/**
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* @file SquareMatrix.hpp
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*
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* A square matrix
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*
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* @author James Goppert <james.goppert@gmail.com>
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*/
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#pragma once
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#include <stdio.h>
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#include <stddef.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include "math.hpp"
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namespace matrix
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{
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template <typename Type, size_t M, size_t N>
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class Matrix;
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template <typename Type, size_t M>
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class Vector;
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template<typename Type, size_t M>
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class SquareMatrix : public Matrix<Type, M, M>
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{
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public:
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SquareMatrix() :
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Matrix<Type, M, M>()
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{
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}
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SquareMatrix(const Type *data_) :
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Matrix<Type, M, M>(data_)
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{
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}
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SquareMatrix(const Matrix<Type, M, M> &other) :
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Matrix<Type, M, M>(other)
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{
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}
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// inverse alias
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inline SquareMatrix<Type, M> I() const
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{
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return inv(*this);
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}
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Vector<Type, M> diag() const
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{
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Vector<Type, M> res;
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const SquareMatrix<Type, M> &self = *this;
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for (size_t i = 0; i < M; i++) {
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res(i) = self(i, i);
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}
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return res;
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}
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Type trace() const
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{
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Type res = 0;
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const SquareMatrix<Type, M> &self = *this;
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for (size_t i = 0; i < M; i++) {
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res += self(i, i);
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}
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return res;
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}
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};
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typedef SquareMatrix<float, 3> SquareMatrix3f;
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template<typename Type, size_t M>
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SquareMatrix<Type, M> eye() {
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SquareMatrix<Type, M> m;
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m.setIdentity();
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return m;
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}
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template<typename Type, size_t M>
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SquareMatrix<Type, M> diag(Vector<Type, M> d) {
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SquareMatrix<Type, M> m;
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for (size_t i=0; i<M; i++) {
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m(i,i) = d(i);
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}
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return m;
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}
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template<typename Type, size_t M>
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SquareMatrix<Type, M> expm(const Matrix<Type, M, M> & A, size_t order=5)
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{
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SquareMatrix<Type, M> res;
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SquareMatrix<Type, M> A_pow = A;
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res.setIdentity();
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size_t i_factorial = 1;
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for (size_t i=1; i<=order; i++) {
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i_factorial *= i;
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res += A_pow / Type(i_factorial);
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A_pow *= A_pow;
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}
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return res;
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}
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/**
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* inverse based on LU factorization with partial pivotting
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*/
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template<typename Type, size_t M>
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SquareMatrix <Type, M> inv(const SquareMatrix<Type, M> & A)
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{
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SquareMatrix<Type, M> L;
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L.setIdentity();
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SquareMatrix<Type, M> U = A;
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SquareMatrix<Type, M> P;
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P.setIdentity();
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//printf("A:\n"); A.print();
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// for all diagonal elements
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for (size_t n = 0; n < M; n++) {
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// if diagonal is zero, swap with row below
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if (fabsf(U(n, n)) < 1e-8f) {
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//printf("trying pivot for row %d\n",n);
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for (size_t i = 0; i < M; i++) {
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if (i == n) {
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continue;
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}
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//printf("\ttrying row %d\n",i);
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if (fabsf(U(i, n)) > 1e-8f) {
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//printf("swapped %d\n",i);
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U.swapRows(i, n);
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P.swapRows(i, n);
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}
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}
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}
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#ifdef MATRIX_ASSERT
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//printf("A:\n"); A.print();
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//printf("U:\n"); U.print();
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//printf("P:\n"); P.print();
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//fflush(stdout);
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ASSERT(fabsf(U(n, n)) > 1e-8f);
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#endif
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// failsafe, return zero matrix
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if (fabsf(U(n, n)) < 1e-8f) {
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SquareMatrix<Type, M> zero;
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zero.setZero();
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return zero;
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}
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// for all rows below diagonal
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for (size_t i = (n + 1); i < M; i++) {
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L(i, n) = U(i, n) / U(n, n);
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// add i-th row and n-th row
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// multiplied by: -a(i,n)/a(n,n)
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for (size_t k = n; k < M; k++) {
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U(i, k) -= L(i, n) * U(n, k);
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}
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}
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}
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//printf("L:\n"); L.print();
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//printf("U:\n"); U.print();
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// solve LY=P*I for Y by forward subst
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SquareMatrix<Type, M> Y = P;
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// for all columns of Y
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for (size_t c = 0; c < M; c++) {
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// for all rows of L
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for (size_t i = 0; i < M; i++) {
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// for all columns of L
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for (size_t j = 0; j < i; j++) {
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// for all existing y
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// subtract the component they
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// contribute to the solution
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Y(i, c) -= L(i, j) * Y(j, c);
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}
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// divide by the factor
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// on current
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// term to be solved
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// Y(i,c) /= L(i,i);
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// but L(i,i) = 1.0
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}
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}
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//printf("Y:\n"); Y.print();
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// solve Ux=y for x by back subst
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SquareMatrix<Type, M> X = Y;
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// for all columns of X
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for (size_t c = 0; c < M; c++) {
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// for all rows of U
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for (size_t k = 0; k < M; k++) {
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// have to go in reverse order
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size_t i = M - 1 - k;
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// for all columns of U
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for (size_t j = i + 1; j < M; j++) {
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// for all existing x
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// subtract the component they
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// contribute to the solution
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X(i, c) -= U(i, j) * X(j, c);
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}
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// divide by the factor
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// on current
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// term to be solved
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X(i, c) /= U(i, i);
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}
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}
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//printf("X:\n"); X.print();
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return X;
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}
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typedef SquareMatrix<float, 3> Matrix3f;
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} // namespace matrix
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/* vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 : */
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