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/******************************************************************************
*
* Project: GDAL
* Purpose: Linear system solver
* Author: VIZRT Development Team.
*
* This code was provided by Gilad Ronnen (gro at visrt dot com) with
* permission to reuse under the following license.
*
******************************************************************************
* Copyright (c) 2004, VIZRT Inc.
* Copyright (c) 2008-2014, Even Rouault <even dot rouault at spatialys.com>
* Copyright (c) 2019, Martin Franzke <martin dot franzke at telekom dot de>
*
* SPDX-License-Identifier: MIT
****************************************************************************/
/*! @cond Doxygen_Suppress */
#include "cpl_port.h"
#include "cpl_conv.h"
#include "gdallinearsystem.h"
#ifdef HAVE_ARMADILLO
#include "armadillo_headers.h"
#endif
#include <cstdio>
#include <algorithm>
#include <cassert>
#include <cmath>
namespace
{
// LU decomposition of the quadratic matrix A
// see https://en.wikipedia.org/wiki/LU_decomposition#C_code_examples
bool solve(GDALMatrix &A, GDALMatrix &RHS, GDALMatrix &X, double eps)
{
assert(A.getNumRows() == A.getNumCols());
if (eps < 0)
return false;
int const m = A.getNumRows();
int const n = RHS.getNumCols();
// row permutations
std::vector<int> perm(m);
for (int iRow = 0; iRow < m; ++iRow)
perm[iRow] = iRow;
// Arbitrary threshold to trigger progress in debug mode
const bool bDebug = (m > 10000);
int nLastPct = -1;
for (int step = 0; step < m - 1; ++step)
{
if (bDebug)
{
const int nPct = (step * 100 * 10 / m) / 2;
if (nPct != nLastPct)
{
CPLDebug("GDAL", "solve(): %d.%d %%", nPct / 10, nPct % 10);
nLastPct = nPct;
}
}
// determine pivot element
int iMax = step;
double dMax = std::abs(A(step, step));
for (int i = step + 1; i < m; ++i)
{
if (std::abs(A(i, step)) > dMax)
{
iMax = i;
dMax = std::abs(A(i, step));
}
}
if (dMax <= eps)
{
CPLError(CE_Failure, CPLE_AppDefined,
"GDALLinearSystemSolve: matrix not invertible");
return false;
}
// swap rows
if (iMax != step)
{
std::swap(perm[iMax], perm[step]);
for (int iCol = 0; iCol < m; ++iCol)
{
std::swap(A(iMax, iCol), A(step, iCol));
}
}
for (int iRow = step + 1; iRow < m; ++iRow)
{
A(iRow, step) /= A(step, step);
}
for (int iCol = step + 1; iCol < m; ++iCol)
{
for (int iRow = step + 1; iRow < m; ++iRow)
{
A(iRow, iCol) -= A(iRow, step) * A(step, iCol);
}
}
}
// LUP solve;
for (int iCol = 0; iCol < n; ++iCol)
{
if (bDebug)
{
const int nPct = 500 + (iCol * 100 * 10 / n) / 2;
if (nPct != nLastPct)
{
CPLDebug("GDAL", "solve(): %d.%d %%", nPct / 10, nPct % 10);
nLastPct = nPct;
}
}
for (int iRow = 0; iRow < m; ++iRow)
{
X(iRow, iCol) = RHS(perm[iRow], iCol);
for (int k = 0; k < iRow; ++k)
{
X(iRow, iCol) -= A(iRow, k) * X(k, iCol);
}
}
for (int iRow = m - 1; iRow >= 0; --iRow)
{
for (int k = iRow + 1; k < m; ++k)
{
X(iRow, iCol) -= A(iRow, k) * X(k, iCol);
}
X(iRow, iCol) /= A(iRow, iRow);
}
}
if (bDebug)
{
CPLDebug("GDAL", "solve(): 100.0 %%");
}
return true;
}
} // namespace
/************************************************************************/
/* GDALLinearSystemSolve() */
/* */
/* Solves the linear system A*X_i = RHS_i for each column i */
/* where A is a square matrix. */
/************************************************************************/
bool GDALLinearSystemSolve(GDALMatrix &A, GDALMatrix &RHS, GDALMatrix &X,
[[maybe_unused]] bool bForceBuiltinMethod)
{
assert(A.getNumRows() == RHS.getNumRows());
assert(A.getNumCols() == X.getNumRows());
assert(RHS.getNumCols() == X.getNumCols());
#ifdef HAVE_ARMADILLO
if (!bForceBuiltinMethod)
{
try
{
arma::mat matA(A.data(), A.getNumRows(), A.getNumCols(), false,
true);
arma::mat matRHS(RHS.data(), RHS.getNumRows(), RHS.getNumCols(),
false, true);
arma::mat matOut(X.data(), X.getNumRows(), X.getNumCols(), false,
true);
#if ARMA_VERSION_MAJOR > 6 || \
(ARMA_VERSION_MAJOR == 6 && ARMA_VERSION_MINOR >= 500)
// Perhaps available in earlier versions, but didn't check
return arma::solve(matOut, matA, matRHS,
arma::solve_opts::equilibrate +
arma::solve_opts::no_approx);
#else
return arma::solve(matOut, matA, matRHS);
#endif
}
catch (std::exception const &e)
{
CPLError(CE_Failure, CPLE_AppDefined, "GDALLinearSystemSolve: %s",
e.what());
return false;
}
}
#endif // HAVE_ARMADILLO
return solve(A, RHS, X, 0);
}
/*! @endcond */
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