1299 lines
36 KiB
C++
1299 lines
36 KiB
C++
/*! \file pimathmatrix.h
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* \ingroup Math
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* \~\brief
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* \~english Math matrix
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* \~russian Математическая матрица
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*/
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/*
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PIP - Platform Independent Primitives
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PIMathMatrix
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Ivan Pelipenko peri4ko@yandex.ru, Andrey Bychkov work.a.b@yandex.ru
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef PIMATHMATRIX_H
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#define PIMATHMATRIX_H
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#include "pimathvector.h"
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#include "pimathcomplex.h"
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/// Matrix templated
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#define PIMM_FOR for (uint r = 0; r < Rows; ++r) for (uint c = 0; c < Cols; ++c)
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#define PIMM_FOR_C for (uint i = 0; i < Cols; ++i)
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#define PIMM_FOR_R for (uint i = 0; i < Rows; ++i)
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#pragma pack(push, 1)
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//! \brief A class that works with square matrix operations, the input data of which are columns, rows and the data type of the matrix
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//! @tparam Rows rows number of matrix
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//! @tparam Сols columns number of matrix
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//! @tparam Type is the data type of the matrix. There are can be basic C++ language data and different classes where the arithmetic operators(=, +=, -=, *=, /=, ==, !=, +, -, *, /)
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//! of the C++ language are implemented
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template<uint Rows, uint Cols = Rows, typename Type = double>
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class PIP_EXPORT PIMathMatrixT {
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typedef PIMathMatrixT<Rows, Cols, Type> _CMatrix;
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typedef PIMathMatrixT<Cols, Rows, Type> _CMatrixI;
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typedef PIMathVectorT<Rows, Type> _CMCol;
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typedef PIMathVectorT<Cols, Type> _CMRow;
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static_assert(std::is_arithmetic<Type>::value, "Type must be arithmetic");
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static_assert(Rows > 0, "Row count must be > 0");
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static_assert(Cols > 0, "Column count must be > 0");
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public:
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/**
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* \brief Constructs PIMathMatrixT that is filled by \a new_value
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*/
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PIMathMatrixT(const Type &new_value = Type()) {PIMM_FOR m[r][c] = new_value;}
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/**
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* \brief Contructs PIMathMatrixT from PIVector
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*/
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PIMathMatrixT(const PIVector<Type> &val) {
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assert(Rows*Cols == val.size());
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int i = 0;
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PIMM_FOR m[r][c] = val[i++];
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}
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/**
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* \brief Contructs PIMathMatrixT from C++11 initializer list
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*/
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PIMathMatrixT(std::initializer_list<Type> init_list) {
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assert(Rows*Cols == init_list.size());
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int i = 0;
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PIMM_FOR m[r][c] = init_list.begin()[i++];
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}
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/**
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* \brief Сreates a matrix whose main diagonal is filled with ones and the remaining elements are zeros
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*
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* @return identity matrix of type PIMathMatrixT
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*/
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static _CMatrix identity() {
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_CMatrix tm = _CMatrix();
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PIMM_FOR tm.m[r][c] = (c == r ? Type(1) : Type(0));
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return tm;
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}
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/**
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* \brief Method which returns number of columns in matrix
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*
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* @return type uint shows number of columns
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*/
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constexpr uint cols() const {return Cols;}
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/**
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* \brief Method which returns number of rows in matrix
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*
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* @return type uint shows number of rows
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*/
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constexpr uint rows() const {return Rows;}
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/**
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* \brief Method which returns the selected column in PIMathVectorT format.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param index is the number of the selected column
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* @return column in PIMathVectorT format
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*/
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_CMCol col(uint index) {
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_CMCol tv;
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PIMM_FOR_R tv[i] = m[i][index];
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return tv;
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}
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/**
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* \brief Method which returns the selected row in PIMathVectorT format
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param index is the number of the selected row
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* @return row in PIMathVectorT format
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*/
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_CMRow row(uint index) {
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_CMRow tv;
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PIMM_FOR_C tv[i] = m[index][i];
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return tv;
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}
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/**
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* \brief Set the selected column in matrix.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param index is the number of the selected column
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* @param v is a vector of the type _CMCol that needs to fill the column
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* @return matrix type _CMatrix
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*/
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_CMatrix &setCol(uint index, const _CMCol &v) {
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PIMM_FOR_R m[i][index] = v[i];
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return *this;
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}
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/**
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* \brief Set the selected row in matrix
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param index is the number of the selected row
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* @param v is a vector of the type _CMCol that needs to fill the row
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* @return matrix type _CMatrix
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*/
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_CMatrix &setRow(uint index, const _CMRow &v) {
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PIMM_FOR_C m[index][i] = v[i];
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return *this;
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}
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/**
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* \brief Method which changes selected rows in a matrix.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param rf is the number of the first selected row
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* @param rs is the number of the second selected row
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* @return matrix type _CMatrix
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*/
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_CMatrix &swapRows(uint rf, uint rs) {
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PIMM_FOR_C piSwap<Type>(m[rf][i], m[rs][i]);
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return *this;
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}
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/**
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* \brief Method which changes selected columns in a matrix.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param cf is the number of the first selected column
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* @param cs is the number of the second selected column
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* @return matrix type _CMatrix
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*/
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_CMatrix &swapCols(uint cf, uint cs) {
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PIMM_FOR_R piSwap<Type>(m[i][cf], m[i][cs]);
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return *this;
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}
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/**
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* \brief Method which fills the matrix with selected value
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*
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* @param v is a parameter the type and value of which is selected and later filled into the matrix
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* @return filled matrix type _CMatrix
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*/
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_CMatrix &fill(const Type &v) {
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PIMM_FOR m[r][c] = v;
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return *this;
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}
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/**
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* \brief Method which checks if matrix is square
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*
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* @return true if matrix is square, else false
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*/
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constexpr bool isSquare() const { return Rows == Cols; }
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/**
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* \brief Method which checks if main diagonal of matrix consists of ones and another elements are zeros
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*
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* @return true if matrix is identitied, else false
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*/
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bool isIdentity() const {
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PIMM_FOR if ((c == r) ? m[r][c] != Type(1) : m[r][c] != Type(0)) return false;
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return true;
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}
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/**
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* \brief Method which checks if every elements of matrix are zeros
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*
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* @return true if matrix is null, else false
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*/
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bool isNull() const {
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PIMM_FOR if (m[r][c] != Type(0)) return false;
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return true;
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}
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/**
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* \brief Read-only access to element by \a row and \a col.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param row of matrix
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* @param col of matrix
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* @return copy of element of matrix
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*/
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Type at(uint row, uint col) const { return m[row][col]; }
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/**
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* \brief Full access to element by \a row and \a col.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param row of matrix
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* @param col of matrix
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* @return element of matrix
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*/
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inline Type & element(uint row, uint col) {return m[row][col];}
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/**
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* \brief Read-only access to element by \a row and \a col.
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* If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param row of matrix
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* @param col of matrix
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* @return element of matrix
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*/
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inline const Type & element(uint row, uint col) const {return m[row][col];}
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/**
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* \brief Full access to the matrix row pointer. If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param row of matrix
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* @return matrix row pointer
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*/
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Type *operator[](uint row) { return m[row]; }
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/**
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* \brief Read-only access to the matrix row pointer. If you enter an index out of the border of the matrix there will be "undefined behavior"
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*
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* @param row of matrix
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* @return matrix row pointer
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*/
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const Type *operator[](uint row) const {return m[row];}
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/**
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* \brief Matrix compare
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*
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* @param sm matrix for compare
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* @return if matrices are equal true, else false
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*/
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bool operator==(const _CMatrix &sm) const {
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PIMM_FOR if (m[r][c] != sm.m[r][c]) return false;
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return true;
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}
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/**
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* \brief Matrix negative compare
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*
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* @param sm matrix for compare
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* @return if matrices are not equal true, else false
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*/
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bool operator!=(const _CMatrix &sm) const { return !(*this == sm); }
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/**
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* \brief Addition assignment with matrix "sm"
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*
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* @param sm matrix for the addition assigment
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*/
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void operator+=(const _CMatrix &sm) {PIMM_FOR m[r][c] += sm.m[r][c];}
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/**
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* \brief Subtraction assignment with matrix "sm"
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*
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* @param sm matrix for the subtraction assigment
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*/
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void operator-=(const _CMatrix &sm) {PIMM_FOR m[r][c] -= sm.m[r][c];}
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/**
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* \brief Multiplication assignment with value "v"
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*
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* @param v value for the multiplication assigment
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*/
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void operator*=(const Type &v) {
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PIMM_FOR m[r][c] *= v;
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}
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/**
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* \brief Division assignment with value "v"
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*
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* @param v value for the division assigment
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*/
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void operator/=(const Type &v) {
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assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
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PIMM_FOR m[r][c] /= v;
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}
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/**
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* \brief Matrix substraction
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*
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* @return the result of matrix substraction
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*/
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_CMatrix operator-() const {
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_CMatrix tm;
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PIMM_FOR tm.m[r][c] = -m[r][c];
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return tm;
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}
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/**
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* \brief Matrix addition
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*
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* @param sm is matrix term
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* @return the result of matrix addition
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*/
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_CMatrix operator+(const _CMatrix &sm) const {
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_CMatrix tm = _CMatrix(*this);
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PIMM_FOR tm.m[r][c] += sm.m[r][c];
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return tm;
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}
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/**
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* \brief Matrix substraction
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*
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* @param sm is matrix subtractor
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* @return the result of matrix substraction
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*/
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_CMatrix operator-(const _CMatrix &sm) const {
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_CMatrix tm = _CMatrix(*this);
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PIMM_FOR tm.m[r][c] -= sm.m[r][c];
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return tm;
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}
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/**
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* \brief Matrix multiplication
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*
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* @param v is value factor
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* @return the result of matrix multiplication
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*/
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_CMatrix operator*(const Type &v) const {
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_CMatrix tm = _CMatrix(*this);
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PIMM_FOR tm.m[r][c] *= v;
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return tm;
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}
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/**
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* \brief Matrix division
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*
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* @param v is value divider
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* @return the result of matrix division
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*/
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_CMatrix operator/(const Type &v) const {
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assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
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_CMatrix tm = _CMatrix(*this);
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PIMM_FOR tm.m[r][c] /= v;
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return tm;
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}
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/**
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* \brief Determinant of the matrix is calculated. Works only with square matrix, nonzero matrices and invertible matrix
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*
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* @param ok is a parameter with which we can find out if the method worked correctly
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* @return matrix determinant
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*/
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Type determinant(bool *ok = 0) const {
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_CMatrix m(*this);
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bool k;
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Type ret = Type(0);
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m.toUpperTriangular(&k);
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if (ok) *ok = k;
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if (!k) return ret;
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ret = Type(1);
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PIMM_FOR if (r == c) ret *= m[r][c];
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return ret;
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}
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/**
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* \brief Trace of the matrix is calculated. Works only with square matrix, nonzero matrices and invertible matrix
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*
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* @return matrix trace
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*/
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Type trace() const {
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static_assert(Rows == Cols, "Works only with square matrix");
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Type ret = Type(0);
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for (uint i = 0; i < Cols; ++i) {
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ret += m[i][i];
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}
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return ret;
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}
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/**
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* \brief Transforming matrix to upper triangular. Works only with square matrix, nonzero matrices and invertible matrix
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*
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* @param ok is a parameter with which we can find out if the method worked correctly
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* @return copy of transformed upper triangular matrix
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*/
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_CMatrix &toUpperTriangular(bool *ok = 0) {
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static_assert(Rows == Cols, "Works only with square matrix");
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_CMatrix smat(*this);
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bool ndet;
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uint crow;
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Type mul;
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for (uint i = 0; i < Cols; ++i) {
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ndet = true;
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for (uint j = 0; j < Rows; ++j) if (smat.m[i][j] != 0) ndet = false;
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if (ndet) {
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if (ok != 0) *ok = false;
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return *this;
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}
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}
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for (uint i = 0; i < Cols; ++i) {
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crow = i;
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while (smat.m[i][i] == Type(0))
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smat.swapRows(i, ++crow);
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for (uint j = i + 1; j < Rows; ++j) {
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mul = smat.m[i][j] / smat.m[i][i];
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for (uint k = i; k < Cols; ++k) smat.m[k][j] -= mul * smat.m[k][i];
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}
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if (i < Cols - 1) {
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if (piAbs<Type>(smat.m[i + 1][i + 1]) < Type(1E-200)) {
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if (ok != 0) *ok = false;
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return *this;
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}
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}
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}
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if (ok != 0) *ok = true;
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memcpy(m, smat.m, sizeof(Type) * Cols * Rows);
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return *this;
|
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}
|
||
|
||
/**
|
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* \brief Matrix inversion operation. Works only with square matrix, nonzero matrices and invertible matrix
|
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*
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* @param ok is a parameter with which we can find out if the method worked correctly
|
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* @return copy of inverted matrix
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*/
|
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_CMatrix &invert(bool *ok = 0) {
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static_assert(Rows == Cols, "Works only with square matrix");
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_CMatrix mtmp = _CMatrix::identity(), smat(*this);
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bool ndet;
|
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uint crow;
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Type mul, iddiv;
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for (uint i = 0; i < Cols; ++i) {
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ndet = true;
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for (uint j = 0; j < Rows; ++j) if (smat.m[i][j] != 0) ndet = false;
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if (ndet) {
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if (ok != 0) *ok = false;
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return *this;
|
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}
|
||
}
|
||
for (uint i = 0; i < Cols; ++i) {
|
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crow = i;
|
||
while (smat.m[i][i] == Type(0)) {
|
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++crow;
|
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smat.swapRows(i, crow);
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mtmp.swapRows(i, crow);
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||
}
|
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for (uint j = i + 1; j < Rows; ++j) {
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mul = smat.m[i][j] / smat.m[i][i];
|
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for (uint k = i; k < Cols; ++k) smat.m[k][j] -= mul * smat.m[k][i];
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for (uint k = 0; k < Cols; ++k) mtmp.m[k][j] -= mul * mtmp.m[k][i];
|
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}
|
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if (i < Cols - 1) {
|
||
if (piAbs<Type>(smat.m[i + 1][i + 1]) < Type(1E-200)) {
|
||
if (ok != 0) *ok = false;
|
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return *this;
|
||
}
|
||
}
|
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iddiv = smat.m[i][i];
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for (uint j = i; j < Cols; ++j) smat.m[j][i] /= iddiv;
|
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for (uint j = 0; j < Cols; ++j) mtmp.m[j][i] /= iddiv;
|
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}
|
||
for (uint i = Cols - 1; i > 0; --i) {
|
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for (uint j = 0; j < i; ++j) {
|
||
mul = smat.m[i][j];
|
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smat.m[i][j] -= mul;
|
||
for (uint k = 0; k < Cols; ++k) mtmp.m[k][j] -= mtmp.m[k][i] * mul;
|
||
}
|
||
}
|
||
if (ok != 0) *ok = true;
|
||
memcpy(m, mtmp.m, sizeof(Type) * Cols * Rows);
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix inversion operation. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @param ok is a parameter with which we can find out if the method worked correctly
|
||
* @return inverted matrix
|
||
*/
|
||
_CMatrix inverted(bool *ok = 0) const {
|
||
_CMatrix tm(*this);
|
||
tm.invert(ok);
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix transposition operation. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @return transposed matrix
|
||
*/
|
||
_CMatrixI transposed() const {
|
||
_CMatrixI tm;
|
||
PIMM_FOR tm[c][r] = m[r][c];
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix rotation operation. Works only with 2x2 matrix
|
||
*
|
||
* @return rotated matrix
|
||
*/
|
||
_CMatrix rotate(Type angle) {
|
||
static_assert(Rows == 2 && Cols == 2, "Works only with 2x2 matrix");
|
||
Type c = std::cos(angle);
|
||
Type s = std::sin(angle);
|
||
PIMathMatrixT<2u, 2u> tm;
|
||
tm[0][0] = tm[1][1] = c;
|
||
tm[0][1] = -s;
|
||
tm[1][0] = s;
|
||
*this = *this * tm;
|
||
return *this;
|
||
}
|
||
|
||
private:
|
||
Type m[Rows][Cols];
|
||
};
|
||
|
||
#pragma pack(pop)
|
||
|
||
|
||
#ifdef PIP_STD_IOSTREAM
|
||
template<uint Rows, uint Cols, typename Type>
|
||
inline std::ostream & operator <<(std::ostream & s, const PIMathMatrixT<Rows, Cols, Type> & m) {
|
||
s << "{";
|
||
for (uint r = 0; r < Rows; ++r) {
|
||
for (uint c = 0; c < Cols; ++c) {
|
||
s << m[r][c];
|
||
if (c < Cols - 1 || r < Rows - 1) s << ", ";
|
||
}
|
||
if (r < Rows - 1) s << std::endl << " ";
|
||
}
|
||
s << "}";
|
||
return s;
|
||
}
|
||
#endif
|
||
|
||
/**
|
||
* \brief Add matrix "m" at the end of matrix and return reference to matrix
|
||
*
|
||
* @param s PICout type
|
||
* @param m PIMathMatrixT type
|
||
* @return bitwise left PICout
|
||
*/
|
||
template<uint Rows, uint Cols, typename Type>
|
||
inline PICout operator<<(PICout s, const PIMathMatrixT<Rows, Cols, Type> &m) {
|
||
s << "{";
|
||
for (uint r = 0; r < Rows; ++r) {
|
||
for (uint c = 0; c < Cols; ++c) {
|
||
s << m[r][c];
|
||
if (c < Cols - 1 || r < Rows - 1) s << ", ";
|
||
}
|
||
if (r < Rows - 1) s << PICoutManipulators::NewLine << " ";
|
||
}
|
||
s << "}";
|
||
return s;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying matrices by each other. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param fm first matrix multiplier
|
||
* @param sm second matrix multiplier
|
||
* @return matrix that is the result of multiplication
|
||
*/
|
||
template<uint CR, uint Rows0, uint Cols1, typename Type>
|
||
inline PIMathMatrixT<Rows0, Cols1, Type> operator*(const PIMathMatrixT<Rows0, CR, Type> &fm,
|
||
const PIMathMatrixT<CR, Cols1, Type> &sm) {
|
||
PIMathMatrixT<Rows0, Cols1, Type> tm;
|
||
Type t;
|
||
for (uint j = 0; j < Rows0; ++j) {
|
||
for (uint i = 0; i < Cols1; ++i) {
|
||
t = Type(0);
|
||
for (uint k = 0; k < CR; ++k)
|
||
t += fm[j][k] * sm[k][i];
|
||
tm[j][i] = t;
|
||
}
|
||
}
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying matrix and vector. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param fm first matrix multiplier
|
||
* @param sv second vector multiplier
|
||
* @return vector that is the result of multiplication
|
||
*/
|
||
template<uint Cols, uint Rows, typename Type>
|
||
inline PIMathVectorT<Rows, Type> operator*(const PIMathMatrixT<Rows, Cols, Type> &fm,
|
||
const PIMathVectorT<Cols, Type> &sv) {
|
||
PIMathVectorT<Rows, Type> tv;
|
||
Type t;
|
||
for (uint j = 0; j < Rows; ++j) {
|
||
t = Type(0);
|
||
for (uint i = 0; i < Cols; ++i)
|
||
t += fm[j][i] * sv[i];
|
||
tv[j] = t;
|
||
}
|
||
return tv;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying vector and matrix. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param sv first vector multiplier
|
||
* @param fm second matrix multiplier
|
||
* @return vector that is the result of multiplication
|
||
*/
|
||
template<uint Cols, uint Rows, typename Type>
|
||
inline PIMathVectorT<Cols, Type> operator*(const PIMathVectorT<Rows, Type> &sv,
|
||
const PIMathMatrixT<Rows, Cols, Type> &fm) {
|
||
PIMathVectorT<Cols, Type> tv;
|
||
Type t;
|
||
for (uint j = 0; j < Cols; ++j) {
|
||
t = Type(0);
|
||
for (uint i = 0; i < Rows; ++i)
|
||
t += fm[i][j] * sv[i];
|
||
tv[j] = t;
|
||
}
|
||
return tv;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying value of type Type and matrix
|
||
*
|
||
* @param x first multiplier of type Type
|
||
* @param fm second matrix multiplier
|
||
* @return matrix that is the result of multiplication
|
||
*/
|
||
template<uint Cols, uint Rows, typename Type>
|
||
inline PIMathMatrixT<Rows, Cols, Type> operator*(const Type &x, const PIMathMatrixT<Rows, Cols, Type> &v) {
|
||
return v * x;
|
||
}
|
||
|
||
|
||
typedef PIMathMatrixT<2u, 2u, int> PIMathMatrixT22i;
|
||
typedef PIMathMatrixT<3u, 3u, int> PIMathMatrixT33i;
|
||
typedef PIMathMatrixT<4u, 4u, int> PIMathMatrixT44i;
|
||
typedef PIMathMatrixT<2u, 2u, double> PIMathMatrixT22d;
|
||
typedef PIMathMatrixT<3u, 3u, double> PIMathMatrixT33d;
|
||
typedef PIMathMatrixT<4u, 4u, double> PIMathMatrixT44d;
|
||
|
||
|
||
template<typename Type>
|
||
class PIMathMatrix;
|
||
|
||
#undef PIMM_FOR
|
||
#undef PIMM_FOR_C
|
||
#undef PIMM_FOR_R
|
||
|
||
|
||
|
||
|
||
|
||
/// Matrix
|
||
|
||
#define PIMM_FOR for (uint r = 0; r < _V2D::rows_; ++r) for (uint c = 0; c < _V2D::cols_; ++c)
|
||
#define PIMM_FOR_A for (uint i = 0; i < _V2D::mat.size(); ++i)
|
||
#define PIMM_FOR_C for (uint i = 0; i < _V2D::cols_; ++i)
|
||
#define PIMM_FOR_R for (uint i = 0; i < _V2D::rows_; ++i)
|
||
|
||
//! \brief A class that works with matrix operations, the input data of which is the data type of the matrix
|
||
//! @tparam There are can be basic C++ language data and different classes where the arithmetic operators(=, +=, -=, *=, /=, ==, !=, +, -, *, /)
|
||
//! of the C++ language are implemented
|
||
template<typename Type>
|
||
class PIP_EXPORT PIMathMatrix : public PIVector2D<Type> {
|
||
typedef PIVector2D<Type> _V2D;
|
||
typedef PIMathMatrix<Type> _CMatrix;
|
||
public:
|
||
/**
|
||
* \brief Constructor of class PIMathMatrix, which creates a matrix
|
||
*
|
||
* @param cols is number of matrix column uint type
|
||
* @param rows is number of matrix row uint type
|
||
* @param f is type of matrix elements
|
||
*/
|
||
PIMathMatrix(const uint cols = 0, const uint rows = 0, const Type &f = Type()) { _V2D::resize(rows, cols, f); }
|
||
|
||
/**
|
||
* \brief Constructor of class PIMathMatrix, which creates a matrix
|
||
*
|
||
* @param cols is number of matrix column uint type
|
||
* @param rows is number of matrix row uint type
|
||
* @param val is PIVector<Type> of matrix elements
|
||
*/
|
||
PIMathMatrix(const uint cols, const uint rows, const PIVector<Type> &val) {
|
||
_V2D::resize(rows, cols);
|
||
int i = 0;
|
||
PIMM_FOR _V2D::element(r, c) = val[i++];
|
||
}
|
||
|
||
/**
|
||
* \brief Constructor of class PIMathMatrix, which creates a matrix
|
||
*
|
||
* @param val is PIVector<Type> of PIVector, which creates matrix
|
||
*/
|
||
PIMathMatrix(const PIVector<PIVector<Type> > &val) {
|
||
if (!val.isEmpty()) {
|
||
_V2D::resize(val.size(), val[0].size());
|
||
for (uint r = 0; r < _V2D::rows_; ++r) {
|
||
assert(val[r].size() == _V2D::cols_);
|
||
for (uint c = 0; c < _V2D::cols_; ++c)
|
||
_V2D::element(r, c) = val[r][c];
|
||
}
|
||
}
|
||
}
|
||
|
||
/**
|
||
* \brief Constructor of class PIMathMatrix, which creates a matrix
|
||
*
|
||
* @param val is PIVector2D<Type>, which creates matrix
|
||
*/
|
||
PIMathMatrix(const PIVector2D<Type> &val) {
|
||
if (!val.isEmpty()) {
|
||
_V2D::resize(val.rows(), val.cols());
|
||
PIMM_FOR _V2D::element(r, c) = val.element(r, c);
|
||
}
|
||
}
|
||
|
||
/**
|
||
* \brief Creates a matrix whose main diagonal is filled with ones and the remaining elements are zeros
|
||
*
|
||
* @param cols is number of matrix column uint type
|
||
* @param rows is number of matrix row uint type
|
||
* @return identity matrix(cols,rows)
|
||
*/
|
||
static _CMatrix identity(const uint cols, const uint rows) {
|
||
_CMatrix tm(cols, rows);
|
||
for (uint r = 0; r < rows; ++r) for (uint c = 0; c < cols; ++c) tm.element(r, c) = (c == r ? Type(1) : Type(0));
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Creates a row matrix of every element that is equal to every element of the vector
|
||
*
|
||
* @param val is the vector type PIMathVector
|
||
* @return row matrix of every element that is equal to every element of the vector
|
||
*/
|
||
static _CMatrix matrixRow(const PIMathVector<Type> &val) {return _CMatrix(val.size(), 1, val.toVector());}
|
||
|
||
/**
|
||
* \brief Creates a column matrix of every element that is equal to every element of the vector
|
||
*
|
||
* @param val is the vector type PIMathVector
|
||
* @return column matrix of every element that is equal to every element of the vector
|
||
*/
|
||
static _CMatrix matrixCol(const PIMathVector<Type> &val) {return _CMatrix(1, val.size(), val.toVector());}
|
||
|
||
/**
|
||
* \brief Set the selected column in matrix. If there are more elements of the vector than elements in the column of the matrix
|
||
* or index larger than the number of columns otherwise there will be "undefined behavior"
|
||
*
|
||
* @param index is the number of the selected column
|
||
* @param v is a vector of the type _CMCol that needs to fill the column
|
||
* @return matrix type _CMatrix
|
||
*/
|
||
_CMatrix &setCol(uint index, const PIMathVector<Type> &v) {
|
||
assert(_V2D::rows() == v.size());
|
||
PIMM_FOR_R _V2D::element(i, index) = v[i];
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Set the selected row in matrix. If there are more elements of the vector than elements in the row of the matrix,
|
||
* or index larger than the number of rows otherwise there will be "undefined behavior"
|
||
* @param index is the number of the selected row
|
||
* @param v is a vector of the type _CMCol that needs to fill the row
|
||
* @return matrix type _CMatrix
|
||
*/
|
||
_CMatrix &setRow(uint index, const PIMathVector<Type> &v) {
|
||
assert(_V2D::cols() == v.size());
|
||
PIMM_FOR_C _V2D::element(index, i) = v[i];
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which replace selected columns in a matrix. You cannot use an index larger than the number of columns,
|
||
* otherwise there will be "undefined behavior"
|
||
*
|
||
* @param r0 is the number of the first selected row
|
||
* @param r1 is the number of the second selected row
|
||
* @return matrix type _CMatrix
|
||
*/
|
||
_CMatrix &swapCols(uint r0, uint r1) {
|
||
PIMM_FOR_C piSwap<Type>(_V2D::element(i, r0), _V2D::element(i, r1));
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which replace selected rows in a matrix. You cannot use an index larger than the number of rows,
|
||
* otherwise there will be "undefined behavior"
|
||
*
|
||
* @param c0 is the number of the first selected row
|
||
* @param c1 is the number of the second selected row
|
||
* @return matrix type _CMatrix
|
||
*/
|
||
_CMatrix &swapRows(uint c0, uint c1) {
|
||
PIMM_FOR_R piSwap<Type>(_V2D::element(c0, i), _V2D::element(c1, i));
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which fills the matrix with selected value
|
||
*
|
||
* @param v is a parameter the type and value of which is selected and later filled into the matrix
|
||
* @return filled matrix type _CMatrix
|
||
*/
|
||
_CMatrix &fill(const Type &v) {
|
||
PIMM_FOR_A _V2D::mat[i] = v;
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which checks if matrix is square
|
||
*
|
||
* @return true if matrix is square, else false
|
||
*/
|
||
bool isSquare() const { return _V2D::cols_ == _V2D::rows_; }
|
||
|
||
/**
|
||
* \brief Method which checks if main diagonal of matrix consists of ones and another elements are zeros
|
||
*
|
||
* @return true if matrix is identity, else false
|
||
*/
|
||
bool isIdentity() const {
|
||
PIMM_FOR if ((c == r) ? _V2D::element(r, c) != Type(1) : _V2D::element(r, c) != Type(0))return false;
|
||
return true;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which checks if every elements of matrix are zeros
|
||
*
|
||
* @return true if matrix elements equal to zero, else false
|
||
*/
|
||
bool isNull() const {
|
||
PIMM_FOR_A if (_V2D::mat[i] != Type(0)) return false;
|
||
return true;
|
||
}
|
||
|
||
/**
|
||
* \brief Method which checks if matrix is empty
|
||
*
|
||
* @return true if matrix is valid, else false
|
||
*/
|
||
bool isValid() const { return !PIVector2D<Type>::isEmpty(); }
|
||
|
||
/**
|
||
* \brief Addition assignment with matrix "sm"
|
||
*
|
||
* @param sm matrix for the addition assigment
|
||
*/
|
||
void operator+=(const _CMatrix &sm) {
|
||
assert(_V2D::rows() == sm.rows());
|
||
assert(_V2D::cols() == sm.cols());
|
||
PIMM_FOR_A _V2D::mat[i] += sm.mat[i];
|
||
}
|
||
|
||
/**
|
||
* \brief Subtraction assignment with matrix "sm"
|
||
*
|
||
* @param sm matrix for the subtraction assigment
|
||
*/
|
||
void operator-=(const _CMatrix &sm) {
|
||
assert(_V2D::rows() == sm.rows());
|
||
assert(_V2D::cols() == sm.cols());
|
||
PIMM_FOR_A _V2D::mat[i] -= sm.mat[i];
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplication assignment with value "v"
|
||
*
|
||
* @param v value for the multiplication assigment
|
||
*/
|
||
void operator*=(const Type &v) {
|
||
PIMM_FOR_A _V2D::mat[i] *= v;
|
||
}
|
||
|
||
/**
|
||
* \brief Division assignment with value "v"
|
||
*
|
||
* @param v value for the division assigment
|
||
*/
|
||
void operator/=(const Type &v) {
|
||
assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
|
||
PIMM_FOR_A _V2D::mat[i] /= v;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix substraction
|
||
*
|
||
* @return the result of matrix substraction
|
||
*/
|
||
_CMatrix operator-() const {
|
||
_CMatrix tm(*this);
|
||
PIMM_FOR_A tm.mat[i] = -_V2D::mat[i];
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix addition
|
||
*
|
||
* @param sm is matrix term
|
||
* @return the result of matrix addition
|
||
*/
|
||
_CMatrix operator+(const _CMatrix &sm) const {
|
||
_CMatrix tm(*this);
|
||
assert(tm.rows() == sm.rows());
|
||
assert(tm.cols() == sm.cols());
|
||
PIMM_FOR_A tm.mat[i] += sm.mat[i];
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix subtraction
|
||
*
|
||
* @param sm is matrix subtractor
|
||
* @return the result of matrix subtraction
|
||
*/
|
||
_CMatrix operator-(const _CMatrix &sm) const {
|
||
_CMatrix tm(*this);
|
||
assert(tm.rows() == sm.rows());
|
||
assert(tm.cols() == sm.cols());
|
||
PIMM_FOR_A tm.mat[i] -= sm.mat[i];
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix multiplication
|
||
*
|
||
* @param v is value factor
|
||
* @return the result of matrix multiplication
|
||
*/
|
||
_CMatrix operator*(const Type &v) const {
|
||
_CMatrix tm(*this);
|
||
PIMM_FOR_A tm.mat[i] *= v;
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix division
|
||
*
|
||
* @param v is value divider
|
||
* @return the result of matrix division
|
||
*/
|
||
_CMatrix operator/(const Type &v) const {
|
||
assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
|
||
_CMatrix tm(*this);
|
||
PIMM_FOR_A tm.mat[i] /= v;
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Determinant of the self matrix is calculated. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @param ok is a parameter with which we can find out if the method worked correctly
|
||
* @return matrix determinant
|
||
*/
|
||
Type determinant(bool *ok = 0) const {
|
||
_CMatrix m(*this);
|
||
bool k;
|
||
m.toUpperTriangular(&k);
|
||
Type ret = Type(0);
|
||
if (ok) *ok = k;
|
||
if (!k) return ret;
|
||
ret = Type(1);
|
||
for (uint c = 0; c < _V2D::cols_; ++c)
|
||
for (uint r = 0; r < _V2D::rows_; ++r)
|
||
if (r == c)
|
||
ret *= m.element(r, c);
|
||
return ret;
|
||
}
|
||
|
||
/**
|
||
* \brief Trace of the matrix is calculated. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @return matrix trace
|
||
*/
|
||
Type trace() const {
|
||
assert(isSquare());
|
||
Type ret = Type(0);
|
||
for (uint i = 0; i < _V2D::cols_; ++i) {
|
||
ret += _V2D::element(i, i);
|
||
}
|
||
return ret;
|
||
}
|
||
|
||
/**
|
||
* \brief Transforming matrix to upper triangular. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @param ok is a parameter with which we can find out if the method worked correctly
|
||
* @return copy of transformed upper triangular matrix
|
||
*/
|
||
_CMatrix &toUpperTriangular(bool *ok = 0) {
|
||
assert(isSquare());
|
||
_CMatrix smat(*this);
|
||
bool ndet;
|
||
uint crow;
|
||
Type mul;
|
||
for (uint i = 0; i < _V2D::cols_; ++i) {
|
||
ndet = true;
|
||
for (uint j = 0; j < _V2D::rows_; ++j) if (smat.element(i, j) != 0) ndet = false;
|
||
if (ndet) {
|
||
if (ok != 0) *ok = false;
|
||
return *this;
|
||
}
|
||
}
|
||
for (uint i = 0; i < _V2D::cols_; ++i) {
|
||
crow = i;
|
||
while (smat.element(i, i) == Type(0))
|
||
smat.swapRows(i, ++crow);
|
||
for (uint j = i + 1; j < _V2D::rows_; ++j) {
|
||
mul = smat.element(i, j) / smat.element(i, i);
|
||
for (uint k = i; k < _V2D::cols_; ++k) smat.element(k, j) -= mul * smat.element(k, i);
|
||
}
|
||
if (i < _V2D::cols_ - 1) {
|
||
if (PIMathFloatNullCompare(smat.element(i + 1, i + 1))) {
|
||
if (ok != 0) *ok = false;
|
||
return *this;
|
||
}
|
||
}
|
||
}
|
||
if (ok != 0) *ok = true;
|
||
_V2D::mat.swap(smat.mat);
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix inversion operation. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @param ok is a parameter with which we can find out if the method worked correctly
|
||
* @param sv is a vector multiplier
|
||
* @return copy of inverted matrix
|
||
*/
|
||
_CMatrix &invert(bool *ok = 0, PIMathVector<Type> *sv = 0) {
|
||
assert(isSquare());
|
||
_CMatrix mtmp = _CMatrix::identity(_V2D::cols_, _V2D::rows_), smat(*this);
|
||
bool ndet;
|
||
uint crow;
|
||
Type mul, iddiv;
|
||
for (uint i = 0; i < _V2D::cols_; ++i) {
|
||
ndet = true;
|
||
for (uint j = 0; j < _V2D::rows_; ++j) if (smat.element(i, j) != Type(0)) ndet = false;
|
||
if (ndet) {
|
||
if (ok != 0) *ok = false;
|
||
return *this;
|
||
}
|
||
}
|
||
for (uint i = 0; i < _V2D::cols_; ++i) {
|
||
crow = i;
|
||
while (smat.element(i, i) == Type(0)) {
|
||
++crow;
|
||
smat.swapRows(i, crow);
|
||
mtmp.swapRows(i, crow);
|
||
if (sv != 0) sv->swapElements(i, crow);
|
||
}
|
||
for (uint j = i + 1; j < _V2D::rows_; ++j) {
|
||
mul = smat.element(i, j) / smat.element(i, i);
|
||
for (uint k = i; k < _V2D::cols_; ++k) smat.element(k, j) -= mul * smat.element(k, i);
|
||
for (uint k = 0; k < _V2D::cols_; ++k) mtmp.element(k, j) -= mul * mtmp.element(k, i);
|
||
if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
|
||
}
|
||
if (i < _V2D::cols_ - 1) {
|
||
if (PIMathFloatNullCompare(smat.element(i + 1, i + 1))) {
|
||
if (ok != 0) *ok = false;
|
||
return *this;
|
||
}
|
||
}
|
||
iddiv = smat.element(i, i);
|
||
for (uint j = i; j < _V2D::cols_; ++j) smat.element(j, i) /= iddiv;
|
||
for (uint j = 0; j < _V2D::cols_; ++j) mtmp.element(j, i) /= iddiv;
|
||
if (sv != 0) (*sv)[i] /= iddiv;
|
||
}
|
||
for (uint i = _V2D::cols_ - 1; i > 0; --i) {
|
||
for (uint j = 0; j < i; ++j) {
|
||
mul = smat.element(i, j);
|
||
smat.element(i, j) -= mul;
|
||
for (uint k = 0; k < _V2D::cols_; ++k) mtmp.element(k, j) -= mul * mtmp.element(k, i);
|
||
if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
|
||
}
|
||
}
|
||
if (ok != 0) *ok = true;
|
||
PIVector2D<Type>::swap(mtmp);
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix inversion operation. Works only with square matrix, nonzero matrices and invertible matrix
|
||
*
|
||
* @param ok is a parameter with which we can find out if the method worked correctly
|
||
* @return inverted matrix
|
||
*/
|
||
_CMatrix inverted(bool *ok = 0) const {
|
||
_CMatrix tm(*this);
|
||
tm.invert(ok);
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Matrix transposition operation
|
||
*
|
||
* @return transposed matrix
|
||
*/
|
||
_CMatrix transposed() const {
|
||
_CMatrix tm(_V2D::rows_, _V2D::cols_);
|
||
PIMM_FOR tm.element(c, r) = _V2D::element(r, c);
|
||
return tm;
|
||
}
|
||
};
|
||
|
||
|
||
#ifdef PIP_STD_IOSTREAM
|
||
template<typename Type>
|
||
inline std::ostream & operator <<(std::ostream & s, const PIMathMatrix<Type> & m) {s << "{"; for (uint r = 0; r < m.rows(); ++r) { for (uint c = 0; c < m.cols(); ++c) { s << m.element(r, c); if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";} if (r < m.rows() - 1) s << std::endl << " ";} s << "}"; return s;}
|
||
#endif
|
||
|
||
/**
|
||
* \brief Inline operator for outputting the matrix to the console
|
||
*
|
||
* @param s PICout type
|
||
* @param the matrix type PIMathMatrix that we print to the console
|
||
* @return PIMathMatrix printed to the console
|
||
*/
|
||
template<typename Type>
|
||
inline PICout operator<<(PICout s, const PIMathMatrix<Type> &m) {
|
||
s << "Matrix{";
|
||
for (uint r = 0; r < m.rows(); ++r) {
|
||
for (uint c = 0; c < m.cols(); ++c) {
|
||
s << m.element(r, c);
|
||
if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";
|
||
}
|
||
if (r < m.rows() - 1) s << PICoutManipulators::NewLine << " ";
|
||
}
|
||
s << "}";
|
||
return s;
|
||
}
|
||
|
||
/**
|
||
* \brief Inline operator for serializing a matrix into a PIByteArray
|
||
*
|
||
* @param s PIByteArray type
|
||
* @param v PIMathMatrix type
|
||
* @return PIBiteArray serialized PIMathMatrix
|
||
*/
|
||
template <typename P, typename T>
|
||
inline PIBinaryStream<P> & operator <<(PIBinaryStream<P> & s, const PIMathMatrix<T> & v) {
|
||
s << (const PIVector2D<T> &) v;
|
||
return s;
|
||
}
|
||
|
||
/**
|
||
* \brief Inline operator to deserialize matrix from PIByteArray
|
||
*
|
||
* @param s PIByteArray type
|
||
* @param v PIMathMatrix type
|
||
* @return PIMathMatrix deserialized from PIByteArray
|
||
*/
|
||
template <typename P, typename T>
|
||
inline PIBinaryStream<P> & operator >>(PIBinaryStream<P> & s, PIMathMatrix<T> & v) {
|
||
s >> (PIVector2D<T> &) v;
|
||
return s;
|
||
}
|
||
|
||
|
||
/**
|
||
* \brief Multiplying matrices by each other. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param fm first matrix multiplier
|
||
* @param sm second matrix multiplier
|
||
* @return matrix that is the result of multiplication
|
||
*/
|
||
template<typename Type>
|
||
inline PIMathMatrix<Type> operator*(const PIMathMatrix<Type> &fm,
|
||
const PIMathMatrix<Type> &sm) {
|
||
assert(fm.cols() == sm.rows());
|
||
PIMathMatrix<Type> tm(sm.cols(), fm.rows());
|
||
Type t;
|
||
for (uint j = 0; j < fm.rows(); ++j) {
|
||
for (uint i = 0; i < sm.cols(); ++i) {
|
||
t = Type(0);
|
||
for (uint k = 0; k < fm.cols(); ++k)
|
||
t += fm.element(j, k) * sm.element(k, i);
|
||
tm.element(j, i) = t;
|
||
}
|
||
}
|
||
return tm;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying matrix and vector. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param fm first matrix multiplier
|
||
* @param sv second vector multiplier
|
||
* @return vector that is the result of multiplication
|
||
*/
|
||
template<typename Type>
|
||
inline PIMathVector<Type> operator*(const PIMathMatrix<Type> &fm,
|
||
const PIMathVector<Type> &sv) {
|
||
assert(fm.cols() == sv.size());
|
||
PIMathVector<Type> tv(fm.rows());
|
||
Type t;
|
||
for (uint j = 0; j < fm.rows(); ++j) {
|
||
t = Type(0);
|
||
for (uint i = 0; i < fm.cols(); ++i)
|
||
t += fm.element(j, i) * sv[i];
|
||
tv[j] = t;
|
||
}
|
||
return tv;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying vector and matrix. If you enter an index out of the border of the matrix there will be "undefined behavior"
|
||
*
|
||
* @param sv first vector multiplier
|
||
* @param fm second matrix multiplier
|
||
* @return vector that is the result of multiplication
|
||
*/
|
||
template<typename Type>
|
||
inline PIMathVector<Type> operator*(const PIMathVector<Type> &sv,
|
||
const PIMathMatrix<Type> &fm) {
|
||
PIMathVector<Type> tv(fm.cols());
|
||
assert(fm.rows() == sv.size());
|
||
Type t;
|
||
for (uint j = 0; j < fm.cols(); ++j) {
|
||
t = Type(0);
|
||
for (uint i = 0; i < fm.rows(); ++i)
|
||
t += fm.element(i, j) * sv[i];
|
||
tv[j] = t;
|
||
}
|
||
return tv;
|
||
}
|
||
|
||
/**
|
||
* \brief Multiplying value of type Type and matrix
|
||
*
|
||
* @param x first multiplier of type Type
|
||
* @param v second matrix multiplier
|
||
* @return matrix that is the result of multiplication
|
||
*/
|
||
template<typename Type>
|
||
inline PIMathMatrix<Type> operator*(const Type &x, const PIMathMatrix<Type> &v) {
|
||
return v * x;
|
||
}
|
||
|
||
typedef PIMathMatrix<int> PIMathMatrixi;
|
||
typedef PIMathMatrix<double> PIMathMatrixd;
|
||
|
||
/**
|
||
* \brief Searching hermitian matrix
|
||
*
|
||
* @param m conjugate transpose matrix
|
||
* @return result of the hermitian
|
||
*/
|
||
template<typename T>
|
||
PIMathMatrix<complex<T> > hermitian(const PIMathMatrix<complex<T> > &m) {
|
||
PIMathMatrix<complex<T> > ret(m);
|
||
for (uint r = 0; r < ret.rows(); ++r)
|
||
for (uint c = 0; c < ret.cols(); ++c)
|
||
ret.element(r, c).imag(-(ret.element(r, c).imag()));
|
||
return ret.transposed();
|
||
}
|
||
|
||
#undef PIMM_FOR
|
||
#undef PIMM_FOR_A
|
||
#undef PIMM_FOR_C
|
||
#undef PIMM_FOR_R
|
||
|
||
#endif // PIMATHMATRIX_H
|