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/**
* @file Matrix.h
*
* matrix code
*/
#pragma once
#include <inttypes.h>
#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <math.h>
#include "../Vector.hpp"
#include "../Matrix.hpp"
namespace math
{
class __EXPORT Matrix
{
public:
// constructor
Matrix(size_t rows, size_t cols) :
_rows(rows),
_cols(cols),
_data((float *)calloc(rows *cols, sizeof(float))) {
}
Matrix(size_t rows, size_t cols, const float *data) :
_rows(rows),
_cols(cols),
_data((float *)malloc(getSize())) {
memcpy(getData(), data, getSize());
}
// deconstructor
virtual ~Matrix() {
delete [] getData();
}
// copy constructor (deep)
Matrix(const Matrix &right) :
_rows(right.getRows()),
_cols(right.getCols()),
_data((float *)malloc(getSize())) {
memcpy(getData(), right.getData(),
right.getSize());
}
// assignment
inline Matrix &operator=(const Matrix &right) {
#ifdef MATRIX_ASSERT
ASSERT(getRows() == right.getRows());
ASSERT(getCols() == right.getCols());
#endif
if (this != &right) {
memcpy(getData(), right.getData(),
right.getSize());
}
return *this;
}
// element accessors
inline float &operator()(size_t i, size_t j) {
#ifdef MATRIX_ASSERT
ASSERT(i < getRows());
ASSERT(j < getCols());
#endif
return getData()[i * getCols() + j];
}
inline const float &operator()(size_t i, size_t j) const {
#ifdef MATRIX_ASSERT
ASSERT(i < getRows());
ASSERT(j < getCols());
#endif
return getData()[i * getCols() + j];
}
// output
inline void print() const {
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
float sig;
int exp;
float num = (*this)(i, j);
float2SigExp(num, sig, exp);
printf("%6.3fe%03.3d,", (double)sig, exp);
}
printf("\n");
}
}
// boolean ops
inline bool operator==(const Matrix &right) const {
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
if (fabsf((*this)(i, j) - right(i, j)) > 1e-30f)
return false;
}
}
return true;
}
// scalar ops
inline Matrix operator+(const float &right) const {
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) + right;
}
}
return result;
}
inline Matrix operator-(const float &right) const {
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) - right;
}
}
return result;
}
inline Matrix operator*(const float &right) const {
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) * right;
}
}
return result;
}
inline Matrix operator/(const float &right) const {
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) / right;
}
}
return result;
}
// vector ops
inline Vector operator*(const Vector &right) const {
#ifdef MATRIX_ASSERT
ASSERT(getCols() == right.getRows());
#endif
Vector result(getRows());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i) += (*this)(i, j) * right(j);
}
}
return result;
}
// matrix ops
inline Matrix operator+(const Matrix &right) const {
#ifdef MATRIX_ASSERT
ASSERT(getRows() == right.getRows());
ASSERT(getCols() == right.getCols());
#endif
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) + right(i, j);
}
}
return result;
}
inline Matrix operator-(const Matrix &right) const {
#ifdef MATRIX_ASSERT
ASSERT(getRows() == right.getRows());
ASSERT(getCols() == right.getCols());
#endif
Matrix result(getRows(), getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(i, j) = (*this)(i, j) - right(i, j);
}
}
return result;
}
inline Matrix operator*(const Matrix &right) const {
#ifdef MATRIX_ASSERT
ASSERT(getCols() == right.getRows());
#endif
Matrix result(getRows(), right.getCols());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < right.getCols(); j++) {
for (size_t k = 0; k < right.getRows(); k++) {
result(i, j) += (*this)(i, k) * right(k, j);
}
}
}
return result;
}
inline Matrix operator/(const Matrix &right) const {
#ifdef MATRIX_ASSERT
ASSERT(right.getRows() == right.getCols());
ASSERT(getCols() == right.getCols());
#endif
return (*this) * right.inverse();
}
// other functions
inline Matrix transpose() const {
Matrix result(getCols(), getRows());
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
result(j, i) = (*this)(i, j);
}
}
return result;
}
inline void swapRows(size_t a, size_t b) {
if (a == b) return;
for (size_t j = 0; j < getCols(); j++) {
float tmp = (*this)(a, j);
(*this)(a, j) = (*this)(b, j);
(*this)(b, j) = tmp;
}
}
inline void swapCols(size_t a, size_t b) {
if (a == b) return;
for (size_t i = 0; i < getRows(); i++) {
float tmp = (*this)(i, a);
(*this)(i, a) = (*this)(i, b);
(*this)(i, b) = tmp;
}
}
/**
* inverse based on LU factorization with partial pivotting
*/
Matrix inverse() const {
#ifdef MATRIX_ASSERT
ASSERT(getRows() == getCols());
#endif
size_t N = getRows();
Matrix L = identity(N);
const Matrix &A = (*this);
Matrix U = A;
Matrix P = identity(N);
//printf("A:\n"); A.print();
// for all diagonal elements
for (size_t n = 0; n < N; n++) {
// if diagonal is zero, swap with row below
if (fabsf(U(n, n)) < 1e-8f) {
//printf("trying pivot for row %d\n",n);
for (size_t i = 0; i < N; i++) {
if (i == n) continue;
//printf("\ttrying row %d\n",i);
if (fabsf(U(i, n)) > 1e-8f) {
//printf("swapped %d\n",i);
U.swapRows(i, n);
P.swapRows(i, n);
}
}
}
#ifdef MATRIX_ASSERT
//printf("A:\n"); A.print();
//printf("U:\n"); U.print();
//printf("P:\n"); P.print();
//fflush(stdout);
ASSERT(fabsf(U(n, n)) > 1e-8f);
#endif
// failsafe, return zero matrix
if (fabsf(U(n, n)) < 1e-8f) {
return Matrix::zero(n);
}
// for all rows below diagonal
for (size_t i = (n + 1); i < N; i++) {
L(i, n) = U(i, n) / U(n, n);
// add i-th row and n-th row
// multiplied by: -a(i,n)/a(n,n)
for (size_t k = n; k < N; k++) {
U(i, k) -= L(i, n) * U(n, k);
}
}
}
//printf("L:\n"); L.print();
//printf("U:\n"); U.print();
// solve LY=P*I for Y by forward subst
Matrix Y = P;
// for all columns of Y
for (size_t c = 0; c < N; c++) {
// for all rows of L
for (size_t i = 0; i < N; i++) {
// for all columns of L
for (size_t j = 0; j < i; j++) {
// for all existing y
// subtract the component they
// contribute to the solution
Y(i, c) -= L(i, j) * Y(j, c);
}
// divide by the factor
// on current
// term to be solved
// Y(i,c) /= L(i,i);
// but L(i,i) = 1.0
}
}
//printf("Y:\n"); Y.print();
// solve Ux=y for x by back subst
Matrix X = Y;
// for all columns of X
for (size_t c = 0; c < N; c++) {
// for all rows of U
for (size_t k = 0; k < N; k++) {
// have to go in reverse order
size_t i = N - 1 - k;
// for all columns of U
for (size_t j = i + 1; j < N; j++) {
// for all existing x
// subtract the component they
// contribute to the solution
X(i, c) -= U(i, j) * X(j, c);
}
// divide by the factor
// on current
// term to be solved
X(i, c) /= U(i, i);
}
}
//printf("X:\n"); X.print();
return X;
}
inline void setAll(const float &val) {
for (size_t i = 0; i < getRows(); i++) {
for (size_t j = 0; j < getCols(); j++) {
(*this)(i, j) = val;
}
}
}
inline void set(const float *data) {
memcpy(getData(), data, getSize());
}
inline size_t getRows() const { return _rows; }
inline size_t getCols() const { return _cols; }
inline static Matrix identity(size_t size) {
Matrix result(size, size);
for (size_t i = 0; i < size; i++) {
result(i, i) = 1.0f;
}
return result;
}
inline static Matrix zero(size_t size) {
Matrix result(size, size);
result.setAll(0.0f);
return result;
}
inline static Matrix zero(size_t m, size_t n) {
Matrix result(m, n);
result.setAll(0.0f);
return result;
}
protected:
inline size_t getSize() const { return sizeof(float) * getRows() * getCols(); }
inline float *getData() { return _data; }
inline const float *getData() const { return _data; }
inline void setData(float *data) { _data = data; }
private:
size_t _rows;
size_t _cols;
float *_data;
};
} // namespace math