al_Mat.hpp

#ifndef INCLUDE_AL_MAT_HPP
#define INCLUDE_AL_MAT_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  Generic fixed-size n-by-n matrix
 
  File author(s):
  Lance Putnam, 2010, putnam.lance@gmail.com
  Graham Wakefield, 2010, grrrwaaa@gmail.com
*/
 
#include <stdio.h>
#include <cmath>
#include "al/math/al_Vec.hpp"
 
namespace al {
 
template <int N, class T>
class Mat;
 
typedef Mat<2, float> Mat2f;   
typedef Mat<2, double> Mat2d;  
typedef Mat<2, int> Mat2i;     
typedef Mat<3, float> Mat3f;   
typedef Mat<3, double> Mat3d;  
typedef Mat<3, int> Mat3i;     
typedef Mat<4, float> Mat4f;   
typedef Mat<4, double> Mat4d;  
typedef Mat<4, int> Mat4i;     
 
// Forward iterates from 0 to n-1. Current index is 'i'.
#define IT(n) for (int i = 0; i < (n); ++i)
 
static struct MatNoInit {
} MAT_NO_INIT;
 
 
template <int N, class T>
class Mat {
 public:
  T mElems[N * N];
 
  //--------------------------------------------------------------------------
  // Constructors
 
  Mat() { set(T(0)); }
 
  template <class U>
  Mat(const U* arr) {
    set(arr);
  }
 
  template <class U>
  Mat(const Mat<N, U>& src) {
    set(src.elems());
  }
 
  Mat(const MatNoInit& v) {}
 
  Mat(const T& r1c1, const T& r1c2, const T& r2c1, const T& r2c2) {
    set(r1c1, r1c2, r2c1, r2c2);
  }
 
  Mat(const T& r1c1, const T& r1c2, const T& r1c3, const T& r2c1, const T& r2c2,
      const T& r2c3, const T& r3c1, const T& r3c2, const T& r3c3) {
    set(r1c1, r1c2, r1c3, r2c1, r2c2, r2c3, r3c1, r3c2, r3c3);
  }
 
  Mat(const T& r1c1, const T& r1c2, const T& r1c3, const T& r1c4, const T& r2c1,
      const T& r2c2, const T& r2c3, const T& r2c4, const T& r3c1, const T& r3c2,
      const T& r3c3, const T& r3c4, const T& r4c1, const T& r4c2, const T& r4c3,
      const T& r4c4) {
    set(r1c1, r1c2, r1c3, r1c4, r2c1, r2c2, r2c3, r2c4, r3c1, r3c2, r3c3, r3c4,
        r4c1, r4c2, r4c3, r4c4);
  }
 
  //--------------------------------------------------------------------------
  // Factory Methods
 
  static Mat identity() { return Mat(MAT_NO_INIT).setIdentity(); }
 
  static Mat rotation(double angle, int dim1, int dim2) {
    double cs = cos(angle);
    double sn = sin(angle);
 
    Mat m(MAT_NO_INIT);
    m.setIdentity();
    m(dim1, dim1) = cs;
    m(dim1, dim2) = -sn;
    m(dim2, dim1) = sn;
    m(dim2, dim2) = cs;
    return m;
  }
 
  template <class V>
  static Mat scaling(const Vec<N - 1, V>& v) {
    Mat m;
    for (int r = 0; r < N - 1; ++r) m(r, r) = v[r];
    m(N - 1, N - 1) = T(1);
    return m;
  }
 
  template <class V>
  static Mat scaling(V v) {
    return scaling(Vec<N - 1, V>(v));
  }
 
  template <typename... Vals>
  static Mat scaling(Vals... vals) {
    return scaling(Vec<(sizeof...(Vals)), T>(vals...));
  }
 
  template <class V>
  static Mat translation(const Vec<N - 1, V>& v) {
    Mat m(MAT_NO_INIT);
    m.setIdentity();
    for (int r = 0; r < N - 1; ++r) m(r, N - 1) = v[r];
    return m;
  }
 
  template <typename... Vals>
  static Mat translation(Vals... vals) {
    return translation(Vec<(sizeof...(Vals)), T>(vals...));
  }
 
  //--------------------------------------------------------------------------
  // Memory Operations
 
  static Mat& pun(T* src) { return *(Mat*)(src); }
  static const Mat& pun(const T* src) { return *(const Mat*)(src); }
 
  static int size() { return N * N; }
 
  const T* elems() const { return mElems; }
 
  T* elems() { return mElems; }
 
  T& operator[](int i) { return elems()[i]; }
 
  const T& operator[](int i) const { return elems()[i]; }
 
  T& operator()(int i, int j) { return (*this)[j * N + i]; }
 
  const T& operator()(int i, int j) const { return (*this)[j * N + i]; }
 
  Vec<N, T> col(int i) const { return Vec<N, T>(elems() + i * N); }
 
  Vec<N, T> row(int i) const { return Vec<N, T>(elems() + i, N); }
 
  Vec<N, T> diagonal() const { return Vec<N, T>(elems(), N + 1); }
 
  Mat& transpose() {
    for (int j = 0; j < N - 1; ++j) {    // row and column
      for (int i = j + 1; i < N; ++i) {  // offset into row or column
        T& a = (*this)(i, j);
        T& b = (*this)(j, i);
        T c = a;
        a = b;
        b = c;  // swap elements
      }
    }
    return *this;
  }
 
  template <int M>
  Mat<M, T> sub(int row = 0, int col = 0) const {
    Mat<M, T> res(MAT_NO_INIT);
    for (int j = 0; j < M; ++j) {
      for (int i = 0; i < M; ++i) {
        res(j, i) = (*this)(j + row, i + col);
      }
    }
    return res;
  }
 
  Mat<N - 1, T> submatrix(int row, int col) const {
    Mat<N - 1, T> res(MAT_NO_INIT);
    for (int j = 0, js = 0; j < N - 1; ++j, ++js) {
      js += int(js == row);
      for (int i = 0, is = 0; i < N - 1; ++i, ++is) {
        is += int(is == col);
        res(j, i) = (*this)(js, is);
      }
    }
    return res;
  }
 
  Vec<N * N, T>& vec() { return *(Vec<N * N, T>*)(this); }
 
  //--------------------------------------------------------------------------
  // Basic Arithmetic Operations
 
  Mat& operator*=(const Mat& v) { return multiply(*this, Mat(*this), v); }
  Mat& operator+=(const Mat& v) {
    IT(size()) { (*this)[i] += v[i]; }
    return *this;
  }
  Mat& operator-=(const Mat& v) {
    IT(size()) { (*this)[i] -= v[i]; }
    return *this;
  }
  Mat& operator+=(const T& v) {
    IT(size()) { (*this)[i] += v; }
    return *this;
  }
  Mat& operator-=(const T& v) {
    IT(size()) { (*this)[i] -= v; }
    return *this;
  }
  Mat& operator*=(const T& v) {
    IT(size()) { (*this)[i] *= v; }
    return *this;
  }
  Mat& operator/=(const T& v) {
    IT(size()) { (*this)[i] /= v; }
    return *this;
  }
 
  Mat operator-() const {
    Mat r(MAT_NO_INIT);
    IT(size()) { r[i] = -(*this)[i]; }
    return r;
  }
  Mat operator+(const Mat& v) const { return Mat(*this) += v; }
  Mat operator-(const Mat& v) const { return Mat(*this) -= v; }
  Mat operator*(const Mat& v) const { return Mat(*this) *= v; }
  Mat operator+(const T& v) const { return Mat(*this) += v; }
  Mat operator-(const T& v) const { return Mat(*this) -= v; }
  Mat operator*(const T& v) const { return Mat(*this) *= v; }
  Mat operator/(const T& v) const { return Mat(*this) /= v; }
 
 
  static Mat& multiply(Mat& r, const Mat& a, const Mat& b) {
    for (int j = 0; j < N; ++j) {
      const Vec<N, T>& bcol = b.col(j);
      for (int i = 0; i < N; ++i) {
        r(i, j) = a.row(i).dot(bcol);
      }
    }
    return r;
  }
 
  template <class U>
  static Vec<N, U>& multiply(Vec<N, U>& r, const Mat& m,
                             const Vec<N, U>& vCol) {
    IT(N) { r[i] = m.row(i).dot(vCol); }
    return r;
  }
 
  template <class U>
  static Vec<N, U>& multiply(Vec<N, U>& r, const Vec<N, U>& vRow,
                             const Mat& m) {
    IT(N) { r[i] = vRow.dot(m.col(i)); }
    return r;
  }
 
  Mat& set(const T& v) {
    IT(size()) { (*this)[i] = v; }
    return *this;
  }
 
  template <class U>
  Mat& set(const Mat<N, U>& v) {
    return set(v.elems());
  }
 
  template <class U>
  Mat& set(const U* arr) {
    IT(size()) { (*this)[i] = arr[i]; }
    return *this;
  }
 
 
  template <class U>
  Mat& set(const U* arr, int numElements, int matOffset, int matStride = 1) {
    IT(numElements) { (*this)[i * matStride + matOffset] = arr[i]; }
    return *this;
  }
 
  Mat& set(const T& r1c1, const T& r1c2, const T& r2c1, const T& r2c2,
           int row = 0, int col = 0) {
    setCol2(r1c1, r2c1, col, row);
    setCol2(r1c2, r2c2, col + 1, row);
    return *this;
  }
 
  Mat& set(const T& r1c1, const T& r1c2, const T& r1c3, const T& r2c1,
           const T& r2c2, const T& r2c3, const T& r3c1, const T& r3c2,
           const T& r3c3, int row = 0, int col = 0) {
    setCol3(r1c1, r2c1, r3c1, col, row);
    setCol3(r1c2, r2c2, r3c2, col + 1, row);
    setCol3(r1c3, r2c3, r3c3, col + 2, row);
    return *this;
  }
 
  Mat& set(const T& r1c1, const T& r1c2, const T& r1c3, const T& r1c4,
           const T& r2c1, const T& r2c2, const T& r2c3, const T& r2c4,
           const T& r3c1, const T& r3c2, const T& r3c3, const T& r3c4,
           const T& r4c1, const T& r4c2, const T& r4c3, const T& r4c4,
           int row = 0, int col = 0) {
    setCol4(r1c1, r2c1, r3c1, r4c1, col, row);
    setCol4(r1c2, r2c2, r3c2, r4c2, col + 1, row);
    setCol4(r1c3, r2c3, r3c3, r4c3, col + 2, row);
    setCol4(r1c4, r2c4, r3c4, r4c4, col + 3, row);
    return *this;
  }
 
  Mat& setCol2(const T& v1, const T& v2, int col = 0, int row = 0) {
    (*this)(row, col) = v1;
    (*this)(row + 1, col) = v2;
    return *this;
  }
 
  Mat& setCol3(const T& v1, const T& v2, const T& v3, int col = 0,
               int row = 0) {
    (*this)(row, col) = v1;
    (*this)(row + 1, col) = v2;
    (*this)(row + 2, col) = v3;
    return *this;
  }
 
  Mat& setCol4(const T& v1, const T& v2, const T& v3, const T& v4, int col = 0,
               int row = 0) {
    (*this)(row, col) = v1;
    (*this)(row + 1, col) = v2;
    (*this)(row + 2, col) = v3;
    (*this)(row + 3, col) = v4;
    return *this;
  }
 
  Mat& setIdentity() {
    for (int i = 0; i < N; ++i) (*this)[i * (N + 1)] = T(1);
 
    for (int i = 0; i < N - 1; ++i) {
      for (int j = i + 1; j < N + i + 1; ++j) {
        (*this)[i * N + j] = T(0);
      }
    }
    return *this;
  }
 
  //--------------------------------------------------------------------------
  // Linear Operations
 
  T cofactor(int row, int col) const {
    T minor = determinant(submatrix(row, col));
    T cofactors[] = {minor, -minor};
    // cofactor sign: + if row+col even, - otherwise
    int sign = (row ^ col) & 1;
    return cofactors[sign];
  }
 
  Mat<N, T> cofactorMatrix() const {
    Mat<N, T> res(MAT_NO_INIT);
    for (int r = 0; r < N; ++r) {
      for (int c = 0; c < N; ++c) {
        res(r, c) = cofactor(r, c);
      }
    }
    return res;
  }
 
  T trace() const { return diagonal().sum(); }
 
  Mat<N, T> inversed() const {
    Mat<N, T> res(*this);
    invert(res);
    return res;
  }
 
  // Affine transformations
 
 
  Mat& rotate(double angle, int dim1, int dim2) {
    double cs = cos(angle);
    double sn = sin(angle);
    for (int R = 0; R < N - 1; ++R) {
      const T& v1 = (*this)(R, dim1);
      const T& v2 = (*this)(R, dim2);
      T t = v1 * cs + v2 * sn;
      (*this)(R, dim2) = v2 * cs - v1 * sn;
      (*this)(R, dim1) = t;
    }
    return *this;
  }
 
  template <int M>
  Mat& rotateGlobal(double angle, int dim1, int dim2) {
    double cs = cos(angle);
    double sn = sin(angle);
    for (int C = 0; C < M; ++C) {
      const T& v1 = (*this)(dim1, C);
      const T& v2 = (*this)(dim2, C);
      T t = v1 * cs - v2 * sn;
      (*this)(dim2, C) = v2 * cs + v1 * sn;
      (*this)(dim1, C) = t;
    }
    return *this;
  }
 
  Mat& rotateGlobal(double angle, int dim1, int dim2) {
    return rotateGlobal<N - 1>(angle, dim1, dim2);
  }
 
  template <class V>
  Mat& scale(const Vec<N - 1, V>& amount) {
    for (int C = 0; C < N - 1; ++C) {
      for (int R = 0; R < N - 1; ++R) {
        (*this)(R, C) *= amount[C];
      }
    }
    return *this;
  }
 
  template <class V>
  Mat& scale(const V& amount) {
    return scale(Vec<N - 1, V>(amount));
  }
 
  template <typename... Vals>
  Mat& scale(Vals... vals) {
    return scale(Vec<(sizeof...(Vals)), T>(vals...));
  }
 
  template <class V>
  Mat& scaleGlobal(const Vec<N - 1, V>& amount) {
    for (int R = 0; R < N - 1; ++R) {
      for (int C = 0; C < N - 1; ++C) {
        (*this)(R, C) *= amount[R];
      }
    }
    return *this;
  }
 
  template <class V>
  Mat& translate(const Vec<N - 1, V>& amount) {
    for (int R = 0; R < N - 1; ++R) {
      (*this)(R, N - 1) += amount[R];
    }
    return *this;
  }
 
  template <class V>
  Mat& translate(const V& amount) {
    return translate(Vec<N - 1, V>(amount));
  }
 
  template <typename... Vals>
  Mat& translate(Vals... vals) {
    return translate(Vec<(sizeof...(Vals)), T>(vals...));
  }
 
  void print(std::ostream& stream) const;
};
 
// -----------------------------------------------------------------------------
// The following are functions that either cannot be defined as class methods
// (due to syntax rules or specialization) or simply are not object oriented.
 
// Non-member binary arithmetic operations
template <int N, class T>
inline Mat<N, T> operator+(const T& s, const Mat<N, T>& v) {
  return v + s;
}
 
template <int N, class T>
inline Mat<N, T> operator-(const T& s, const Mat<N, T>& v) {
  return -v + s;
}
 
template <int N, class T>
inline Mat<N, T> operator*(const T& s, const Mat<N, T>& v) {
  return v * s;
}
 
// Basic Vec/Mat Arithmetic
template <int N, class T, class U>
inline Vec<N, U> operator*(const Mat<N, T>& m, const Vec<N, U>& vCol) {
  Vec<N, U> r;
  return Mat<N, T>::multiply(r, m, vCol);
}
 
template <int N, class T, class U>
inline Vec<N, U> operator*(const Vec<N, U>& vRow, const Mat<N, T>& m) {
  Vec<N, U> r;
  return Mat<N, T>::multiply(r, vRow, m);
}
 
template <class T>
T determinant(const Mat<1, T>& m) {
  return m(0, 0);
}
 
template <class T>
T determinant(const Mat<2, T>& m) {
  return m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0);
}
 
template <class T>
T determinant(const Mat<3, T>& m) {
  return m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) +
         m(0, 1) * (m(1, 2) * m(2, 0) - m(1, 0) * m(2, 2)) +
         m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0));
}
 
 
template <int N, class T>
T determinant(const Mat<N, T>& m) {
  T res = 0;
  for (int i = 0; i < N; ++i) {
    T entry = m(0, i);
    if (entry != T(0)) {
      res += entry * m.cofactor(0, i);
    }
  }
  return res;
}
 
template <class T>
bool invert(Mat<1, T>& m) {
  T det = determinant(m);
  if (det != 0) {
    m(0, 0) /= det;
    return true;
  }
  return false;
}
 
template <class T>
bool invert(Mat<2, T>& m) {
  T det = determinant(m);
  if (det != 0) {
    m = Mat<2, T>(m(1, 1), -m(0, 1), -m(1, 0), m(0, 0)) /= det;
    return true;
  }
  return false;
}
 
template <int N, class T>
bool invert(Mat<N, T>& m) {
  // Get cofactor matrix, C
  Mat<N, T> C = m.cofactorMatrix();
 
  // Compute determinant
  T det = T(0);
  for (int i = 0; i < N; ++i) {
    det += m(0, i) * C(0, i);
  }
 
  // Divide adjugate matrix, C^T, by determinant
  if (det != T(0)) {
    m = (C.transpose() *= T(1) / det);
    return true;
  }
 
  return false;
}
 
//----------------------------
// Member function definitions
 
template <int N, class T>
void Mat<N, T>::print(std::ostream& stream) const {
  for (int R = 0; R < N; ++R) {
    stream << (R == 0 ? " {" : "");
    for (int C = 0; C < N; ++C) {
      stream << "% " << double((*this)(R, C))
             << ((R != N - 1) || (C != N - 1) ? ", " : "}");
    }
    stream << std::endl;
  }
}
 
#undef IT
}  // namespace al
#endif