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+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed
+ * with this work for additional information regarding copyright
+ * ownership. The ASF licenses this file to you under the Apache
+ * License, Version 2.0 (the "License"); you may not use this file
+ * except in compliance with the License. You may obtain a copy of
+ * the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/types.h>
+#include <basegfx/numeric/ftools.hxx>
+#include <cmath>
+#include <string.h>
+
+#include <memory>
+
+namespace basegfx::internal
+ {
+
+ inline double implGetDefaultValue(sal_uInt16 nRow, sal_uInt16 nColumn)
+ {
+ if(nRow == nColumn)
+ return 1.0;
+ return 0.0;
+ }
+
+ template < sal_uInt16 RowSize > class ImplMatLine
+ {
+ double mfValue[RowSize];
+
+ public:
+ ImplMatLine()
+ {
+ }
+
+ explicit ImplMatLine(sal_uInt16 nRow, ImplMatLine< RowSize >* pToBeCopied)
+ {
+ if(pToBeCopied)
+ {
+ memcpy(&mfValue, pToBeCopied, sizeof(double) * RowSize);
+ }
+ else
+ {
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ mfValue[a] = implGetDefaultValue(nRow, a);
+ }
+ }
+ }
+
+ double get(sal_uInt16 nColumn) const
+ {
+ return mfValue[nColumn];
+ }
+
+ void set(sal_uInt16 nColumn, const double& rValue)
+ {
+ mfValue[nColumn] = rValue;
+ }
+ };
+
+ template < sal_uInt16 RowSize > class ImplHomMatrixTemplate
+ {
+ ImplMatLine< RowSize > maLine[RowSize - 1];
+ std::unique_ptr<ImplMatLine< RowSize >> mutable mpLine;
+
+ public:
+ // Is last line used?
+ bool isLastLineDefault() const
+ {
+ if(!mpLine)
+ return true;
+
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ const double fDefault(implGetDefaultValue((RowSize - 1), a));
+ const double fLineValue(mpLine->get(a));
+
+ if(!::basegfx::fTools::equal(fDefault, fLineValue))
+ {
+ return false;
+ }
+ }
+
+ // reset last line, it equals default
+ mpLine.reset();
+
+ return true;
+ }
+
+ ImplHomMatrixTemplate()
+ {
+ // complete initialization with identity matrix, all lines
+ // were initialized with a trailing 1 followed by 0's.
+ for(sal_uInt16 a(0); a < RowSize-1; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ maLine[a].set(b, implGetDefaultValue(a, b) );
+ }
+ }
+
+ ImplHomMatrixTemplate(const ImplHomMatrixTemplate& rToBeCopied)
+ {
+ operator=(rToBeCopied);
+ }
+
+ ImplHomMatrixTemplate& operator=(const ImplHomMatrixTemplate& rToBeCopied)
+ {
+ if (this != &rToBeCopied)
+ {
+ // complete initialization using copy
+ for(sal_uInt16 a(0); a < (RowSize - 1); a++)
+ {
+ memcpy(&maLine[a], &rToBeCopied.maLine[a], sizeof(ImplMatLine< RowSize >));
+ }
+ if(rToBeCopied.mpLine)
+ {
+ mpLine.reset( new ImplMatLine< RowSize >((RowSize - 1), rToBeCopied.mpLine.get()) );
+ }
+ }
+ return *this;
+ }
+
+ static sal_uInt16 getEdgeLength() { return RowSize; }
+
+ double get(sal_uInt16 nRow, sal_uInt16 nColumn) const
+ {
+ if(nRow < (RowSize - 1))
+ {
+ return maLine[nRow].get(nColumn);
+ }
+
+ if(mpLine)
+ {
+ return mpLine->get(nColumn);
+ }
+
+ return implGetDefaultValue((RowSize - 1), nColumn);
+ }
+
+ void set(sal_uInt16 nRow, sal_uInt16 nColumn, const double& rValue)
+ {
+ if(nRow < (RowSize - 1))
+ {
+ maLine[nRow].set(nColumn, rValue);
+ }
+ else if(mpLine)
+ {
+ mpLine->set(nColumn, rValue);
+ }
+ else
+ {
+ const double fDefault(implGetDefaultValue((RowSize - 1), nColumn));
+
+ if(!::basegfx::fTools::equal(fDefault, rValue))
+ {
+ mpLine.reset(new ImplMatLine< RowSize >((RowSize - 1), nullptr));
+ mpLine->set(nColumn, rValue);
+ }
+ }
+ }
+
+ void testLastLine()
+ {
+ if(!mpLine)
+ return;
+
+ bool bNecessary(false);
+
+ for(sal_uInt16 a(0);!bNecessary && a < RowSize; a++)
+ {
+ const double fDefault(implGetDefaultValue((RowSize - 1), a));
+ const double fLineValue(mpLine->get(a));
+
+ if(!::basegfx::fTools::equal(fDefault, fLineValue))
+ {
+ bNecessary = true;
+ }
+ }
+
+ if(!bNecessary)
+ {
+ mpLine.reset();
+ }
+ }
+
+ // Left-upper decomposition
+ bool ludcmp(sal_uInt16 nIndex[], sal_Int16& nParity)
+ {
+ double fBig, fSum, fDum;
+ double fStorage[RowSize];
+ sal_uInt16 a, b, c;
+
+ // #i30874# Initialize nAMax (compiler warns)
+ sal_uInt16 nAMax = 0;
+
+ nParity = 1;
+
+ // Calc the max of each line. If a line is empty,
+ // stop immediately since matrix is not invertible then.
+ for(a = 0; a < RowSize; a++)
+ {
+ fBig = 0.0;
+
+ for(b = 0; b < RowSize; b++)
+ {
+ double fTemp(fabs(get(a, b)));
+
+ if(::basegfx::fTools::more(fTemp, fBig))
+ {
+ fBig = fTemp;
+ }
+ }
+
+ if(::basegfx::fTools::equalZero(fBig))
+ {
+ return false;
+ }
+
+ fStorage[a] = 1.0 / fBig;
+ }
+
+ // start normalizing
+ for(b = 0; b < RowSize; b++)
+ {
+ for(a = 0; a < b; a++)
+ {
+ fSum = get(a, b);
+
+ for(c = 0; c < a; c++)
+ {
+ fSum -= get(a, c) * get(c, b);
+ }
+
+ set(a, b, fSum);
+ }
+
+ fBig = 0.0;
+
+ for(a = b; a < RowSize; a++)
+ {
+ fSum = get(a, b);
+
+ for(c = 0; c < b; c++)
+ {
+ fSum -= get(a, c) * get(c, b);
+ }
+
+ set(a, b, fSum);
+ fDum = fStorage[a] * fabs(fSum);
+
+ if(::basegfx::fTools::moreOrEqual(fDum, fBig))
+ {
+ fBig = fDum;
+ nAMax = a;
+ }
+ }
+
+ if(b != nAMax)
+ {
+ for(c = 0; c < RowSize; c++)
+ {
+ fDum = get(nAMax, c);
+ set(nAMax, c, get(b, c));
+ set(b, c, fDum);
+ }
+
+ nParity = -nParity;
+ fStorage[nAMax] = fStorage[b];
+ }
+
+ nIndex[b] = nAMax;
+
+ // here the failure of precision occurs
+ const double fValBB(fabs(get(b, b)));
+
+ if(::basegfx::fTools::equalZero(fValBB))
+ {
+ return false;
+ }
+
+ if(b != (RowSize - 1))
+ {
+ fDum = 1.0 / get(b, b);
+
+ for(a = b + 1; a < RowSize; a++)
+ {
+ set(a, b, get(a, b) * fDum);
+ }
+ }
+ }
+
+ return true;
+ }
+
+ void lubksb(const sal_uInt16 nIndex[], double fRow[]) const
+ {
+ sal_uInt16 b, ip;
+ sal_Int16 a, a2 = -1;
+ double fSum;
+
+ for(a = 0; a < RowSize; a++)
+ {
+ ip = nIndex[a];
+ fSum = fRow[ip];
+ fRow[ip] = fRow[a];
+
+ if(a2 >= 0)
+ {
+ for(b = a2; b < a; b++)
+ {
+ fSum -= get(a, b) * fRow[b];
+ }
+ }
+ else if(!::basegfx::fTools::equalZero(fSum))
+ {
+ a2 = a;
+ }
+
+ fRow[a] = fSum;
+ }
+
+ for(a = (RowSize - 1); a >= 0; a--)
+ {
+ fSum = fRow[a];
+
+ for(b = a + 1; b < RowSize; b++)
+ {
+ fSum -= get(a, b) * fRow[b];
+ }
+
+ const double fValueAA(get(a, a));
+
+ if(!::basegfx::fTools::equalZero(fValueAA))
+ {
+ fRow[a] = fSum / get(a, a);
+ }
+ }
+ }
+
+ bool isIdentity() const
+ {
+ // last line needs no testing if not existing
+ const sal_uInt16 nMaxLine(
+ sal::static_int_cast<sal_uInt16>(mpLine ? RowSize : (RowSize - 1)) );
+
+ for(sal_uInt16 a(0); a < nMaxLine; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ {
+ const double fDefault(implGetDefaultValue(a, b));
+ const double fValueAB(get(a, b));
+
+ if(!::basegfx::fTools::equal(fDefault, fValueAB))
+ {
+ return false;
+ }
+ }
+ }
+
+ return true;
+ }
+
+ bool isInvertible() const
+ {
+ ImplHomMatrixTemplate aWork(*this);
+ sal_uInt16 nIndex[RowSize];
+ sal_Int16 nParity;
+
+ return aWork.ludcmp(nIndex, nParity);
+ }
+
+ void doInvert(const ImplHomMatrixTemplate& rWork, const sal_uInt16 nIndex[])
+ {
+ double fArray[RowSize];
+
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ // prepare line
+ sal_uInt16 b;
+ for( b = 0; b < RowSize; b++)
+ {
+ fArray[b] = implGetDefaultValue(a, b);
+ }
+
+ // expand line
+ rWork.lubksb(nIndex, fArray);
+
+ // copy line transposed to this matrix
+ for( b = 0; b < RowSize; b++)
+ {
+ set(b, a, fArray[b]);
+ }
+ }
+
+ // evtl. get rid of last matrix line
+ testLastLine();
+ }
+
+ double doDeterminant() const
+ {
+ ImplHomMatrixTemplate aWork(*this);
+ sal_uInt16 nIndex[RowSize];
+ sal_Int16 nParity;
+ double fRetval(0.0);
+
+ if(aWork.ludcmp(nIndex, nParity))
+ {
+ fRetval = static_cast<double>(nParity);
+
+ // last line needs no multiply if not existing; default value would be 1.
+ const sal_uInt16 nMaxLine(
+ sal::static_int_cast<sal_uInt16>(aWork.mpLine ? RowSize : (RowSize - 1)) );
+
+ for(sal_uInt16 a(0); a < nMaxLine; a++)
+ {
+ fRetval *= aWork.get(a, a);
+ }
+ }
+
+ return fRetval;
+ }
+
+ void doAddMatrix(const ImplHomMatrixTemplate& rMat)
+ {
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ {
+ set(a, b, get(a, b) + rMat.get(a, b));
+ }
+ }
+
+ testLastLine();
+ }
+
+ void doSubMatrix(const ImplHomMatrixTemplate& rMat)
+ {
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ {
+ set(a, b, get(a, b) - rMat.get(a, b));
+ }
+ }
+
+ testLastLine();
+ }
+
+ void doMulMatrix(const double& rfValue)
+ {
+ for(sal_uInt16 a(0); a < RowSize; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ {
+ set(a, b, get(a, b) * rfValue);
+ }
+ }
+
+ testLastLine();
+ }
+
+ void doMulMatrix(const ImplHomMatrixTemplate& rMat)
+ {
+ // create a copy as source for the original values
+ const ImplHomMatrixTemplate aCopy(*this);
+
+ // TODO: maybe optimize cases where last line is [0 0 1].
+
+ double fValue(0.0);
+
+ for(sal_uInt16 a(0); a < RowSize; ++a)
+ {
+ for(sal_uInt16 b(0); b < RowSize; ++b)
+ {
+ fValue = 0.0;
+
+ for(sal_uInt16 c(0); c < RowSize; ++c)
+ fValue += aCopy.get(c, b) * rMat.get(a, c);
+
+ set(a, b, fValue);
+ }
+ }
+
+ testLastLine();
+ }
+
+ bool isEqual(const ImplHomMatrixTemplate& rMat) const
+ {
+ const sal_uInt16 nMaxLine(
+ sal::static_int_cast<sal_uInt16>((mpLine || rMat.mpLine) ? RowSize : (RowSize - 1)) );
+
+ for(sal_uInt16 a(0); a < nMaxLine; a++)
+ {
+ for(sal_uInt16 b(0); b < RowSize; b++)
+ {
+ const double fValueA(get(a, b));
+ const double fValueB(rMat.get(a, b));
+
+ if(!::basegfx::fTools::equal(fValueA, fValueB))
+ {
+ return false;
+ }
+ }
+ }
+
+ return true;
+ }
+ };
+
+} // namespace basegfx::internal
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
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