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Matrix data structures, linear solvers, least squares methods, eigenvalue,
and singular value decompositions. For larger random dense matrices (above ~ 350 x 350)
matrix-matrix multiplication C = A.B is about 50% faster than MTJ.
/*
* Copyright (C) 2003-2006 Bjørn-Ove Heimsund
*
* This file is part of MTJ.
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by the
* Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* This library is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
* for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
package no.uib.cipr.matrix.sparse;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Set;
import no.uib.cipr.matrix.AbstractMatrix;
import no.uib.cipr.matrix.DenseVector;
import no.uib.cipr.matrix.Matrix;
import no.uib.cipr.matrix.MatrixEntry;
import no.uib.cipr.matrix.Vector;
import no.uib.cipr.matrix.io.MatrixInfo;
import no.uib.cipr.matrix.io.MatrixSize;
import no.uib.cipr.matrix.io.MatrixVectorReader;
/**
* Compressed row storage (CRS) matrix.
*
* Only use this class if the matrix structure (the
* location of non-zeros) is known and static (does
* not change).
*/
public class CompRowMatrix extends AbstractMatrix {
/**
* Matrix data
*/
double[] data;
/**
* Column indices. These are kept sorted within each row.
*/
int[] columnIndex;
/**
* Indices to the start of each row
*/
int[] rowPointer;
/**
* Constructor for CompRowMatrix.
*
* @param r
* Reader to get sparse matrix from
*/
public CompRowMatrix(MatrixVectorReader r) throws IOException {
// Start with a zero-sized matrix
super(0, 0);
// Get matrix information. Use the header if present, else just assume
// that the matrix stores real numbers without any symmetry
MatrixInfo info = null;
if (r.hasInfo())
info = r.readMatrixInfo();
else
info = new MatrixInfo(true, MatrixInfo.MatrixField.Real,
MatrixInfo.MatrixSymmetry.General);
// Check that the matrix is in an acceptable format
if (info.isPattern())
throw new UnsupportedOperationException(
"Pattern matrices are not supported");
if (info.isDense())
throw new UnsupportedOperationException(
"Dense matrices are not supported");
if (info.isComplex())
throw new UnsupportedOperationException(
"Complex matrices are not supported");
// Resize the matrix to correct size
MatrixSize size = r.readMatrixSize(info);
numRows = size.numRows();
numColumns = size.numColumns();
// Start reading entries
int numEntries = size.numEntries();
int[] row = new int[numEntries];
int[] column = new int[numEntries];
double[] entry = new double[numEntries];
r.readCoordinate(row, column, entry);
// Shift the indices from 1 based to 0 based
r.add(-1, row);
r.add(-1, column);
// Find the number of entries on each row
List> rnz = new ArrayList>(numRows);
for (int i = 0; i < numRows; ++i)
rnz.add(new HashSet());
for (int i = 0; i < numEntries; ++i)
rnz.get(row[i]).add(column[i]);
// Allocate some more in case of symmetry
if (info.isSymmetric() || info.isSkewSymmetric())
for (int i = 0; i < numEntries; ++i)
if (row[i] != column[i])
rnz.get(column[i]).add(row[i]);
int[][] nz = new int[numRows][];
for (int i = 0; i < numRows; ++i) {
nz[i] = new int[rnz.get(i).size()];
int j = 0;
for (Integer colind : rnz.get(i))
nz[i][j++] = colind;
}
// Create the sparse matrix structure
construct(nz);
// Insert the entries
for (int i = 0; i < size.numEntries(); ++i)
set(row[i], column[i], entry[i]);
// Put in extra entries from symmetry or skew symmetry
if (info.isSymmetric())
for (int i = 0; i < numEntries; ++i) {
if (row[i] != column[i])
set(column[i], row[i], entry[i]);
}
else if (info.isSkewSymmetric())
for (int i = 0; i < numEntries; ++i) {
if (row[i] != column[i])
set(column[i], row[i], -entry[i]);
}
}
/**
* Constructor for CompRowMatrix.
*
* @param numRows
* Number of rows
* @param numColumns
* Number of columns
* @param nz
* The nonzero column indices on each row
*/
public CompRowMatrix(int numRows, int numColumns, int[][] nz) {
super(numRows, numColumns);
construct(nz);
}
private void construct(int[][] nz) {
int nnz = 0;
for (int i = 0; i < nz.length; ++i)
nnz += nz[i].length;
rowPointer = new int[numRows + 1];
columnIndex = new int[nnz];
data = new double[nnz];
if (nz.length != numRows)
throw new IllegalArgumentException("nz.length != numRows");
for (int i = 1; i <= numRows; ++i) {
rowPointer[i] = rowPointer[i - 1] + nz[i - 1].length;
for (int j = rowPointer[i - 1], k = 0; j < rowPointer[i]; ++j, ++k) {
columnIndex[j] = nz[i - 1][k];
if (nz[i - 1][k] < 0 || nz[i - 1][k] >= numColumns)
throw new IllegalArgumentException("nz[" + (i - 1) + "]["
+ k + "]=" + nz[i - 1][k]
+ ", which is not a valid column index");
}
Arrays.sort(columnIndex, rowPointer[i - 1], rowPointer[i]);
}
}
private void construct(Matrix A, boolean deep) {
if (deep) {
if (A instanceof CompRowMatrix) {
CompRowMatrix Ac = (CompRowMatrix) A;
data = new double[Ac.data.length];
columnIndex = new int[Ac.columnIndex.length];
rowPointer = new int[Ac.rowPointer.length];
System.arraycopy(Ac.data, 0, data, 0, data.length);
System.arraycopy(Ac.columnIndex, 0, columnIndex, 0,
columnIndex.length);
System.arraycopy(Ac.rowPointer, 0, rowPointer, 0,
rowPointer.length);
} else {
List> rnz = new ArrayList>(numRows);
for (int i = 0; i < numRows; ++i)
rnz.add(new HashSet());
for (MatrixEntry e : A)
rnz.get(e.row()).add(e.column());
int[][] nz = new int[numRows][];
for (int i = 0; i < numRows; ++i) {
nz[i] = new int[rnz.get(i).size()];
int j = 0;
for (Integer colind : rnz.get(i))
nz[i][j++] = colind;
}
construct(nz);
set(A);
}
} else {
CompRowMatrix Ac = (CompRowMatrix) A;
columnIndex = Ac.getColumnIndices();
rowPointer = Ac.getRowPointers();
data = Ac.getData();
}
}
/**
* Constructor for CompRowMatrix.
*
* @param A
* Copies from this matrix
* @param deep
* True if the copy is to be deep. If it is a shallow copy,
* A must be a CompRowMatrix
*/
public CompRowMatrix(Matrix A, boolean deep) {
super(A);
construct(A, deep);
}
/**
* Constructor for CompRowMatrix.
*
* @param A
* Copies from this matrix. The copy will be deep
*/
public CompRowMatrix(Matrix A) {
this(A, true);
}
/**
* Returns the column indices
*/
public int[] getColumnIndices() {
return columnIndex;
}
/**
* Returns the row pointers
*/
public int[] getRowPointers() {
return rowPointer;
}
/**
* Returns the internal data storage
*/
public double[] getData() {
return data;
}
@Override
public Matrix mult(Matrix B, Matrix C) {
checkMultAdd(B, C);
C.zero();
// optimised a little bit to avoid zeros in rows, but not to
// exploit sparsity of matrix B
for (int i = 0; i < numRows; ++i) {
for (int j = 0; j < C.numColumns(); ++j) {
double dot = 0;
for (int k = rowPointer[i]; k < rowPointer[i + 1]; ++k) {
dot += data[k] * B.get(columnIndex[k], j);
}
if (dot != 0) {
C.set(i, j, dot);
}
}
}
return C;
}
@Override
public Vector mult(Vector x, Vector y) {
// check dimensions
checkMultAdd(x, y);
// can't assume this, unfortunately
y.zero();
if (x instanceof DenseVector) {
// DenseVector optimisations
double[] xd = ((DenseVector) x).getData();
for (int i = 0; i < numRows; ++i) {
double dot = 0;
for (int j = rowPointer[i]; j < rowPointer[i + 1]; j++) {
dot += data[j] * xd[columnIndex[j]];
}
if (dot != 0) {
y.set(i, dot);
}
}
return y;
}
// use sparsity of matrix (not vector), as get(,) is slow
// TODO: additional optimisations for mult(ISparseVector, Vector)
// note that this would require Sparse BLAS, e.g. BLAS_DUSDOT(,,,,)
// @see http://www.netlib.org/blas/blast-forum/chapter3.pdf
for (int i = 0; i < numRows; ++i) {
double dot = 0;
for (int j = rowPointer[i]; j < rowPointer[i + 1]; j++) {
dot += data[j] * x.get(columnIndex[j]);
}
y.set(i, dot);
}
return y;
}
@Override
public Vector multAdd(double alpha, Vector x, Vector y) {
if (!(x instanceof DenseVector) || !(y instanceof DenseVector))
return super.multAdd(alpha, x, y);
checkMultAdd(x, y);
double[] xd = ((DenseVector) x).getData();
double[] yd = ((DenseVector) y).getData();
for (int i = 0; i < numRows; ++i) {
double dot = 0;
for (int j = rowPointer[i]; j < rowPointer[i + 1]; ++j)
dot += data[j] * xd[columnIndex[j]];
yd[i] += alpha * dot;
}
return y;
}
@Override
public Vector transMult(Vector x, Vector y) {
if (!(x instanceof DenseVector) || !(y instanceof DenseVector))
return super.transMult(x, y);
checkTransMultAdd(x, y);
double[] xd = ((DenseVector) x).getData();
double[] yd = ((DenseVector) y).getData();
y.zero();
for (int i = 0; i < numRows; ++i)
for (int j = rowPointer[i]; j < rowPointer[i + 1]; ++j)
yd[columnIndex[j]] += data[j] * xd[i];
return y;
}
@Override
public Vector transMultAdd(double alpha, Vector x, Vector y) {
if (!(x instanceof DenseVector) || !(y instanceof DenseVector))
return super.transMultAdd(alpha, x, y);
checkTransMultAdd(x, y);
double[] xd = ((DenseVector) x).getData();
double[] yd = ((DenseVector) y).getData();
// y = 1/alpha * y
y.scale(1. / alpha);
// y = A'x + y
for (int i = 0; i < numRows; ++i)
for (int j = rowPointer[i]; j < rowPointer[i + 1]; ++j)
yd[columnIndex[j]] += data[j] * xd[i];
// y = alpha*y = alpha*A'x + y
return y.scale(alpha);
}
@Override
public void set(int row, int column, double value) {
check(row, column);
int index = getIndex(row, column);
data[index] = value;
}
@Override
public void add(int row, int column, double value) {
check(row, column);
int index = getIndex(row, column);
data[index] += value;
}
@Override
public double get(int row, int column) {
check(row, column);
int index = no.uib.cipr.matrix.sparse.Arrays.binarySearch(columnIndex,
column, rowPointer[row], rowPointer[row + 1]);
if (index >= 0)
return data[index];
else
return 0;
}
/**
* Finds the insertion index
*/
private int getIndex(int row, int column) {
int i = no.uib.cipr.matrix.sparse.Arrays.binarySearch(columnIndex,
column, rowPointer[row], rowPointer[row + 1]);
if (i >= 0 && columnIndex[i] == column)
return i;
else
throw new IndexOutOfBoundsException("Entry (" + (row + 1) + ", "
+ (column + 1) + ") is not in the matrix structure");
}
@Override
public CompRowMatrix copy() {
return new CompRowMatrix(this);
}
@Override
public Iterator iterator() {
return new CompRowMatrixIterator();
}
@Override
public CompRowMatrix zero() {
Arrays.fill(data, 0);
return this;
}
@Override
public Matrix set(Matrix B) {
if (!(B instanceof CompRowMatrix))
return super.set(B);
checkSize(B);
CompRowMatrix Bc = (CompRowMatrix) B;
// Reallocate matrix structure, if necessary
if (Bc.columnIndex.length != columnIndex.length
|| Bc.rowPointer.length != rowPointer.length) {
data = new double[Bc.data.length];
columnIndex = new int[Bc.columnIndex.length];
rowPointer = new int[Bc.rowPointer.length];
}
System.arraycopy(Bc.data, 0, data, 0, data.length);
System.arraycopy(Bc.columnIndex, 0, columnIndex, 0, columnIndex.length);
System.arraycopy(Bc.rowPointer, 0, rowPointer, 0, rowPointer.length);
return this;
}
/**
* Iterator over a compressed row matrix
*/
private final class CompRowMatrixIterator implements Iterator {
private int row, cursor;
private CompRowMatrixEntry entry = new CompRowMatrixEntry();
public CompRowMatrixIterator() {
// Find first non-empty row
nextNonEmptyRow();
}
/**
* Locates the first non-empty row, starting at the current. After the
* new row has been found, the cursor is also updated
*/
private void nextNonEmptyRow() {
while (row < numRows() && rowPointer[row] == rowPointer[row + 1])
row++;
cursor = rowPointer[row];
}
public boolean hasNext() {
return cursor < data.length;
}
public MatrixEntry next() {
entry.update(row, cursor);
// Next position is in the same row
if (cursor < rowPointer[row + 1] - 1)
cursor++;
// Next position is at the following (non-empty) row
else {
row++;
nextNonEmptyRow();
}
return entry;
}
public void remove() {
entry.set(0);
}
}
/**
* Entry of a compressed row matrix
*/
private final class CompRowMatrixEntry implements MatrixEntry {
private int row, cursor;
/**
* Updates the entry
*/
public void update(int row, int cursor) {
this.row = row;
this.cursor = cursor;
}
public int row() {
return row;
}
public int column() {
return columnIndex[cursor];
}
public double get() {
return data[cursor];
}
public void set(double value) {
data[cursor] = value;
}
}
}
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