// 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
#include
#include
#include
class math_IntegerVector;
class math_Vector;
class math_Matrix;
class Message_ProgressIndicator;
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 Handle(Message_ProgressIndicator) & aProgress = Handle(Message_ProgressIndicator)());
// 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 wether 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 Handle(Message_ProgressIndicator) & aProgress = Handle(Message_ProgressIndicator)());
// 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