620 lines
15 KiB
C
620 lines
15 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 SIMPLEMATHDYNAMIC_H
|
|
#define SIMPLEMATHDYNAMIC_H
|
|
|
|
#include <sstream>
|
|
#include <cstdlib>
|
|
#include <assert.h>
|
|
#include <algorithm>
|
|
|
|
#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 Fixed {
|
|
template <typename val_type, unsigned int ncols, unsigned int nrows> class Matrix;
|
|
}
|
|
|
|
|
|
/** \brief Namespace for elements of varying size.
|
|
*/
|
|
namespace Dynamic {
|
|
|
|
// forward declaration
|
|
template <typename val_type>
|
|
class Matrix;
|
|
|
|
/** \brief Class for both matrices and vectors.
|
|
*/
|
|
template <typename val_type>
|
|
class Matrix {
|
|
public:
|
|
typedef Matrix<val_type> matrix_type;
|
|
typedef val_type value_type;
|
|
|
|
Matrix() :
|
|
nrows (0),
|
|
ncols (0),
|
|
mapped_data (false),
|
|
mData (NULL) {};
|
|
Matrix(unsigned int rows) :
|
|
nrows (rows),
|
|
ncols (1),
|
|
mapped_data (false) {
|
|
mData = new val_type[rows];
|
|
}
|
|
Matrix(unsigned int rows, unsigned int cols) :
|
|
nrows (rows),
|
|
ncols (cols),
|
|
mapped_data (false) {
|
|
mData = new val_type[rows * cols];
|
|
}
|
|
Matrix(unsigned int rows, unsigned int cols, val_type *data_ptr) :
|
|
nrows (rows),
|
|
ncols (cols),
|
|
mapped_data (true) {
|
|
mData = data_ptr;
|
|
}
|
|
|
|
unsigned int rows() const {
|
|
return nrows;
|
|
}
|
|
|
|
unsigned int cols() const {
|
|
return ncols;
|
|
}
|
|
|
|
unsigned int size() const {
|
|
return nrows * ncols;
|
|
}
|
|
void resize (unsigned int rows, unsigned int cols=1) {
|
|
if (nrows * ncols > 0 && mData != NULL && mapped_data == false) {
|
|
delete[] mData;
|
|
}
|
|
|
|
nrows = rows;
|
|
ncols = cols;
|
|
|
|
mData = new val_type[nrows * ncols];
|
|
}
|
|
|
|
void conservativeResize (unsigned int rows, unsigned int cols = 1) {
|
|
Matrix <val_type> result = Matrix<val_type>::Zero(rows, cols);
|
|
|
|
unsigned int arows = std::min (rows, nrows);
|
|
unsigned int acols = std::min (cols, ncols);
|
|
|
|
for (unsigned int i = 0; i < arows; i++) {
|
|
for (unsigned int j = 0; j < acols; j++) {
|
|
result(i,j) = (*this)(i,j);
|
|
}
|
|
}
|
|
|
|
*this = result;
|
|
}
|
|
|
|
Matrix(const Matrix &matrix) :
|
|
nrows (matrix.nrows),
|
|
ncols (matrix.ncols),
|
|
mapped_data (false) {
|
|
unsigned int i;
|
|
|
|
mData = new val_type[nrows * ncols];
|
|
|
|
for (i = 0; i < nrows * ncols; i++)
|
|
mData[i] = matrix.mData[i];
|
|
}
|
|
Matrix& operator=(const Matrix &matrix) {
|
|
if (this != &matrix) {
|
|
if (!mapped_data) {
|
|
delete[] mData;
|
|
|
|
nrows = matrix.nrows;
|
|
ncols = matrix.ncols;
|
|
mapped_data = false;
|
|
|
|
mData = new val_type[nrows * ncols];
|
|
|
|
unsigned int i;
|
|
for (i = 0; i < nrows * ncols; i++)
|
|
mData[i] = matrix.mData[i];
|
|
} else {
|
|
// we overwrite any existing data
|
|
nrows = matrix.nrows;
|
|
ncols = matrix.ncols;
|
|
mapped_data = true;
|
|
|
|
unsigned int i;
|
|
for (i = 0; i < nrows * ncols; i++)
|
|
mData[i] = matrix.mData[i];
|
|
}
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
CommaInitializer<matrix_type> operator<< (const val_type& value) {
|
|
return CommaInitializer<matrix_type> (*this, value);
|
|
}
|
|
|
|
// conversion different val_types
|
|
template <typename other_type>
|
|
Matrix (const Matrix<other_type> &matrix) :
|
|
nrows (matrix.rows()),
|
|
ncols (matrix.cols()),
|
|
mapped_data(false) {
|
|
|
|
mData = new val_type[nrows * ncols];
|
|
|
|
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));
|
|
}
|
|
}
|
|
}
|
|
|
|
// conversion from a fixed size matrix
|
|
template <typename other_type, unsigned int fnrows, unsigned int fncols>
|
|
Matrix (const Fixed::Matrix<other_type, fnrows, fncols> &fixed_matrix) :
|
|
nrows (fnrows),
|
|
ncols (fncols),
|
|
mapped_data (false),
|
|
mData (NULL) {
|
|
mData = new val_type[nrows * ncols];
|
|
|
|
for (unsigned int i = 0; i < nrows; i++) {
|
|
for (unsigned int j = 0; j < ncols; j++) {
|
|
(*this)(i,j) = static_cast<val_type>(fixed_matrix(i,j));
|
|
}
|
|
}
|
|
}
|
|
|
|
template <typename other_matrix_type>
|
|
explicit Matrix (const Block<other_matrix_type, value_type> &block) :
|
|
nrows(block.rows()),
|
|
ncols(block.cols()),
|
|
mapped_data (false) {
|
|
mData = new val_type[nrows * ncols];
|
|
|
|
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));
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
~Matrix() {
|
|
if (nrows * ncols > 0 && mData != NULL && mapped_data == false) {
|
|
delete[] mData;
|
|
mData = NULL;
|
|
}
|
|
|
|
nrows = 0;
|
|
ncols = 0;
|
|
};
|
|
|
|
// comparison
|
|
bool operator==(const Matrix &matrix) const {
|
|
if (nrows != matrix.nrows || ncols != matrix.ncols)
|
|
return false;
|
|
|
|
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 {
|
|
if (nrows != matrix.nrows || ncols != matrix.ncols)
|
|
return true;
|
|
|
|
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);
|
|
assert (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 {
|
|
if (!(row >= 0 && row < nrows && col >= 0 && col < ncols)) {
|
|
std::cout << "row = " << row << " col = " << col << std::endl;
|
|
std::cout << "nrows = " << nrows << " ncols = " << ncols << std::endl;
|
|
std::cout << "invalid read = " << mData[100000] << std::endl;
|
|
}
|
|
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());
|
|
}
|
|
|
|
void normalize() {
|
|
val_type length = this->norm();
|
|
|
|
for (unsigned int i = 0; i < ncols * nrows; i++)
|
|
mData[i] /= length;
|
|
}
|
|
|
|
Matrix<val_type> normalized() const {
|
|
return Matrix<val_type> (*this) / this->norm();
|
|
}
|
|
|
|
Matrix<val_type> cross(const Matrix<val_type> &other_vector) {
|
|
assert (nrows * ncols == 3);
|
|
assert (other_vector.nrows * other_vector.ncols == 3);
|
|
|
|
Matrix<val_type> result (3, 1);
|
|
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;
|
|
}
|
|
|
|
static matrix_type Zero() {
|
|
matrix_type result;
|
|
result.setZero();
|
|
return result;
|
|
}
|
|
|
|
static matrix_type Zero(int rows, int cols = 1) {
|
|
matrix_type result (rows, cols);
|
|
result.setZero();
|
|
return result;
|
|
}
|
|
|
|
static matrix_type Constant (int rows, val_type value) {
|
|
matrix_type result (rows, 1);
|
|
unsigned int i;
|
|
for (i = 0; i < result.size(); i++)
|
|
result[i] = value;
|
|
|
|
return result;
|
|
}
|
|
|
|
static matrix_type Constant (int rows, int cols, val_type value) {
|
|
matrix_type result (rows, cols);
|
|
unsigned int i;
|
|
for (i = 0; i < result.size(); i++)
|
|
result[i] = value;
|
|
|
|
return result;
|
|
}
|
|
|
|
static matrix_type Identity (int rows, int cols = 1) {
|
|
assert (rows == cols);
|
|
|
|
matrix_type result (rows, cols);
|
|
result.identity();
|
|
|
|
return result;
|
|
}
|
|
|
|
void identity() {
|
|
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 {
|
|
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 {
|
|
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
|
|
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);
|
|
}
|
|
|
|
template <unsigned int row_count, unsigned int 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, row_count, col_count);
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
template <unsigned int row_count, unsigned int col_count>
|
|
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, row_count, col_count);
|
|
}
|
|
|
|
// 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];
|
|
}
|
|
|
|
Matrix<val_type> operator*(const Matrix<val_type> &other_matrix) const {
|
|
assert (ncols == other_matrix.nrows);
|
|
|
|
Matrix<val_type> result(nrows, other_matrix.ncols);
|
|
|
|
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] * other_matrix(k,j);
|
|
}
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
template <unsigned int _nrows, unsigned int _ncols>
|
|
Matrix<val_type> operator*(const Fixed::Matrix<val_type, _nrows, _ncols> &other_matrix) const {
|
|
assert (ncols == other_matrix.rows());
|
|
|
|
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] * other_matrix(k,j);
|
|
}
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
Matrix<val_type> operator*(const Block<matrix_type, val_type> &other_matrix) const {
|
|
assert (ncols == other_matrix.rows());
|
|
|
|
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] * 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;
|
|
}
|
|
|
|
// regular transpose of a 6 dimensional matrix
|
|
Matrix<val_type> transpose() const {
|
|
Matrix<val_type> result(ncols, nrows);
|
|
|
|
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() {
|
|
assert (nrows == 1);
|
|
assert (nrows == 1);
|
|
|
|
return mData[0];
|
|
}
|
|
|
|
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:
|
|
unsigned int nrows;
|
|
unsigned int ncols;
|
|
bool mapped_data;
|
|
|
|
val_type* mData;
|
|
};
|
|
|
|
template <typename val_type>
|
|
inline Matrix<val_type> operator*(val_type scalar, const Matrix<val_type> &matrix) {
|
|
Matrix<val_type> result (matrix);
|
|
|
|
for (unsigned int i = 0; i < matrix.rows() * matrix.cols(); i++)
|
|
result.data()[i] *= scalar;
|
|
|
|
return result;
|
|
}
|
|
|
|
template <typename val_type, typename other_type>
|
|
inline Matrix<val_type> operator*(const Matrix<val_type> &matrix, other_type scalar) {
|
|
Matrix<val_type> result (matrix);
|
|
|
|
for (unsigned int i = 0; i < matrix.rows() * matrix.cols(); i++)
|
|
result.data()[i] *= static_cast<val_type>(scalar);
|
|
|
|
return result;
|
|
}
|
|
|
|
template <typename val_type>
|
|
inline std::ostream& operator<<(std::ostream& output, const Matrix<val_type> &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 /* SIMPLEMATHDYNAMIC_H */
|