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pmlpp/MLPP/LinAlg/LinAlg.cpp

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//
// LinAlg.cpp
//
// Created by Marc Melikyan on 1/8/21.
//
#include "LinAlg.hpp"
#include "Stat/Stat.hpp"
#include <iostream>
#include <random>
#include <map>
#include <cmath>
namespace MLPP{
std::vector<std::vector<double>> LinAlg::gramMatrix(std::vector<std::vector<double>> A){
return matmult(transpose(A), A); // AtA
}
bool LinAlg::linearIndependenceChecker(std::vector<std::vector<double>> A){
if (det(gramMatrix(A), A.size()) == 0){
return false;
}
return true;
}
std::vector<std::vector<double>> LinAlg::gaussianNoise(int n, int m){
std::random_device rd;
std::default_random_engine generator(rd());
std::vector<std::vector<double>> A;
A.resize(n);
for(int i = 0; i < n; i++){
A[i].resize(m);
for(int j = 0; j < m; j++){
std::normal_distribution<double> distribution(0, 1); // Standard normal distribution. Mean of 0, std of 1.
A[i][j] = distribution(generator);
}
}
return A;
}
std::vector<std::vector<double>> LinAlg::addition(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[0].size(); j++){
C[i][j] = A[i][j] + B[i][j];
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::subtraction(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[0].size(); j++){
C[i][j] = A[i][j] - B[i][j];
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::matmult(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(B[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int k = 0; k < B.size(); k++){
for(int j = 0; j < B[0].size(); j++){
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::hadamard_product(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[0].size(); j++){
C[i][j] = A[i][j] * B[i][j];
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::kronecker_product(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
// [1,1,1,1] [1,2,3,4,5]
// [1,1,1,1] [1,2,3,4,5]
// [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5] [1,2,3,4,5]
// Resulting matrix: A.size() * B.size()
// A[0].size() * B[0].size()
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < B.size(); j++){
std::vector<std::vector<double>> row;
for(int k = 0; k < A[0].size(); k++){
row.push_back(scalarMultiply(A[i][k], B[j]));
}
C.push_back(flatten(row));
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::elementWiseDivision(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
C[i][j] = A[i][j] / B[i][j];
}
}
return C;
}
std::vector<std::vector<double>> LinAlg::transpose(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> AT;
AT.resize(A[0].size());
for(int i = 0; i < AT.size(); i++){
AT[i].resize(A.size());
}
for(int i = 0; i < A[0].size(); i++){
for(int j = 0; j < A.size(); j++){
AT[i][j] = A[j][i];
}
}
return AT;
}
std::vector<std::vector<double>> LinAlg::scalarMultiply(double scalar, std::vector<std::vector<double>> A){
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
A[i][j] *= scalar;
}
}
return A;
}
std::vector<std::vector<double>> LinAlg::scalarAdd(double scalar, std::vector<std::vector<double>> A){
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
A[i][j] += scalar;
}
}
return A;
}
std::vector<std::vector<double>> LinAlg::log(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::log(A[i][j]);
}
}
return B;
}
std::vector<std::vector<double>> LinAlg::log10(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::log10(A[i][j]);
}
}
return B;
}
std::vector<std::vector<double>> LinAlg::exp(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::exp(A[i][j]);
}
}
return B;
}
std::vector<std::vector<double>> LinAlg::erf(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::erf(A[i][j]);
}
}
return B;
}
std::vector<std::vector<double>> LinAlg::exponentiate(std::vector<std::vector<double>> A, double p){
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
A[i][j] = std::pow(A[i][j], p);
}
}
return A;
}
std::vector<std::vector<double>> LinAlg::sqrt(std::vector<std::vector<double>> A){
return exponentiate(A, 0.5);
}
std::vector<std::vector<double>> LinAlg::cbrt(std::vector<std::vector<double>> A){
return exponentiate(A, double(1)/double(3));
}
std::vector<std::vector<double>> LinAlg::matrixPower(std::vector<std::vector<double>> A, int n){
std::vector<std::vector<double>> B = identity(A.size());
if(n == 0){
return identity(A.size());
}
else if(n < 0){
A = inverse(A);
}
for(int i = 0; i < std::abs(n); i++){
B = matmult(B, A);
}
return B;
}
std::vector<std::vector<double>> LinAlg::abs(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < B.size(); i++){
for(int j = 0; j < B[i].size(); j++){
B[i][j] = std::abs(A[i][j]);
}
}
return B;
}
double LinAlg::det(std::vector<std::vector<double>> A, int d){
double deter = 0;
std::vector<std::vector<double>> B;
B.resize(d);
for(int i = 0; i < d; i++){
B[i].resize(d);
}
/* This is the base case in which the input is a 2x2 square matrix.
Recursion is performed unless and until we reach this base case,
such that we recieve a scalar as the result. */
if(d == 2){
return A[0][0] * A[1][1] - A[0][1] * A[1][0];
}
else{
for(int i = 0; i < d; i++){
int sub_i = 0;
for(int j = 1; j < d; j++){
int sub_j = 0;
for(int k = 0; k < d; k++){
if(k == i){
continue;
}
B[sub_i][sub_j] = A[j][k];
sub_j++;
}
sub_i++;
}
deter += std::pow(-1, i) * A[0][i] * det(B, d-1);
}
}
return deter;
}
double LinAlg::trace(std::vector<std::vector<double>> A){
double trace = 0;
for(int i = 0; i < A.size(); i++){
trace += A[i][i];
}
return trace;
}
std::vector<std::vector<double>> LinAlg::cofactor(std::vector<std::vector<double>> A, int n, int i, int j){
std::vector<std::vector<double>> cof;
cof.resize(A.size());
for(int i = 0; i < cof.size(); i++){
cof[i].resize(A.size());
}
int sub_i = 0, sub_j = 0;
for (int row = 0; row < n; row++){
for (int col = 0; col < n; col++){
if (row != i && col != j) {
cof[sub_i][sub_j++] = A[row][col];
if (sub_j == n - 1){
sub_j = 0;
sub_i++;
}
}
}
}
return cof;
}
std::vector<std::vector<double>> LinAlg::adjoint(std::vector<std::vector<double>> A){
//Resizing the initial adjoint matrix
std::vector<std::vector<double>> adj;
adj.resize(A.size());
for(int i = 0; i < adj.size(); i++){
adj[i].resize(A.size());
}
// Checking for the case where the given N x N matrix is a scalar
if(A.size() == 1){
adj[0][0] = 1;
return adj;
}
if(A.size() == 2){
adj[0][0] = A[1][1];
adj[1][1] = A[0][0];
adj[0][1] = -A[0][1];
adj[1][0] = -A[1][0];
return adj;
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A.size(); j++){
std::vector<std::vector<double>> cof = cofactor(A, int(A.size()), i, j);
// 1 if even, -1 if odd
int sign = (i + j) % 2 == 0 ? 1 : -1;
adj[j][i] = sign * det(cof, int(A.size()) - 1);
}
}
return adj;
}
// The inverse can be computed as (1 / determinant(A)) * adjoint(A)
std::vector<std::vector<double>> LinAlg::inverse(std::vector<std::vector<double>> A){
return scalarMultiply(1/det(A, int(A.size())), adjoint(A));
}
// This is simply the Moore-Penrose least squares approximation of the inverse.
std::vector<std::vector<double>> LinAlg::pinverse(std::vector<std::vector<double>> A){
return matmult(inverse(matmult(transpose(A), A)), transpose(A));
}
std::vector<std::vector<double>> LinAlg::zeromat(int n, int m){
std::vector<std::vector<double>> zeromat;
zeromat.resize(n);
for(int i = 0; i < zeromat.size(); i++){
zeromat[i].resize(m);
}
return zeromat;
}
std::vector<std::vector<double>> LinAlg::onemat(int n, int m){
return full(n, m, 1);
}
std::vector<std::vector<double>> LinAlg::full(int n, int m, int k){
std::vector<std::vector<double>> full;
full.resize(n);
for(int i = 0; i < full.size(); i++){
full[i].resize(m);
}
for(int i = 0; i < full.size(); i++){
for(int j = 0; j < full[i].size(); j++){
full[i][j] = k;
}
}
return full;
}
std::vector<std::vector<double>> LinAlg::sin(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::sin(A[i][j]);
}
}
return B;
}
std::vector<std::vector<double>> LinAlg::cos(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::cos(A[i][j]);
}
}
return B;
}
std::vector<double> LinAlg::max(std::vector<double> a, std::vector<double> b){
std::vector<double> c;
c.resize(a.size());
for(int i = 0; i < c.size(); i++){
if(a[i] >= b[i]) {
c[i] = a[i];
}
else { c[i] = b[i]; }
}
return c;
}
double LinAlg::max(std::vector<std::vector<double>> A){
return max(flatten(A));
}
double LinAlg::min(std::vector<std::vector<double>> A){
return min(flatten(A));
}
std::vector<std::vector<double>> LinAlg::round(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
B[i][j] = std::round(A[i][j]);
}
}
return B;
}
double LinAlg::norm_2(std::vector<std::vector<double>> A){
double sum = 0;
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
sum += A[i][j] * A[i][j];
}
}
return std::sqrt(sum);
}
std::vector<std::vector<double>> LinAlg::identity(double d){
std::vector<std::vector<double>> identityMat;
identityMat.resize(d);
for(int i = 0; i < identityMat.size(); i++){
identityMat[i].resize(d);
}
for(int i = 0; i < identityMat.size(); i++){
for(int j = 0; j < identityMat.size(); j++){
if(i == j){
identityMat[i][j] = 1;
}
else { identityMat[i][j] = 0; }
}
}
return identityMat;
}
std::vector<std::vector<double>> LinAlg::cov(std::vector<std::vector<double>> A){
Stat stat;
std::vector<std::vector<double>> covMat;
covMat.resize(A.size());
for(int i = 0; i < covMat.size(); i++){
covMat[i].resize(A.size());
}
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A.size(); j++){
covMat[i][j] = stat.covariance(A[i], A[j]);
}
}
return covMat;
}
std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>> LinAlg::eig(std::vector<std::vector<double>> A){
/*
A (the entered parameter) in most use cases will be X'X, XX', etc. and must be symmetric.
That simply means that 1) X' = X and 2) X is a square matrix. This function that computes the
eigenvalues of a matrix is utilizing Jacobi's method.
*/
double diagonal = true; // Perform the iterative Jacobi algorithm unless and until we reach a diagonal matrix which yields us the eigenvals.
std::map<int, int> val_to_vec;
std::vector<std::vector<double>> a_new;
std::vector<std::vector<double>> eigenvectors = identity(A.size());
do{
double a_ij = A[0][1];
double sub_i = 0;
double sub_j = 1;
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
if(i != j && std::abs(A[i][j]) > a_ij){
a_ij = A[i][j];
sub_i = i;
sub_j = j;
}
else if(i != j && std::abs(A[i][j]) == a_ij){
if(i < sub_i){
a_ij = A[i][j];
sub_i = i;
sub_j = j;
}
}
}
}
double a_ii = A[sub_i][sub_i];
double a_jj = A[sub_j][sub_j];
double a_ji = A[sub_j][sub_i];
double theta;
if(a_ii == a_jj) {
theta = M_PI / 4;
}
else{
theta = 0.5 * atan(2 * a_ij / (a_ii - a_jj));
}
std::vector<std::vector<double>> P = identity(A.size());
P[sub_i][sub_j] = -std::sin(theta);
P[sub_i][sub_i] = std::cos(theta);
P[sub_j][sub_j] = std::cos(theta);
P[sub_j][sub_i] = std::sin(theta);
a_new = matmult(matmult(inverse(P), A), P);
for(int i = 0; i < a_new.size(); i++){
for(int j = 0; j < a_new[i].size(); j++){
if(i != j && std::round(a_new[i][j]) == 0){
a_new[i][j] = 0;
}
}
}
bool non_zero = false;
for(int i = 0; i < a_new.size(); i++){
for(int j = 0; j < a_new[i].size(); j++){
if(i != j && std::round(a_new[i][j]) != 0){
non_zero = true;
}
}
}
if(non_zero) {
diagonal = false;
}
else{
diagonal = true;
}
if(a_new == A){
diagonal = true;
for(int i = 0; i < a_new.size(); i++){
for(int j = 0; j < a_new[i].size(); j++){
if(i != j){
a_new[i][j] = 0;
}
}
}
}
eigenvectors = matmult(eigenvectors, P);
A = a_new;
} while(!diagonal);
std::vector<std::vector<double>> a_new_prior = a_new;
// Bubble Sort. Should change this later.
for(int i = 0; i < a_new.size() - 1; i++){
for(int j = 0; j < a_new.size() - 1 - i; j++){
if(a_new[j][j] < a_new[j + 1][j + 1]){
double temp = a_new[j + 1][j + 1];
a_new[j + 1][j + 1] = a_new[j][j];
a_new[j][j] = temp;
}
}
}
for(int i = 0; i < a_new.size(); i++){
for(int j = 0; j < a_new.size(); j++){
if(a_new[i][i] == a_new_prior[j][j]){
val_to_vec[i] = j;
}
}
}
std::vector<std::vector<double>> eigen_temp = eigenvectors;
for(int i = 0; i < eigenvectors.size(); i++){
for(int j = 0; j < eigenvectors[i].size(); j++){
eigenvectors[i][j] = eigen_temp[i][val_to_vec[j]];
}
}
return {eigenvectors, a_new};
}
std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>, std::vector<std::vector<double>>> LinAlg::SVD(std::vector<std::vector<double>> A){
auto [left_eigenvecs, eigenvals] = eig(matmult(A, transpose(A)));
auto [right_eigenvecs, right_eigenvals] = eig(matmult(transpose(A), A));
std::vector<std::vector<double>> singularvals = sqrt(eigenvals);
std::vector<std::vector<double>> sigma = zeromat(A.size(), A[0].size());
for(int i = 0; i < singularvals.size(); i++){
for(int j = 0; j < singularvals[i].size(); j++){
sigma[i][j] = singularvals[i][j];
}
}
return {left_eigenvecs, sigma, right_eigenvecs};
}
std::vector<double> LinAlg::vectorProjection(std::vector<double> a, std::vector<double> b){
double product = dot(a, b)/dot(a, a);
return scalarMultiply(product, a); // Projection of vector a onto b. Denotated as proj_a(b).
}
std::vector<std::vector<double>> LinAlg::gramSchmidtProcess(std::vector<std::vector<double>> A){
A = transpose(A); // C++ vectors lack a mechanism to directly index columns. So, we transpose *a copy* of A for this purpose for ease of use.
std::vector<std::vector<double>> B;
B.resize(A.size());
for(int i = 0; i < B.size(); i++){
B[i].resize(A[0].size());
}
B[0] = A[0]; // We set a_1 = b_1 as an initial condition.
B[0] = scalarMultiply(1/norm_2(B[0]), B[0]);
for(int i = 1; i < B.size(); i++){
B[i] = A[i];
for(int j = i-1; j >= 0; j--){
B[i] = subtraction(B[i], vectorProjection(B[j], A[i]));
}
B[i] = scalarMultiply(1/norm_2(B[i]), B[i]); // Very simply multiply all elements of vec B[i] by 1/||B[i]||_2
}
return transpose(B); // We re-transpose the marix.
}
std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>> LinAlg::QRD(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> Q = gramSchmidtProcess(A);
std::vector<std::vector<double>> R = matmult(transpose(Q), A);
return {Q, R};
}
std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>> LinAlg::chol(std::vector<std::vector<double>> A){
std::vector<std::vector<double>> L = zeromat(A.size(), A[0].size());
for(int j = 0; j < L.size(); j++){ // Matrices entered must be square. No problem here.
for(int i = j; i < L.size(); i++){
if(i == j){
double sum = 0;
for(int k = 0; k < j; k++){
sum += L[i][k] * L[i][k];
}
L[i][j] = std::sqrt(A[i][j] - sum);
}
else{ // That is, i!=j
double sum = 0;
for(int k = 0; k < j; k++){
sum += L[i][k] * L[j][k];
}
L[i][j] = (A[i][j] - sum)/L[j][j];
}
}
}
return {L, transpose(L)}; // Indeed, L.T is our upper triangular matrix.
}
double LinAlg::sum_elements(std::vector<std::vector<double>> A){
double sum = 0;
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
sum += A[i][j];
}
}
return sum;
}
std::vector<double> LinAlg::flatten(std::vector<std::vector<double>> A){
std::vector<double> a;
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
a.push_back(A[i][j]);
}
}
return a;
}
std::vector<double> LinAlg::solve(std::vector<std::vector<double>> A, std::vector<double> b){
return mat_vec_mult(inverse(A), b);
}
bool LinAlg::positiveDefiniteChecker(std::vector<std::vector<double>> A){
auto [eigenvectors, eigenvals] = eig(A);
std::vector<double> eigenvals_vec;
for(int i = 0; i < eigenvals.size(); i++){
eigenvals_vec.push_back(eigenvals[i][i]);
}
for(int i = 0; i < eigenvals_vec.size(); i++){
if(eigenvals_vec[i] <= 0){ // Simply check to ensure all eigenvalues are positive.
return false;
}
}
return true;
}
bool LinAlg::negativeDefiniteChecker(std::vector<std::vector<double>> A){
auto [eigenvectors, eigenvals] = eig(A);
std::vector<double> eigenvals_vec;
for(int i = 0; i < eigenvals.size(); i++){
eigenvals_vec.push_back(eigenvals[i][i]);
}
for(int i = 0; i < eigenvals_vec.size(); i++){
if(eigenvals_vec[i] >= 0){ // Simply check to ensure all eigenvalues are negative.
return false;
}
}
return true;
}
bool LinAlg::zeroEigenvalue(std::vector<std::vector<double>> A){
auto [eigenvectors, eigenvals] = eig(A);
std::vector<double> eigenvals_vec;
for(int i = 0; i < eigenvals.size(); i++){
eigenvals_vec.push_back(eigenvals[i][i]);
}
for(int i = 0; i < eigenvals_vec.size(); i++){
if(eigenvals_vec[i] == 0){
return true;
}
}
return false;
}
void LinAlg::printMatrix(std::vector<std::vector<double>> A){
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
std::cout << A[i][j] << " ";
}
std::cout << std::endl;
}
}
std::vector<std::vector<double>> LinAlg::outerProduct(std::vector<double> a, std::vector<double> b){
std::vector<std::vector<double>> C;
C.resize(a.size());
for(int i = 0; i < C.size(); i++){
C[i] = scalarMultiply(a[i], b);
}
return C;
}
std::vector<double> LinAlg::hadamard_product(std::vector<double> a, std::vector<double> b){
std::vector<double> c;
c.resize(a.size());
for(int i = 0; i < a.size(); i++){
c[i] = a[i] * b[i];
}
return c;
}
std::vector<double> LinAlg::elementWiseDivision(std::vector<double> a, std::vector<double> b){
std::vector<double> c;
c.resize(a.size());
for(int i = 0; i < a.size(); i++){
c[i] = a[i] / b[i];
}
return c;
}
std::vector<double> LinAlg::scalarMultiply(double scalar, std::vector<double> a){
for(int i = 0; i < a.size(); i++){
a[i] *= scalar;
}
return a;
}
std::vector<double> LinAlg::scalarAdd(double scalar, std::vector<double> a){
for(int i = 0; i < a.size(); i++){
a[i] += scalar;
}
return a;
}
std::vector<double> LinAlg::addition(std::vector<double> a, std::vector<double> b){
std::vector<double> c;
c.resize(a.size());
for(int i = 0; i < a.size(); i++){
c[i] = a[i] + b[i];
}
return c;
}
std::vector<double> LinAlg::subtraction(std::vector<double> a, std::vector<double> b){
std::vector<double> c;
c.resize(a.size());
for(int i = 0; i < a.size(); i++){
c[i] = a[i] - b[i];
}
return c;
}
std::vector<double> LinAlg::subtractMatrixRows(std::vector<double> a, std::vector<std::vector<double>> B){
for(int i = 0; i < B.size(); i++){
a = subtraction(a, B[i]);
}
return a;
}
std::vector<double> LinAlg::log(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::log(a[i]);
}
return b;
}
std::vector<double> LinAlg::log10(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::log10(a[i]);
}
return b;
}
std::vector<double> LinAlg::exp(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::exp(a[i]);
}
return b;
}
std::vector<double> LinAlg::erf(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::erf(a[i]);
}
return b;
}
std::vector<double> LinAlg::exponentiate(std::vector<double> a, double p){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < b.size(); i++){
b[i] = std::pow(a[i], p);
}
return b;
}
std::vector<double> LinAlg::sqrt(std::vector<double> a){
return exponentiate(a, 0.5);
}
std::vector<double> LinAlg::cbrt(std::vector<double> a){
return exponentiate(a, double(1)/double(3));
}
double LinAlg::dot(std::vector<double> a, std::vector<double> b){
double c = 0;
for(int i = 0; i < a.size(); i++){
c += a[i] * b[i];
}
return c;
}
std::vector<double> LinAlg::cross(std::vector<double> a, std::vector<double> b){
// Cross products exist in R^7 also. Though, I will limit it to R^3 as Wolfram does this.
std::vector<std::vector<double>> mat = {onevec(3), a, b};
double det1 = det({{a[1], a[2]}, {b[1], b[2]}}, 2);
double det2 = -det({{a[0], a[2]}, {b[0], b[2]}}, 2);
double det3 = det({{a[0], a[1]}, {b[0], b[1]}}, 2);
return {det1, det2, det3};
}
std::vector<double> LinAlg::abs(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < b.size(); i++){
b[i] = std::abs(a[i]);
}
return b;
}
std::vector<double> LinAlg::zerovec(int n){
std::vector<double> zerovec;
zerovec.resize(n);
return zerovec;
}
std::vector<double> LinAlg::onevec(int n){
return full(n, 1);
}
std::vector<std::vector<double>> LinAlg::diag(std::vector<double> a){
std::vector<std::vector<double>> B = zeromat(a.size(), a.size());
for(int i = 0; i < B.size(); i++){
B[i][i] = a[i];
}
return B;
}
std::vector<double> LinAlg::full(int n, int k){
std::vector<double> full;
full.resize(n);
for(int i = 0; i < full.size(); i++){
full[i] = k;
}
return full;
}
std::vector<double> LinAlg::sin(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::sin(a[i]);
}
return b;
}
std::vector<double> LinAlg::cos(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::cos(a[i]);
}
return b;
}
std::vector<std::vector<double>> LinAlg::rotate(std::vector<std::vector<double>> A, double theta, int axis){
std::vector<std::vector<double>> rotationMatrix = {{std::cos(theta), -std::sin(theta)}, {std::sin(theta), std::cos(theta)}};
if(axis == 0) {rotationMatrix = {{1, 0, 0}, {0, std::cos(theta), -std::sin(theta)}, {0, std::sin(theta), std::cos(theta)}};}
else if(axis == 1) {rotationMatrix = {{std::cos(theta), 0, std::sin(theta)}, {0, 1, 0}, {-std::sin(theta), 0, std::cos(theta)}};}
else if (axis == 2) {rotationMatrix = {{std::cos(theta), -std::sin(theta), 0}, {std::sin(theta), std::cos(theta), 0}, {1, 0, 0}};}
return matmult(A, rotationMatrix);
}
std::vector<std::vector<double>> LinAlg::max(std::vector<std::vector<double>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < A.size(); i++){
C[i] = max(A[i], B[i]);
}
return C;
}
double LinAlg::max(std::vector<double> a){
int max = a[0];
for(int i = 0; i < a.size(); i++){
if(a[i] > max){
max = a[i];
}
}
return max;
}
double LinAlg::min(std::vector<double> a){
int min = a[0];
for(int i = 0; i < a.size(); i++){
if(a[i] < min){
min = a[i];
}
}
return min;
}
std::vector<double> LinAlg::round(std::vector<double> a){
std::vector<double> b;
b.resize(a.size());
for(int i = 0; i < a.size(); i++){
b[i] = std::round(a[i]);
}
return b;
}
// Multidimensional Euclidean Distance
double LinAlg::euclideanDistance(std::vector<double> a, std::vector<double> b){
double dist = 0;
for(int i = 0; i < a.size(); i++){
dist += (a[i] - b[i])*(a[i] - b[i]);
}
return std::sqrt(dist);
}
double LinAlg::norm_2(std::vector<double> a){
return std::sqrt(norm_sq(a));
}
double LinAlg::norm_sq(std::vector<double> a){
double n_sq = 0;
for(int i = 0; i < a.size(); i++){
n_sq += a[i] * a[i];
}
return n_sq;
}
double LinAlg::sum_elements(std::vector<double> a){
double sum = 0;
for(int i = 0; i < a.size(); i++){
sum += a[i];
}
return sum;
}
double LinAlg::cosineSimilarity(std::vector<double> a, std::vector<double> b){
return dot(a, b) / (norm_2(a) * norm_2(b));
}
void LinAlg::printVector(std::vector<double> a){
for(int i = 0; i < a.size(); i++){
std::cout << a[i] << " ";
}
std::cout << std::endl;
}
std::vector<std::vector<double>> LinAlg::mat_vec_add(std::vector<std::vector<double>> A, std::vector<double> b){
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
A[i][j] += b[j];
}
}
return A;
}
std::vector<double> LinAlg::mat_vec_mult(std::vector<std::vector<double>> A, std::vector<double> b){
std::vector<double> c;
c.resize(A.size());
for(int i = 0; i < A.size(); i++){
for(int k = 0; k < b.size(); k++){
c[i] += A[i][k] * b[k];
}
}
return c;
}
std::vector<std::vector<std::vector<double>>> LinAlg::addition(std::vector<std::vector<std::vector<double>>> A, std::vector<std::vector<std::vector<double>>> B){
for(int i = 0; i < A.size(); i++){
A[i] = addition(A[i], B[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::elementWiseDivision(std::vector<std::vector<std::vector<double>>> A, std::vector<std::vector<std::vector<double>>> B){
for(int i = 0; i < A.size(); i++){
A[i] = elementWiseDivision(A[i], B[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::sqrt(std::vector<std::vector<std::vector<double>>> A){
for(int i = 0; i < A.size(); i++){
A[i] = sqrt(A[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::exponentiate(std::vector<std::vector<std::vector<double>>> A, double p){
for(int i = 0; i < A.size(); i++){
A[i] = exponentiate(A[i], p);
}
return A;
}
std::vector<std::vector<double>> LinAlg::tensor_vec_mult(std::vector<std::vector<std::vector<double>>> A, std::vector<double> b){
std::vector<std::vector<double>> C;
C.resize(A.size());
for(int i = 0; i < C.size(); i++){
C[i].resize(A[0].size());
}
for(int i = 0; i < C.size(); i++){
for(int j = 0; j < C[i].size(); j++){
C[i][j] = dot(A[i][j], b);
}
}
return C;
}
std::vector<double> LinAlg::flatten(std::vector<std::vector<std::vector<double>>> A){
std::vector<double> c;
for(int i = 0; i < A.size(); i++){
std::vector<double> flattenedVec = flatten(A[i]);
c.insert(c.end(), flattenedVec.begin(), flattenedVec.end());
}
return c;
}
void LinAlg::printTensor(std::vector<std::vector<std::vector<double>>> A){
for(int i = 0; i < A.size(); i++){
printMatrix(A[i]);
if(i != A.size() - 1) { std::cout << std::endl; }
}
}
std::vector<std::vector<std::vector<double>>> LinAlg::scalarMultiply(double scalar, std::vector<std::vector<std::vector<double>>> A){
for(int i = 0; i < A.size(); i++){
A[i] = scalarMultiply(scalar, A[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::scalarAdd(double scalar, std::vector<std::vector<std::vector<double>>> A){
for(int i = 0; i < A.size(); i++){
A[i] = scalarAdd(scalar, A[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::resize(std::vector<std::vector<std::vector<double>>> A, std::vector<std::vector<std::vector<double>>> B){
A.resize(B.size());
for(int i = 0; i < B.size(); i++){
A[i].resize(B[i].size());
for(int j = 0; j < B[i].size(); j++){
A[i][j].resize(B[i][j].size());
}
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::max(std::vector<std::vector<std::vector<double>>> A, std::vector<std::vector<std::vector<double>>> B){
for(int i = 0; i < A.size(); i++){
A[i] = max(A[i], B[i]);
}
return A;
}
std::vector<std::vector<std::vector<double>>> LinAlg::abs(std::vector<std::vector<std::vector<double>>> A){
for(int i = 0; i < A.size(); i++){
A[i] = abs(A[i]);
}
return A;
}
double LinAlg::norm_2(std::vector<std::vector<std::vector<double>>> A){
double sum = 0;
for(int i = 0; i < A.size(); i++){
for(int j = 0; j < A[i].size(); j++){
for(int k = 0; k < A[i][j].size(); k++){
sum += A[i][j][k] * A[i][j][k];
}
}
}
return std::sqrt(sum);
}
// Bad implementation. Change this later.
std::vector<std::vector<std::vector<double>>> LinAlg::vector_wise_tensor_product(std::vector<std::vector<std::vector<double>>> A, std::vector<std::vector<double>> B){
std::vector<std::vector<std::vector<double>>> C;
C = resize(C, A);
for(int i = 0; i < A[0].size(); i++){
for(int j = 0; j < A[0][i].size(); j++){
std::vector<double> currentVector;
currentVector.resize(A.size());
for(int k = 0; k < C.size(); k++){
currentVector[k] = A[k][i][j];
}
currentVector = mat_vec_mult(B, currentVector);
for(int k = 0; k < C.size(); k++){
C[k][i][j] = currentVector[k];
}
}
}
return C;
}
}
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