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 // Copyright (c) 1997-1999 Matra Datavision
 // Copyright (c) 1999-2014 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.
 
 #ifndef math_Recipes_HeaderFile
 #define math_Recipes_HeaderFile
 
 #include <Message_ProgressRange.hxx>
 
 #include <NCollection_Allocator.hxx>
 
 template<typename T> class math_VectorBase;
 using math_IntegerVector = math_VectorBase<int>;
 using math_Vector = math_VectorBase<double>;
 class math_Matrix;
 
 const Standard_Integer math_Status_UserAborted         = -1;
 const Standard_Integer math_Status_OK                  = 0;
 const Standard_Integer math_Status_SingularMatrix      = 1;
 const Standard_Integer math_Status_ArgumentError       = 2;
 const Standard_Integer math_Status_NoConvergence       = 3;
 
 Standard_EXPORT Standard_Integer  LU_Decompose(math_Matrix& a, 
                                         math_IntegerVector& indx,
                                         Standard_Real&   d,
                                         Standard_Real    TINY = 1.0e-20,
                                         const Message_ProgressRange& theProgress = Message_ProgressRange());
 
 // Given a matrix a(1..n, 1..n), this routine computes its LU decomposition, 
 // The matrix a is replaced by this LU decomposition and the vector indx(1..n)
 // is an output which records the row permutation effected by the partial
 // pivoting; d is output as +1 or -1 depending on whether the number of row
 // interchanges was even or odd.
 
 Standard_EXPORT Standard_Integer LU_Decompose(math_Matrix& a, 
                                         math_IntegerVector& indx,
                                         Standard_Real&   d,
                                         math_Vector& vv,
                                         Standard_Real    TINY = 1.0e-30,
                                         const Message_ProgressRange& theProgress = Message_ProgressRange());
 
 // Idem to the previous LU_Decompose function. But the input Vector vv(1..n) is
 // used internally as a scratch area.
 
 
 Standard_EXPORT void LU_Solve(const math_Matrix& a,
               const math_IntegerVector& indx, 
               math_Vector& b);
 
 // Solves a * x = b for a vector x, where x is specified by a(1..n, 1..n),
 // indx(1..n) as returned by LU_Decompose. n is the dimension of the 
 // square matrix A. b(1..n) is the input right-hand side and will be 
 // replaced by the solution vector.Neither a and indx are destroyed, so 
 // the routine may be called sequentially with different b's.
 
 
 Standard_EXPORT Standard_Integer LU_Invert(math_Matrix& a);
 
 // Given a matrix a(1..n, 1..n) this routine computes its inverse. The matrix
 // a is replaced by its inverse.
 
 
 Standard_EXPORT Standard_Integer SVD_Decompose(math_Matrix& a,
                       math_Vector& w,                    
                       math_Matrix& v);
 
 // Given a matrix a(1..m, 1..n), this routine computes its singular value 
 // decomposition, a = u * w * transposed(v). The matrix u replaces a on 
 // output. The diagonal matrix of singular values w is output as a vector 
 // w(1..n). The matrix v is output as v(1..n, 1..n). m must be greater or
 // equal to n; if it is smaller, then a should be filled up to square with
 // zero rows.
 
 
 Standard_EXPORT Standard_Integer SVD_Decompose(math_Matrix& a,
                       math_Vector& w,
                       math_Matrix& v,
                       math_Vector& rv1);
 
 
 // Idem to the previous LU_Decompose function. But the input Vector vv(1..m) 
 // (the number of rows a(1..m, 1..n)) is used internally as a scratch area.
 
 
 Standard_EXPORT void SVD_Solve(const math_Matrix& u,
               const math_Vector& w,
               const math_Matrix& v,
               const math_Vector& b,
               math_Vector& x);
 
 // Solves a * x = b for a vector x, where x is specified by u(1..m, 1..n),
 // w(1..n), v(1..n, 1..n) as returned by SVD_Decompose. m and n are the 
 // dimensions of A, and will be equal for square matrices. b(1..m) is the 
 // input right-hand side. x(1..n) is the output solution vector.
 // No input quantities are destroyed, so the routine may be called 
 // sequentially with different b's.
 
 
 
 Standard_EXPORT Standard_Integer DACTCL_Decompose(math_Vector& a, const math_IntegerVector& indx,
                          const Standard_Real MinPivot = 1.e-20);
 
 // Given a SYMMETRIC matrix a, this routine computes its 
 // LU decomposition. 
 // a is given through a vector of its non zero components of the upper
 // triangular matrix.
 // indx is the indice vector of the diagonal elements of a.
 // a is replaced by its LU decomposition.
 // The range of the matrix is n = indx.Length(), 
 // and a.Length() = indx(n).
 
 
 
 Standard_EXPORT Standard_Integer DACTCL_Solve(const math_Vector& a, math_Vector& b, 
                      const math_IntegerVector& indx, 
                      const Standard_Real MinPivot = 1.e-20);
 
 // Solves a * x = b for a vector x and a matrix a coming from DACTCL_Decompose.
 // indx is the same vector as in DACTCL_Decompose.
 // the vector b is replaced by the vector solution x.
 
 
 
 
 Standard_EXPORT Standard_Integer Jacobi(math_Matrix& a, math_Vector& d, math_Matrix& v, Standard_Integer& nrot);
 
 // Computes all eigenvalues and eigenvectors of a real symmetric matrix
 // a(1..n, 1..n). On output, elements of a above the diagonal are destroyed. 
 // d(1..n) returns the eigenvalues of a. v(1..n, 1..n) is a matrix whose 
 // columns contain, on output, the normalized eigenvectors of a. nrot returns
 // the number of Jacobi rotations that were required.
 // Eigenvalues are sorted into descending order, and eigenvectors are 
 // arranges correspondingly.
 
 #endif
 
 
 
 
 
 
 
 
 

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