/*
* Copyright (C) 2011 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#ifndef ANDROID_MAT_H
#define ANDROID_MAT_H
#include "vec.h"
#include "traits.h"
// -----------------------------------------------------------------------
namespace android {
template <typename TYPE, size_t C, size_t R>
class mat;
namespace helpers {
template <typename TYPE, size_t C, size_t R>
mat<TYPE, C, R>& doAssign(
mat<TYPE, C, R>& lhs,
typename TypeTraits<TYPE>::ParameterType rhs) {
for (size_t i=0 ; i<C ; i++)
for (size_t j=0 ; j<R ; j++)
lhs[i][j] = (i==j) ? rhs : 0;
return lhs;
}
template <typename TYPE, size_t C, size_t R, size_t D>
mat<TYPE, C, R> PURE doMul(
const mat<TYPE, D, R>& lhs,
const mat<TYPE, C, D>& rhs)
{
mat<TYPE, C, R> res;
for (size_t c=0 ; c<C ; c++) {
for (size_t r=0 ; r<R ; r++) {
TYPE v(0);
for (size_t k=0 ; k<D ; k++) {
v += lhs[k][r] * rhs[c][k];
}
res[c][r] = v;
}
}
return res;
}
template <typename TYPE, size_t R, size_t D>
vec<TYPE, R> PURE doMul(
const mat<TYPE, D, R>& lhs,
const vec<TYPE, D>& rhs)
{
vec<TYPE, R> res;
for (size_t r=0 ; r<R ; r++) {
TYPE v(0);
for (size_t k=0 ; k<D ; k++) {
v += lhs[k][r] * rhs[k];
}
res[r] = v;
}
return res;
}
template <typename TYPE, size_t C, size_t R>
mat<TYPE, C, R> PURE doMul(
const vec<TYPE, R>& lhs,
const mat<TYPE, C, 1>& rhs)
{
mat<TYPE, C, R> res;
for (size_t c=0 ; c<C ; c++) {
for (size_t r=0 ; r<R ; r++) {
res[c][r] = lhs[r] * rhs[c][0];
}
}
return res;
}
template <typename TYPE, size_t C, size_t R>
mat<TYPE, C, R> PURE doMul(
const mat<TYPE, C, R>& rhs,
typename TypeTraits<TYPE>::ParameterType v)
{
mat<TYPE, C, R> res;
for (size_t c=0 ; c<C ; c++) {
for (size_t r=0 ; r<R ; r++) {
res[c][r] = rhs[c][r] * v;
}
}
return res;
}
template <typename TYPE, size_t C, size_t R>
mat<TYPE, C, R> PURE doMul(
typename TypeTraits<TYPE>::ParameterType v,
const mat<TYPE, C, R>& rhs)
{
mat<TYPE, C, R> res;
for (size_t c=0 ; c<C ; c++) {
for (size_t r=0 ; r<R ; r++) {
res[c][r] = v * rhs[c][r];
}
}
return res;
}
}; // namespace helpers
// -----------------------------------------------------------------------
template <typename TYPE, size_t C, size_t R>
class mat : public vec< vec<TYPE, R>, C > {
typedef typename TypeTraits<TYPE>::ParameterType pTYPE;
typedef vec< vec<TYPE, R>, C > base;
public:
// STL-like interface.
typedef TYPE value_type;
typedef TYPE& reference;
typedef TYPE const& const_reference;
typedef size_t size_type;
size_type size() const { return R*C; }
enum { ROWS = R, COLS = C };
// -----------------------------------------------------------------------
// default constructors
mat() { }
mat(const mat& rhs) : base(rhs) { }
mat(const base& rhs) : base(rhs) { } // NOLINT(google-explicit-constructor)
// -----------------------------------------------------------------------
// conversion constructors
// sets the diagonal to the value, off-diagonal to zero
mat(pTYPE rhs) { // NOLINT(google-explicit-constructor)
helpers::doAssign(*this, rhs);
}
// -----------------------------------------------------------------------
// Assignment
mat& operator=(const mat& rhs) {
base::operator=(rhs);
return *this;
}
mat& operator=(const base& rhs) {
base::operator=(rhs);
return *this;
}
mat& operator=(pTYPE rhs) {
return helpers::doAssign(*this, rhs);
}
// -----------------------------------------------------------------------
// non-member function declaration and definition
friend inline mat PURE operator + (const mat& lhs, const mat& rhs) {
return helpers::doAdd(
static_cast<const base&>(lhs),
static_cast<const base&>(rhs));
}
friend inline mat PURE operator - (const mat& lhs, const mat& rhs) {
return helpers::doSub(
static_cast<const base&>(lhs),
static_cast<const base&>(rhs));
}
// matrix*matrix
template <size_t D>
friend mat PURE operator * (
const mat<TYPE, D, R>& lhs,
const mat<TYPE, C, D>& rhs) {
return helpers::doMul(lhs, rhs);
}
// matrix*vector
friend vec<TYPE, R> PURE operator * (
const mat& lhs, const vec<TYPE, C>& rhs) {
return helpers::doMul(lhs, rhs);
}
// vector*matrix
friend mat PURE operator * (
const vec<TYPE, R>& lhs, const mat<TYPE, C, 1>& rhs) {
return helpers::doMul(lhs, rhs);
}
// matrix*scalar
friend inline mat PURE operator * (const mat& lhs, pTYPE v) {
return helpers::doMul(lhs, v);
}
// scalar*matrix
friend inline mat PURE operator * (pTYPE v, const mat& rhs) {
return helpers::doMul(v, rhs);
}
// -----------------------------------------------------------------------
// streaming operator to set the columns of the matrix:
// example:
// mat33_t m;
// m << v0 << v1 << v2;
// column_builder<> stores the matrix and knows which column to set
template<size_t PREV_COLUMN>
struct column_builder {
mat& matrix;
explicit column_builder(mat& matrix) : matrix(matrix) { }
};
// operator << is not a method of column_builder<> so we can
// overload it for unauthorized values (partial specialization
// not allowed in class-scope).
// we just set the column and return the next column_builder<>
template<size_t PREV_COLUMN>
friend column_builder<PREV_COLUMN+1> operator << (
const column_builder<PREV_COLUMN>& lhs,
const vec<TYPE, R>& rhs) {
lhs.matrix[PREV_COLUMN+1] = rhs;
return column_builder<PREV_COLUMN+1>(lhs.matrix);
}
// we return void here so we get a compile-time error if the
// user tries to set too many columns
friend void operator << (
const column_builder<C-2>& lhs,
const vec<TYPE, R>& rhs) {
lhs.matrix[C-1] = rhs;
}
// this is where the process starts. we set the first columns and
// return the next column_builder<>
column_builder<0> operator << (const vec<TYPE, R>& rhs) {
(*this)[0] = rhs;
return column_builder<0>(*this);
}
};
// Specialize column matrix so they're exactly equivalent to a vector
template <typename TYPE, size_t R>
class mat<TYPE, 1, R> : public vec<TYPE, R> {
typedef vec<TYPE, R> base;
public:
// STL-like interface.
typedef TYPE value_type;
typedef TYPE& reference;
typedef TYPE const& const_reference;
typedef size_t size_type;
size_type size() const { return R; }
enum { ROWS = R, COLS = 1 };
mat() { }
explicit mat(const base& rhs) : base(rhs) { }
mat(const mat& rhs) : base(rhs) { }
explicit mat(const TYPE& rhs) { helpers::doAssign(*this, rhs); }
mat& operator=(const mat& rhs) { base::operator=(rhs); return *this; }
mat& operator=(const base& rhs) { base::operator=(rhs); return *this; }
mat& operator=(const TYPE& rhs) { return helpers::doAssign(*this, rhs); }
// we only have one column, so ignore the index
const base& operator[](size_t) const { return *this; }
base& operator[](size_t) { return *this; }
void operator << (const vec<TYPE, R>& rhs) { base::operator[](0) = rhs; }
};
// -----------------------------------------------------------------------
// matrix functions
// transpose. this handles matrices of matrices
inline int PURE transpose(int v) { return v; }
inline float PURE transpose(float v) { return v; }
inline double PURE transpose(double v) { return v; }
// Transpose a matrix
template <typename TYPE, size_t C, size_t R>
mat<TYPE, R, C> PURE transpose(const mat<TYPE, C, R>& m) {
mat<TYPE, R, C> r;
for (size_t i=0 ; i<R ; i++)
for (size_t j=0 ; j<C ; j++)
r[i][j] = transpose(m[j][i]);
return r;
}
// Calculate the trace of a matrix
template <typename TYPE, size_t C> static TYPE trace(const mat<TYPE, C, C>& m) {
TYPE t;
for (size_t i=0 ; i<C ; i++)
t += m[i][i];
return t;
}
// Test positive-semidefiniteness of a matrix
template <typename TYPE, size_t C>
static bool isPositiveSemidefinite(const mat<TYPE, C, C>& m, TYPE tolerance) {
for (size_t i=0 ; i<C ; i++)
if (m[i][i] < 0)
return false;
for (size_t i=0 ; i<C ; i++)
for (size_t j=i+1 ; j<C ; j++)
if (fabs(m[i][j] - m[j][i]) > tolerance)
return false;
return true;
}
// Transpose a vector
template <
template<typename T, size_t S> class VEC,
typename TYPE,
size_t SIZE
>
mat<TYPE, SIZE, 1> PURE transpose(const VEC<TYPE, SIZE>& v) {
mat<TYPE, SIZE, 1> r;
for (size_t i=0 ; i<SIZE ; i++)
r[i][0] = transpose(v[i]);
return r;
}
// -----------------------------------------------------------------------
// "dumb" matrix inversion
template<typename T, size_t N>
mat<T, N, N> PURE invert(const mat<T, N, N>& src) {
T t;
size_t swap;
mat<T, N, N> tmp(src);
mat<T, N, N> inverse(1);
for (size_t i=0 ; i<N ; i++) {
// look for largest element in column
swap = i;
for (size_t j=i+1 ; j<N ; j++) {
if (fabs(tmp[j][i]) > fabs(tmp[i][i])) {
swap = j;
}
}
if (swap != i) {
/* swap rows. */
for (size_t k=0 ; k<N ; k++) {
t = tmp[i][k];
tmp[i][k] = tmp[swap][k];
tmp[swap][k] = t;
t = inverse[i][k];
inverse[i][k] = inverse[swap][k];
inverse[swap][k] = t;
}
}
t = 1 / tmp[i][i];
for (size_t k=0 ; k<N ; k++) {
tmp[i][k] *= t;
inverse[i][k] *= t;
}
for (size_t j=0 ; j<N ; j++) {
if (j != i) {
t = tmp[j][i];
for (size_t k=0 ; k<N ; k++) {
tmp[j][k] -= tmp[i][k] * t;
inverse[j][k] -= inverse[i][k] * t;
}
}
}
}
return inverse;
}
// -----------------------------------------------------------------------
typedef mat<float, 2, 2> mat22_t;
typedef mat<float, 3, 3> mat33_t;
typedef mat<float, 4, 4> mat44_t;
// -----------------------------------------------------------------------
}; // namespace android
#endif /* ANDROID_MAT_H */