occt/src/FoundationClasses/TKMath/GTests/math_Matrix_Test.cxx

// Copyright (c) 2025 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.

#include <math_Matrix.hxx>

#include <gtest/gtest.h>

#include <Standard_Real.hxx>
#include <Standard_Integer.hxx>
#include <math_Vector.hxx>
#include <Precision.hxx>

namespace
{
// Helper function for comparing matrices with tolerance
void checkMatricesEqual(const math_Matrix&  theM1,
                        const math_Matrix&  theM2,
                        const Standard_Real theTolerance = Precision::Confusion())
{
  ASSERT_EQ(theM1.RowNumber(), theM2.RowNumber());
  ASSERT_EQ(theM1.ColNumber(), theM2.ColNumber());
  ASSERT_EQ(theM1.LowerRow(), theM2.LowerRow());
  ASSERT_EQ(theM1.LowerCol(), theM2.LowerCol());

  for (Standard_Integer anI = theM1.LowerRow(); anI <= theM1.UpperRow(); anI++)
  {
    for (Standard_Integer aJ = theM1.LowerCol(); aJ <= theM1.UpperCol(); aJ++)
    {
      EXPECT_NEAR(theM1(anI, aJ), theM2(anI, aJ), theTolerance);
    }
  }
}
} // namespace

// Tests for constructors
TEST(MathMatrixTest, Constructors)
{
  // Test standard constructor
  math_Matrix aMatrix1(1, 3, 1, 4);
  EXPECT_EQ(aMatrix1.RowNumber(), 3);
  EXPECT_EQ(aMatrix1.ColNumber(), 4);
  EXPECT_EQ(aMatrix1.LowerRow(), 1);
  EXPECT_EQ(aMatrix1.UpperRow(), 3);
  EXPECT_EQ(aMatrix1.LowerCol(), 1);
  EXPECT_EQ(aMatrix1.UpperCol(), 4);

  // Test constructor with initial value
  math_Matrix aMatrix2(2, 4, 3, 5, 2.5);
  EXPECT_EQ(aMatrix2.RowNumber(), 3);
  EXPECT_EQ(aMatrix2.ColNumber(), 3);

  for (Standard_Integer anI = 2; anI <= 4; anI++)
  {
    for (Standard_Integer aJ = 3; aJ <= 5; aJ++)
    {
      EXPECT_EQ(aMatrix2(anI, aJ), 2.5);
    }
  }

  // Test copy constructor
  math_Matrix aMatrix3(aMatrix2);
  checkMatricesEqual(aMatrix2, aMatrix3);
}

// Tests for initialization and access
TEST(MathMatrixTest, InitAndAccess)
{
  math_Matrix aMatrix(1, 3, 1, 3);

  // Test Init
  aMatrix.Init(5.0);

  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aMatrix(anI, aJ), 5.0);
    }
  }

  // Test direct value access and modification
  aMatrix(2, 2) = 10.0;
  EXPECT_EQ(aMatrix(2, 2), 10.0);

  // Test Value method
  aMatrix.Value(3, 3) = 15.0;
  EXPECT_EQ(aMatrix(3, 3), 15.0);
}

// Tests for matrix operations
TEST(MathMatrixTest, MatrixOperations)
{
  math_Matrix aMatrix1(1, 3, 1, 3);
  math_Matrix aMatrix2(1, 3, 1, 3);

  // Initialize matrices
  aMatrix1.Init(2.0);
  aMatrix2.Init(3.0);

  // Test addition
  math_Matrix anAddResult = aMatrix1.Added(aMatrix2);
  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(anAddResult(anI, aJ), 5.0);
    }
  }

  // Test subtraction
  math_Matrix aSubResult = aMatrix1.Subtracted(aMatrix2);
  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aSubResult(anI, aJ), -1.0);
    }
  }

  // Test multiplication by scalar
  math_Matrix aMulResult = aMatrix1.Multiplied(2.5);
  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aMulResult(anI, aJ), 5.0);
    }
  }
  // Test division by scalar
  math_Matrix aDivResult = aMatrix1.Divided(0.5);
  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aDivResult(anI, aJ), 4.0);
    }
  }

  // Test in-place multiplication by scalar using Multiply method
  math_Matrix aInPlaceMul(1, 3, 1, 3);
  aInPlaceMul.Init(3.0);
  aInPlaceMul.Multiply(2.0);

  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aInPlaceMul(anI, aJ), 6.0);
    }
  }

  // Test in-place multiplication by scalar using operator*=
  math_Matrix aInPlaceOp(1, 3, 1, 3);
  aInPlaceOp.Init(2.0);
  aInPlaceOp *= 3.0;

  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      EXPECT_EQ(aInPlaceOp(anI, aJ), 6.0);
    }
  }
}

// Tests for matrix multiplication
TEST(MathMatrixTest, MatrixMultiplication)
{
  // Create identity matrix
  math_Matrix anIdentity(1, 3, 1, 3);
  anIdentity.Init(0.0);
  anIdentity(1, 1) = 1.0;
  anIdentity(2, 2) = 1.0;
  anIdentity(3, 3) = 1.0;

  // Create test matrix
  math_Matrix aMatrix(1, 3, 1, 3);
  for (Standard_Integer anI = 1; anI <= 3; anI++)
  {
    for (Standard_Integer aJ = 1; aJ <= 3; aJ++)
    {
      aMatrix(anI, aJ) = anI + aJ;
    }
  }

  // Test matrix multiplication with identity
  math_Matrix aResult = aMatrix.Multiplied(anIdentity);
  checkMatricesEqual(aResult, aMatrix);

  // Test matrix multiplication
  math_Matrix aMatA(1, 2, 1, 3);
  math_Matrix aMatB(1, 3, 1, 2);

  aMatA(1, 1) = 1.0;
  aMatA(1, 2) = 2.0;
  aMatA(1, 3) = 3.0;
  aMatA(2, 1) = 4.0;
  aMatA(2, 2) = 5.0;
  aMatA(2, 3) = 6.0;

  aMatB(1, 1) = 7.0;
  aMatB(1, 2) = 8.0;
  aMatB(2, 1) = 9.0;
  aMatB(2, 2) = 10.0;
  aMatB(3, 1) = 11.0;
  aMatB(3, 2) = 12.0;

  math_Matrix aMatC = aMatA.Multiplied(aMatB);

  EXPECT_EQ(aMatC(1, 1), 1 * 7 + 2 * 9 + 3 * 11);
  EXPECT_EQ(aMatC(1, 2), 1 * 8 + 2 * 10 + 3 * 12);
  EXPECT_EQ(aMatC(2, 1), 4 * 7 + 5 * 9 + 6 * 11);
  EXPECT_EQ(aMatC(2, 2), 4 * 8 + 5 * 10 + 6 * 12);

  // Test in-place matrix multiplication using Multiply method
  math_Matrix aInPlaceMulMat1(1, 2, 1, 2);
  math_Matrix aInPlaceMulMat2(1, 2, 1, 2);

  // Set matrix values
  aInPlaceMulMat1(1, 1) = 1.0;
  aInPlaceMulMat1(1, 2) = 2.0;
  aInPlaceMulMat1(2, 1) = 3.0;
  aInPlaceMulMat1(2, 2) = 4.0;

  aInPlaceMulMat2(1, 1) = 2.0;
  aInPlaceMulMat2(1, 2) = 0.0;
  aInPlaceMulMat2(2, 1) = 1.0;
  aInPlaceMulMat2(2, 2) = 3.0;

  // Store original matrix for comparison
  math_Matrix aOrigMat(aInPlaceMulMat1);

  // Perform in-place multiplication
  aInPlaceMulMat1.Multiply(aInPlaceMulMat2);

  // Expected result: [1 2; 3 4] * [2 0; 1 3] = [4 6; 10 12]
  EXPECT_EQ(aInPlaceMulMat1(1, 1), 1 * 2 + 2 * 1); // 4
  EXPECT_EQ(aInPlaceMulMat1(1, 2), 1 * 0 + 2 * 3); // 6
  EXPECT_EQ(aInPlaceMulMat1(2, 1), 3 * 2 + 4 * 1); // 10
  EXPECT_EQ(aInPlaceMulMat1(2, 2), 3 * 0 + 4 * 3); // 12

  // Test in-place matrix multiplication using operator*=
  math_Matrix aInPlaceOpMat(aOrigMat);
  aInPlaceOpMat *= aInPlaceMulMat2;

  // Check same result as with direct Multiply method
  EXPECT_EQ(aInPlaceOpMat(1, 1), 4);
  EXPECT_EQ(aInPlaceOpMat(1, 2), 6);
  EXPECT_EQ(aInPlaceOpMat(2, 1), 10);
  EXPECT_EQ(aInPlaceOpMat(2, 2), 12);
}

// Tests for transpose and inverse operations
TEST(MathMatrixTest, TransposeAndInverse)
{
  // Test transpose
  math_Matrix aMatrix(1, 2, 1, 3);
  aMatrix(1, 1) = 1.0;
  aMatrix(1, 2) = 2.0;
  aMatrix(1, 3) = 3.0;
  aMatrix(2, 1) = 4.0;
  aMatrix(2, 2) = 5.0;
  aMatrix(2, 3) = 6.0;

  math_Matrix aTransposed = aMatrix.Transposed();

  EXPECT_EQ(aTransposed.RowNumber(), aMatrix.ColNumber());
  EXPECT_EQ(aTransposed.ColNumber(), aMatrix.RowNumber());
  EXPECT_EQ(aTransposed(1, 1), aMatrix(1, 1));
  EXPECT_EQ(aTransposed(2, 1), aMatrix(1, 2));
  EXPECT_EQ(aTransposed(3, 1), aMatrix(1, 3));
  EXPECT_EQ(aTransposed(1, 2), aMatrix(2, 1));
  EXPECT_EQ(aTransposed(2, 2), aMatrix(2, 2));
  EXPECT_EQ(aTransposed(3, 2), aMatrix(2, 3));

  // Test inverse of a matrix
  math_Matrix anInvertible(1, 3, 1, 3);
  anInvertible(1, 1) = 1.0;
  anInvertible(1, 2) = 0.0;
  anInvertible(1, 3) = 0.0;
  anInvertible(2, 1) = 0.0;
  anInvertible(2, 2) = 2.0;
  anInvertible(2, 3) = 0.0;
  anInvertible(3, 1) = 0.0;
  anInvertible(3, 2) = 0.0;
  anInvertible(3, 3) = 4.0;

  math_Matrix anInverse = anInvertible.Inverse();

  EXPECT_EQ(anInverse(1, 1), 1.0);
  EXPECT_EQ(anInverse(2, 2), 0.5);
  EXPECT_EQ(anInverse(3, 3), 0.25);

  // Test identity after multiplication
  math_Matrix anIdentity = anInvertible.Multiplied(anInverse);

  EXPECT_NEAR(anIdentity(1, 1), 1.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(2, 2), 1.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(3, 3), 1.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(1, 2), 0.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(1, 3), 0.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(2, 1), 0.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(2, 3), 0.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(3, 1), 0.0, Precision::Confusion());
  EXPECT_NEAR(anIdentity(3, 2), 0.0, Precision::Confusion());
}

// Tests for determinant calculation
TEST(MathMatrixTest, Determinant)
{
  // Test determinant of identity matrix
  math_Matrix anIdentity(1, 3, 1, 3);
  anIdentity.Init(0.0);
  anIdentity(1, 1) = 1.0;
  anIdentity(2, 2) = 1.0;
  anIdentity(3, 3) = 1.0;

  EXPECT_NEAR(anIdentity.Determinant(), 1.0, Precision::Confusion());

  // Test determinant of diagonal matrix
  math_Matrix aDiagonal(1, 3, 1, 3);
  aDiagonal.Init(0.0);
  aDiagonal(1, 1) = 2.0;
  aDiagonal(2, 2) = 3.0;
  aDiagonal(3, 3) = 4.0;

  EXPECT_NEAR(aDiagonal.Determinant(), 24.0, Precision::Confusion());

  // Test determinant of a non-singular matrix
  math_Matrix aMatrix(1, 3, 1, 3);
  aMatrix(1, 1) = 3.0;
  aMatrix(1, 2) = 8.0;
  aMatrix(1, 3) = 5.0;
  aMatrix(2, 1) = 6.0;
  aMatrix(2, 2) = 2.0;
  aMatrix(2, 3) = 7.0;
  aMatrix(3, 1) = 4.0;
  aMatrix(3, 2) = 1.0;
  aMatrix(3, 3) = 9.0;

  // det = 3*(2*9-7*1) - 8*(6*9-7*4) + 5*(6*1-2*4) = 3*11 - 8*26 + 5*-2 = 33 - 208 - 10 = -185
  EXPECT_NEAR(aMatrix.Determinant(), -185.0, Precision::Confusion());
}

// Tests for Row and Column operations
TEST(MathMatrixTest, RowAndColumnOperations)
{
  math_Matrix aMatrix(1, 3, 1, 3);
  aMatrix.Init(0.0);

  // Setup matrix rows
  aMatrix(1, 1) = 1.0;
  aMatrix(1, 2) = 2.0;
  aMatrix(1, 3) = 3.0;
  aMatrix(2, 1) = 4.0;
  aMatrix(2, 2) = 5.0;
  aMatrix(2, 3) = 6.0;
  aMatrix(3, 1) = 7.0;
  aMatrix(3, 2) = 8.0;
  aMatrix(3, 3) = 9.0;

  // Test Row method
  math_Vector aRow = aMatrix.Row(2);
  EXPECT_EQ(aRow.Length(), 3);
  EXPECT_EQ(aRow(1), 4.0);
  EXPECT_EQ(aRow(2), 5.0);
  EXPECT_EQ(aRow(3), 6.0);

  // Test Col method
  math_Vector aCol = aMatrix.Col(3);
  EXPECT_EQ(aCol.Length(), 3);
  EXPECT_EQ(aCol(1), 3.0);
  EXPECT_EQ(aCol(2), 6.0);
  EXPECT_EQ(aCol(3), 9.0);

  // Test SetRow
  math_Vector aNewRow(1, 3);
  aNewRow(1) = 10.0;
  aNewRow(2) = 11.0;
  aNewRow(3) = 12.0;
  aMatrix.SetRow(2, aNewRow);

  EXPECT_EQ(aMatrix(2, 1), 10.0);
  EXPECT_EQ(aMatrix(2, 2), 11.0);
  EXPECT_EQ(aMatrix(2, 3), 12.0);

  // Test SetCol
  math_Vector aNewCol(1, 3);
  aNewCol(1) = 13.0;
  aNewCol(2) = 14.0;
  aNewCol(3) = 15.0;
  aMatrix.SetCol(1, aNewCol);

  EXPECT_EQ(aMatrix(1, 1), 13.0);
  EXPECT_EQ(aMatrix(2, 1), 14.0);
  EXPECT_EQ(aMatrix(3, 1), 15.0);

  // Test SwapRow
  aMatrix.SwapRow(1, 3);
  EXPECT_EQ(aMatrix(1, 1), 15.0);
  EXPECT_EQ(aMatrix(1, 2), 8.0);
  EXPECT_EQ(aMatrix(1, 3), 9.0);
  EXPECT_EQ(aMatrix(3, 1), 13.0);
  EXPECT_EQ(aMatrix(3, 2), 2.0);
  EXPECT_EQ(aMatrix(3, 3), 3.0);

  // Test SwapCol
  aMatrix.SwapCol(2, 3);
  EXPECT_EQ(aMatrix(1, 2), 9.0);
  EXPECT_EQ(aMatrix(1, 3), 8.0);
  EXPECT_EQ(aMatrix(2, 2), 12.0);
  EXPECT_EQ(aMatrix(2, 3), 11.0);
  EXPECT_EQ(aMatrix(3, 2), 3.0);
  EXPECT_EQ(aMatrix(3, 3), 2.0);
}

// Tests for SetDiag method
TEST(MathMatrixTest, SetDiag)
{
  math_Matrix aMatrix(1, 3, 1, 3);
  aMatrix.Init(0.0);

  // Set diagonal elements to 5.0
  aMatrix.SetDiag(5.0);

  EXPECT_EQ(aMatrix(1, 1), 5.0);
  EXPECT_EQ(aMatrix(2, 2), 5.0);
  EXPECT_EQ(aMatrix(3, 3), 5.0);

  // Check non-diagonal elements remain 0
  EXPECT_EQ(aMatrix(1, 2), 0.0);
  EXPECT_EQ(aMatrix(1, 3), 0.0);
  EXPECT_EQ(aMatrix(2, 1), 0.0);
  EXPECT_EQ(aMatrix(2, 3), 0.0);
  EXPECT_EQ(aMatrix(3, 1), 0.0);
  EXPECT_EQ(aMatrix(3, 2), 0.0);
}

// Tests for vector-matrix operations
TEST(MathMatrixTest, VectorMatrixOperations)
{
  // Create test matrix
  math_Matrix aMatrix(1, 3, 1, 3);
  aMatrix(1, 1) = 1;
  aMatrix(1, 2) = 2;
  aMatrix(1, 3) = 3;
  aMatrix(2, 1) = 4;
  aMatrix(2, 2) = 5;
  aMatrix(2, 3) = 6;
  aMatrix(3, 1) = 7;
  aMatrix(3, 2) = 8;
  aMatrix(3, 3) = 9;

  // Create test vector
  math_Vector aVector(1, 3);
  aVector(1) = 2;
  aVector(2) = 3;
  aVector(3) = 4;

  // Test matrix * vector
  math_Vector aResult = aMatrix * aVector;

  EXPECT_EQ(aResult.Length(), 3);
  // For row 1: 1*2 + 2*3 + 3*4 = 2 + 6 + 12 = 20
  EXPECT_EQ(aResult(1), 20);
  // For row 2: 4*2 + 5*3 + 6*4 = 8 + 15 + 24 = 47
  EXPECT_EQ(aResult(2), 47);
  // For row 3: 7*2 + 8*3 + 9*4 = 14 + 24 + 36 = 74
  EXPECT_EQ(aResult(3), 74);

  // Test Multiply method with two vectors
  math_Vector aVec1(1, 2), aVec2(1, 3);
  aVec1(1) = 1;
  aVec1(2) = 2;
  aVec2(1) = 3;
  aVec2(2) = 4;
  aVec2(3) = 5;

  math_Matrix aMat(1, 2, 1, 3);
  aMat.Multiply(aVec1, aVec2);

  // The result should be the outer product of v1 and v2
  EXPECT_EQ(aMat(1, 1), 1 * 3); // aVec1(1) * aVec2(1)
  EXPECT_EQ(aMat(1, 2), 1 * 4); // aVec1(1) * aVec2(2)
  EXPECT_EQ(aMat(1, 3), 1 * 5); // aVec1(1) * aVec2(3)
  EXPECT_EQ(aMat(2, 1), 2 * 3); // aVec1(2) * aVec2(1)
  EXPECT_EQ(aMat(2, 2), 2 * 4); // aVec1(2) * aVec2(2)
  EXPECT_EQ(aMat(2, 3), 2 * 5); // aVec1(2) * aVec2(3)
}

// Special test to ensure that the matrix multiplication bug is fixed
// Bug description: In-place matrix multiplication modifies matrix elements
// that are still needed for the computation of remaining elements
TEST(MathMatrixTest, InPlaceMatrixMultiplication)
{
  // Create a test matrix with specific values to reveal the bug
  math_Matrix aMatrix(1, 2, 1, 2);
  aMatrix(1, 1) = 1.0;
  aMatrix(1, 2) = 2.0;
  aMatrix(2, 1) = 3.0;
  aMatrix(2, 2) = 4.0;

  // Create a copy of the matrix for comparison
  math_Matrix aMatrixCopy(aMatrix);

  // Expected result of matrix * matrix (calculated by hand)
  // [1 2] * [1 2] = [7 10]
  // [3 4]   [3 4]   [15 22]
  math_Matrix aExpectedResult(1, 2, 1, 2);
  aExpectedResult(1, 1) = 7.0;
  aExpectedResult(1, 2) = 10.0;
  aExpectedResult(2, 1) = 15.0;
  aExpectedResult(2, 2) = 22.0;

  // Non-in-place multiplication result (known to be correct)
  math_Matrix aCorrectResult = aMatrixCopy.Multiplied(aMatrixCopy);

  // Verify that the non-in-place multiplication gives the correct result
  EXPECT_EQ(aCorrectResult(1, 1), 7.0);
  EXPECT_EQ(aCorrectResult(1, 2), 10.0);
  EXPECT_EQ(aCorrectResult(2, 1), 15.0);
  EXPECT_EQ(aCorrectResult(2, 2), 22.0);

  // Perform in-place multiplication with self
  aMatrix.Multiply(aMatrix);

  // If the bug is fixed, both results should be identical
  EXPECT_NEAR(aMatrix(1, 1), aCorrectResult(1, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrix(1, 2), aCorrectResult(1, 2), Precision::Confusion());
  EXPECT_NEAR(aMatrix(2, 1), aCorrectResult(2, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrix(2, 2), aCorrectResult(2, 2), Precision::Confusion());

  // Also test the operator*= version with self
  aMatrixCopy *= aMatrixCopy;

  // Verify the operator*= with self gives correct results
  EXPECT_NEAR(aMatrixCopy(1, 1), aCorrectResult(1, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixCopy(1, 2), aCorrectResult(1, 2), Precision::Confusion());
  EXPECT_NEAR(aMatrixCopy(2, 1), aCorrectResult(2, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixCopy(2, 2), aCorrectResult(2, 2), Precision::Confusion());

  // Create two different matrices
  math_Matrix aMatrixA(1, 2, 1, 2);
  aMatrixA(1, 1) = 1.0;
  aMatrixA(1, 2) = 2.0;
  aMatrixA(2, 1) = 3.0;
  aMatrixA(2, 2) = 4.0;

  math_Matrix aMatrixB(1, 2, 1, 2);
  aMatrixB(1, 1) = 5.0;
  aMatrixB(1, 2) = 6.0;
  aMatrixB(2, 1) = 7.0;
  aMatrixB(2, 2) = 8.0;

  // Create copies for non-in-place calculation
  math_Matrix aMatrixACopy(aMatrixA);
  math_Matrix aMatrixBCopy(aMatrixB);

  // Calculate expected result using non-in-place multiplication
  math_Matrix aExpectedAB = aMatrixACopy.Multiplied(aMatrixBCopy);

  // Expected result: [1 2] * [5 6] = [19 22]
  //                  [3 4]   [7 8]   [43 50]
  EXPECT_EQ(aExpectedAB(1, 1), 19.0);
  EXPECT_EQ(aExpectedAB(1, 2), 22.0);
  EXPECT_EQ(aExpectedAB(2, 1), 43.0);
  EXPECT_EQ(aExpectedAB(2, 2), 50.0);

  // Test in-place multiplication with different matrix
  aMatrixA.Multiply(aMatrixB);

  // Check results match expected values
  EXPECT_NEAR(aMatrixA(1, 1), aExpectedAB(1, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixA(1, 2), aExpectedAB(1, 2), Precision::Confusion());
  EXPECT_NEAR(aMatrixA(2, 1), aExpectedAB(2, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixA(2, 2), aExpectedAB(2, 2), Precision::Confusion());

  // Test operator*= with different matrices
  aMatrixACopy *= aMatrixBCopy;

  // Check results match expected values
  EXPECT_NEAR(aMatrixACopy(1, 1), aExpectedAB(1, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixACopy(1, 2), aExpectedAB(1, 2), Precision::Confusion());
  EXPECT_NEAR(aMatrixACopy(2, 1), aExpectedAB(2, 1), Precision::Confusion());
  EXPECT_NEAR(aMatrixACopy(2, 2), aExpectedAB(2, 2), Precision::Confusion());
}