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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;
import java.util.Iterator;
import com.github.fommil.netlib.BLAS;
import com.github.fommil.netlib.LAPACK;
import org.netlib.util.intW;
/**
* Partial implementation of a triangular, dense matrix
*/
abstract class AbstractTriangDenseMatrix extends AbstractDenseMatrix {
/**
* If the matrix is upper triangular
*/
UpLo uplo;
/**
* If the matrix is unit diagonal or not unit
*/
Diag diag;
/**
* Leading dimension of the matrix
*/
int ld;
/**
* Constructor for AbstractTriangDenseMatrix
*
* @param n
* Size of the matrix. Since the matrix must be square, this
* equals both the number of rows and columns
*/
AbstractTriangDenseMatrix(int n, UpLo uplo, Diag diag) {
super(n, n);
ld = n;
this.uplo = uplo;
this.diag = diag;
}
/**
* Constructor for AbstractTriangDenseMatrix
*
* @param A
* Matrix to copy from
*/
AbstractTriangDenseMatrix(Matrix A, UpLo uplo, Diag diag) {
this(A, Math.min(A.numRows(), A.numColumns()), uplo, diag);
}
/**
* Constructor for AbstractTriangDenseMatrix
*
* @param A
* Matrix to copy from
* @param deep
* If true, A is copied, else a shallow copy is made
* and the matrices share underlying storage. For this,
* A must be a dense matrix
*/
AbstractTriangDenseMatrix(Matrix A, boolean deep, UpLo uplo, Diag diag) {
this(A, Math.min(A.numRows(), A.numColumns()), deep, uplo, diag);
}
/**
* Constructor for AbstractTriangDenseMatrix
*
* @param A
* Matrix to copy from
* @param k
* Size of matrix to refer.
* k<min(numRows,numColumns)
*/
AbstractTriangDenseMatrix(Matrix A, int k, UpLo uplo, Diag diag) {
this(A, k, true, uplo, diag);
}
/**
* Constructor for AbstractTriangDenseMatrix
*
* @param A
* Matrix to copy from
* @param k
* Size of matrix to refer.
* k<min(numRows,numColumns)
* @param deep
* If true, A is copied, else a shallow copy is made
* and the matrices share underlying storage. For this,
* A must be a dense matrix
*/
AbstractTriangDenseMatrix(Matrix A, int k, boolean deep, UpLo uplo,
Diag diag) {
super(A, deep);
if (deep && !A.isSquare())
throw new IllegalArgumentException("deep && !A.isSquare()");
ld = A.numRows();
numRows = numColumns = k;
this.uplo = uplo;
this.diag = diag;
}
@Override
public Vector mult(double alpha, Vector x, Vector y) {
if (!(y instanceof DenseVector))
return super.mult(alpha, x, y);
checkMultAdd(x, y);
double[] yd = ((DenseVector) y).getData();
// y = alpha*x
y.set(alpha, x);
// y = A*z
BLAS.getInstance().dtrmv(uplo.netlib(), Transpose.NoTranspose.netlib(),
diag.netlib(), numRows, data, Math.max(1, ld), yd, 1);
return y;
}
@Override
public Vector transMult(double alpha, Vector x, Vector y) {
if (!(y instanceof DenseVector))
return super.transMult(alpha, x, y);
checkTransMultAdd(x, y);
double[] yd = ((DenseVector) y).getData();
// y = alpha*x
y.set(alpha, x);
// y = A'*y
BLAS.getInstance().dtrmv(uplo.netlib(), Transpose.Transpose.netlib(),
diag.netlib(), numRows, data, Math.max(1, ld), yd, 1);
return y;
}
@Override
public Matrix mult(double alpha, Matrix B, Matrix C) {
if (!(C instanceof DenseMatrix))
return super.mult(alpha, B, C);
checkMultAdd(B, C);
double[] Cd = ((DenseMatrix) C).getData();
C.set(B);
// C = alpha*A*C
BLAS.getInstance().dtrmm(Side.Left.netlib(), uplo.netlib(),
Transpose.NoTranspose.netlib(), diag.netlib(), C.numRows(),
C.numColumns(), alpha, data, Math.max(1, ld), Cd,
Math.max(1, C.numRows()));
return C;
}
@Override
public Matrix transAmult(double alpha, Matrix B, Matrix C) {
if (!(C instanceof DenseMatrix))
return super.transAmult(alpha, B, C);
checkTransAmultAdd(B, C);
double[] Cd = ((DenseMatrix) C).getData();
C.set(B);
// C = alpha*A'*C
BLAS.getInstance().dtrmm(Side.Left.netlib(), uplo.netlib(),
Transpose.Transpose.netlib(), diag.netlib(), C.numRows(),
C.numColumns(), alpha, data, Math.max(1, ld), Cd,
Math.max(1, C.numRows()));
return C;
}
@Override
public Matrix solve(Matrix B, Matrix X) {
return solve(B, X, Transpose.NoTranspose);
}
@Override
public Vector solve(Vector b, Vector x) {
DenseMatrix B = new DenseMatrix(b, false), X = new DenseMatrix(x, false);
solve(B, X);
return x;
}
@Override
public Matrix transSolve(Matrix B, Matrix X) {
return solve(B, X, Transpose.Transpose);
}
@Override
public Vector transSolve(Vector b, Vector x) {
DenseMatrix B = new DenseMatrix(b, false), X = new DenseMatrix(x, false);
transSolve(B, X);
return x;
}
Matrix solve(Matrix B, Matrix X, Transpose trans) {
if (!(X instanceof DenseMatrix))
throw new UnsupportedOperationException("X must be a DenseMatrix");
// Different argument checking to support Hessenberg type matrices for
// solvers such as GMRES
if (B.numRows() < numRows)
throw new IllegalArgumentException("B.numRows() < A.numRows()");
if (B.numColumns() != X.numColumns())
throw new IllegalArgumentException(
"B.numColumns() != X.numColumns()");
if (X.numRows() < numRows)
throw new IllegalArgumentException("X.numRows() < A.numRows()");
double[] Xd = ((DenseMatrix) X).getData();
X.set(B);
intW info = new intW(0);
LAPACK.getInstance().dtrtrs(uplo.netlib(), trans.netlib(),
diag.netlib(), numRows, X.numColumns(), data, Math.max(1, ld),
Xd, Matrices.ld(numRows), info);
if (info.val > 0)
throw new MatrixSingularException();
else if (info.val < 0)
throw new IllegalArgumentException();
return X;
}
@Override
int getIndex(int row, int column) {
check(row, column);
return row + column * Math.max(ld, numRows);
}
@Override
public Iterator iterator() {
return new TriangDenseMatrixIterator();
}
private class TriangDenseMatrixIterator extends RefMatrixIterator {
@Override
public MatrixEntry next() {
entry.update(row, column);
if (uplo == UpLo.Lower)
if (row < numRows - 1)
row++;
else {
column++;
row = column;
}
else { // uplo == UpLo.Upper
if (row < column)
row++;
else {
column++;
row = 0;
}
}
return entry;
}
}
}
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