmetry
TriangularSolver_FDRB.solveL(blockLength, L, B, 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);
}
/**
* Divides the elements at the specified column by 'val'. Takes in account
* leading zeros and one.
*/
public static void divideElementsCol(int blockLength,
FSubmatrixD1 Y, int col, float val)
{
int width = Math.Min(blockLength, Y.col1 - Y.col0);
float[] dataY = Y.original.data;
for (int i = Y.row0; i < Y.row1; i += blockLength)
{
int height = Math.Min(blockLength, Y.row1 - i);
int index = i * Y.original.numCols + height * Y.col0 + col;
if (i == Y.row0)
{
index += width * (col + 1);
for (int k = col + 1; k < height; k++, index += width)
{
dataY[index] /= val;
}
}
else
{
int endIndex = index + width * height;
//for( int k = 0; k < height; k++
for (; index != endIndex; index += width)
{
dataY[index] /= val;
}
}
}
}
/**
* <p>
* Sets W to its initial value using the first column of 'y' and the value of 'b':
* <br>
* W = -βv<br>
* <br>
* where v = Y(:,0).
* </p>
*
* @param blockLength size of the inner block
* @param W Submatrix being initialized.
* @param Y Contains householder vector
* @param widthB How wide the W block matrix is.
* @param b beta
*/
public static void initializeW(int blockLength,
FSubmatrixD1 W, FSubmatrixD1 Y,
int widthB, float b)
{
float[] dataW = W.original.data;
float[] dataY = Y.original.data;
for (int i = W.row0; i < W.row1; i += blockLength)
{
int heightW = Math.Min(blockLength, W.row1 - i);
int indexW = i * W.original.numCols + heightW * W.col0;
int indexY = i * Y.original.numCols + heightW * Y.col0;
// take in account the first element in V being 1
if (i == W.row0)
{
dataW[indexW] = -b;
indexW += widthB;
indexY += widthB;
for (int k = 1; k < heightW; k++, indexW += widthB, indexY += widthB)
{
dataW[indexW] = -b * dataY[indexY];
}
}
else
{
for (int k = 0; k < heightW; k++, indexW += widthB, indexY += widthB)
{
dataW[indexW] = -b * dataY[indexY];
}
}
}
}
public static float innerProdRowSymm(int blockLength,
FSubmatrixD1 A,
int rowA,
FSubmatrixD1 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'
float total = B.get(offset, rowB);
total += VectorOps_FDRB.dot_row_col(blockLength, A, rowA, B, rowB, offset + 1, rowB);
total += VectorOps_FDRB.dot_row(blockLength, A, rowA, B, rowB, rowB, A.col1 - A.col0);
return(total);
}
else
{
// take in account the one in 'A'
float total = B.get(rowB, offset);
total += VectorOps_FDRB.dot_row(blockLength, A, rowA, B, rowB, offset + 1, A.col1 - A.col0);
return(total);
}
}
/**
* <p>
* Performs a matrix multiplication with a transpose on {@link FMatrixRBlock} submatrices.<br>
* <br>
* c = a * b <sup>T</sup> <br>
* <br>
* </p>
*
* <p>
* It is assumed that all submatrices start at the beginning of a block and end at the end of a block.
* </p>
*
* @param blockLength Length of the blocks in the submatrix.
* @param A A submatrix. Not modified.
* @param B A submatrix. Not modified.
* @param C Result of the operation. Modified,
*/
public static void multTransB(int blockLength,
FSubmatrixD1 A, FSubmatrixD1 B,
FSubmatrixD1 C)
{
for (int i = A.row0; i < A.row1; i += blockLength)
{
int heightA = Math.Min(blockLength, A.row1 - i);
for (int j = B.row0; j < B.row1; j += blockLength)
{
int widthC = Math.Min(blockLength, B.row1 - j);
int indexC = (i - A.row0 + C.row0) * C.original.numCols + (j - B.row0 + C.col0) * heightA;
for (int k = A.col0; k < A.col1; k += blockLength)
{
int widthA = Math.Min(blockLength, A.col1 - k);
int indexA = i * A.original.numCols + k * heightA;
int indexB = j * B.original.numCols + (k - A.col0 + B.col0) * widthC;
if (k == A.col0)
{
InnerMultiplication_FDRB.blockMultSetTransB(A.original.data, B.original.data, C.original.data,
indexA, indexB, indexC, heightA, widthA, widthC);
}
else
{
InnerMultiplication_FDRB.blockMultPlusTransB(A.original.data, B.original.data, C.original.data,
indexA, indexB, indexC, heightA, widthA, widthC);
}
}
}
}
}
/**
* Special multiplication that takes in account the zeros and one in Y, which
* is the matrix that stores the householder vectors.
*
*/
public static void multAdd_zeros(int blockLength,
FSubmatrixD1 Y, FSubmatrixD1 B,
FSubmatrixD1 C)
{
int widthY = Y.col1 - Y.col0;
for (int i = Y.row0; i < Y.row1; i += blockLength)
{
int heightY = Math.Min(blockLength, Y.row1 - i);
for (int j = B.col0; j < B.col1; j += blockLength)
{
int widthB = Math.Min(blockLength, B.col1 - j);
int indexC = (i - Y.row0 + C.row0) * C.original.numCols + (j - B.col0 + C.col0) * heightY;
for (int k = Y.col0; k < Y.col1; k += blockLength)
{
int indexY = i * Y.original.numCols + k * heightY;
int indexB = (k - Y.col0 + B.row0) * B.original.numCols + j * widthY;
if (i == Y.row0)
{
multBlockAdd_zerosone(Y.original.data, B.original.data, C.original.data,
indexY, indexB, indexC, heightY, widthY, widthB);
}
else
{
InnerMultiplication_FDRB.blockMultPlus(Y.original.data, B.original.data, C.original.data,
indexY, indexB, indexC, heightY, widthY, widthB);
}
}
}
}
}
/**
* <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>
* 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(FSubmatrixD1 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_FDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
MatrixMult_FDRB.multTransA(blockLength, W, A, WTA);
BlockHouseHolder_FDRB.multAdd_zeros(blockLength, Y, WTA, A);
}
else if (saveW)
{
BlockHouseHolder_FDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
}
/**
* Computes Y<sup>T</sup>v<sup>(j)</sup>. Where Y are the columns before 'col' and v is the column
* at 'col'. The zeros and ones are taken in account. The solution is a vector with 'col' elements.
*
* width of Y must be along the block of original matrix A
*
* @param temp Temporary storage of least length 'col'
*/
public static void computeY_t_V(int blockLength, FSubmatrixD1 Y,
int col, float[] temp)
{
int widthB = Y.col1 - Y.col0;
for (int j = 0; j < col; j++)
{
temp[j] = innerProdCol(blockLength, Y, col, widthB, j, widthB);
}
}
/**
* 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,
FSubmatrixD1 A,
float[] gammasU,
float[] 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_FDRB.computeHouseHolderCol(blockLength, A, gammasU, i))
{
return(false);
}
// apply to rest of the columns in the column block
BlockHouseHolder_FDRB.rank1UpdateMultR_Col(blockLength, A, i, gammasU[A.col0 + i]);
// apply to the top row block
BlockHouseHolder_FDRB.rank1UpdateMultR_TopRow(blockLength, A, i, gammasU[A.col0 + i]);
Console.WriteLine("After column stuff");
A.original.print();
//-- Apply reflector to the row
if (!BlockHouseHolder_FDRB.computeHouseHolderRow(blockLength, A, gammasV, i))
{
return(false);
}
// apply to rest of the rows in the row block
BlockHouseHolder_FDRB.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>
* From the specified row of Y tau is computed and each element is divided by 'max'.
* See code below:
* </p>
*
* <pre>
* for j=row:Y.numCols
* Y[row][j] = u[row][j] / max
* tau = tau + u[row][j]*u[row][j]
* end
* tau = sqrt(tau)
* if( Y[row][row] < 0 )
* tau = -tau;
* </pre>
*
* @param row Which row in the block will be processed
* @param colStart The first column that computation of tau will start at
* @param max used to normalize and prevent buffer over flow
*
*/
public static float computeTauAndDivideRow(int blockLength,
FSubmatrixD1 Y,
int row, int colStart, float max)
{
int height = Math.Min(blockLength, Y.row1 - Y.row0);
float[] dataY = Y.original.data;
float top = 0;
float norm2 = 0;
int startJ = Y.col0 + colStart - colStart % blockLength;
colStart = colStart % blockLength;
for (int j = startJ; j < Y.col1; j += blockLength)
{
int width = Math.Min(blockLength, Y.col1 - j);
int index = Y.row0 * Y.original.numCols + height * j + row * width;
if (j == startJ)
{
index += colStart;
// save this value so that the sign can be determined later on
top = dataY[index] /= max;
norm2 += top * top;
index++;
for (int k = colStart + 1; k < width; k++)
{
float val = dataY[index++] /= max;
norm2 += val * val;
}
}
else
{
for (int k = 0; k < width; k++)
{
float val = dataY[index++] /= max;
norm2 += val * val;
}
}
}
norm2 = (float)Math.Sqrt(norm2);
if (top < 0)
{
norm2 = -norm2;
}
return(norm2);
}
/**
* <p>
* Computes the inner product of column vector 'colA' against column vector 'colB' while taking account leading zeros and one.<br>
* <br>
* ret = a<sup>T</sup>*b
* </p>
*
* <p>
* Column A is assumed to be a householder vector. Element at 'colA' is one and previous ones are zero.
* </p>
*
* @param blockLength
* @param A block aligned submatrix.
* @param colA Column inside the block of first column vector.
* @param widthA how wide the column block that colA is inside of.
* @param colB Column inside the block of second column vector.
* @param widthB how wide the column block that colB is inside of.
* @return dot product of the two vectors.
*/
public static float innerProdCol(int blockLength, FSubmatrixD1 A,
int colA, int widthA,
int colB, int widthB)
{
float total = 0;
float[] data = A.original.data;
// first column in the blocks
int colBlockA = A.col0 + colA - colA % blockLength;
int colBlockB = A.col0 + colB - colB % blockLength;
colA = colA % blockLength;
colB = colB % blockLength;
// compute dot product down column vectors
for (int i = A.row0; i < A.row1; i += blockLength)
{
int height = Math.Min(blockLength, A.row1 - i);
int indexA = i * A.original.numCols + height * colBlockA + colA;
int indexB = i * A.original.numCols + height * colBlockB + colB;
if (i == A.row0)
{
// handle leading zeros
indexA += widthA * (colA + 1);
indexB += widthB * colA;
// handle leading one
total = data[indexB];
indexB += widthB;
// standard vector dot product
int endA = indexA + (height - colA - 1) * widthA;
for (; indexA != endA; indexA += widthA, indexB += widthB)
{
// for( int k = col+1; k < height; k++ , indexU += width, indexA += width ) {
total += data[indexA] * data[indexB];
}
}
else
{
// standard vector dot product
int endA = indexA + widthA * height;
// for( int k = 0; k < height; k++ ) {
for (; indexA != endA; indexA += widthA, indexB += widthB)
{
total += data[indexA] * data[indexB];
}
}
}
return(total);
}
/**
* Inverts an upper or lower triangular block submatrix.
*
* @param blockLength
* @param upper Is it upper or lower triangular.
* @param T Triangular matrix that is to be inverted. Overwritten with solution. Modified.
* @param temp Work space variable that is size blockLength*blockLength.
*/
public static void invert(int blockLength,
bool upper,
FSubmatrixD1 T,
float[] temp)
{
if (upper)
{
throw new ArgumentException("Upper triangular matrices not supported yet");
}
if (temp.Length < blockLength * blockLength)
{
throw new ArgumentException("Temp must be at least blockLength*blockLength long.");
}
int M = T.row1 - T.row0;
float[] dataT = T.original.data;
int offsetT = T.row0 * T.original.numCols + M * T.col0;
for (int i = 0; i < M; i += blockLength)
{
int heightT = Math.Min(T.row1 - (i + T.row0), blockLength);
int indexII = offsetT + T.original.numCols * (i + T.row0) + heightT * (i + T.col0);
for (int j = 0; j < i; j += blockLength)
{
int widthX = Math.Min(T.col1 - (j + T.col0), blockLength);
for (int w = 0; w < temp.Length; w++)
{
temp[w] = 0;
}
for (int k = j; k < i; k += blockLength)
{
int widthT = Math.Min(T.col1 - (k + T.col0), blockLength);
int indL = offsetT + T.original.numCols * (i + T.row0) + heightT * (k + T.col0);
int indX = offsetT + T.original.numCols * (k + T.row0) + widthT * (j + T.col0);
InnerMultiplication_FDRB.blockMultMinus(dataT, dataT, temp, indL, indX, 0, heightT, widthT, widthX);
}
int indexX = offsetT + T.original.numCols * (i + T.row0) + heightT * (j + T.col0);
InnerTriangularSolver_FDRB.solveL(dataT, temp, heightT, widthX, heightT, indexII, 0);
Array.Copy(temp, 0, dataT, indexX, widthX * heightT);
}
InnerTriangularSolver_FDRB.invertLower(dataT, heightT, indexII);
}
}
/**
* <p>
* Row vector scale:<br>
* scale: b<sub>i</sub> = α*a<sub>i</sub><br>
* where 'a' and 'b' are row vectors within the row block vector A and B.
* </p>
*
* @param A submatrix. Not modified.
* @param rowA which row in A the vector is contained in.
* @param alpha scale factor.
* @param B submatrix that the results are written to. Modified.
* @param offset Index at which the vectors start at.
* @param end Index at which the vectors end at.
*/
public static void scale_row(int blockLength,
FSubmatrixD1 A, int rowA,
float alpha, FSubmatrixD1 B, int rowB,
int offset, int end)
{
float[] dataA = A.original.data;
float[] dataB = B.original.data;
// handle the case where offset is more than a block
int startI = offset - offset % blockLength;
offset = offset % blockLength;
// handle rows in any block
int rowBlockA = A.row0 + rowA - rowA % blockLength;
rowA = rowA % blockLength;
int rowBlockB = B.row0 + rowB - rowB % blockLength;
rowB = rowB % blockLength;
int heightA = Math.Min(blockLength, A.row1 - rowBlockA);
int heightB = Math.Min(blockLength, B.row1 - rowBlockB);
for (int i = startI; i < end; i += blockLength)
{
int segment = Math.Min(blockLength, end - i);
int widthA = Math.Min(blockLength, A.col1 - A.col0 - i);
int widthB = Math.Min(blockLength, B.col1 - B.col0 - i);
int indexA = rowBlockA * A.original.numCols + (A.col0 + i) * heightA + rowA * widthA;
int indexB = rowBlockB * B.original.numCols + (B.col0 + i) * heightB + rowB * widthB;
if (i == startI)
{
indexA += offset;
indexB += offset;
for (int j = offset; j < segment; j++)
{
dataB[indexB++] = alpha * dataA[indexA++];
}
}
else
{
for (int j = 0; j < segment; j++)
{
dataB[indexB++] = alpha * dataA[indexA++];
}
}
}
}
/**
* <p>
* Row vector add:<br>
* add: c<sub>i</sub> = α*a<sub>i</sub> + βB<sub>i</sub><br>
* where 'a', 'b', and 'c' are row vectors within the row block vectors of A, B, and C respectively.
* </p>
*
* @param blockLength Length of each inner matrix block.
* @param A submatrix. Not modified.
* @param rowA which row in A the vector is contained in.
* @param alpha scale factor of A
* @param B submatrix. Not modified.
* @param rowB which row in B the vector is contained in.
* @param beta scale factor of B
* @param C submatrix where the results are written to. Modified.
* @param rowC which row in C is the vector contained.
* @param offset Index at which the vectors start at.
* @param end Index at which the vectors end at.
*/
public static void add_row(int blockLength,
FSubmatrixD1 A, int rowA, float alpha,
FSubmatrixD1 B, int rowB, float beta,
FSubmatrixD1 C, int rowC,
int offset, int end)
{
int heightA = Math.Min(blockLength, A.row1 - A.row0);
int heightB = Math.Min(blockLength, B.row1 - B.row0);
int heightC = Math.Min(blockLength, C.row1 - C.row0);
// handle the case where offset is more than a block
int startI = offset - offset % blockLength;
offset = offset % blockLength;
float[] dataA = A.original.data;
float[] dataB = B.original.data;
float[] dataC = C.original.data;
for (int i = startI; i < end; i += blockLength)
{
int segment = Math.Min(blockLength, end - i);
int widthA = Math.Min(blockLength, A.col1 - A.col0 - i);
int widthB = Math.Min(blockLength, B.col1 - B.col0 - i);
int widthC = Math.Min(blockLength, C.col1 - C.col0 - i);
int indexA = A.row0 * A.original.numCols + (A.col0 + i) * heightA + rowA * widthA;
int indexB = B.row0 * B.original.numCols + (B.col0 + i) * heightB + rowB * widthB;
int indexC = C.row0 * C.original.numCols + (C.col0 + i) * heightC + rowC * widthC;
if (i == startI)
{
indexA += offset;
indexB += offset;
indexC += offset;
for (int j = offset; j < segment; j++)
{
dataC[indexC++] = alpha * dataA[indexA++] + beta * dataB[indexB++];
}
}
else
{
for (int j = 0; j < segment; j++)
{
dataC[indexC++] = alpha * dataA[indexA++] + beta * dataB[indexB++];
}
}
}
}
/**
* <p>
* Rank N update function for a symmetric inner submatrix and only operates on the upper
* triangular portion of the submatrix.<br>
* <br>
* A = A - B <sup>T</sup>B
* </p>
*/
public static void symmRankNMinus_U(int blockLength,
FSubmatrixD1 A, FSubmatrixD1 B)
{
int heightB = B.row1 - B.row0;
if (heightB > blockLength)
{
throw new ArgumentException("Height of B cannot be greater than the block length");
}
int N = B.col1 - B.col0;
if (A.col1 - A.col0 != N)
{
throw new ArgumentException("A does not have the expected number of columns based on B's width");
}
if (A.row1 - A.row0 != N)
{
throw new ArgumentException("A does not have the expected number of rows based on B's width");
}
for (int i = B.col0; i < B.col1; i += blockLength)
{
int indexB_i = B.row0 * B.original.numCols + i * heightB;
int widthB_i = Math.Min(blockLength, B.col1 - i);
int rowA = i - B.col0 + A.row0;
int heightA = Math.Min(blockLength, A.row1 - rowA);
for (int j = i; j < B.col1; j += blockLength)
{
int widthB_j = Math.Min(blockLength, B.col1 - j);
int indexA = rowA * A.original.numCols + (j - B.col0 + A.col0) * heightA;
int indexB_j = B.row0 * B.original.numCols + j * heightB;
if (i == j)
{
// only the upper portion of this block needs to be modified since it is along a diagonal
multTransABlockMinus_U(B.original.data, A.original.data,
indexB_i, indexB_j, indexA, heightB, widthB_i, widthB_j);
}
else
{
multTransABlockMinus(B.original.data, A.original.data,
indexB_i, indexB_j, indexA, heightB, widthB_i, widthB_j);
}
}
}
}
/**
* <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 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);
}
/**
* <p>
* From the specified column of Y tau is computed and each element is divided by 'max'.
* See code below:
* </p>
*
* <pre>
* for i=col:Y.numRows
* Y[i][col] = u[i][col] / max
* tau = tau + u[i][col]*u[i][col]
* end
* tau = sqrt(tau)
* if( Y[col][col] < 0 )
* tau = -tau;
* </pre>
*
*/
public static float computeTauAndDivideCol(int blockLength,
FSubmatrixD1 Y,
int col, float max)
{
int width = Math.Min(blockLength, Y.col1 - Y.col0);
float[] dataY = Y.original.data;
float top = 0;
float norm2 = 0;
for (int i = Y.row0; i < Y.row1; i += blockLength)
{
int height = Math.Min(blockLength, Y.row1 - i);
int index = i * Y.original.numCols + height * Y.col0 + col;
if (i == Y.row0)
{
index += width * col;
// save this value so that the sign can be determined later on
top = dataY[index] /= max;
norm2 += top * top;
index += width;
for (int k = col + 1; k < height; k++, index += width)
{
float val = dataY[index] /= max;
norm2 += val * val;
}
}
else
{
for (int k = 0; k < height; k++, index += width)
{
float val = dataY[index] /= max;
norm2 += val * val;
}
}
}
norm2 = (float)Math.Sqrt(norm2);
if (top < 0)
{
norm2 = -norm2;
}
return(norm2);
}
/**
* <p>
* Rank N update function for a symmetric inner submatrix and only operates on the lower
* triangular portion of the submatrix.<br>
* <br>
* A = A - B*B<sup>T</sup><br>
* </p>
*/
public static void symmRankNMinus_L(int blockLength,
FSubmatrixD1 A, FSubmatrixD1 B)
{
int widthB = B.col1 - B.col0;
if (widthB > blockLength)
{
throw new ArgumentException("Width of B cannot be greater than the block length");
}
int N = B.row1 - B.row0;
if (A.col1 - A.col0 != N)
{
throw new ArgumentException("A does not have the expected number of columns based on B's height");
}
if (A.row1 - A.row0 != N)
{
throw new ArgumentException("A does not have the expected number of rows based on B's height");
}
for (int i = B.row0; i < B.row1; i += blockLength)
{
int heightB_i = Math.Min(blockLength, B.row1 - i);
int indexB_i = i * B.original.numCols + heightB_i * B.col0;
int rowA = i - B.row0 + A.row0;
int heightA = Math.Min(blockLength, A.row1 - rowA);
for (int j = B.row0; j <= i; j += blockLength)
{
int widthB_j = Math.Min(blockLength, B.row1 - j);
int indexA = rowA * A.original.numCols + (j - B.row0 + A.col0) * heightA;
int indexB_j = j * B.original.numCols + widthB_j * B.col0;
if (i == j)
{
multTransBBlockMinus_L(B.original.data, A.original.data,
indexB_i, indexB_j, indexA, widthB, heightB_i, widthB_j);
}
else
{
multTransBBlockMinus(B.original.data, A.original.data,
indexB_i, indexB_j, indexA, widthB, heightB_i, widthB_j);
}
}
}
}
/**
* 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(FMatrixRBlock B, bool isIdentity)
{
int minDimen = Math.Min(dataA.numCols, dataA.numRows);
FSubmatrixD1 subB = new FSubmatrixD1(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_FDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0);
}
// Apply the Qi to Q
BlockHouseHolder_FDRB.multTransA_vecCol(blockLength, Y, subB, WTA);
MatrixMult_FDRB.multPlus(blockLength, W, WTA, subB);
}
}
