使用OpenCASCADE的Math功能解线性方程组

Use Math Utilities in the OpenCASCADE

OpenCASCADE由七个模块组成，分别如下：

• Module FoundationClasses; 基础类；
• Module ModelingData; 造型数据；
• Module ModelingAlgorihtms; 造型算法；
• Module Visualization; 可视化；
• Module ApplicationFramework; 程序框架；
• Module DataExchange; 数据交换；
• Module Draw;

其中基础类模块有三个工具箱：

• Toolkit TKAdvTools; 高级工具箱；
• Toolkit TKMath; 数学工具箱；
• Toolkit TKernel; 核心工具箱；

根据OpenCASCADE的Reference文档，查到math_Gauss类，描述如下：

This class implements the Gauss LU decomposition (Crout algorithm) with partial pivoting (rows interchange) of a square matrix and the different possible derived calculation :

• Solution of a set of linear equations.
• Inverse of a matrix.
• Determinant of a matrix.

主要根据矩阵的三角分解中的LU分解方法，可作如下计算：

• 线性方程组的求解；
• 矩阵的逆；
• 矩阵的行列式；

为简单起见，先做个简单的测试，求以下方程组的解：

OpenCASCADE的C++代码如下：(新建一个控制台程序，需要包含TKernel.lib;TKMath.lib两个库；)

   1:  //------------------------------------------------------------------------------

   2:  //    Copyright (c) 2012 eryar All Rights Reserved.

   3:  //

   4:  //        File    : Main.cpp

   5:  //        Author  : [email protected]

   6:  //        Date    : 2012-6-20 20:06

   7:  //        Version : 1.0v

   8:  //

   9:  //    Description : Learn to use OpenCASCADE Math Utilities.

  10:  //

  11:  //==============================================================================

  12:   

  13:  #include <math_Gauss.hxx>

  14:   

  15:  int main(int argc, char* argv[])

  16:  {

  17:      math_Matrix aMatrix(1, 3, 1, 3);

  18:      math_Vector b1(1, 3);

  22:   

  23:      //aMatrix, b1 and b2 are set here to the appropriate values

  24:      aMatrix(1, 1)   = 10;

  25:      aMatrix(2, 2)   = 2;

  26:      aMatrix(3, 3)   = 8;

  27:   

  28:      b1.Init(1);

  29:   

  30:      // Use Gause method

  31:      math_Gauss  sol(aMatrix);

  32:   

  33:      // LU decomposition of A

  34:      if (sol.IsDone())

  35:      {

  36:          sol.Solve(b1, x1);

  37:      }

  38:      else

  39:      {

  40:          // Fix up

  41:          try 

  42:          {

  43:              sol.Solve(b1, x1);

  44:          }

  45:          catch (Standard_Failure)

  46:          {

  47:              Handle(Standard_Failure) error = Standard_Failure::Caught();

  48:              cout<<error<<endl;

  49:          }

  50:      }

  51:   

  52:      cout<<aMatrix;

  53:      cout<<b1;

  54:      cout<<x1;

  55:   

  56:      return 0;

  57:  }

输出结果如下所示：

   1:  math_Matrix of RowNumber = 3 and ColNumber = 3

   2:  math_Matrix ( 1, 1 ) = 10

   3:  math_Matrix ( 1, 2 ) = 0

   4:  math_Matrix ( 1, 3 ) = 0

   5:  math_Matrix ( 2, 1 ) = 0

   6:  math_Matrix ( 2, 2 ) = 2

   7:  math_Matrix ( 2, 3 ) = 0

   8:  math_Matrix ( 3, 1 ) = 0

   9:  math_Matrix ( 3, 2 ) = 0

  10:  math_Matrix ( 3, 3 ) = 8

  11:  math_Vector of Length = 3

  12:  math_Vector(1) = 1

  13:  math_Vector(2) = 1

  14:  math_Vector(3) = 1

  15:  math_Vector of Length = 3

  16:  math_Vector(1) = 0.1

  17:  math_Vector(2) = 0.5

  18:  math_Vector(3) = 0.125

  19:  Press any key to continue . . .

结论

通过对基础类模块中数学工具箱的使用，对OpenCASCADE慢慢进行了解。