linalg.h

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#pragma once

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include <assert.h>
#include <iostream>

#define MAT(m, x, y) (m->data[(x * m->col) + y])
#define VEC(v, x) (v->data[x])

typedef struct _vector {
    size_t size;
    size_t padding;
    double data[];
    inline friend std::ostream& operator<< (std::ostream &out, const _vector & vector) {
        for(size_t i = 0; i < vector.size; i ++) {
            out << (vector.data)[i];
            out << " ";
        }
        out << std::endl;
        return out;
    }
} vector;

typedef struct _matrix {
    size_t row;
    size_t col;
    double data[];
    inline friend std::ostream& operator<< (std::ostream &out, const _matrix & matrix) {
        for(size_t i = 0; i < matrix.row; i ++) {
            for(size_t j = 0; j < matrix.col; j ++) {
                out << (matrix.data)[(i * matrix.col) + j];
                out << " ";
            }
            out << std::endl;
        }
        out << std::endl;
        return out;
    }
} matrix;


vector* vector_create(size_t size);

matrix* matrix_create(size_t row, size_t col);

matrix* vec_to_mat(vector* vec, int orientation);

vector* mat_to_vec(matrix* mat);

void matrix_reshape(matrix* mat, size_t row, size_t col);

double dot_product(const double* left, const double* right, int length);

vector* vecscalar_multiply(const vector* vec, const double scalar);

 vector* vecscalar_divide(const vector* vec, const double scalar);


 vector* vecmat_multiply(const vector* vec, const matrix* mat);

vector* matvec_multiply(const matrix* mat, const vector* vec);

void mat_print(const matrix* mat);

void vec_print (const vector* vec);

matrix* matmat_multiply(const matrix* left, const matrix* right);

matrix* matmat_addition(const matrix* left, const matrix* right);

matrix* matmat_subtraction(const matrix* left, const matrix* right);

matrix* matscalar_multiply(const matrix* mat, const double scalar);

matrix* matscalar_divide(const matrix* mat, const double scalar);

matrix* mat_transpose(const matrix* mat);

void vec_append(vector** vec_a, vector* vec_b);

void eigen(int N, double a[], int it_max, double v[], double d[], int* it_num, int* rot_num);

void mat_identity(int n, double a[]);

void diag_vector(int n, double a[], double v[]);

double frobenius_norm(int n, int k, double a[], double x[], double lambda[]);

matrix* covmat(matrix* mat);