org.ejml.dense.block.decomposition.qr.BlockHouseHolder_DDRB Maven / Gradle / Ivy
/*
* Copyright (c) 2009-2017, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.dense.block.decomposition.qr;
import org.ejml.data.DMatrixRBlock;
import org.ejml.data.DSubmatrixD1;
import org.ejml.dense.block.InnerMultiplication_DDRB;
import org.ejml.dense.block.VectorOps_DDRB;
/**
*
*
* Contains various helper functions for performing a block matrix QR decomposition.
*
*
*
* Assumptions:
*
* - All submatrices are aligned along the inner blocks of the {@link DMatrixRBlock}.
*
- Some times vectors are assumed to have leading zeros and a one.
*
*
* @author Peter Abeles
*/
public class BlockHouseHolder_DDRB {
/**
* Performs a standard QR decomposition on the specified submatrix that is one block wide.
*
* @param blockLength
* @param Y
* @param gamma
*/
public static boolean decomposeQR_block_col( final int blockLength ,
final DSubmatrixD1 Y ,
final double gamma[] )
{
int width = Y.col1-Y.col0;
int height = Y.row1-Y.row0;
int min = Math.min(width,height);
for( int i = 0; i < min; i++ ) {
// compute the householder vector
if (!computeHouseHolderCol(blockLength, Y, gamma, i))
return false;
// apply to rest of the columns in the block
rank1UpdateMultR_Col(blockLength,Y,i,gamma[Y.col0+i]);
}
return true;
}
/**
*
* Computes the householder vector that is used to create reflector for the column.
* The results are stored in the original matrix.
*
*
*
* The householder vector 'u' is computed as follows:
*
* u(1) = 1
* u(i) = x(i)/(τ + x(1))
*
*
* 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 boolean computeHouseHolderCol( final int blockLength, final DSubmatrixD1 Y,
final double[] gamma, final int i) {
double max = BlockHouseHolder_DDRB.findMaxCol(blockLength,Y,i);
if( max == 0.0 ) {
return false;
} else {
// computes tau and normalizes u by max
double tau = computeTauAndDivideCol(blockLength, Y, i, max);
// divide u by u_0
double 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;
}
/**
*
* Computes the householder vector from the specified row
*
*
*
* The householder vector 'u' is computed as follows:
*
* u(1) = 1
* u(i) = x(i)/(τ + x(1))
*
*
* 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 boolean computeHouseHolderRow( final int blockLength, final DSubmatrixD1 Y,
final double[] gamma, final 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;
}
/**
*
* Applies a householder reflector stored in column 'col' to the remainder of the columns
* in the block after it. Takes in account leading zeros and one.
*
* A = (I - γ*u*uT)*A
*
*
* @param A submatrix that is at most one block wide and aligned along inner blocks
* @param col The column in A containing 'u'
*
*/
public static void rank1UpdateMultR_Col(final int blockLength ,
final DSubmatrixD1 A , final int col , final double gamma )
{
final int width = Math.min(blockLength,A.col1 - A.col0);
final double dataA[] = A.original.data;
for( int j = col+1; j < width; j++ ) {
// total = U^T * A(:,j)
double total = innerProdCol(blockLength, A, col, width, j, width);
total *= gamma;
// A(:,j) - gamma*U*total
for( int i = A.row0; i < A.row1; i += blockLength ) {
int height = Math.min( blockLength , A.row1 - i );
int indexU = i*A.original.numCols + height*A.col0 + col;
int indexA = i*A.original.numCols + height*A.col0 + j;
if( i == A.row0 ) {
indexU += width*(col+1);
indexA += width*col;
dataA[ indexA ] -= total;
indexA += width;
for( int k = col+1; k < height; k++ , indexU += width, indexA += width ) {
dataA[ indexA ] -= total*dataA[ indexU ];
}
} else {
int endU = indexU + width*height;
// for( int k = 0; k < height; k++
for( ; indexU != endU; indexU += width, indexA += width ) {
dataA[ indexA ] -= total*dataA[ indexU ];
}
}
}
}
}
/**
*
* Applies a householder reflector stored in column 'col' to the top block row (excluding
* the first column) of A. Takes in account leading zeros and one.
*
* A = (I - γ*u*uT)*A
*
*
* @param A submatrix that is at most one block wide and aligned along inner blocks
* @param col The column in A containing 'u'
*
*/
public static void rank1UpdateMultR_TopRow(final int blockLength ,
final DSubmatrixD1 A , final int col , final double gamma )
{
final double dataA[] = A.original.data;
final int widthCol = Math.min( blockLength , A.col1 - col );
// step through columns in top block, skipping over the first block
for( int colStartJ = A.col0 + blockLength; colStartJ < A.col1; colStartJ += blockLength ) {
final int widthJ = Math.min( blockLength , A.col1 - colStartJ);
for( int j = 0; j < widthJ; j++ ) {
// total = U^T * A(:,j) * gamma
double total = innerProdCol(blockLength, A, col, widthCol, (colStartJ-A.col0)+j, widthJ)*gamma;
// A(:,j) - gamma*U*total
// just update the top most block
int i = A.row0;
int height = Math.min( blockLength , A.row1 - i );
int indexU = i*A.original.numCols + height*A.col0 + col;
int indexA = i*A.original.numCols + height*colStartJ + j;
// take in account zeros and one
indexU += widthCol*(col+1);
indexA += widthJ*col;
dataA[ indexA ] -= total;
indexA += widthJ;
for( int k = col+1; k < height; k++ , indexU += widthCol, indexA += widthJ ) {
dataA[ indexA ] -= total*dataA[ indexU ];
}
}
}
}
/**
*
* Applies a householder reflector stored in row 'row' to the remainder of the row
* in the block after it. Takes in account leading zeros and one.
*
* A = A*(I - γ*u*uT)
*
*
* @param A submatrix that is block aligned
* @param row The row in A containing 'u'
* @param colStart First index in 'u' that the reflector starts at
*
*/
public static void rank1UpdateMultL_Row( final int blockLength ,
final DSubmatrixD1 A ,
final int row , final int colStart , final double gamma )
{
final int height = Math.min(blockLength,A.row1 - A.row0);
final double dataA[] = A.original.data;
int zeroOffset = colStart-row;
for( int i = row+1; i < height; i++ ) {
// total = U^T * A(i,:)
double total = innerProdRow(blockLength, A, row, A , i, zeroOffset );
total *= gamma;
// A(i,:) - gamma*U*total
for( int j = A.col0; j < A.col1; j += blockLength ) {
int width = Math.min( blockLength , A.col1 - j );
int indexU = A.row0*A.original.numCols + height*j + row*width;
int indexA = A.row0*A.original.numCols + height*j + i*width;
if( j == A.col0 ) {
indexU += colStart+1;
indexA += colStart;
dataA[indexA++] -= total;
for( int k = colStart+1; k < width; k++ ) {
dataA[ indexA++ ] -= total*dataA[ indexU++ ];
}
} else {
for( int k = 0; k < width; k++ ) {
dataA[ indexA++ ] -= total*dataA[ indexU++ ];
}
}
}
}
}
/**
*
* Applies a householder reflector stored in row 'row' to the left column block.
* Takes in account leading zeros and one.
*
* A = A*(I - γ*u*uT)
*
*
* @param A submatrix that is block aligned
* @param row The row in A containing 'u'
* @param zeroOffset How far off the diagonal is the first element in 'u'
*
*/
public static void rank1UpdateMultL_LeftCol( final int blockLength ,
final DSubmatrixD1 A ,
final int row , final double gamma , int zeroOffset )
{
final int heightU = Math.min(blockLength,A.row1 - A.row0);
final int width = Math.min(blockLength,A.col1-A.col0);
final double data[] = A.original.data;
for( int blockStart = A.row0+blockLength; blockStart < A.row1; blockStart += blockLength) {
final int heightA = Math.min(blockLength,A.row1 - blockStart);
for( int i = 0; i < heightA; i++ ) {
// total = U^T * A(i,:)
double total = innerProdRow(blockLength, A, row, A, i+(blockStart-A.row0), zeroOffset);
total *= gamma;
// A(i,:) - gamma*U*total
// plusScale_row(blockLength,);
int indexU = A.row0*A.original.numCols + heightU*A.col0 + row*width;
int indexA = blockStart*A.original.numCols + heightA*A.col0 + i*width;
// skip over zeros and assume first element in U is 1
indexU += zeroOffset+1;
indexA += zeroOffset;
data[indexA++] -= total;
for( int k = zeroOffset+1; k < width; k++ ) {
data[ indexA++ ] -= total*data[ indexU++ ];
}
}
}
}
/**
*
* Computes the inner product of column vector 'colA' against column vector 'colB' while taking account leading zeros and one.
*
* ret = aT*b
*
*
*
* Column A is assumed to be a householder vector. Element at 'colA' is one and previous ones are zero.
*
*
* @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 double innerProdCol( int blockLength, DSubmatrixD1 A,
int colA, int widthA,
int colB, int widthB ) {
double total = 0;
final double data[] = A.original.data;
// first column in the blocks
final int colBlockA = A.col0 + colA - colA % blockLength;
final 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;
}
/**
*
* Computes the inner product of row vector 'rowA' against row vector 'rowB' while taking account leading zeros and one.
*
* ret = aT*b
*
*
*
* Row A is assumed to be a householder vector. Element at 'colStartA' is one and previous elements are zero.
*
*
* @param blockLength
* @param A block aligned submatrix.
* @param rowA Row index inside the sub-matrix of first row vector has zeros and ones..
* @param rowB Row index inside the sub-matrix of second row vector.
* @return dot product of the two vectors.
*/
public static double innerProdRow(int blockLength,
DSubmatrixD1 A,
int rowA,
DSubmatrixD1 B,
int rowB, int zeroOffset ) {
int offset = rowA + zeroOffset;
if( offset + B.col0 >= B.col1 )
return 0;
// 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;
}
public static void add_row(final 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);
}
/**
* Divides the elements at the specified column by 'val'. Takes in account
* leading zeros and one.
*/
public static void divideElementsCol(final int blockLength ,
final DSubmatrixD1 Y , final int col , final double val ) {
final int width = Math.min(blockLength,Y.col1-Y.col0);
final double 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;
}
}
}
}
/**
* Scales the elements in the specified row starting at element colStart by 'val'.
* 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( final int blockLength ,
final DSubmatrixD1 Y ,
final DSubmatrixD1 W ,
final int row ,
final int zeroOffset,
final 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);
}
/**
*
* From the specified column of Y tau is computed and each element is divided by 'max'.
* See code below:
*
*
*
* 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;
*
*
*/
public static double computeTauAndDivideCol( final int blockLength ,
final DSubmatrixD1 Y ,
final int col , final double max ) {
final int width = Math.min(blockLength,Y.col1-Y.col0);
final double dataY[] = Y.original.data;
double top=0;
double 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 ) {
double val = dataY[index] /= max;
norm2 += val*val;
}
} else {
for( int k = 0; k < height; k++ , index += width ) {
double val = dataY[index] /= max;
norm2 += val*val;
}
}
}
norm2 = Math.sqrt(norm2);
if( top < 0 )
norm2 = -norm2;
return norm2;
}
/**
*
* From the specified row of Y tau is computed and each element is divided by 'max'.
* See code below:
*
*
*
* 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;
*
*
* @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 double computeTauAndDivideRow( final int blockLength ,
final DSubmatrixD1 Y ,
final int row , int colStart , final double max ) {
final int height = Math.min(blockLength , Y.row1-Y.row0);
final double dataY[] = Y.original.data;
double top=0;
double 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++ ) {
double val = dataY[index++] /= max;
norm2 += val*val;
}
} else {
for( int k = 0; k < width; k++ ) {
double val = dataY[index++] /= max;
norm2 += val*val;
}
}
}
norm2 = Math.sqrt(norm2);
if( top < 0 )
norm2 = -norm2;
return norm2;
}
/**
* Finds the element in the column with the largest absolute value. The offset
* from zero is automatically taken in account based on the column.
*/
public static double findMaxCol(final int blockLength , final DSubmatrixD1 Y , final int col )
{
final int width = Math.min(blockLength,Y.col1-Y.col0);
final double dataY[] = Y.original.data;
double max = 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;
for( int k = col; k < height; k++ , index += width ) {
double v = Math.abs(dataY[index]);
if( v > max ) {
max = v;
}
}
} else {
for( int k = 0; k < height; k++ , index += width ) {
double v = Math.abs(dataY[index]);
if( v > max ) {
max = v;
}
}
}
}
return max;
}
/**
* Finds the element in the column with the largest absolute value. The offset
* from zero is automatically taken in account based on the column.
*/
public static double findMaxRow( final int blockLength ,
final DSubmatrixD1 Y ,
final int row , final int colStart ) {
final int height = Math.min(blockLength , Y.row1-Y.row0);
final double dataY[] = Y.original.data;
double max = 0;
for( int j = Y.col0; 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 == Y.col0 ) {
index += colStart;
for( int k = colStart; k < width; k++ ) {
double v = Math.abs(dataY[index++]);
if( v > max ) {
max = v;
}
}
} else {
for( int k = 0; k < width; k++ ) {
double v = Math.abs(dataY[index++]);
if( v > max ) {
max = v;
}
}
}
}
return max;
}
/**
*
* Computes W from the householder reflectors stored in the columns of the column block
* submatrix Y.
*
*
*
* Y = v(1)
* W = -β1v(1)
* for j=2:r
* z = -β(I +WYT)v(j)
* W = [W z]
* Y = [Y v(j)]
* end
*
* where v(.) 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.
*
*
*
* Y and W are assumed to have the same number of rows and columns.
*
*
* @param Y Input matrix containing householder vectors. Not modified.
* @param W Resulting W matrix. Modified.
* @param temp Used internally. Must have W.numCols elements.
* @param beta Beta's for householder vectors.
* @param betaIndex Index of first relevant beta.
*/
public static void computeW_Column(final int blockLength ,
final DSubmatrixD1 Y , final DSubmatrixD1 W ,
final double temp[], final double beta[] , int betaIndex ) {
final int widthB = W.col1-W.col0;
// set the first column in W
initializeW(blockLength, W, Y, widthB, beta[betaIndex++]);
final int min = Math.min(widthB,W.row1-W.row0);
// set up rest of the columns
for( int j = 1; j < min; j++ ) {
//compute the z vector and insert it into W
computeY_t_V(blockLength,Y,j,temp);
computeZ(blockLength,Y,W,j,temp,beta[betaIndex++]);
}
}
/**
*
* Sets W to its initial value using the first column of 'y' and the value of 'b':
*
* W = -βv
*
* where v = Y(:,0).
*
*
* @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(final int blockLength,
final DSubmatrixD1 W, final DSubmatrixD1 Y,
final int widthB, final double b) {
final double dataW[] = W.original.data;
final double 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];
}
}
}
}
/**
* Computes the vector z and inserts it into 'W':
*
* z = - βj*(Vj + W*h)
*
* where h is a vector of length 'col' and was computed using {@link #computeY_t_V}.
* V is a column in the Y matrix. Z is a column in the W matrix. Both Z and V are
* column 'col'.
*/
public static void computeZ(final int blockLength , final DSubmatrixD1 Y , final DSubmatrixD1 W,
final int col , final double []temp , final double beta )
{
final int width = Y.col1-Y.col0;
final double dataW[] = W.original.data;
final double dataY[] = Y.original.data;
final int colsW = W.original.numCols;
final double beta_neg = -beta;
for( int i = Y.row0; i < Y.row1; i += blockLength ) {
int heightW = Math.min( blockLength , Y.row1 - i );
int indexW = i*colsW + heightW*W.col0;
int indexZ = i*colsW + heightW*W.col0 + col;
int indexV = i*Y.original.numCols + heightW*Y.col0 + col;
if( i == Y.row0 ) {
// handle the triangular portion with the leading zeros and the one
for( int k = 0; k < heightW; k++ , indexZ += width, indexW += width , indexV += width ) {
// compute the rows of W * h
double total = 0;
for( int j = 0; j < col; j++ ) {
total += dataW[indexW+j] * temp[j];
}
// add the two vectors together and multiply by -beta
if( k < col ) { // zeros
dataW[indexZ] = -beta*total;
} else if( k == col ) { // one
dataW[indexZ] = beta_neg*(1.0 + total);
} else { // normal data
dataW[indexZ] = beta_neg*(dataY[indexV] + total);
}
}
} else {
int endZ = indexZ + width*heightW;
// for( int k = 0; k < heightW; k++ ,
while( indexZ != endZ ) {
// compute the rows of W * h
double total = 0;
for( int j = 0; j < col; j++ ) {
total += dataW[indexW+j] * temp[j];
}
// add the two vectors together and multiply by -beta
dataW[indexZ] = beta_neg*(dataY[indexV] + total);
indexZ += width; indexW += width; indexV += width;
}
}
}
}
/**
* Computes YTv(j). 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( final int blockLength , final DSubmatrixD1 Y ,
final int col , final double []temp )
{
final int widthB = Y.col1-Y.col0;
for( int j = 0; j < col; j++ ) {
temp[j] = innerProdCol(blockLength,Y,col,widthB,j,widthB);
}
}
/**
* 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(final int blockLength ,
final DSubmatrixD1 Y , final DSubmatrixD1 B ,
final DSubmatrixD1 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_DDRB.blockMultPlus(Y.original.data,B.original.data,C.original.data,
indexY,indexB,indexC,heightY,widthY,widthB);
}
}
}
}
}
/**
*
* Inner block mult add operation that takes in account the zeros and on in dataA,
* which is the top part of the Y block vector that has the householder vectors.
*
* C = C + A * B
*
*/
public static void multBlockAdd_zerosone( double[] dataA, double []dataB, double []dataC,
int indexA, int indexB, int indexC,
final int heightA, final int widthA, final int widthC) {
for( int i = 0; i < heightA; i++ ) {
for( int j = 0; j < widthC; j++ ) {
double val = i < widthA ? dataB[i*widthC+j+indexB] : 0;
int end = Math.min(i,widthA);
for( int k = 0; k < end; k++ ) {
val += dataA[i*widthA + k + indexA] * dataB[k*widthC + j + indexB];
}
dataC[ i*widthC + j + indexC ] += val;
}
}
}
/**
*
* Performs a matrix multiplication on the block aligned submatrices. A is
* assumed to be block column vector that is lower triangular with diagonal elements set to 1.
*
* C = A^T * B
*
*/
public static void multTransA_vecCol(final int blockLength ,
DSubmatrixD1 A , DSubmatrixD1 B ,
DSubmatrixD1 C )
{
int widthA = A.col1 - A.col0;
if( widthA > blockLength )
throw new IllegalArgumentException("A is expected to be at most one block wide.");
for( int j = B.col0; j < B.col1; j += blockLength ) {
int widthB = Math.min( blockLength , B.col1 - j );
int indexC = C.row0*C.original.numCols + (j-B.col0+C.col0)*widthA;
for( int k = A.row0; k < A.row1; k += blockLength ) {
int heightA = Math.min( blockLength , A.row1 - k );
int indexA = k*A.original.numCols + A.col0*heightA;
int indexB = (k-A.row0+B.row0)*B.original.numCols + j*heightA;
if( k == A.row0 )
multTransABlockSet_lowerTriag(A.original.data,B.original.data,C.original.data,
indexA,indexB,indexC,heightA,widthA,widthB);
else
InnerMultiplication_DDRB.blockMultPlusTransA(A.original.data,B.original.data,C.original.data,
indexA,indexB,indexC,heightA,widthA,widthB);
}
}
}
/**
* Performs a matrix multiplication on an single inner block where A is assumed to be lower triangular with diagonal
* elements equal to 1.
*
* C = A^T * B
*/
protected static void multTransABlockSet_lowerTriag( double[] dataA, double []dataB, double []dataC,
int indexA, int indexB, int indexC,
final int heightA, final int widthA, final int widthC) {
for( int i = 0; i < widthA; i++ ) {
for( int j = 0; j < widthC; j++ ) {
double val = i < heightA ? dataB[i*widthC + j + indexB] : 0;
for( int k = i+1; k < heightA; k++ ) {
val += dataA[k*widthA + i + indexA] * dataB[k*widthC + j + indexB];
}
dataC[ i*widthC + j + indexC ] = val;
}
}
}
}