From e9199c6e14ddef7b19d0d791b3986701ecba86f9 Mon Sep 17 00:00:00 2001
From: Henry Weller <http://cfd.direct>
Date: Thu, 24 Mar 2016 14:49:25 +0000
Subject: [PATCH] QRMatrix: New class to provide QR-decomposition by
Householder reflection
This development is sponsored by Carnegie Wave Energy Ltd.
---
applications/test/Matrix/Test-Matrix.C | 27 +++
src/OpenFOAM/matrices/QRMatrix/QRMatrix.C | 249 +++++++++++++++++++++
src/OpenFOAM/matrices/QRMatrix/QRMatrix.H | 133 +++++++++++
src/OpenFOAM/matrices/QRMatrix/QRMatrixI.H | 51 +++++
4 files changed, 460 insertions(+)
create mode 100644 src/OpenFOAM/matrices/QRMatrix/QRMatrix.C
create mode 100644 src/OpenFOAM/matrices/QRMatrix/QRMatrix.H
create mode 100644 src/OpenFOAM/matrices/QRMatrix/QRMatrixI.H
diff --git a/applications/test/Matrix/Test-Matrix.C b/applications/test/Matrix/Test-Matrix.C
index c8691e81b50..87a39386fc1 100644
--- a/applications/test/Matrix/Test-Matrix.C
+++ b/applications/test/Matrix/Test-Matrix.C
@@ -25,6 +25,7 @@ License
#include "scalarMatrices.H"
#include "LLTMatrix.H"
+#include "QRMatrix.H"
#include "vector.H"
#include "tensor.H"
#include "IFstream.H"
@@ -161,6 +162,32 @@ int main(int argc, char *argv[])
Info<< "LLT solve residual " << (squareMatrix*x - source) << endl;
}
+ {
+ scalarSquareMatrix squareMatrix(3, Zero);
+
+ squareMatrix(0, 0) = 4;
+ squareMatrix(0, 1) = 12;
+ squareMatrix(0, 2) = -16;
+ squareMatrix(1, 0) = 12;
+ squareMatrix(1, 1) = 37;
+ squareMatrix(1, 2) = -43;
+ squareMatrix(2, 0) = -16;
+ squareMatrix(2, 1) = -43;
+ squareMatrix(2, 2) = 98;
+
+ scalarField source(3, 1);
+
+ QRMatrix<scalarSquareMatrix> QR(squareMatrix);
+ scalarField x(QR.solve(source));
+
+ Info<< "QR solve residual "
+ << (squareMatrix*x - source) << endl;
+
+ Info<< "QR inverse solve residual "
+ << (x - QR.inverse()*source) << endl;
+
+ }
+
Info<< "\nEnd\n" << endl;
return 0;
diff --git a/src/OpenFOAM/matrices/QRMatrix/QRMatrix.C b/src/OpenFOAM/matrices/QRMatrix/QRMatrix.C
new file mode 100644
index 00000000000..80e33b0fb2a
--- /dev/null
+++ b/src/OpenFOAM/matrices/QRMatrix/QRMatrix.C
@@ -0,0 +1,249 @@
+/*---------------------------------------------------------------------------*\
+ ========= |
+ \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
+ \\ / O peration |
+ \\ / A nd | Copyright (C) 2016 OpenFOAM Foundation
+ \\/ M anipulation |
+-------------------------------------------------------------------------------
+License
+ This file is part of OpenFOAM.
+
+ OpenFOAM is free software: you can redistribute it and/or modify it
+ under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ OpenFOAM 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 General Public License
+ for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "QRMatrix.H"
+
+// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
+
+template<class MatrixType>
+Foam::QRMatrix<MatrixType>::QRMatrix(const MatrixType& M)
+{
+ decompose(M);
+}
+
+
+// * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * * //
+
+template<class MatrixType>
+void Foam::QRMatrix<MatrixType>::decompose(const MatrixType& M)
+{
+ const label m = M.m();
+ const label n = M.n();
+
+ // Initialize the R-matrix to M
+ R_ = M;
+
+ // Initialize the Q-matrix to I
+ Q_.setSize(m);
+ Q_ = I;
+
+ // Pre-allocate temporary storage for the Householder steps
+ QMatrixType Qk(m);
+ QMatrixType Rk(m);
+ Field<cmptType> uk(m);
+
+ for (label k=0; k<n; k++)
+ {
+ // alpha = -|column k of Rk|
+ cmptType alpha = Zero;
+ for (label bi=k; bi<m; bi++)
+ {
+ alpha += sqr(R_(bi, k));
+ }
+ alpha = sqrt(alpha);
+
+ if (R_(k, k) > 0)
+ {
+ alpha = -alpha;
+ }
+
+ // uk = column k of Rk - alpha*ek
+ // rSumSqrUk = 2/sum(sqr(uk))
+ uk[k] = R_(k, k) - alpha;
+ cmptType rSumSqrUk = sqr(uk[k]);
+ for (label bi=k+1; bi<m; bi++)
+ {
+ uk[bi] = R_(bi, k);
+ rSumSqrUk += sqr(uk[bi]);
+ }
+ rSumSqrUk = 2/rSumSqrUk;
+
+ // Qk = I - 2*u*uT/sum(sqr(uk))
+ for (label bi=k; bi<m; bi++)
+ {
+ for (label bj=k; bj<m; bj++)
+ {
+ Qk(bi, bj) = -rSumSqrUk*uk[bi]*uk[bj];
+ }
+ Qk(bi, bi) += 1;
+ }
+
+ // Rk = Qk*R
+ for (label bi=k; bi<m; bi++)
+ {
+ for (label bk=k; bk<n; bk++)
+ {
+ Rk(bi, bk) = Zero;
+ for (label bj=k; bj<n; bj++)
+ {
+ Rk(bi, bk) += Qk(bi, bj)*R_(bj, bk);
+ }
+ }
+ }
+
+ // Ensure diagonal is positive
+ if (R_(k, k) < 0)
+ {
+ // R = -Rk
+ // Q = -Q
+ for (label bi=k; bi<m; bi++)
+ {
+ for (label bj=k; bj<n; bj++)
+ {
+ R_(bi, bj) = -Rk(bi, bj);
+ }
+ for (label bj=k; bj<m; bj++)
+ {
+ Q_(bi, bj) = -Q_(bi, bj);
+ }
+ }
+ }
+ else
+ {
+ // R = Rk
+ for (label bi=k; bi<m; bi++)
+ {
+ for (label bj=k; bj<n; bj++)
+ {
+ R_(bi, bj) = Rk(bi, bj);
+ }
+ }
+ }
+
+ // Q = Q*Qk (using Rk as temporary storage)
+ for (label bi=0; bi<m; bi++)
+ {
+ for (label bk=k; bk<m; bk++)
+ {
+ Rk(bi, bk) = Zero;
+ for (label bj=k; bj<m; bj++)
+ {
+ Rk(bi, bk) += Q_(bi, bj)*Qk(bj, bk);
+ }
+ }
+ }
+ for (label bi=0; bi<m; bi++)
+ {
+ for (label bj=k; bj<n; bj++)
+ {
+ Q_(bi, bj) = Rk(bi, bj);
+ }
+ }
+ }
+}
+
+
+template<class MatrixType>
+void Foam::QRMatrix<MatrixType>::solvex
+(
+ Field<cmptType>& x
+) const
+{
+ const label n = R_.n();
+
+ for (int i=n-1; i>=0; i--)
+ {
+ cmptType sum = x[i];
+
+ for (label j=i+1; j<n; j++)
+ {
+ sum -= x[j]*R_(i, j);
+ }
+
+ if (mag(R_(i, i)) < SMALL)
+ {
+ FatalErrorInFunction
+ << "Back-substitution failed due to small diagonal"
+ << abort(FatalError);
+ }
+
+ x[i] = sum/R_(i, i);
+ }
+}
+
+
+template<class MatrixType>
+void Foam::QRMatrix<MatrixType>::solve
+(
+ Field<cmptType>& x,
+ const Field<cmptType>& source
+) const
+{
+ const label m = Q_.m();
+
+ // x = Q_.T()*source;
+ for (label i=0; i<m; i++)
+ {
+ x[i] = 0;
+ for (label j=0; j<m; j++)
+ {
+ x[i] += Q_(j, i)*source[j];
+ }
+ }
+
+ solvex(x);
+}
+
+
+template<class MatrixType>
+Foam::tmp<Foam::Field<typename MatrixType::cmptType>>
+Foam::QRMatrix<MatrixType>::solve
+(
+ const Field<cmptType>& source
+) const
+{
+ tmp<Field<cmptType>> tx(new Field<cmptType>(Q_.m()));
+ Field<cmptType>& x = tx.ref();
+
+ solve(x, source);
+
+ return tx;
+}
+
+
+template<class MatrixType>
+typename Foam::QRMatrix<MatrixType>::QMatrixType
+Foam::QRMatrix<MatrixType>::inverse() const
+{
+ const label m = Q_.m();
+
+ Field<cmptType> x(m);
+ QMatrixType inv(m);
+
+ for (label i=0; i<m; i++)
+ {
+ for (label j=0; j<m; j++)
+ {
+ x[j] = Q_(i, j);
+ }
+ solvex(x);
+ inv.block(m, 1, 0, i) = x;
+ }
+
+ return inv;
+}
+
+
+// ************************************************************************* //
diff --git a/src/OpenFOAM/matrices/QRMatrix/QRMatrix.H b/src/OpenFOAM/matrices/QRMatrix/QRMatrix.H
new file mode 100644
index 00000000000..bbad659be26
--- /dev/null
+++ b/src/OpenFOAM/matrices/QRMatrix/QRMatrix.H
@@ -0,0 +1,133 @@
+/*---------------------------------------------------------------------------*\
+ ========= |
+ \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
+ \\ / O peration |
+ \\ / A nd | Copyright (C) 2016 OpenFOAM Foundation
+ \\/ M anipulation |
+-------------------------------------------------------------------------------
+License
+ This file is part of OpenFOAM.
+
+ OpenFOAM is free software: you can redistribute it and/or modify it
+ under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ OpenFOAM 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 General Public License
+ for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
+
+Class
+ Foam::QRMatrix
+
+Description
+ Class templated on matrix type to perform the QR decomposition using
+ Householder reflections on a square or rectangular matrix.
+
+SourceFiles
+ QRMatrixI.H
+ QRMatrix.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef QRMatrix_H
+#define QRMatrix_H
+
+#include "SquareMatrix.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+ Class QRMatrix Declaration
+\*---------------------------------------------------------------------------*/
+
+template<class MatrixType>
+class QRMatrix
+{
+
+public:
+
+ typedef typename MatrixType::cmptType cmptType;
+ typedef SquareMatrix<cmptType> QMatrixType;
+ typedef MatrixType RMatrixType;
+
+private:
+
+ // Private data
+
+ //- The Q-matrix
+ QMatrixType Q_;
+
+ //- The R-matrix
+ RMatrixType R_;
+
+
+ // Private member functions
+
+ //- Solve the linear system with the Field argument x initialized to
+ // the appropriate transformed source (e.g. Q.T()*source)
+ // and return the solution in x
+ void solvex(Field<cmptType>& x) const;
+
+
+public:
+
+ // Constructors
+
+ //- Construct null
+ inline QRMatrix();
+
+ //- Construct decomposing given matrix
+ QRMatrix(const MatrixType& M);
+
+
+ // Member Functions
+
+ //- Return Q-matrix
+ inline const QMatrixType& Q() const;
+
+ //- Return R-matrix
+ inline const RMatrixType& R() const;
+
+ //- Decompose given matrix
+ void decompose(const MatrixType& M);
+
+ //- Solve the linear system with the given source
+ // and returning the solution in the Field argument x
+ void solve(Field<cmptType>& x, const Field<cmptType>& source) const;
+
+ //- Solve the linear system with the given source
+ // returning the solution
+ tmp<Field<cmptType>> solve(const Field<cmptType>& source) const;
+
+ //- Return the inverse of a square matrix
+ QMatrixType inverse() const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#include "QRMatrixI.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#ifdef NoRepository
+ #include "QRMatrix.C"
+#endif
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/OpenFOAM/matrices/QRMatrix/QRMatrixI.H b/src/OpenFOAM/matrices/QRMatrix/QRMatrixI.H
new file mode 100644
index 00000000000..1d9ca4b620e
--- /dev/null
+++ b/src/OpenFOAM/matrices/QRMatrix/QRMatrixI.H
@@ -0,0 +1,51 @@
+/*---------------------------------------------------------------------------*\
+ ========= |
+ \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
+ \\ / O peration |
+ \\ / A nd | Copyright (C) 2016 OpenFOAM Foundation
+ \\/ M anipulation |
+-------------------------------------------------------------------------------
+License
+ This file is part of OpenFOAM.
+
+ OpenFOAM is free software: you can redistribute it and/or modify it
+ under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ OpenFOAM 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 General Public License
+ for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
+
+template<class MatrixType>
+inline Foam::QRMatrix<MatrixType>::QRMatrix()
+{}
+
+
+// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
+
+template<class MatrixType>
+inline const typename Foam::QRMatrix<MatrixType>::QMatrixType&
+Foam::QRMatrix<MatrixType>::Q() const
+{
+ return Q_;
+}
+
+
+template<class MatrixType>
+inline const typename Foam::QRMatrix<MatrixType>::RMatrixType&
+Foam::QRMatrix<MatrixType>::R() const
+{
+ return R_;
+}
+
+
+// ************************************************************************* //
--
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