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/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration |
-------------------------------------------------------------------------------
Copyright (C) 2011-2016 OpenFOAM Foundation
Copyright (C) 2019 OpenCFD Ltd.
-------------------------------------------------------------------------------
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 "LUscalarMatrix.H"
#include "LLTMatrix.H"
#include "Random.H"
#include "SortList.H"
using namespace Foam::MatrixTools;
#define isEqual MatrixTools::equal
void horizontalLine()
{
Info<< "+---------+---------+---------+---------+---------+" << nl;
}
// Copy values into matrix
template<class Form, class Type>
void assignMatrix
(
Matrix<Form, Type>& mat,
std::initializer_list<typename Matrix<Form, Type>::cmptType> list
)
{
const label nargs = list.size();
if (nargs != mat.size())
{
FatalErrorInFunction
<< "Mismatch in matrix dimension ("
<< mat.m() << ", "
<< mat.n() << ") and number of args (" << nargs << ')' << nl
<< exit(FatalError);
}
std::copy(list.begin(), list.end(), mat.begin());
}
MatrixType makeRandomMatrix
)
{
MatrixType mat(dims);
std::generate
(
mat.begin(),
mat.end(),
[&]{return rndGen.GaussNormal<typename MatrixType::cmptType>();}
);
template<class MatrixType>
Ostream& operator<<(Ostream& os, const ConstMatrixBlock<MatrixType>& mat)
return MatrixTools::printMatrix(os, mat);
}
template<class MatrixType>
Ostream& operator<<(Ostream& os, const MatrixBlock<MatrixType>& mat)
{
return MatrixTools::printMatrix(os, mat);
// * * * * * * * * * * * * * * * Main Program * * * * * * * * * * * * * * * //
int main(int argc, char *argv[])
{
typedef SquareMatrix<scalar> SMatrix;
typedef SquareMatrix<complex> SCMatrix;
typedef RectangularMatrix<scalar> RMatrix;
typedef RectangularMatrix<complex> RCMatrix;
Random rndGen(1234);
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{
horizontalLine();
Info<< "## Matrix Constructors & Assignments:" << nl << nl;
Info<< "# SquareMatrix<scalar> examples:" << nl;
{
const label mRows = 2;
const label nCols = 2;
Matrix<SMatrix, scalar> MS0(mRows, nCols);
Matrix<SMatrix, scalar> MS1(mRows, nCols, Zero);
Matrix<SMatrix, scalar> MS2(mRows, nCols, 17.44);
Matrix<SMatrix, scalar> MS3(MS2);
SMatrix S0(mRows);
SMatrix S1(mRows, Zero);
SMatrix S2(mRows, I);
SMatrix S3(mRows, 17.44);
SMatrix S4(2, Zero);
SMatrix S5(labelPair{mRows, nCols});
SMatrix S6(mRows, nCols, Zero);
SMatrix S7({mRows, nCols}, Zero);
SMatrix S8({mRows, nCols}, 17.44);
assignMatrix
(
S8,
{
1, 2, // 0th row
3, 4 // 1st row and so on
}
);
S1 = Zero;
S2 = 13.13;
S3 = I;
}
Info<< "# RectangularMatrix<scalar> examples:" << nl;
{
const label mRows = 2;
const label nCols = 3;
Matrix<RMatrix, scalar> MR0(mRows, nCols);
Matrix<RMatrix, scalar> MR1(mRows, nCols, Zero);
Matrix<RMatrix, scalar> MR2(mRows, nCols, 17.44);
RMatrix R0(mRows, nCols);
RMatrix R1(labelPair{mRows, nCols});
RMatrix R2(mRows, nCols, Zero);
RMatrix R3({mRows, nCols}, Zero);
RMatrix R4(mRows, nCols, -17.44);
RMatrix R5({mRows, nCols}, -17.44);
RMatrix R6(3, 4, Zero);
RMatrix R7({3, 4}, Zero);
assignMatrix
(
R7,
{
1, 2, 3, 4,
5, 6, 7, 8.8,
9, 10, 11, 12
}
);
R0 = Zero;
R2 = -13.13;
}
Info<< "# SquareMatrix<complex> examples:" << nl;
{
const label mRows = 2;
const label nCols = 2;
Matrix<SCMatrix, complex> MS0(mRows, nCols);
Matrix<SCMatrix, complex> MS1(mRows, nCols, Zero);
Matrix<SCMatrix, complex> MS2(mRows, nCols, complex(17.44, 44.17));
Matrix<SCMatrix, complex> MS3(MS2);
SCMatrix S0(mRows);
SCMatrix S1(mRows, Zero);
SCMatrix S2(mRows, I);
SCMatrix S3(mRows, complex(17.44,0));
SCMatrix S4(2, Zero);
SCMatrix S5(labelPair{mRows, nCols});
SCMatrix S6(mRows, nCols, Zero);
SCMatrix S7({mRows, nCols}, Zero);
SCMatrix S8({mRows, nCols}, complex(17.44,0));
assignMatrix
(
S8,
{
complex(1,0), complex(2,2),
complex(4,2), complex(5,0)
}
);
S1 = Zero;
S2 = complex(13.13,0);
S3 = I;
}
Info<< nl;
horizontalLine();
}
#endif
{
horizontalLine();
Info<< "## Access Functions:" << nl;
SMatrix S(3, Zero);
assignMatrix
(
S,
{
-3, 11, -4,
2, 3, 10,
2, 6, 1
}
);
S(0,1) = 10;
Info<< "# SquareMatrix<scalar> example:" << nl;
printMatrix(Info, S) << nl;
Info
<< "Number of rows =" << tab << S.m() << nl
<< "Number of columns = " << tab << S.n() << nl
<< "Number of elements = " << tab << S.size() << nl
<< "Number of rows/columns = " << tab << S.sizes() << nl
<< "Matrix is empty = " << tab << Switch(S.empty()) << nl
<< "Constant pointer = " << tab << name(S.cdata()) << nl
<< "Pointer = " << tab << name(S.data()) << nl
<< nl;
horizontalLine();
}
#endif
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{
horizontalLine();
Info<< "## Block Access Functions:" << nl;
RMatrix R(4, 3, Zero);
assignMatrix
(
R,
{
-3, 11, -4,
2, 3, 10,
2, 6, 1,
1, 2, 3
}
);
Info<< "# RectangularMatrix<scalar> example:" << nl;
printMatrix(Info, R) << nl;
// Indices begin at 0
const label columnI = 1;
const label rowI = 2;
const label colStartI = 1;
const label rowStartI = 1;
const label szRows = 2;
const label szCols = 2;
Info
<< "column: " << R.subColumn(columnI) << nl
<< "sub-column: " << R.subColumn(columnI, rowStartI) << nl
<< "sub-sub-column: " << R.subColumn(columnI, rowStartI, szRows) << nl
<< "row: " << R.subRow(rowI) << nl
<< "sub-row: " << R.subRow(rowI, colStartI) << nl
<< "sub-sub-row: " << R.subRow(rowI, colStartI, szCols) << nl
<< "sub-block: " << R.subMatrix(rowStartI, colStartI) << nl
<< "sub-block with row size: " << R.subMatrix(rowStartI, colStartI, szRows) << nl
<< "sub-block with row|col size: " << R.subMatrix(rowStartI, colStartI, szRows, szCols) << nl;
horizontalLine();
}
#endif
horizontalLine();
Info<< "## Edit Functions:" << nl;
RMatrix R(2, 2, Zero);
assignMatrix
(
R,
{
1, 2,
3, 4
}
);
Info<< "# Before Matrix.clear():" << nl << R << nl;
R.clear();
Info<< "# After Matrix.clear():" << nl << R << nl;
Info<< "# Before Matrix.resize(m, n):" << nl << R;
R.resize(3, 2);
Info<< "# After Matrix.resize(m, n):" << nl << R << nl << nl;
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// Steal matrix contents
Info<< "# Before Matrix.release():" << nl << R << nl;
List<scalar> newOwner(R.release());
Info<< "# After Matrix.release():" << nl << R
<< "& corresponding List content:" << nl << newOwner << nl << nl;
R.resize(3, 2);
assignMatrix
(
R,
{
1, 2,
5, 6,
9e-19, 1e-17
}
);
Info<< "# Before Matrix.round():" << nl << R << nl;
R.round();
Info<< "# After Matrix.round():" << nl << R << nl << nl;
Info<< "# Before Matrix.T() (Transpose):" << nl << R << nl;
RMatrix RT = R.T();
Info<< "# After Matrix.T():" << nl << RT << nl << nl;
RCMatrix RC(3, 2, Zero);
complex(1, 0), complex(2,5),
complex(4, 3), complex(1,-1),
complex(1, 2), complex(2,9)
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Info<< "# Before Matrix.T() (Hermitian transpose):" << nl << RC << nl;
RCMatrix RCH = RC.T();
Info<< "# After Matrix.T():" << nl << RCH << nl << nl;
Info<< "# Diagonal and trace:" << nl;
RMatrix R1(5, 7, 3.4);
{
List<scalar> diagR = R1.diag();
scalar traceR = R1.trace();
Info<< "RectangularMatrix<scalar>:"
<< nl << R1 << nl
<< "Major diagonal of RectangularMatrix:"
<< nl << diagR << nl
<< "Trace of RectangularMatrix:"
<< nl << traceR << nl << nl;
}
Info<< "# List assignment to the main diagonal of Matrix:" << nl;
{
SMatrix S1(5, I);
Info<< "Before List assignment:" << nl;
printMatrix(Info, S1);
List<scalar> lst(5, 2.0);
S1.diag(lst);
Info<< "After List assignment:" << nl;
printMatrix(Info, S1);
}
Info<< "# Diagonal sort of Matrix:" << nl;
makeRandomMatrix<SMatrix>
List<scalar> diag = S1.diag();
SortList<scalar> incrDiag(diag);
incrDiag.sort();
Info<< "Diagonal list:" << diag << nl
<< "Ascending diagonal list: " << incrDiag << nl << nl;
}
horizontalLine();
}
#endif
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{
horizontalLine();
Info<< "## Transpose Verifications:" << nl;
const label numberOfTests = 10;
for (label i = 0; i < numberOfTests; ++i)
{
const label mRows = rndGen.position(1,10);
const label nCols = rndGen.position(1,10);
Info << "# SquareMatrix<scalar> example:" << nl;
{
Info<< "A(mxm) where m = " << mRows << nl;
auto A(makeRandomMatrix<SMatrix>({mRows, mRows}, rndGen));
auto B(makeRandomMatrix<SMatrix>({mRows, mRows}, rndGen));
Info<< nl << "# (A.T()).T() = A:" << nl;
isEqual((A.T()).T(), A, true);
Info<< nl << "# (A + B).T() = A.T() + B.T():" << nl;
isEqual((A + B).T(), A.T() + B.T(), true);
Info<< nl << "# (A*B).T() = B.T()*A.T():" << nl;
isEqual((A*B).T(), B.T()*A.T(), true);
Info<< nl << nl;
}
Info << "# RectangularMatrix<scalar> example:" << nl;
{
Info<< "A(mxn) where"
<< " m = " << mRows << ","
<< " n = " << nCols << nl;
auto A(makeRandomMatrix<RMatrix>({mRows, nCols}, rndGen));
auto B(makeRandomMatrix<RMatrix>({mRows, nCols}, rndGen));
auto C(makeRandomMatrix<RMatrix>({nCols, mRows}, rndGen));
Info<< nl << "# (A.T()).T() = A:" << nl;
isEqual((A.T()).T(), A, true);
Info<< nl << "# (A + B).T() = A.T() + B.T():" << nl;
isEqual((A + B).T(), A.T() + B.T(), true);
Info<< nl << "# (A*C).T() = C.T()*C.T():" << nl;
isEqual((A*C).T(), C.T()*A.T(), true);
Info<< nl << nl;
}
Info << "# SquareMatrix<complex> example:" << nl;
{
Info<< "A(mxm) where m = " << mRows << nl;
SCMatrix A(mRows);
SCMatrix B(mRows);
for (auto& val : A)
{
val.Re() = rndGen.GaussNormal<scalar>();
val.Im() = rndGen.GaussNormal<scalar>();
}
for (auto& val : B)
{
val.Re() = rndGen.GaussNormal<scalar>();
val.Im() = rndGen.GaussNormal<scalar>();
}
Info<< nl << "# (A.T()).T() = A:" << nl;
isEqual((A.T()).T(), A, true);
Info<< nl << "# (A + B).T() = A.T() + B.T():" << nl;
isEqual((A + B).T(), A.T() + B.T(), true);
Info<< nl << "# (A*B).T() = B.T()*A.T():" << nl;
isEqual((A*B).T(), B.T()*A.T(), true);
Info<< nl << nl;
}
}
horizontalLine();
}
#endif
{
horizontalLine();
Info<< "## Scalar Arithmetic Operations:" << nl;
if (true)
{
SMatrix S1(3, Zero);
assignMatrix
S1,
{
4.1, 12.5, -16.3,
-192.3, -9.1, -3.0,
1.0, 5.02, -4.4
}
SMatrix S2 = S1;
SMatrix S3(3, Zero);
Info<< "SquareMatrix<scalar> S1 = " << S1 << nl;
Info<< "SquareMatrix<scalar> S2 = " << S2 << nl;
Info<< "SquareMatrix<scalar> S3 = " << S3 << nl;
S3 = S1*S2;
Info<< "S1*S2 = " << S3 << nl;
S3 = S1 - S2;
Info<< "S1 - S2 = " << S3 << nl;
S3 = S1 + S2;
Info<< "S1 + S2 = " << S3 << nl;
// S3 *= S1; // Not Implemented
S3 -= S1;
Info<< "S3 -= S1; S3 = " << S3 << nl;
S3 += S1;
Info<< "S3 += S1; S3 = " << S3 << nl;
Info<< nl << "# Scalar broadcasting:" << nl;
S3 *= 5.0;
Info<< "S3 *= 5.0; S3 = " << S3 << nl;
S3 /= 5.0;
Info<< "S3 /= 5.0; S3 = " << S3 << nl;
S3 -= 1.0;
Info<< "S3 -= 1.0; S3 = " << S3 << nl;
S3 += 1.0;
Info<< "S3 += 1.0; S3 = " << S3 << nl;
Info<< nl << "# Operations between different matrix types:" << nl;
RMatrix R1 = S1;
Info<< "RectangularMatrix<scalar> R1 = " << R1 << nl;
// RectangularMatrix*SquareMatrix returns RectangularMatrix
// S3 = S3*R1; // Not implemented
R1 = S3*R1;
Info<< "R1 = S3*R1; R1 = " << R1 << nl;
S3 = S3 - R1;
Info<< "S3 = S3 - R1; S3 = " << S3 << nl;
S3 = S3 + R1;
Info<< "S3 = S3 + R1; S3 = " << S3 << nl;
R1 = S3 + R1;
Info<< "R1 = S3 + R1; R1 = " << R1 << nl;
Info<< nl << "# Extrema operations:" << nl;
Info<< "min(S3) = " << min(S3) << nl
<< "max(S3) = " << max(S3) << nl
<< "minMax(S3) = " << minMax(S3) << nl;
}
if (true)
{
Info<< nl << "# Operations with ListTypes<scalar>:" << nl;
SMatrix A(3, Zero);
assignMatrix
(
A,
{
4.1, 12.5, -16.3,
-192.3, -9.1, -3.0,
1.0, 5.02, -4.4
}
);
const List<scalar> lst({1, 2, 3});
RMatrix colVector(3, 1, Zero);
assignMatrix
(
colVector,
{1, 2, 3}
);
RMatrix rowVector(1, 3, Zero);
assignMatrix
(
rowVector,
{1, 2, 3}
);
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Info<< "A = " << A << nl;
Info<< "colVector = " << colVector << nl;
Info<< "rowVector = " << rowVector << nl;
const Field<scalar> field1(A.Amul(lst));
const Field<scalar> field2(A*lst);
const Field<scalar> field3(A.Tmul(lst));
const Field<scalar> field4(lst*A);
Info
<< "Field1 = A*lst = A.Amul(lst):" << nl << field1 << nl
<< "Field2 = A*lst:" << nl << field2 << nl
<< "A*colVector:" << nl << A*colVector << nl
<< "Field3 = lst*A = A.Tmul(lst):" << nl << field3 << nl
<< "Field4 = lst*A:" << nl << field4 << nl
<< "rowVector*A:" << nl << rowVector*A << nl
<< nl;
}
if (true)
{
Info<< nl << "# Implicit inner/outer products:" << nl;
const scalar r = 2.0;
RMatrix A(3, 2, Zero);
assignMatrix
(
A,
{
1, 2,
3, 4,
5, 6
}
);
const RMatrix B(A);
const RMatrix C(B);
Info<< nl << "# Inner product:" << nl;
{
Info<< "- Explicit vs Implicit => A.T()*B == A&B:" << nl;
isEqual(A.T()*B, A&B, true);
Info<< "- Commutative => A&B == B&A:" << nl;
isEqual(A&B, B&A, true);
Info<< "- Distributive => A&(B+C) == A&B + A&C:" << nl;
isEqual(A&(B + C), (A&B) + (A&C), true);
Info<< "- Bilinear => A&(rB+C) == r(A&B) + (A&C):" << nl;
isEqual(A&(r*B + C), r*(A&B) + (A&C), true);
Info<< "- Scalar multiplication => (rA)&(rB) == rr(A&B):" << nl;
isEqual((r*A)&(r*B), r*r*(A&B), true);
}
Info<< nl << "# Outer product:" << nl;
{
Info<< "- Explicit vs Implicit => A*B.T() == A^B:" << nl;
isEqual(A*B.T(), A^B, true);
Info<< "- Commutative => A^B == B^A:" << nl;
isEqual(A^B, B^A, true);
Info<< "- Distributive => A^(B+C) == A^B + A^C:" << nl;
isEqual(A^(B + C), (A^B) + (A^C), true);
Info<< "- Scalar multiplication => r*(A^B) == (r*A)^B:" << nl;
isEqual(r*(A^B), (r*A)^B, true);
}
}
Info<< nl;
horizontalLine();
Henry Weller
committed
}
Henry Weller
committed
Henry Weller
committed
{
laurence
committed
Info<< "## Complex Arithmetic Operations:" << nl;
laurence
committed
if (true)
{
SCMatrix S1(3, Zero);
assignMatrix
(
S1,
{
complex(4.1, 1.0), complex(12.5, -1), complex(-16.3,-3),
complex(-192.3, 5), complex(-9.1, 3), complex(-3.0, 1),
complex(1.0, 3), complex(5.02, 0.3), complex(-4.4, 1)
}
);
SCMatrix S2 = S1;
SCMatrix S3(3, Zero);
laurence
committed
Info<< "SquareMatrix<complex> S1 = " << S1 << nl;
Info<< "SquareMatrix<complex> S2 = " << S2 << nl;
Info<< "SquareMatrix<complex> S3 = " << S3 << nl;
laurence
committed
S3 = S1*S2;
Info<< "S1*S2 = " << S3 << nl;
laurence
committed
S3 = S1 - S2;
Info<< "S1 - S2 = " << S3 << nl;
laurence
committed
S3 = S1 + S2;
Info<< "S1 + S2 = " << S3 << nl;
laurence
committed
// S3 *= S1; // Not Implemented
laurence
committed
S3 -= S1;
Info<< "S3 -= S1; S3 = " << S3 << nl;
laurence
committed
S3 += S1;
Info<< "S3 += S1; S3 = " << S3 << nl;
laurence
committed
Info<< nl << "# Complex broadcasting:" << nl;
laurence
committed
S3 *= complex(5, 0);
Info<< "S3 *= complex(5, 0); S3 = " << S3 << nl;
laurence
committed
S3 /= complex(5, 0);
Info<< "S3 /= complex(5, 0); S3 = " << S3 << nl;
S3 -= complex(1, 0);
Info<< "S3 -= complex(1, 0); S3 = " << S3 << nl;
S3 += complex(1, 0);
Info<< "S3 += complex(1, 0); S3 = " << S3 << nl;
Info<< nl << "# Operations between different matrix types:" << nl;
RCMatrix R1 = S1;
Info<< "RectangularMatrix<complex> R1 = " << R1 << nl;
R1 = S3*R1;
Info<< "R1 = S3*R1; R1 = " << R1 << nl;
S3 = S3 - R1;
Info<< "S3 = S3 - R1; S3 = " << S3 << nl;
S3 = S3 + R1;
Info<< "S3 = S3 + R1:" << S3 << nl;
// Extrama operations // Not Implemented
}
if (true)
{
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Info<< nl << "# Operations with ListTypes<complex>:" << nl;
SCMatrix A(3, Zero);
assignMatrix
(
A,
{
complex(4.1, 1.0), complex(12.5, -1), complex(-16.3,-3),
complex(-192.3, 5), complex(-9.1, 3), complex(-3.0, 1),
complex(1.0, 3), complex(5.02, 0.3), complex(-4.4, 1)
}
);
const List<complex> lst({complex(1,1), complex(2,2), complex(3,3)});
RCMatrix colVector(3, 1, Zero);
assignMatrix
(
colVector,
{complex(1,1), complex(2,2), complex(3,3)}
);
RCMatrix rowVector(1, 3, Zero);
assignMatrix
(
rowVector,
{complex(1,1), complex(2,2), complex(3,3)}
);
Info<< "A = " << A << nl;
Info<< "colVector = " << colVector << nl;
Info<< "rowVector = " << rowVector << nl;
const Field<complex> field1(A.Amul(lst));
const Field<complex> field2(A*lst);
const Field<complex> field3(A.Tmul(lst));
const Field<complex> field4(lst*A);
Info
<< "Field1 = A*lst = A.Amul(lst):" << nl << field1 << nl
<< "Field2 = A*lst:" << nl << field2 << nl
<< "A*colVector:" << nl << A*colVector << nl
<< "Field3 = lst*A = A.Tmul(lst):" << nl << field3 << nl
<< "Field4 = lst*A:" << nl << field4 << nl
<< "rowVector*A:" << nl << rowVector*A << nl
<< nl;
}
laurence
committed
{
Info<< nl << "# Implicit inner/outer products:" << nl;
laurence
committed
const complex r(2.0,1.0);
RCMatrix A(3, 2, Zero);
assignMatrix
(
A,
{
complex(1,0), complex(2,1),
complex(3,-0.3), complex(4,-1),
complex(0.5,-0.1), complex(6,0.4)
}
);
const RCMatrix B(A);
const RCMatrix C(B);
laurence
committed
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Info<< nl << "# Inner product:" << nl;
{
Info<< "- Explicit vs Implicit => A.T()*B == A&B:" << nl;
isEqual(A.T()*B, A&B, true);
Info<< "- Commutative => A&B == B&A:" << nl;
isEqual(A&B, B&A, true);
Info<< "- Distributive => A&(B+C) == A&B + A&C:" << nl;
isEqual(A&(B + C), (A&B) + (A&C), true);
Info<< "- Bilinear => A&(rB+C) == r(A&B) + (A&C):" << nl;
isEqual(A&(r*B + C), r*(A&B) + (A&C), true);
}
Info<< nl << "# Outer product:" << nl;
{
Info<< "- Explicit vs Implicit => A*B.T() == A^B:" << nl;
isEqual(A*B.T(), A^B, true);
Info<< "- Commutative => A^B == B^A:" << nl;
isEqual(A^B, B^A, true);
Info<< "- Distributive => A^(B+C) == A^B + A^C:" << nl;
isEqual(A^(B + C), (A^B) + (A^C), true);
Info<< "- Scalar multiplication => r*(A^B) == (r*A)^B:" << nl;
isEqual(r*(A^B), (r*A)^B, true);
}
}
#endif
Info<< nl;
horizontalLine();
}
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#if (0 | RUNALL)
{
horizontalLine();
Info<< "## Query to determine if a square matrix is symmetric:" << nl;
{
const label mRows = 100;
SMatrix A(makeRandomMatrix<SMatrix>({mRows, mRows}, rndGen));
Info<< "# SquareMatrix<scalar>.symmetric():" << nl
<< A.symmetric() << nl;
// Symmetrise
for (label n = 0; n < A.n() - 1; ++n)
{
for (label m = A.m() - 1; n < m; --m)
{
A(n, m) = A(m, n);
}
}
Info<< "# SquareMatrix<scalar>.symmetric():" << nl
<< A.symmetric() << nl;
}
{
const label mRows = 100;
SCMatrix A(mRows);
for (auto& val : A)
{
val.Re() = rndGen.GaussNormal<scalar>();
val.Im() = rndGen.GaussNormal<scalar>();
}
Info<< "# SquareMatrix<complex>.symmetric():" << nl
<< A.symmetric() << nl;
// Symmetrise
for (label n = 0; n < A.n() - 1; ++n)
{
for (label m = A.m() - 1; n < m; --m)
{
A(n, m) = A(m, n);
}
}
Info<< "# SquareMatrix<complex>.symmetric():" << nl
<< A.symmetric() << nl;
}
horizontalLine();
}
#endif
#if (0 | RUNALL)
{
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horizontalLine();
Info<< "## SymmetricSquareMatrix<scalar> algorithms:" << nl;
scalarSymmetricSquareMatrix symm(3, Zero);
symm(0, 0) = 4;
symm(1, 0) = 12;
symm(1, 1) = 37;
symm(2, 0) = -16;
symm(2, 1) = -43;
symm(2, 2) = 98;
Info<< "SymmetricSquareMatrix = " << nl << symm << nl
<< "Inverse = " << nl << inv(symm) << nl
<< "Determinant = " << det(symm) << nl;
scalarSymmetricSquareMatrix symm2(symm);
LUDecompose(symm2);
Info<< "LU decomposition:" << nl
<< "Inverse = " << nl << invDecomposed(symm2) << nl
<< "Determinant = " << detDecomposed(symm2) << nl;
scalarDiagonalMatrix rhs(3, 0);
rhs[0] = 1;
rhs[1] = 2;
rhs[2] = 3;
LUsolve(symm, rhs);
Info<< "Solving linear system through LU decomposition:" << nl
<< "Decomposition = " << nl << symm << nl
<< "Solution = " << rhs << nl;
{
scalarSquareMatrix squareMatrix(3, Zero);
scalarSquareMatrix S(3, Zero);
assignMatrix
(
S,
{
4, 12, -16,
12, 37, -43,
-16, -43, 98
}
);
const scalarField source(3, 1);
Info<< nl << "Square Matrix = " << S << endl;
if (true)
{
{
scalarSquareMatrix S2(S);
Info<< "Determinant = " << det(S2) << nl;
}
scalarSquareMatrix S2(S);
labelList rhs(3, 0);
label sign;
LUDecompose(S2, rhs, sign);
Info<< "LU decomposition = " << S2 << nl
<< "Pivots = " << rhs << nl
<< "Sign = " << sign << nl
<< "Determinant = " << detDecomposed(S2, sign) << nl;
}
if (true)
{
LUscalarMatrix LU(S);
scalarField x(LU.solve(source));