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d5f74e42d6
License statement text corrected; compiler warnings caused by Bison 2.41 disabled for MSVC; a few other compiler warnings on 54-bit Windows eliminated by appropriate type cast Wrong license statements corrected in several files. Copyright and license statements added in XSD and GLSL files. Copyright year updated in some files. Obsolete documentation files removed from DrawResources.
678 lines
18 KiB
C++
678 lines
18 KiB
C++
// Copyright (c) 1997-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#include <math_Matrix.ixx>
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#include <math_Vector.hxx>
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#include <Standard_DimensionError.hxx>
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#include <Standard_DivideByZero.hxx>
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#include <Standard_RangeError.hxx>
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#include <math_SingularMatrix.hxx>
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#include <math_NotSquare.hxx>
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#include <math_Gauss.hxx>
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void math_Matrix::SetLowerRow(const Standard_Integer LowerRow) {
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Array.SetLowerRow(LowerRow);
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Standard_Integer Rows = RowNumber();
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LowerRowIndex = LowerRow;
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UpperRowIndex = LowerRowIndex + Rows - 1;
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}
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void math_Matrix::SetLowerCol(const Standard_Integer LowerCol) {
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Array.SetLowerCol(LowerCol);
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Standard_Integer Cols = ColNumber();
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LowerColIndex = LowerCol;
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UpperColIndex = LowerColIndex + Cols - 1;
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}
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math_Matrix::math_Matrix (const Standard_Integer LowerRow,
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const Standard_Integer UpperRow,
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const Standard_Integer LowerCol,
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const Standard_Integer UpperCol):
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LowerRowIndex(LowerRow),
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UpperRowIndex(UpperRow),
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LowerColIndex(LowerCol),
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UpperColIndex(UpperCol),
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Array(LowerRow, UpperRow,
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LowerCol, UpperCol)
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{
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Standard_RangeError_Raise_if((LowerRow > UpperRow) ||
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(LowerCol > UpperCol), "");
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}
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math_Matrix::math_Matrix (const Standard_Integer LowerRow,
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const Standard_Integer UpperRow,
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const Standard_Integer LowerCol,
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const Standard_Integer UpperCol,
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const Standard_Real InitialValue):
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LowerRowIndex(LowerRow),
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UpperRowIndex(UpperRow),
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LowerColIndex(LowerCol),
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UpperColIndex(UpperCol),
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Array(LowerRow, UpperRow,
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LowerCol, UpperCol)
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{
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Standard_RangeError_Raise_if((LowerRow > UpperRow) ||
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(LowerCol > UpperCol), "");
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Array.Init(InitialValue);
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}
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math_Matrix::math_Matrix (const Standard_Address Tab,
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const Standard_Integer LowerRow,
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const Standard_Integer UpperRow,
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const Standard_Integer LowerCol,
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const Standard_Integer UpperCol) :
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LowerRowIndex(LowerRow),
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UpperRowIndex(UpperRow),
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LowerColIndex(LowerCol),
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UpperColIndex(UpperCol),
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Array(Tab, LowerRow, UpperRow, LowerCol, UpperCol)
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{
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Standard_RangeError_Raise_if((LowerRow > UpperRow) ||
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(LowerCol > UpperCol), "");
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}
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void math_Matrix::Init(const Standard_Real InitialValue)
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{
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Array.Init(InitialValue);
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}
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math_Matrix::math_Matrix (const math_Matrix& Other):
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LowerRowIndex(Other.LowerRow()),
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UpperRowIndex(Other.UpperRow()),
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LowerColIndex(Other.LowerCol()),
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UpperColIndex(Other.UpperCol()),
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Array(Other.Array)
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{
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}
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math_Matrix math_Matrix::Divided (const Standard_Real Right) const
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{
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Standard_DivideByZero_Raise_if(Abs(Right) <= RealEpsilon(), "");
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math_Matrix temp = Multiplied(1./Right);
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return temp;
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}
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Standard_Real math_Matrix::Determinant() const
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{
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math_Gauss Sol(*this);
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if(Sol.IsDone()) {
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return Sol.Determinant();
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}
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else {
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return 0.0;
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}
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}
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void math_Matrix::Transpose()
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{
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math_NotSquare_Raise_if(RowNumber() != ColNumber(), "");
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Standard_Integer Row = LowerRowIndex;
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Standard_Integer Col = LowerColIndex;
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SetLowerCol(LowerRowIndex);
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Standard_Real Temp;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = I; J <= UpperColIndex; J++) {
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Temp = Array(I, J);
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Array(I, J) = Array(J, I);
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Array(J, I) = Temp;
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}
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}
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SetLowerRow(Col);
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SetLowerCol(Row);
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}
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math_Matrix math_Matrix::Transposed() const
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{
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math_Matrix Result(LowerColIndex, UpperColIndex,
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LowerRowIndex, UpperRowIndex);
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(J, I) = Array(I, J);
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}
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}
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return Result;
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}
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void math_Matrix::Invert()
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{
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math_NotSquare_Raise_if(RowNumber() != ColNumber(), "");
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math_Gauss Sol(*this);
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if(Sol.IsDone()) {
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Sol.Invert(*this);
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}
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else {
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math_SingularMatrix::Raise(); // SingularMatrix Exception;
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}
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}
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math_Matrix math_Matrix::Inverse() const
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{
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math_Matrix Result = *this;
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Result.Invert();
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return Result;
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}
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void math_Matrix::Multiply (const Standard_Real Right)
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{
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Array(I, J) = Array(I, J) * Right;
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}
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}
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}
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math_Matrix math_Matrix::Multiplied (const Standard_Real Right) const
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{
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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LowerColIndex, UpperColIndex);
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(I, J) = Array(I, J) * Right;
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}
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}
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return Result;
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}
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math_Matrix math_Matrix::TMultiplied (const Standard_Real Right) const
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{
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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LowerColIndex, UpperColIndex);
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(I, J) = Array(I, J) * Right;
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}
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}
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return Result;
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}
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void math_Matrix::Divide (const Standard_Real Right)
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{
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Standard_DivideByZero_Raise_if(Abs(Right) <= RealEpsilon(), "");
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Array(I, J) = Array(I, J) / Right;
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}
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}
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}
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void math_Matrix::Add (const math_Matrix& Right)
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{
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Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
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(ColNumber() != Right.ColNumber()),
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"");
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Standard_Integer J2 = Right.LowerColIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Array(I, J) = Array(I, J) + Right.Array(I2, J2);
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J2++;
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}
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I2++;
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}
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}
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void math_Matrix::Subtract (const math_Matrix& Right)
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{
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Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
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(ColNumber() != Right.ColNumber()),
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"");
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Standard_Integer J2 = Right.LowerColIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Array(I, J) = Array(I, J) - Right.Array(I2, J2);
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J2++;
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}
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I2++;
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}
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}
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void math_Matrix::Set(const Standard_Integer I1,const Standard_Integer I2,
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const Standard_Integer J1,const Standard_Integer J2,
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const math_Matrix& M)
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{
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Standard_DimensionError_Raise_if((I1 < LowerRowIndex) ||
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(I2 > UpperRowIndex) ||
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(J1 < LowerColIndex) ||
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(J2 > UpperColIndex) ||
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(I1 > I2) || (J1 > J2) ||
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(I2-I1+1 != M.RowNumber()) ||
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(J2-J1+1 != M.ColNumber()), "");
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Standard_Integer II = M.LowerRow();
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for(Standard_Integer I = I1; I <= I2; I++) {
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Standard_Integer JJ = M.LowerCol();
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for(Standard_Integer J = J1; J <= J2; J++) {
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Array(I, J) = M.Array(II, JJ);
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JJ++;
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}
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II++;
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}
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}
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void math_Matrix::SetRow (const Standard_Integer Row,
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const math_Vector& V)
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{
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Standard_RangeError_Raise_if((Row < LowerRowIndex) ||
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(Row > UpperRowIndex) , "");
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Standard_DimensionError_Raise_if(ColNumber() != V.Length(), "");
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Standard_Integer I = V.LowerIndex;
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for(Standard_Integer Index = LowerColIndex; Index <= UpperColIndex; Index++) {
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Array(Row, Index) = V.Array(I);
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I++;
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}
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}
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void math_Matrix::SetCol (const Standard_Integer Col,
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const math_Vector& V)
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{
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Standard_RangeError_Raise_if((Col < LowerColIndex) ||
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(Col > UpperColIndex) , "");
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Standard_DimensionError_Raise_if(RowNumber() != V.Length(), "");
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Standard_Integer I = V.LowerIndex;
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for(Standard_Integer Index = LowerRowIndex; Index <= UpperRowIndex; Index++) {
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Array(Index, Col) = V.Array(I);
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I++;
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}
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}
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void math_Matrix::SetDiag(const Standard_Real Value)
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{
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math_NotSquare_Raise_if(RowNumber() != ColNumber(), "");
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Array(I, I) = Value;
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}
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}
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math_Vector math_Matrix::Row (const Standard_Integer Row) const
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{
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math_Vector Result(LowerColIndex, UpperColIndex);
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for(Standard_Integer Index = LowerColIndex; Index <= UpperColIndex; Index++) {
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Result.Array(Index) = Array(Row, Index);
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}
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return Result;
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}
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math_Vector math_Matrix::Col (const Standard_Integer Col) const
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{
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math_Vector Result(LowerRowIndex, UpperRowIndex);
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for(Standard_Integer Index = LowerRowIndex; Index <= UpperRowIndex; Index++) {
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Result.Array(Index) = Array(Index, Col);
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}
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return Result;
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}
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void math_Matrix::SwapRow(const Standard_Integer Row1,
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const Standard_Integer Row2)
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{
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Standard_RangeError_Raise_if((Row1 < LowerRowIndex) ||
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(Row1 > UpperRowIndex) ||
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(Row2 < LowerRowIndex) ||
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(Row2 > UpperRowIndex), "");
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math_Vector V1 = Row(Row1);
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math_Vector V2 = Row(Row2);
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SetRow(Row1,V2);
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SetRow(Row2,V1);
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}
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void math_Matrix::SwapCol(const Standard_Integer Col1,
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const Standard_Integer Col2)
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{
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Standard_RangeError_Raise_if((Col1 < LowerColIndex) ||
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(Col1 > UpperColIndex) ||
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(Col2 < LowerColIndex) ||
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(Col2 > UpperColIndex), "");
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math_Vector V1 = Col(Col1);
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math_Vector V2 = Col(Col2);
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SetCol(Col1,V2);
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SetCol(Col2,V1);
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}
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math_Matrix math_Matrix::Multiplied (const math_Matrix& Right) const
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{
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Standard_DimensionError_Raise_if(ColNumber() != Right.RowNumber(), "");
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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Right.LowerColIndex, Right.UpperColIndex);
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Standard_Real Som;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J2 = Right.LowerColIndex; J2 <= Right.UpperColIndex; J2++) {
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Som = 0.0;
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Som = Som + Array(I, J) * Right.Array(I2, J2);
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I2++;
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}
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Result.Array(I, J2) = Som;
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}
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}
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return Result;
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}
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math_Matrix math_Matrix::TMultiply (const math_Matrix& Right) const
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{
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Standard_DimensionError_Raise_if(RowNumber() != Right.RowNumber(), "");
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math_Matrix Result(LowerColIndex, UpperColIndex,
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Right.LowerColIndex, Right.UpperColIndex);
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Standard_Real Som;
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for(Standard_Integer I = LowerColIndex; I <= UpperColIndex; I++) {
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for(Standard_Integer J2 = Right.LowerColIndex; J2 <= Right.UpperColIndex; J2++) {
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Som = 0.0;
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer J = LowerRowIndex; J <= UpperRowIndex; J++) {
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Som = Som + Array(J, I) * Right.Array(I2, J2);
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I2++;
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}
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Result.Array(I, J2) = Som;
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}
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}
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return Result;
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}
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math_Matrix math_Matrix::Added (const math_Matrix& Right) const
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{
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Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
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(ColNumber() != Right.ColNumber()),
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"");
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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LowerColIndex, UpperColIndex);
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Standard_Integer J2 = Right.LowerColIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(I, J) = Array(I, J) + Right.Array(I2, J2);
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J2++;
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}
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I2++;
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}
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return Result;
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}
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math_Matrix math_Matrix::Opposite ()
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{
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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LowerColIndex, UpperColIndex);
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(I, J) = - Array(I, J);
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}
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}
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return Result;
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}
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math_Matrix math_Matrix::Subtracted (const math_Matrix& Right) const
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{
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Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
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(ColNumber() != Right.ColNumber()),
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"");
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math_Matrix Result(LowerRowIndex, UpperRowIndex,
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LowerColIndex, UpperColIndex);
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Standard_Integer J2 = Right.LowerColIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Result.Array(I, J) = Array(I, J) - Right.Array(I2, J2);
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J2++;
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}
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I2++;
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}
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return Result;
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}
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void math_Matrix::Multiply(const math_Vector& Left,
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const math_Vector& Right)
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{
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Standard_DimensionError_Raise_if((RowNumber() != Left.Length()) ||
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(ColNumber() != Right.Length()),
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"");
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Array(I, J) = Left.Array(I) * Right.Array(J);
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}
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}
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}
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void math_Matrix::Multiply(const math_Matrix& Left,
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const math_Matrix& Right)
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{
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Standard_DimensionError_Raise_if((Left.ColNumber() != Right.RowNumber()) ||
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(RowNumber() != Left.RowNumber()) ||
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(ColNumber() != Right.ColNumber()),
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"");
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Standard_Real Som;
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Standard_Integer I1 = Left.LowerRowIndex;
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for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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Standard_Integer J2 = Right.LowerColIndex;
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for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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Som = 0.0;
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Standard_Integer J1 = Left.LowerColIndex;
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Standard_Integer I2 = Right.LowerRowIndex;
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for(Standard_Integer K = Left.LowerColIndex; K <= Left.UpperColIndex; K++) {
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Som = Som + Left.Array(I1, J1) * Right.Array(I2, J2);
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J1++;
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I2++;
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}
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Array(I, J) = Som;
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J2++;
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}
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I1++;
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}
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}
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void math_Matrix::TMultiply(const math_Matrix& TLeft,
|
|
const math_Matrix& Right)
|
|
{
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|
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|
Standard_DimensionError_Raise_if((TLeft.RowNumber() != Right.RowNumber()) ||
|
|
(RowNumber() != TLeft.ColNumber()) ||
|
|
(ColNumber() != Right.ColNumber()),
|
|
"");
|
|
|
|
Standard_Real Som;
|
|
Standard_Integer I1 = TLeft.LowerColIndex;
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|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
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|
Standard_Integer J2 = Right.LowerColIndex;
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
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|
Som = 0.0;
|
|
Standard_Integer J1 = TLeft.LowerRowIndex;
|
|
Standard_Integer I2 = Right.LowerRowIndex;
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|
for(Standard_Integer K = TLeft.LowerRowIndex; K <= TLeft.UpperRowIndex; K++) {
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|
Som = Som + TLeft.Array(J1, I1) * Right.Array(I2, J2);
|
|
J1++;
|
|
I2++;
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|
}
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|
Array(I, J) = Som;
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|
J2++;
|
|
}
|
|
I1++;
|
|
}
|
|
}
|
|
|
|
void math_Matrix::Add (const math_Matrix& Left,
|
|
const math_Matrix& Right)
|
|
{
|
|
|
|
Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
|
|
(ColNumber() != Right.ColNumber()) ||
|
|
(Right.RowNumber() != Left.RowNumber()) ||
|
|
(Right.ColNumber() != Left.ColNumber()),
|
|
"");
|
|
|
|
Standard_Integer I1 = Left.LowerRowIndex;
|
|
Standard_Integer I2 = Right.LowerRowIndex;
|
|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
|
|
Standard_Integer J1 = Left.LowerColIndex;
|
|
Standard_Integer J2 = Right.LowerColIndex;
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
|
|
Array(I, J) = Left.Array(I1, J1) + Right.Array(I2, J2);
|
|
J1++;
|
|
J2++;
|
|
}
|
|
I1++;
|
|
I2++;
|
|
}
|
|
}
|
|
|
|
void math_Matrix::Subtract(const math_Matrix& Left,
|
|
const math_Matrix& Right)
|
|
{
|
|
|
|
Standard_DimensionError_Raise_if((RowNumber() != Right.RowNumber()) ||
|
|
(ColNumber() != Right.ColNumber()) ||
|
|
(Right.RowNumber() != Left.RowNumber()) ||
|
|
(Right.ColNumber() != Left.ColNumber()),
|
|
"");
|
|
|
|
Standard_Integer I1 = Left.LowerRowIndex;
|
|
Standard_Integer I2 = Right.LowerRowIndex;
|
|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
|
|
Standard_Integer J1 = Left.LowerColIndex;
|
|
Standard_Integer J2 = Right.LowerColIndex;
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
|
|
Array(I, J) = Left.Array(I1, J1) - Right.Array(I2, J2);
|
|
J1++;
|
|
J2++;
|
|
}
|
|
I1++;
|
|
I2++;
|
|
}
|
|
}
|
|
|
|
|
|
void math_Matrix::Multiply(const math_Matrix& Right)
|
|
{
|
|
|
|
Standard_DimensionError_Raise_if(ColNumber() != Right.RowNumber(), "");
|
|
|
|
Standard_Real Som;
|
|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
|
|
for(Standard_Integer J2 = Right.LowerColIndex; J2 <= Right.UpperColIndex; J2++) {
|
|
Som = 0.0;
|
|
Standard_Integer I2 = Right.LowerRowIndex;
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
|
|
Som = Som + Array(I, J) * Right.Array(I2, J2);
|
|
I2++;
|
|
}
|
|
Array(I, J2) = Som;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
math_Vector math_Matrix::Multiplied(const math_Vector& Right)const
|
|
{
|
|
|
|
Standard_DimensionError_Raise_if(ColNumber() != Right.Length(), "");
|
|
|
|
math_Vector Result(LowerRowIndex, UpperRowIndex);
|
|
|
|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
|
|
Result.Array(I) = 0.0;
|
|
Standard_Integer II = Right.LowerIndex;
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
|
|
Result.Array(I) = Result.Array(I) + Array(I, J) * Right.Array(II);
|
|
II++;
|
|
}
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
math_Matrix& math_Matrix::Initialized(const math_Matrix& Other)
|
|
{
|
|
|
|
Standard_DimensionError_Raise_if((RowNumber() != Other.RowNumber()) ||
|
|
(ColNumber() != Other.ColNumber()), "");
|
|
|
|
(Other.Array).Copy(Array);
|
|
return *this;
|
|
}
|
|
|
|
|
|
|
|
|
|
void math_Matrix::Dump(Standard_OStream& o)const
|
|
|
|
{
|
|
o << "math_Matrix of RowNumber = " << RowNumber();
|
|
o << " and ColNumber = " << ColNumber() << "\n";
|
|
|
|
for(Standard_Integer I = LowerRowIndex; I <= UpperRowIndex; I++) {
|
|
for(Standard_Integer J = LowerColIndex; J <= UpperColIndex; J++) {
|
|
o << "math_Matrix ( " << I << ", " << J << " ) = ";
|
|
o << Array(I, J) << "\n";
|
|
}
|
|
}
|
|
}
|
|
|