protot/src/SimpleMath/SimpleMathFixed.h

867 lines
21 KiB
C++

/**
* This is a highly inefficient math library. It was conceived by Martin
* Felis <martin.felis@iwr.uni-heidelberg.de> while he was compiling code
* that uses a highly efficient math library.
*
* It is intended to be used as a fast compiling substitute for the
* blazingly fast Eigen3 library and tries to mimic its API to a certain
* extend.
*
* Feel free to use it wherever you like. However, no guarantees are given
* that this code does what it says it would.
*/
#ifndef SIMPLEMATHFIXED_H
#define SIMPLEMATHFIXED_H
#include <sstream>
#include <cstdlib>
#include <cmath>
#include <assert.h>
#include <algorithm>
#include <string.h>
#include "compileassert.h"
#include "SimpleMathBlock.h"
/** \brief Namespace for a highly inefficient math library
*
*/
namespace SimpleMath {
template <typename matrix_type>
class LLT;
template <typename matrix_type>
class HouseholderQR;
template <typename matrix_type>
class ColPivHouseholderQR;
template <typename matrix_type>
class CommaInitializer;
namespace Dynamic {
template <typename val_type> class Matrix;
}
/** \brief Namespace for fixed size elements
*/
namespace Fixed {
// forward declaration
template <typename val_type, unsigned int nrows, unsigned int ncols>
class Matrix;
/** \brief Fixed size matrix class
*/
template <typename val_type, unsigned int nrows, unsigned int ncols>
class Matrix {
public:
typedef Matrix<val_type, nrows, ncols> matrix_type;
typedef val_type value_type;
unsigned int rows() const {
return nrows;
}
unsigned int cols() const {
return ncols;
}
unsigned int size() const {
return nrows * ncols;
}
Matrix() {};
Matrix(const Matrix &matrix) {
unsigned int i;
for (i = 0; i < nrows * ncols; i++)
mData[i] = matrix.mData[i];
}
Matrix(unsigned int _nrows, unsigned int _ncols, const value_type* values) {
assert(nrows == _nrows);
assert(ncols == _ncols);
memcpy (mData, values, sizeof(value_type) * nrows * ncols);
}
Matrix& operator=(const Matrix &matrix) {
if (this != &matrix) {
unsigned int i;
for (i = 0; i < nrows * ncols; i++)
mData[i] = matrix.mData[i];
}
return *this;
}
// conversion different val_types
template <typename other_matrix_type>
Matrix (const Block<other_matrix_type, val_type> &block) {
assert (nrows == block.rows());
assert (ncols == block.cols());
for (unsigned int i = 0; i < nrows; i++) {
for (unsigned int j = 0; j < ncols; j++) {
(*this)(i,j) = static_cast<val_type>(block(i,j));
}
}
}
template <typename other_matrix_type>
Matrix& operator= (const Block<other_matrix_type, val_type> &block) {
assert (nrows == block.rows());
assert (ncols == block.cols());
for (unsigned int i = 0; i < nrows; i++) {
for (unsigned int j = 0; j < ncols; j++) {
(*this)(i,j) = static_cast<value_type>(block(i,j));
}
}
return *this;
}
template <typename other_type>
Matrix (const Matrix<other_type, nrows, ncols> &matrix) {
for (unsigned int i = 0; i < nrows; i++) {
for (unsigned int j = 0; j < ncols; j++) {
(*this)(i,j) = static_cast<val_type>(matrix(i,j));
}
}
}
template <typename other_type>
Matrix& operator=(const Matrix<other_type, nrows, ncols> &matrix) {
for (unsigned int i = 0; i < nrows; i++) {
for (unsigned int j = 0; j < ncols; j++) {
(*this)(i,j) = static_cast<val_type>(matrix(i,j));
}
}
return *this;
}
CommaInitializer<matrix_type> operator<< (const val_type& value) {
return CommaInitializer<matrix_type> (*this, value);
}
// conversion Dynamic->Fixed
Matrix(const Dynamic::Matrix<val_type> &dynamic_matrix);
Matrix& operator=(const Dynamic::Matrix<val_type> &dynamic_matrix);
~Matrix() {};
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02
) {
assert (nrows == 3);
assert (ncols == 1);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
}
void set(
const val_type &v00, const val_type &v01, const val_type &v02
) {
COMPILE_ASSERT (nrows * ncols == 3);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
}
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02,
const val_type &v10, const val_type &v11, const val_type &v12,
const val_type &v20, const val_type &v21, const val_type &v22
) {
COMPILE_ASSERT (nrows == 3);
COMPILE_ASSERT (ncols == 3);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[1 * 3 + 0] = v10;
mData[1 * 3 + 1] = v11;
mData[1 * 3 + 2] = v12;
mData[2 * 3 + 0] = v20;
mData[2 * 3 + 1] = v21;
mData[2 * 3 + 2] = v22;
}
void set(
const val_type v00, const val_type v01, const val_type v02,
const val_type v10, const val_type v11, const val_type v12,
const val_type v20, const val_type v21, const val_type v22
) {
COMPILE_ASSERT (nrows == 3);
COMPILE_ASSERT (ncols == 3);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[1 * 3 + 0] = v10;
mData[1 * 3 + 1] = v11;
mData[1 * 3 + 2] = v12;
mData[2 * 3 + 0] = v20;
mData[2 * 3 + 1] = v21;
mData[2 * 3 + 2] = v22;
}
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02, const val_type &v03
) {
assert (nrows == 4);
assert (ncols == 1);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
}
void set(
const val_type &v00, const val_type &v01, const val_type &v02, const val_type &v03
) {
COMPILE_ASSERT (nrows * ncols == 4);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
}
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02, const val_type &v03,
const val_type &v10, const val_type &v11, const val_type &v12, const val_type &v13,
const val_type &v20, const val_type &v21, const val_type &v22, const val_type &v23,
const val_type &v30, const val_type &v31, const val_type &v32, const val_type &v33
) {
COMPILE_ASSERT (nrows == 4);
COMPILE_ASSERT (ncols == 4);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[1 * 4 + 0] = v10;
mData[1 * 4 + 1] = v11;
mData[1 * 4 + 2] = v12;
mData[1 * 4 + 3] = v13;
mData[2 * 4 + 0] = v20;
mData[2 * 4 + 1] = v21;
mData[2 * 4 + 2] = v22;
mData[2 * 4 + 3] = v23;
mData[3 * 4 + 0] = v30;
mData[3 * 4 + 1] = v31;
mData[3 * 4 + 2] = v32;
mData[3 * 4 + 3] = v33;
}
void set(
const val_type &v00, const val_type &v01, const val_type &v02, const val_type &v03,
const val_type &v10, const val_type &v11, const val_type &v12, const val_type &v13,
const val_type &v20, const val_type &v21, const val_type &v22, const val_type &v23,
const val_type &v30, const val_type &v31, const val_type &v32, const val_type &v33
) {
COMPILE_ASSERT (nrows == 4);
COMPILE_ASSERT (ncols == 4);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[1 * 4 + 0] = v10;
mData[1 * 4 + 1] = v11;
mData[1 * 4 + 2] = v12;
mData[1 * 4 + 3] = v13;
mData[2 * 4 + 0] = v20;
mData[2 * 4 + 1] = v21;
mData[2 * 4 + 2] = v22;
mData[2 * 4 + 3] = v23;
mData[3 * 4 + 0] = v30;
mData[3 * 4 + 1] = v31;
mData[3 * 4 + 2] = v32;
mData[3 * 4 + 3] = v33;
}
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02,
const val_type &v03, const val_type &v04, const val_type &v05
) {
COMPILE_ASSERT (nrows == 6);
COMPILE_ASSERT (ncols == 1);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[4] = v04;
mData[5] = v05;
}
void set(
const val_type &v00, const val_type &v01, const val_type &v02,
const val_type &v03, const val_type &v04, const val_type &v05
) {
COMPILE_ASSERT (nrows * ncols == 6);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[4] = v04;
mData[5] = v05;
}
Matrix (
const val_type &v00, const val_type &v01, const val_type &v02,
const val_type &v03, const val_type &v04, const val_type &v05,
const val_type &v10, const val_type &v11, const val_type &v12,
const val_type &v13, const val_type &v14, const val_type &v15,
const val_type &v20, const val_type &v21, const val_type &v22,
const val_type &v23, const val_type &v24, const val_type &v25,
const val_type &v30, const val_type &v31, const val_type &v32,
const val_type &v33, const val_type &v34, const val_type &v35,
const val_type &v40, const val_type &v41, const val_type &v42,
const val_type &v43, const val_type &v44, const val_type &v45,
const val_type &v50, const val_type &v51, const val_type &v52,
const val_type &v53, const val_type &v54, const val_type &v55
) {
COMPILE_ASSERT (nrows == 6);
COMPILE_ASSERT (ncols == 6);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[4] = v04;
mData[5] = v05;
mData[6 + 0] = v10;
mData[6 + 1] = v11;
mData[6 + 2] = v12;
mData[6 + 3] = v13;
mData[6 + 4] = v14;
mData[6 + 5] = v15;
mData[12 + 0] = v20;
mData[12 + 1] = v21;
mData[12 + 2] = v22;
mData[12 + 3] = v23;
mData[12 + 4] = v24;
mData[12 + 5] = v25;
mData[18 + 0] = v30;
mData[18 + 1] = v31;
mData[18 + 2] = v32;
mData[18 + 3] = v33;
mData[18 + 4] = v34;
mData[18 + 5] = v35;
mData[24 + 0] = v40;
mData[24 + 1] = v41;
mData[24 + 2] = v42;
mData[24 + 3] = v43;
mData[24 + 4] = v44;
mData[24 + 5] = v45;
mData[30 + 0] = v50;
mData[30 + 1] = v51;
mData[30 + 2] = v52;
mData[30 + 3] = v53;
mData[30 + 4] = v54;
mData[30 + 5] = v55;
};
void set(
const val_type v00, const val_type v01, const val_type v02,
const val_type v03, const val_type v04, const val_type v05,
const val_type v10, const val_type v11, const val_type v12,
const val_type v13, const val_type v14, const val_type v15,
const val_type v20, const val_type v21, const val_type v22,
const val_type v23, const val_type v24, const val_type v25,
const val_type v30, const val_type v31, const val_type v32,
const val_type v33, const val_type v34, const val_type v35,
const val_type v40, const val_type v41, const val_type v42,
const val_type v43, const val_type v44, const val_type v45,
const val_type v50, const val_type v51, const val_type v52,
const val_type v53, const val_type v54, const val_type v55
) {
COMPILE_ASSERT (nrows == 6);
COMPILE_ASSERT (ncols == 6);
mData[0] = v00;
mData[1] = v01;
mData[2] = v02;
mData[3] = v03;
mData[4] = v04;
mData[5] = v05;
mData[6 + 0] = v10;
mData[6 + 1] = v11;
mData[6 + 2] = v12;
mData[6 + 3] = v13;
mData[6 + 4] = v14;
mData[6 + 5] = v15;
mData[12 + 0] = v20;
mData[12 + 1] = v21;
mData[12 + 2] = v22;
mData[12 + 3] = v23;
mData[12 + 4] = v24;
mData[12 + 5] = v25;
mData[18 + 0] = v30;
mData[18 + 1] = v31;
mData[18 + 2] = v32;
mData[18 + 3] = v33;
mData[18 + 4] = v34;
mData[18 + 5] = v35;
mData[24 + 0] = v40;
mData[24 + 1] = v41;
mData[24 + 2] = v42;
mData[24 + 3] = v43;
mData[24 + 4] = v44;
mData[24 + 5] = v45;
mData[30 + 0] = v50;
mData[30 + 1] = v51;
mData[30 + 2] = v52;
mData[30 + 3] = v53;
mData[30 + 4] = v54;
mData[30 + 5] = v55;
}
// comparison
bool operator==(const Matrix &matrix) const {
for (unsigned int i = 0; i < nrows * ncols; i++) {
if (mData[i] != matrix.mData[i])
return false;
}
return true;
}
bool operator!=(const Matrix &matrix) const {
for (unsigned int i = 0; i < nrows * ncols; i++) {
if (mData[i] != matrix.mData[i])
return true;
}
return false;
}
// access operators
const val_type& operator[](const unsigned int &index) const {
assert (index >= 0 && index < nrows * ncols);
return mData[index];
};
val_type& operator[](const unsigned int &index) {
assert (index >= 0 && index < nrows * ncols);
return mData[index];
}
const val_type& operator()(const unsigned int &row, const unsigned int &col) const {
assert (row >= 0 && row < nrows && col >= 0 && col < ncols);
return mData[row*ncols + col];
};
val_type& operator()(const unsigned int &row, const unsigned int &col) {
assert (row >= 0 && row < nrows && col >= 0 && col < ncols);
return mData[row*ncols + col];
};
void zero() {
for (unsigned int i = 0; i < ncols * nrows; i++)
mData[i] = 0.;
}
void setZero() {
zero();
}
val_type norm() const {
return sqrt(this->squaredNorm());
}
matrix_type normalize() {
val_type length = this->norm();
for (unsigned int i = 0; i < ncols * nrows; i++)
mData[i] /= length;
return *this;
}
matrix_type normalized() const {
return matrix_type (*this) / this->norm();
}
Matrix<val_type, 3, 1> cross(const Matrix<val_type, 3, 1> &other_vector) const {
COMPILE_ASSERT (nrows * ncols == 3);
Matrix<val_type, 3, 1> result;
result[0] = mData[1] * other_vector[2] - mData[2] * other_vector[1];
result[1] = mData[2] * other_vector[0] - mData[0] * other_vector[2];
result[2] = mData[0] * other_vector[1] - mData[1] * other_vector[0];
return result;
}
val_type trace() const {
COMPILE_ASSERT(nrows == ncols);
val_type result = 0.;
for (unsigned int i = 0; i < rows(); i++) {
result += operator()(i,i);
}
return result;
}
val_type mean() const {
COMPILE_ASSERT(nrows == 1 || ncols == 1);
val_type result = 0.;
for (unsigned int i = 0; i < rows() * cols(); i++) {
result += operator[](i);
}
return result / static_cast<val_type>(nrows * ncols);
}
static matrix_type Zero() {
matrix_type result;
result.setZero();
return result;
}
static matrix_type Zero(int ignore_me) {
matrix_type result;
result.setZero();
return result;
}
static matrix_type Zero(int ignore_me, int ignore_me_too) {
matrix_type result;
result.setZero();
return result;
}
static matrix_type Identity() {
matrix_type result;
result.identity();
return result;
}
static matrix_type Identity(int ignore_me, int ignore_me_too) {
matrix_type result;
result.identity();
return result;
}
void identity() {
COMPILE_ASSERT (nrows == ncols);
setZero();
for (unsigned int i = 0; i < ncols; i++)
mData[i * ncols + i] = 1.;
}
void random() {
for (unsigned int i = 0; i < nrows * ncols; i++)
mData[i] = static_cast<val_type> (rand()) / static_cast<val_type> (RAND_MAX);
}
val_type squaredNorm() const {
COMPILE_ASSERT (ncols == 1 || nrows == 1);
val_type result = 0;
for (unsigned int i = 0; i < nrows * ncols; i++)
result += mData[i] * mData[i];
return result;
}
val_type dot(const matrix_type &matrix) const {
COMPILE_ASSERT (ncols == 1 || nrows == 1);
val_type result = 0;
for (unsigned int i = 0; i < nrows * ncols; i++)
result += mData[i] * matrix[i];
return result;
}
// Blocks using block(i,j,r,c) syntax
Block<matrix_type, val_type>
block (unsigned int row_start, unsigned int col_start, unsigned int row_count, unsigned int col_count) {
return Block<matrix_type, val_type>(*this, row_start, col_start, row_count, col_count);
}
const Block<matrix_type, val_type>
block (unsigned int row_start, unsigned int col_start, unsigned int row_count, unsigned int col_count) const {
return Block<matrix_type, val_type>(*this, row_start, col_start, row_count, col_count);
}
// Blocks using block<r,c>(i,j) syntax
template <unsigned int block_row_count, unsigned int block_col_count>
Block<matrix_type, val_type>
block (unsigned int row_start, unsigned int col_start) {
return Block<matrix_type, val_type>(*this, row_start, col_start, block_row_count, block_col_count);
}
template <unsigned int block_row_count, unsigned int block_col_count>
const Block<matrix_type, val_type>
block (unsigned int row_start, unsigned int col_start) const {
return Block<matrix_type, val_type>(*this, row_start, col_start, block_row_count, block_col_count);
}
// row and col accessors
Block<matrix_type, val_type>
col(unsigned int index) const {
return Block<matrix_type, val_type>(*this, 0, index, rows(), 1);
}
Block<matrix_type, val_type>
col(unsigned int index) {
return Block<matrix_type, val_type>(*this, 0, index, rows(), 1);
}
Block<matrix_type, val_type>
row(unsigned int index) const {
return Block<matrix_type, val_type>(*this, index, 0, 1, cols());
}
Block<matrix_type, val_type>
row(unsigned int index) {
return Block<matrix_type, val_type>(*this, index, 0, 1, cols());
}
// Operators with scalars
void operator*=(const val_type &scalar) {
for (unsigned int i = 0; i < nrows * ncols; i++)
mData[i] *= scalar;
};
void operator/=(const val_type &scalar) {
for (unsigned int i = 0; i < nrows * ncols; i++)
mData[i] /= scalar;
}
Matrix operator/(const val_type& scalar) const {
matrix_type result (*this);
for (unsigned int i = 0; i < nrows * ncols; i++)
result[i] /= scalar;
return result;
}
// Operators with other matrices
Matrix operator+(const Matrix &matrix) const {
matrix_type result (*this);
for (unsigned int i = 0; i < nrows * ncols; i++)
result[i] += matrix[i];
return result;
}
void operator+=(const matrix_type &matrix) {
for (unsigned int i = 0; i < nrows * ncols; i++)
mData[i] += matrix.mData[i];
}
Matrix operator-(const Matrix &matrix) const {
matrix_type result (*this);
for (unsigned int i = 0; i < nrows * ncols; i++)
result[i] -= matrix[i];
return result;
}
void operator-=(const Matrix &matrix) {
for (unsigned int i = 0; i < nrows * ncols; i++)
mData[i] -= matrix.mData[i];
}
template <unsigned int other_rows, unsigned int other_cols>
Matrix<val_type, nrows, other_cols> operator*(const Matrix<val_type, other_rows, other_cols> &matrix) const {
COMPILE_ASSERT (ncols == other_rows);
Matrix<val_type, nrows, other_cols> result;
result.setZero();
unsigned int i,j, k;
for (i = 0; i < nrows; i++) {
for (j = 0; j < other_cols; j++) {
for (k = 0; k < other_rows; k++) {
result(i,j) += mData[i * ncols + k] * matrix(k,j);
}
}
}
return result;
}
// multiplication with dynamic sized matrix
template <typename other_type>
Dynamic::Matrix<val_type> operator*(const Dynamic::Matrix<other_type> &other_matrix) {
assert (ncols == other_matrix.rows());
Dynamic::Matrix<val_type> result(nrows, other_matrix.cols());
result.setZero();
unsigned int i,j, k;
for (i = 0; i < nrows; i++) {
for (j = 0; j < other_matrix.cols(); j++) {
for (k = 0; k < other_matrix.rows(); k++) {
result(i,j) += mData[i * ncols + k] * static_cast<val_type>(other_matrix(k,j));
}
}
}
return result;
}
void operator*=(const Matrix &matrix) {
matrix_type temp (*this);
*this = temp * matrix;
}
// Special operators
val_type *data(){
return mData;
}
const val_type *data() const{
return mData;
}
// regular transpose of a 6 dimensional matrix
Matrix<val_type, ncols, nrows> transpose() const {
Matrix<val_type, ncols, nrows> result;
for (unsigned int i = 0; i < nrows; i++) {
for (unsigned int j = 0; j < ncols; j++) {
result(j,i) = mData[i * ncols + j];
}
}
return result;
}
operator val_type() {
COMPILE_ASSERT (nrows == 1);
COMPILE_ASSERT (nrows == 1);
return mData[0];
}
Matrix operator-() const {
return *this * -1.;
}
Matrix inverse() const {
return colPivHouseholderQr().inverse();
}
const LLT<matrix_type> llt() const {
return LLT<matrix_type>(*this);
}
const HouseholderQR<matrix_type> householderQr() const {
return HouseholderQR<matrix_type>(*this);
}
const ColPivHouseholderQR<matrix_type> colPivHouseholderQr() const {
return ColPivHouseholderQR<matrix_type>(*this);
}
private:
val_type mData[nrows * ncols];
};
template <typename val_type, unsigned int nrows, unsigned int ncols>
inline Matrix<val_type, nrows, ncols> operator*(val_type scalar, const Matrix<val_type, nrows, ncols> &matrix) {
Matrix<val_type, nrows, ncols> result (matrix);
for (unsigned int i = 0; i < nrows * ncols; i++)
result.data()[i] *= scalar;
return result;
}
template <typename val_type, typename other_type, unsigned int nrows, unsigned int ncols>
inline Matrix<val_type, nrows, ncols> operator*(const Matrix<val_type, nrows, ncols> &matrix, other_type scalar) {
Matrix<val_type, nrows, ncols> result (matrix);
for (unsigned int i = 0; i < nrows * ncols; i++)
result.data()[i] *= static_cast<val_type> (scalar);
return result;
}
template <typename val_type, unsigned int nrows, unsigned int ncols>
inline std::ostream& operator<<(std::ostream& output, const Matrix<val_type, nrows, ncols> &matrix) {
size_t max_width = 0;
size_t out_width = output.width();
// get the widest number
for (size_t i = 0; i < matrix.rows(); i++) {
for (size_t j = 0; j < matrix.cols(); j++) {
std::stringstream out_stream;
out_stream << matrix(i,j);
max_width = std::max (out_stream.str().size(),max_width);
}
}
// overwrite width if it was explicitly prescribed
if (out_width != 0) {
max_width = out_width;
}
for (unsigned int i = 0; i < matrix.rows(); i++) {
output.width(0);
output << "[ ";
output.width(out_width);
for (unsigned int j = 0; j < matrix.cols(); j++) {
std::stringstream out_stream;
out_stream.width (max_width);
out_stream << matrix(i,j);
output << out_stream.str();
if (j < matrix.cols() - 1)
output << ", ";
}
output << " ]";
if (matrix.rows() > 1 && i < matrix.rows() - 1)
output << std::endl;
}
return output;
}
}
}
#endif /* SIMPLEMATHFIXED_H */