git-svn-id: svn://db.shs.com.ru/pip@400 12ceb7fc-bf1f-11e4-8940-5bc7170c53b5
This commit is contained in:
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src_main/math/pimathmatrix.h
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src_main/math/pimathmatrix.h
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/*! \file pimathmatrix.h
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* \brief PIMathMatrix
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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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Copyright (C) 2016 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 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 General Public License for more details.
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You should have received a copy of the GNU 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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/// Matrix templated
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#define PIMM_FOR(r, c) for (uint c = 0; c < Cols; ++c) { for (uint r = 0; r < Rows; ++r) {
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#define PIMM_FOR_WB(r, c) for (uint c = 0; c < Cols; ++c) for (uint r = 0; r < Rows; ++r) // without brakes
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#define PIMM_FOR_I(r, c) for (uint r = 0; r < Rows; ++r) { for (uint c = 0; c < Cols; ++c) {
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#define PIMM_FOR_I_WB(r, c) for (uint r = 0; r < Rows; ++r) for (uint c = 0; c < Cols; ++c) // without brakes
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#define PIMM_FOR_C(v) for (uint v = 0; v < Cols; ++v)
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#define PIMM_FOR_R(v) for (uint v = 0; v < Rows; ++v)
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#pragma pack(push, 1)
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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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public:
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PIMathMatrixT() {resize(Rows, Cols);}
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PIMathMatrixT(Type fval, ...) {resize(Rows, Cols); va_list vl; va_start(vl, fval); PIMM_FOR_I_WB(r, c) m[r][c] = (r + c == 0 ? fval : va_arg(vl, Type)); va_end(vl);}
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PIMathMatrixT(const PIVector<Type> & val) {resize(Rows, Cols); int i = 0; PIMM_FOR_I_WB(r, c) m[r][c] = val[i++];}
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//PIMathMatrixT(const _CMatrix & o) {resize(Rows, Cols); int i = 0; PIMM_FOR_I_WB(r, c) m[r][c] = val[i++];}
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static _CMatrix identity() {_CMatrix tm = _CMatrix(); PIMM_FOR_WB(r, c) tm.m[r][c] = (c == r ? Type(1) : Type(0)); return tm;}
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static _CMatrix filled(const Type & v) {_CMatrix tm; PIMM_FOR_WB(r, c) tm.m[r][c] = v; return tm;}
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static _CMatrix rotation(double angle) {return _CMatrix();}
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static _CMatrix rotationX(double angle) {return _CMatrix();}
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static _CMatrix rotationY(double angle) {return _CMatrix();}
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static _CMatrix rotationZ(double angle) {return _CMatrix();}
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static _CMatrix scaleX(double factor) {return _CMatrix();}
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static _CMatrix scaleY(double factor) {return _CMatrix();}
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static _CMatrix scaleZ(double factor) {return _CMatrix();}
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uint cols() const {return Cols;}
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uint rows() const {return Rows;}
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_CMCol col(uint index) {_CMCol tv; PIMM_FOR_R(i) tv[i] = m[i][index]; return tv;}
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_CMRow row(uint index) {_CMRow tv; PIMM_FOR_C(i) tv[i] = m[index][i]; return tv;}
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_CMatrix & setCol(uint index, const _CMCol & v) {PIMM_FOR_R(i) m[i][index] = v[i]; return *this;}
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_CMatrix & setRow(uint index, const _CMRow & v) {PIMM_FOR_C(i) m[index][i] = v[i]; return *this;}
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_CMatrix & swapRows(uint r0, uint r1) {Type t; PIMM_FOR_C(i) {t = m[r0][i]; m[r0][i] = m[r1][i]; m[r1][i] = t;} return *this;}
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_CMatrix & swapCols(uint c0, uint c1) {Type t; PIMM_FOR_R(i) {t = m[i][c0]; m[i][c0] = m[i][c1]; m[i][c1] = t;} return *this;}
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_CMatrix & fill(const Type & v) {PIMM_FOR_WB(r, c) m[r][c] = v; return *this;}
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//inline _CMatrix & set(Type fval, ...) {m[0] = fval; va_list vl; va_start(vl, fval); PIMV_FOR(i, 1) m[i] = va_arg(vl, Type); va_end(vl); return *this;}
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//inline void normalize() {Type tv = length(); if (tv == Type(1)) return; PIMV_FOR(i, 0) m[i] /= tv;}
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bool isSquare() const {return cols() == rows();}
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bool isIdentity() const {PIMM_FOR_WB(r, c) if ((c == r) ? m[r][c] != Type(1) : m[r][c] != Type(0)) return false; return true;}
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bool isNull() const {PIMM_FOR_WB(r, c) if (m[r][c] != Type(0)) return false; return true;}
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Type & at(uint row, uint col) {return m[row][col];}
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Type at(uint row, uint col) const {return m[row][col];}
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Type * operator [](uint row) {return m[row];}
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const Type * operator [](uint row) const {return m[row];}
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_CMatrix & operator =(const _CMatrix & sm) {memcpy(m, sm.m, sizeof(Type) * Cols * Rows); return *this;}
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bool operator ==(const _CMatrix & sm) const {PIMM_FOR_WB(r, c) if (m[r][c] != sm.m[r][c]) return false; return true;}
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bool operator !=(const _CMatrix & sm) const {return !(*this == sm);}
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void operator +=(const _CMatrix & sm) {PIMM_FOR_WB(r, c) m[r][c] += sm.m[r][c];}
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void operator -=(const _CMatrix & sm) {PIMM_FOR_WB(r, c) m[r][c] -= sm.m[r][c];}
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void operator *=(const Type & v) {PIMM_FOR_WB(r, c) m[r][c] *= v;}
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void operator /=(const Type & v) {PIMM_FOR_WB(r, c) m[r][c] /= v;}
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_CMatrix operator -() const {_CMatrix tm; PIMM_FOR_WB(r, c) tm.m[r][c] = -m[r][c]; return tm;}
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_CMatrix operator +(const _CMatrix & sm) const {_CMatrix tm = _CMatrix(*this); PIMM_FOR_WB(r, c) tm.m[r][c] += sm.m[r][c]; return tm;}
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_CMatrix operator -(const _CMatrix & sm) const {_CMatrix tm = _CMatrix(*this); PIMM_FOR_WB(r, c) tm.m[r][c] -= sm.m[r][c]; return tm;}
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_CMatrix operator *(const Type & v) const {_CMatrix tm = _CMatrix(*this); PIMM_FOR_WB(r, c) tm.m[r][c] *= v; return tm;}
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_CMatrix operator /(const Type & v) const {_CMatrix tm = _CMatrix(*this); PIMM_FOR_WB(r, c) tm.m[r][c] /= v; return tm;}
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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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for (uint c = 0; c < Cols; ++c)
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for (uint r = 0; r < Rows; ++r)
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if (r == c)
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ret *= m[r][c];
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return ret;
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}
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_CMatrix & toUpperTriangular(bool * ok = 0) {
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if (Cols != Rows) {
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if (ok != 0) *ok = false;
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return *this;
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}
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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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for (uint j = 0; j < Cols; ++j) if (smat.m[j][i] != 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 (fabs(smat.m[i+1][i+1]) < Type(1E-100)) {
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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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_CMatrix & invert(bool * ok = 0) {
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if (Cols != Rows) {
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if (ok != 0) *ok = false;
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return *this;
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}
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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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}
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for (uint j = 0; j < Cols; ++j) if (smat.m[j][i] != 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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++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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//cout << i << endl << smat << endl;
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if (i < Cols - 1) {
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if (fabs(smat.m[i+1][i+1]) < Type(1E-100)) {
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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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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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}
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for (uint i = Cols - 1; i > 0; --i) {
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for (uint j = 0; j < i; ++j) {
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mul = smat.m[i][j];
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smat.m[i][j] -= mul;
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for (uint k = 0; k < Cols; ++k) mtmp.m[k][j] -= mtmp.m[k][i] * mul;
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}
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}
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if (ok != 0) *ok = true;
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memcpy(m, mtmp.m, sizeof(Type) * Cols * Rows);
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return *this;
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}
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_CMatrix inverted(bool * ok = 0) const {_CMatrix tm(*this); tm.invert(ok); return tm;}
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_CMatrixI transposed() const {_CMatrixI tm; PIMM_FOR_WB(r, c) tm[c][r] = m[r][c]; return tm;}
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private:
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void resize(uint rows_, uint cols_, const Type & new_value = Type()) {r_ = rows_; c_ = cols_; PIMM_FOR_WB(r, c) m[r][c] = new_value;}
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int c_, r_;
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Type m[Rows][Cols];
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};
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#pragma pack(pop)
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template<> inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::rotation(double angle) {double c = cos(angle), s = sin(angle); PIMathMatrixT<2u, 2u> tm; tm[0][0] = tm[1][1] = c; tm[0][1] = -s; tm[1][0] = s; return tm;}
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template<> inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::scaleX(double factor) {PIMathMatrixT<2u, 2u> tm; tm[0][0] = factor; tm[1][1] = 1.; return tm;}
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template<> inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::scaleY(double factor) {PIMathMatrixT<2u, 2u> tm; tm[0][0] = 1.; tm[1][1] = factor; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationX(double angle) {double c = cos(angle), s = sin(angle); PIMathMatrixT<3u, 3u> tm; tm[0][0] = 1.; tm[1][1] = tm[2][2] = c; tm[2][1] = s; tm[1][2] = -s; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationY(double angle) {double c = cos(angle), s = sin(angle); PIMathMatrixT<3u, 3u> tm; tm[1][1] = 1.; tm[0][0] = tm[2][2] = c; tm[2][0] = -s; tm[0][2] = s; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationZ(double angle) {double c = cos(angle), s = sin(angle); PIMathMatrixT<3u, 3u> tm; tm[2][2] = 1.; tm[0][0] = tm[1][1] = c; tm[1][0] = s; tm[0][1] = -s; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleX(double factor) {PIMathMatrixT<3u, 3u> tm; tm[1][1] = tm[2][2] = 1.; tm[0][0] = factor; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleY(double factor) {PIMathMatrixT<3u, 3u> tm; tm[0][0] = tm[2][2] = 1.; tm[1][1] = factor; return tm;}
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template<> inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleZ(double factor) {PIMathMatrixT<3u, 3u> tm; tm[0][0] = tm[1][1] = 1.; tm[2][2] = factor; return tm;}
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#ifdef PIP_STD_IOSTREAM
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template<uint Rows, uint Cols, typename Type>
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inline std::ostream & operator <<(std::ostream & s, const PIMathMatrixT<Rows, Cols, Type> & m) {s << '{'; PIMM_FOR_I(r, c) s << m[r][c]; if (c < Cols - 1 || r < Rows - 1) s << ", ";} if (r < Rows - 1) s << std::endl << ' ';} s << '}'; return s;}
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#endif
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template<uint Rows, uint Cols, typename Type>
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inline PICout operator <<(PICout s, const PIMathMatrixT<Rows, Cols, Type> & m) {s << '{'; PIMM_FOR_I(r, c) s << m[r][c]; if (c < Cols - 1 || r < Rows - 1) s << ", ";} if (r < Rows - 1) s << PICoutManipulators::NewLine << ' ';} s << '}'; return s;}
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/// Multiply matrices {Rows0 x CR} on {CR x Cols1}, result is {Rows0 x Cols1}
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template<uint CR, uint Rows0, uint Cols1, typename Type>
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inline PIMathMatrixT<Rows0, Cols1, Type> operator *(const PIMathMatrixT<Rows0, CR, Type> & fm,
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const PIMathMatrixT<CR, Cols1, Type> & sm) {
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PIMathMatrixT<Rows0, Cols1, Type> tm;
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Type t;
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for (uint j = 0; j < Rows0; ++j) {
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for (uint i = 0; i < Cols1; ++i) {
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t = Type(0);
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for (uint k = 0; k < CR; ++k)
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t += fm[j][k] * sm[k][i];
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tm[j][i] = t;
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}
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}
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return tm;
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}
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/// Multiply matrix {Rows x Cols} on vector {Cols}, result is vector {Rows}
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template<uint Cols, uint Rows, typename Type>
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inline PIMathVectorT<Rows, Type> operator *(const PIMathMatrixT<Rows, Cols, Type> & fm,
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const PIMathVectorT<Cols, Type> & sv) {
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PIMathVectorT<Rows, Type> tv;
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Type t;
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for (uint j = 0; j < Rows; ++j) {
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t = Type(0);
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for (uint i = 0; i < Cols; ++i)
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t += fm[j][i] * sv[i];
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tv[j] = t;
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}
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return tv;
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}
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/// Multiply vector {Rows} on matrix {Rows x Cols}, result is vector {Cols}
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template<uint Cols, uint Rows, typename Type>
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inline PIMathVectorT<Cols, Type> operator *(const PIMathVectorT<Rows, Type> & sv,
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const PIMathMatrixT<Rows, Cols, Type> & fm) {
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PIMathVectorT<Cols, Type> tv;
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Type t;
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for (uint j = 0; j < Cols; ++j) {
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t = Type(0);
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for (uint i = 0; i < Rows; ++i)
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t += fm[i][j] * sv[i];
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tv[j] = t;
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}
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return tv;
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}
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/// Multiply value(T) on matrix {Rows x Cols}, result is vector {Rows}
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template<uint Cols, uint Rows, typename Type>
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inline PIMathMatrixT<Rows, Cols, Type> operator *(const Type & x, const PIMathMatrixT<Rows, Cols, Type> & v) {
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return v * x;
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}
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typedef PIMathMatrixT<2u, 2u, int> PIMathMatrixT22i;
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typedef PIMathMatrixT<3u, 3u, int> PIMathMatrixT33i;
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typedef PIMathMatrixT<4u, 4u, int> PIMathMatrixT44i;
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typedef PIMathMatrixT<2u, 2u, double> PIMathMatrixT22d;
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typedef PIMathMatrixT<3u, 3u, double> PIMathMatrixT33d;
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typedef PIMathMatrixT<4u, 4u, double> PIMathMatrixT44d;
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template<typename Type>
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class PIMathMatrix;
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#undef PIMV_FOR
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#undef PIMM_FOR
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#undef PIMM_FOR_WB
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#undef PIMM_FOR_I
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#undef PIMM_FOR_I_WB
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#undef PIMM_FOR_C
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||||
#undef PIMM_FOR_R
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
/// Matrix
|
||||
|
||||
#define PIMM_FOR(c, r) for (uint c = 0; c < cols_; ++c) { for (uint r = 0; r < rows_; ++r) {
|
||||
#define PIMM_FOR_WB(c, r) for (uint c = 0; c < cols_; ++c) for (uint r = 0; r < rows_; ++r) // without brakes
|
||||
#define PIMM_FOR_I(c, r) for (uint r = 0; r < rows_; ++r) { for (uint c = 0; c < cols_; ++c) {
|
||||
#define PIMM_FOR_I_WB(c, r) for (uint r = 0; r < rows_; ++r) for (uint c = 0; c < cols_; ++c) // without brakes
|
||||
#define PIMM_FOR_C(v) for (uint v = 0; v < cols_; ++v)
|
||||
#define PIMM_FOR_R(v) for (uint v = 0; v < rows_; ++v)
|
||||
|
||||
template<typename Type>
|
||||
class PIP_EXPORT PIMathMatrix {
|
||||
typedef PIMathMatrix<Type> _CMatrix;
|
||||
typedef PIMathVector<Type> _CMCol;
|
||||
typedef PIMathVector<Type> _CMRow;
|
||||
public:
|
||||
PIMathMatrix(const uint cols = 3, const uint rows = 3) {resize(cols, rows);}
|
||||
PIMathMatrix(const uint cols, const uint rows, Type fval, ...) {resize(cols, rows); va_list vl; va_start(vl, fval); PIMM_FOR_I_WB(c, r) m[c][r] = (r + c == 0 ? fval : va_arg(vl, Type)); va_end(vl);}
|
||||
PIMathMatrix(const uint cols, const uint rows, const PIVector<Type> & val) {resize(cols, rows); int i = 0; PIMM_FOR_I_WB(c, r) m[c][r] = val[i++];}
|
||||
|
||||
static _CMatrix identity(const uint cols_, const uint rows_) {_CMatrix tm(cols_, rows_); PIMM_FOR_WB(c, r) tm.m[c][r] = (c == r ? Type(1) : Type(0)); return tm;}
|
||||
|
||||
uint cols() const {return cols_;}
|
||||
uint rows() const {return rows_;}
|
||||
_CMCol col(uint index) {_CMCol tv; PIMM_FOR_R(i) tv[i] = m[index][i]; return tv;}
|
||||
_CMRow row(uint index) {_CMRow tv; PIMM_FOR_C(i) tv[i] = m[i][index]; return tv;}
|
||||
_CMatrix & resize(const uint cols, const uint rows, const Type & new_value = Type()) {cols_ = cols; rows_ = rows; m.resize(cols); PIMM_FOR_C(i) m[i].resize(rows, new_value); return *this;}
|
||||
_CMatrix & setCol(uint index, const _CMCol & v) {PIMM_FOR_R(i) m[index][i] = v[i]; return *this;}
|
||||
_CMatrix & setRow(uint index, const _CMRow & v) {PIMM_FOR_C(i) m[i][index] = v[i]; return *this;}
|
||||
_CMatrix & swapRows(uint r0, uint r1) {Type t; PIMM_FOR_C(i) {t = m[i][r0]; m[i][r0] = m[i][r1]; m[i][r1] = t;} return *this;}
|
||||
_CMatrix & swapCols(uint c0, uint c1) {Type t; PIMM_FOR_R(i) {t = m[c0][i]; m[c0][i] = m[c1][i]; m[c1][i] = t;} return *this;}
|
||||
_CMatrix & fill(const Type & v) {PIMM_FOR_WB(c, r) m[c][r] = v; return *this;}
|
||||
//inline _CMatrix & set(Type fval, ...) {m[0] = fval; va_list vl; va_start(vl, fval); PIMV_FOR(i, 1) m[i] = va_arg(vl, Type); va_end(vl); return *this;}
|
||||
//inline void normalize() {Type tv = length(); if (tv == Type(1)) return; PIMV_FOR(i, 0) m[i] /= tv;}
|
||||
bool isSquare() const {return cols() == rows();}
|
||||
bool isIdentity() const {PIMM_FOR_WB(c, r) if ((c == r) ? m[c][r] != Type(1) : m[c][r] != Type(0)) return false; return true;}
|
||||
bool isNull() const {PIMM_FOR_WB(c, r) if (m[c][r] != Type(0)) return false; return true;}
|
||||
|
||||
Type & at(uint col, uint row) {return m[col][row];}
|
||||
Type at(uint col, uint row) const {return m[col][row];}
|
||||
PIVector<Type> & operator [](uint col) {return m[col];}
|
||||
PIVector<Type> operator [](uint col) const {return m[col];}
|
||||
void operator =(const _CMatrix & sm) {m = sm.m;}
|
||||
bool operator ==(const _CMatrix & sm) const {PIMM_FOR_WB(c, r) if (m[c][r] != sm.m[c][r]) return false; return true;}
|
||||
bool operator !=(const _CMatrix & sm) const {return !(*this == sm);}
|
||||
void operator +=(const _CMatrix & sm) {PIMM_FOR_WB(c, r) m[c][r] += sm.m[c][r];}
|
||||
void operator -=(const _CMatrix & sm) {PIMM_FOR_WB(c, r) m[c][r] -= sm.m[c][r];}
|
||||
void operator *=(const Type & v) {PIMM_FOR_WB(c, r) m[c][r] *= v;}
|
||||
void operator /=(const Type & v) {PIMM_FOR_WB(c, r) m[c][r] /= v;}
|
||||
_CMatrix operator -() {_CMatrix tm(*this); PIMM_FOR_WB(c, r) tm.m[c][r] = -m[c][r]; return tm;}
|
||||
_CMatrix operator +(const _CMatrix & sm) {_CMatrix tm(*this); PIMM_FOR_WB(c, r) tm.m[c][r] += sm.m[c][r]; return tm;}
|
||||
_CMatrix operator -(const _CMatrix & sm) {_CMatrix tm(*this); PIMM_FOR_WB(c, r) tm.m[c][r] -= sm.m[c][r]; return tm;}
|
||||
_CMatrix operator *(const Type & v) {_CMatrix tm(*this); PIMM_FOR_WB(c, r) tm.m[c][r] *= v; return tm;}
|
||||
_CMatrix operator /(const Type & v) {_CMatrix tm(*this); PIMM_FOR_WB(c, r) tm.m[c][r] /= v; return tm;}
|
||||
|
||||
_CMatrix & toUpperTriangular(bool * ok = 0) {
|
||||
if (cols_ != rows_) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
_CMatrix smat(*this);
|
||||
bool ndet;
|
||||
uint crow;
|
||||
Type mul;
|
||||
for (uint i = 0; i < cols_; ++i) {
|
||||
ndet = true;
|
||||
for (uint j = 0; j < rows_; ++j) if (smat.m[i][j] != 0) ndet = false;
|
||||
if (ndet) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
for (uint j = 0; j < cols_; ++j) if (smat.m[j][i] != 0) ndet = false;
|
||||
if (ndet) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
}
|
||||
for (uint i = 0; i < cols_; ++i) {
|
||||
crow = i;
|
||||
while (smat.m[i][i] == Type(0))
|
||||
smat.swapRows(i, ++crow);
|
||||
for (uint j = i + 1; j < rows_; ++j) {
|
||||
mul = smat.m[i][j] / smat.m[i][i];
|
||||
for (uint k = i; k < cols_; ++k) smat.m[k][j] -= mul * smat.m[k][i];
|
||||
}
|
||||
if (i < cols_ - 1) {
|
||||
if (fabs(smat.m[i+1][i+1]) < Type(1E-100)) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
}
|
||||
}
|
||||
if (ok != 0) *ok = true;
|
||||
m = smat.m;
|
||||
return *this;
|
||||
}
|
||||
|
||||
_CMatrix & invert(bool * ok = 0, _CMCol * sv = 0) {
|
||||
if (cols_ != rows_) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
_CMatrix mtmp = _CMatrix::identity(cols_, rows_), smat(*this);
|
||||
bool ndet;
|
||||
uint crow;
|
||||
Type mul, iddiv;
|
||||
for (uint i = 0; i < cols_; ++i) {
|
||||
ndet = true;
|
||||
for (uint j = 0; j < rows_; ++j) if (smat.m[i][j] != 0) ndet = false;
|
||||
if (ndet) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
for (uint j = 0; j < cols_; ++j) if (smat.m[j][i] != 0) ndet = false;
|
||||
if (ndet) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
}
|
||||
for (uint i = 0; i < cols_; ++i) {
|
||||
crow = i;
|
||||
while (smat.m[i][i] == Type(0)) {
|
||||
++crow;
|
||||
smat.swapRows(i, crow);
|
||||
mtmp.swapRows(i, crow);
|
||||
if (sv != 0) sv->swap(i, crow);
|
||||
}
|
||||
for (uint j = i + 1; j < rows_; ++j) {
|
||||
mul = smat.m[i][j] / smat.m[i][i];
|
||||
for (uint k = i; k < cols_; ++k) smat.m[k][j] -= mul * smat.m[k][i];
|
||||
for (uint k = 0; k < cols_; ++k) mtmp.m[k][j] -= mul * mtmp.m[k][i];
|
||||
if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
|
||||
}
|
||||
//cout << i << endl << smat << endl;
|
||||
if (i < cols_ - 1) {
|
||||
if (fabs(smat.m[i+1][i+1]) < Type(1E-100)) {
|
||||
if (ok != 0) *ok = false;
|
||||
return *this;
|
||||
}
|
||||
}
|
||||
iddiv = smat.m[i][i];
|
||||
for (uint j = i; j < cols_; ++j) smat.m[j][i] /= iddiv;
|
||||
for (uint j = 0; j < cols_; ++j) mtmp.m[j][i] /= iddiv;
|
||||
if (sv != 0) (*sv)[i] /= iddiv;
|
||||
}
|
||||
for (uint i = cols_ - 1; i > 0; --i) {
|
||||
for (uint j = 0; j < i; ++j) {
|
||||
mul = smat.m[i][j];
|
||||
smat.m[i][j] -= mul;
|
||||
for (uint k = 0; k < cols_; ++k) mtmp.m[k][j] -= mtmp.m[k][i] * mul;
|
||||
if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
|
||||
}
|
||||
}
|
||||
if (ok != 0) *ok = true;
|
||||
m = mtmp.m;
|
||||
return *this;
|
||||
}
|
||||
_CMatrix inverted(bool * ok = 0) {_CMatrix tm(*this); tm.invert(ok); return tm;}
|
||||
_CMatrix transposed() {_CMatrix tm(rows_, cols_); PIMM_FOR_WB(c, r) tm[r][c] = m[c][r]; return tm;}
|
||||
|
||||
private:
|
||||
uint cols_, rows_;
|
||||
PIVector<PIVector<Type> > m;
|
||||
|
||||
};
|
||||
|
||||
#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[c][r]; if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";} if (r < m.rows() - 1) s << std::endl << ' ';} s << '}'; return s;}
|
||||
#endif
|
||||
|
||||
template<typename Type>
|
||||
inline PICout operator <<(PICout s, const PIMathMatrix<Type> & m) {s << '{'; for (uint r = 0; r < m.rows(); ++r) { for (uint c = 0; c < m.cols(); ++c) { s << m[c][r]; if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";} if (r < m.rows() - 1) s << PICoutManipulators::NewLine << ' ';} s << '}'; return s;}
|
||||
|
||||
/// Multiply matrices {CR x Rows0} on {Cols1 x CR}, result is {Cols1 x Rows0}
|
||||
template<typename Type>
|
||||
inline PIMathMatrix<Type> operator *(const PIMathMatrix<Type> & fm,
|
||||
const PIMathMatrix<Type> & sm) {
|
||||
uint cr = fm.cols(), rows0 = fm.rows(), cols1 = sm.cols();
|
||||
PIMathMatrix<Type> tm(cols1, rows0);
|
||||
if (fm.cols() != sm.rows()) return 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[k][j] * sm[i][k];
|
||||
tm[i][j] = t;
|
||||
}
|
||||
}
|
||||
return tm;
|
||||
}
|
||||
|
||||
/// Multiply matrix {Cols x Rows} on vector {Cols}, result is vector {Rows}
|
||||
template<typename Type>
|
||||
inline PIMathVector<Type> operator *(const PIMathMatrix<Type> & fm,
|
||||
const PIMathVector<Type> & sv) {
|
||||
uint c = fm.cols(), r = fm.rows();
|
||||
PIMathVector<Type> tv(r);
|
||||
if (c != sv.size()) return tv;
|
||||
Type t;
|
||||
for (uint i = 0; i < r; ++i) {
|
||||
t = Type(0);
|
||||
for (uint j = 0; j < c; ++j)
|
||||
t += fm[j][i] * sv[j];
|
||||
tv[i] = t;
|
||||
}
|
||||
return tv;
|
||||
}
|
||||
|
||||
typedef PIMathMatrix<int> PIMathMatrixi;
|
||||
typedef PIMathMatrix<double> PIMathMatrixd;
|
||||
|
||||
#undef PIMV_FOR
|
||||
#undef PIMM_FOR
|
||||
#undef PIMM_FOR_WB
|
||||
#undef PIMM_FOR_I
|
||||
#undef PIMM_FOR_I_WB
|
||||
#undef PIMM_FOR_C
|
||||
#undef PIMM_FOR_R
|
||||
|
||||
#endif // PIMATHMATRIX_H
|
||||
Reference in New Issue
Block a user