// Created on: 1991-05-07
// Created by: Laurent PAINNOT
// Copyright (c) 1991-1999 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_Matrix_HeaderFile
#define _math_Matrix_HeaderFile

#include "Standard.hxx"
#include "Standard_DefineAlloc.hxx"
#include "NCollection_Allocator.hxx"

#include "math_DoubleTab.hxx"
#include "Standard_OStream.hxx"

// resolve name collisions with X11 headers
#ifdef Opposite
  #undef Opposite
#endif

template <typename T = double>
class math_VectorBase;

//! This class implements the real matrix abstract data type.
//! Matrixes can have an arbitrary range which must be defined
//! at the declaration and cannot be changed after this declaration
//! math_Matrix(-3,5,2,4); //a vector with range [-3..5, 2..4]
//! Matrix values may be initialized and
//! retrieved using indexes which must lie within the range
//! of definition of the matrix.
//! Matrix objects follow "value semantics", that is, they
//! cannot be shared and are copied through assignment
//! Matrices are copied through assignment:
//! @code
//! math_Matrix M2(1, 9, 1, 3);
//! ...
//! M2 = M1;
//! M1(1) = 2.0;//the matrix M2 will not be modified.
//! @endcode
//! The exception RangeError is raised when trying to access
//! outside the range of a matrix :
//! @code
//! M1(11, 1)=0.0// --> will raise RangeError.
//! @endcode
//!
//! The exception DimensionError is raised when the dimensions of
//! two matrices or vectors are not compatible.
//! @code
//! math_Matrix M3(1, 2, 1, 2);
//! M3 = M1;   // will raise DimensionError
//! M1.Add(M3) // --> will raise DimensionError.
//! @endcode
//! A Matrix can be constructed with a pointer to "c array".
//! It allows to carry the bounds inside the matrix.
//! Example :
//! @code
//! double tab1[10][20];
//! double tab2[200];
//!
//! math_Matrix A (tab1[0][0], 1, 10, 1, 20);
//! math_Matrix B (tab2[0],    1, 10, 1, 20);
//! @endcode
class math_Matrix
{
public:
  DEFINE_STANDARD_ALLOC

  //! Constructs a non-initialized matrix of range [LowerRow..UpperRow,
  //! LowerCol..UpperCol]
  //! For the constructed matrix:
  //! -   LowerRow and UpperRow are the indexes of the
  //! lower and upper bounds of a row, and
  //! -   LowerCol and UpperCol are the indexes of the
  //! lower and upper bounds of a column.
  inline math_Matrix(const int LowerRow,
                     const int UpperRow,
                     const int LowerCol,
                     const int UpperCol);

  //! constructs a non-initialized matrix of range [LowerRow..UpperRow,
  //! LowerCol..UpperCol]
  //! whose values are all initialized with the value InitialValue.
  inline math_Matrix(const int    LowerRow,
                     const int    UpperRow,
                     const int    LowerCol,
                     const int    UpperCol,
                     const double InitialValue);

  //! constructs a matrix of range [LowerRow..UpperRow,
  //! LowerCol..UpperCol]
  //! Sharing data with a "C array" pointed by Tab.
  inline math_Matrix(void* const Tab,
                     const int   LowerRow,
                     const int   UpperRow,
                     const int   LowerCol,
                     const int   UpperCol);

  //! constructs a matrix for copy in initialization.
  //! An exception is raised if the matrixes have not the same dimensions.
  inline math_Matrix(const math_Matrix& Other);

  //! Move constructor
  inline math_Matrix(math_Matrix&& Other) noexcept;

  //! Initialize all the elements of a matrix to InitialValue.
  inline void Init(const double InitialValue) noexcept;

  //! Returns the number of rows of this matrix.
  //! Note that for a matrix A you always have the following relations:
  //! - A.RowNumber() = A.UpperRow() -   A.LowerRow() + 1
  //! - A.ColNumber() = A.UpperCol() -   A.LowerCol() + 1
  //! - the length of a row of A is equal to the number of columns of A,
  //! - the length of a column of A is equal to the number of
  //! rows of A.returns the row range of a matrix.
  int RowNumber() const noexcept;

  //! Returns the number of rows of this matrix.
  //! Note that for a matrix A you always have the following relations:
  //! - A.RowNumber() = A.UpperRow() -   A.LowerRow() + 1
  //! - A.ColNumber() = A.UpperCol() -   A.LowerCol() + 1
  //! - the length of a row of A is equal to the number of columns of A,
  //! - the length of a column of A is equal to the number of
  //! rows of A.returns the row range of a matrix.
  int ColNumber() const noexcept;

  //! Returns the value of the Lower index of the row
  //! range of a matrix.
  int LowerRow() const noexcept;

  //! Returns the Upper index of the row range
  //! of a matrix.
  int UpperRow() const noexcept;

  //! Returns the value of the Lower index of the
  //! column range of a matrix.
  int LowerCol() const noexcept;

  //! Returns the value of the upper index of the
  //! column range of a matrix.
  int UpperCol() const noexcept;

  //! Computes the determinant of a matrix.
  //! An exception is raised if the matrix is not a square matrix.
  Standard_EXPORT double Determinant() const;

  //! Transposes a given matrix.
  //! An exception is raised if the matrix is not a square matrix.
  inline void Transpose();

  //! Inverts a matrix using Gauss algorithm.
  //! Exception NotSquare is raised if the matrix is not square.
  //! Exception SingularMatrix is raised if the matrix is singular.
  Standard_EXPORT void Invert();

  //! Sets this matrix to the product of the matrix Left, and the matrix Right.
  //! Example
  //! math_Matrix A (1, 3, 1, 3);
  //! math_Matrix B (1, 3, 1, 3);
  //! // A = ... , B = ...
  //! math_Matrix C (1, 3, 1, 3);
  //! C.Multiply(A, B);
  //! Exceptions
  //! Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:
  //! -   the number of columns of matrix Left, or the number of
  //! rows of matrix TLeft is not equal to the number of rows
  //! of matrix Right, or
  //! -   the number of rows of matrix Left, or the number of
  //! columns of matrix TLeft is not equal to the number of
  //! rows of this matrix, or
  //! -   the number of columns of matrix Right is not equal to
  //! the number of columns of this matrix.
  inline void Multiply(const double Right) noexcept;

  void operator*=(const double Right) noexcept { Multiply(Right); }

  //! multiplies all the elements of a matrix by the
  //! value <Right>.
  [[nodiscard]] inline math_Matrix Multiplied(const double Right) const noexcept;

  [[nodiscard]] math_Matrix operator*(const double Right) const noexcept
  {
    return Multiplied(Right);
  }

  //! Sets this matrix to the product of the
  //! transposed matrix TLeft, and the matrix Right.
  //! Example
  //! math_Matrix A (1, 3, 1, 3);
  //! math_Matrix B (1, 3, 1, 3);
  //! // A = ... , B = ...
  //! math_Matrix C (1, 3, 1, 3);
  //! C.Multiply(A, B);
  //! Exceptions
  //! Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:
  //! -   the number of columns of matrix Left, or the number of
  //! rows of matrix TLeft is not equal to the number of rows
  //! of matrix Right, or
  //! -   the number of rows of matrix Left, or the number of
  //! columns of matrix TLeft is not equal to the number of
  //! rows of this matrix, or
  //! -   the number of columns of matrix Right is not equal to
  //! the number of columns of this matrix.
  [[nodiscard]] inline math_Matrix TMultiplied(const double Right) const noexcept;
  friend math_Matrix               operator*(const double Left, const math_Matrix& Right);

  //! divides all the elements of a matrix by the value <Right>.
  //! An exception is raised if <Right> = 0.
  inline void Divide(const double Right);

  void operator/=(const double Right) { Divide(Right); }

  //! divides all the elements of a matrix by the value <Right>.
  //! An exception is raised if <Right> = 0.
  [[nodiscard]] inline math_Matrix Divided(const double Right) const;

  [[nodiscard]] math_Matrix operator/(const double Right) const { return Divided(Right); }

  //! adds the matrix <Right> to a matrix.
  //! An exception is raised if the dimensions are different.
  //! Warning
  //! In order to save time when copying matrices, it is
  //! preferable to use operator += or the function Add
  //! whenever possible.
  inline void Add(const math_Matrix& Right);

  void operator+=(const math_Matrix& Right) { Add(Right); }

  //! adds the matrix <Right> to a matrix.
  //! An exception is raised if the dimensions are different.
  [[nodiscard]] inline math_Matrix Added(const math_Matrix& Right) const;

  [[nodiscard]] math_Matrix operator+(const math_Matrix& Right) const { return Added(Right); }

  //! sets a matrix to the addition of <Left> and <Right>.
  //! An exception is raised if the dimensions are different.
  inline void Add(const math_Matrix& Left, const math_Matrix& Right);

  //! Subtracts the matrix <Right> from <me>.
  //! An exception is raised if the dimensions are different.
  //! Warning
  //! In order to avoid time-consuming copying of matrices, it
  //! is preferable to use operator -= or the function
  //! Subtract whenever possible.
  inline void Subtract(const math_Matrix& Right);

  void operator-=(const math_Matrix& Right) { Subtract(Right); }

  //! Returns the result of the subtraction of <Right> from <me>.
  //! An exception is raised if the dimensions are different.
  [[nodiscard]] inline math_Matrix Subtracted(const math_Matrix& Right) const;

  [[nodiscard]] math_Matrix operator-(const math_Matrix& Right) const { return Subtracted(Right); }

  //! Sets the values of this matrix,
  //! -   from index I1 to index I2 on the row dimension, and
  //! -   from index J1 to index J2 on the column dimension,
  //! to those of matrix M.
  //! Exceptions
  //! Standard_DimensionError if:
  //! -   I1 is less than the index of the lower row bound of this matrix, or
  //! -   I2 is greater than the index of the upper row bound of this matrix, or
  //! -   J1 is less than the index of the lower column bound of this matrix, or
  //! -   J2 is greater than the index of the upper column bound of this matrix, or
  //! -   I2 - I1 + 1 is not equal to the number of rows of matrix M, or
  //! -   J2 - J1 + 1 is not equal to the number of columns of matrix M.
  inline void Set(const int I1, const int I2, const int J1, const int J2, const math_Matrix& M);

  //! Sets the row of index Row of a matrix to the vector <V>.
  //! An exception is raised if the dimensions are different.
  //! An exception is raises if <Row> is inferior to the lower
  //! row of the matrix or <Row> is superior to the upper row.
  Standard_EXPORT void SetRow(const int Row, const math_VectorBase<>& V);

  //! Sets the column of index Col of a matrix to the vector <V>.
  //! An exception is raised if the dimensions are different.
  //! An exception is raises if <Col> is inferior to the lower
  //! column of the matrix or <Col> is superior to the upper
  //! column.
  Standard_EXPORT void SetCol(const int Col, const math_VectorBase<>& V);

  //! Sets the diagonal of a matrix to the value <Value>.
  //! An exception is raised if the matrix is not square.
  inline void SetDiag(const double Value);

  //! Returns the row of index Row of a matrix.
  Standard_EXPORT math_VectorBase<> Row(const int Row) const;

  //! Returns the column of index <Col> of a matrix.
  Standard_EXPORT math_VectorBase<> Col(const int Col) const;

  //! Swaps the rows of index Row1 and Row2.
  //! An exception is raised if <Row1> or <Row2> is out of range.
  Standard_EXPORT void SwapRow(const int Row1, const int Row2);

  //! Swaps the columns of index <Col1> and <Col2>.
  //! An exception is raised if <Col1> or <Col2> is out of range.
  Standard_EXPORT void SwapCol(const int Col1, const int Col2);

  //! Teturns the transposed of a matrix.
  //! An exception is raised if the matrix is not a square matrix.
  [[nodiscard]] inline math_Matrix Transposed() const;

  //! Returns the inverse of a matrix.
  //! Exception NotSquare is raised if the matrix is not square.
  //! Exception SingularMatrix is raised if the matrix is singular.
  Standard_EXPORT math_Matrix Inverse() const;

  //! Returns the product of the transpose of a matrix with
  //! the matrix <Right>.
  //! An exception is raised if the dimensions are different.
  inline math_Matrix TMultiply(const math_Matrix& Right) const;

  //! Computes a matrix as the product of 2 vectors.
  //! An exception is raised if the dimensions are different.
  //! <me> = <Left> * <Right>.
  Standard_EXPORT void Multiply(const math_VectorBase<>& Left, const math_VectorBase<>& Right);

  //! Computes a matrix as the product of 2 matrixes.
  //! An exception is raised if the dimensions are different.
  inline void Multiply(const math_Matrix& Left, const math_Matrix& Right);

  //! Computes a matrix to the product of the transpose of
  //! the matrix <TLeft> with the matrix <Right>.
  //! An exception is raised if the dimensions are different.
  inline void TMultiply(const math_Matrix& TLeft, const math_Matrix& Right);

  //! Sets a matrix to the Subtraction of the matrix <Right>
  //! from the matrix <Left>.
  //! An exception is raised if the dimensions are different.
  inline void Subtract(const math_Matrix& Left, const math_Matrix& Right);

  //! Accesses the value of index <Row>
  //! and <Col> of a matrix.
  //! An exception is raised if <Row> and <Col> are not
  //! in the correct range.
  const double& Value(const int Row, const int Col) const;

  //! Accesses (in read or write mode) the value of index <Row>
  //! and <Col> of a matrix.
  //! An exception is raised if <Row> and <Col> are not
  //! in the correct range.
  double& Value(const int Row, const int Col);

  const double& operator()(const int Row, const int Col) const { return Value(Row, Col); }

  double& operator()(const int Row, const int Col) { return Value(Row, Col); }

  //! Matrixes are copied through assignment.
  //! An exception is raised if the dimensions are different.
  inline math_Matrix& Initialized(const math_Matrix& Other);

  math_Matrix& operator=(const math_Matrix& Other) { return Initialized(Other); }

  //! Move assignment operator
  inline math_Matrix& operator=(math_Matrix&& Other);

  //! Returns the product of 2 matrices.
  //! An exception is raised if the dimensions are different.
  inline void Multiply(const math_Matrix& Right);

  void operator*=(const math_Matrix& Right) { Multiply(Right); }

  //! Returns the product of 2 matrices.
  //! An exception is raised if the dimensions are different.
  [[nodiscard]] inline math_Matrix Multiplied(const math_Matrix& Right) const;

  [[nodiscard]] math_Matrix operator*(const math_Matrix& Right) const { return Multiplied(Right); }

  //! Returns the product of a matrix by a vector.
  //! An exception is raised if the dimensions are different.
  [[nodiscard]] Standard_EXPORT math_VectorBase<> Multiplied(const math_VectorBase<>& Right) const;
  [[nodiscard]] Standard_EXPORT math_VectorBase<> operator*(const math_VectorBase<>& Right) const;

  //! Returns the opposite of a matrix.
  //! An exception is raised if the dimensions are different.
  inline math_Matrix Opposite() const;

  math_Matrix operator-() const { return Opposite(); }

  //! Prints information on the current state of the object.
  //! Is used to redefine the operator <<.
  inline void Dump(Standard_OStream& o) const;

protected:
  //! The new lower row of the matrix is set to <LowerRow>
  inline void SetLowerRow(const int LowerRow) noexcept;

  //! The new lower column of the matrix is set to the column
  //! of range <LowerCol>.
  inline void SetLowerCol(const int LowerCol) noexcept;

  //! The new lower row of the matrix is set to <LowerRow>
  //! and the new lower column of the matrix is set to the column
  //! of range <LowerCol>.
  void SetLower(const int LowerRow, const int LowerCol) noexcept;

private:
  math_DoubleTab Array;
};

#include "math_Matrix.lxx"

#endif // _math_Matrix_HeaderFile