Implementing multivariate linear regression simulation curve with PHP

Multivariate linear regression model: y = b1x1 + b2x2 + b3x3 + ... +bnxn;

We are based on a set of data: similar to arr_x = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]]; Arr_y = [5, 10, 15]; The last we asked for was an array that contained the B1 to Bn;

Methods: Using least squares method

Formula: We only use the first half of the formula, that is, the matrix to calculate

The x in the formula is arr_x, a two-dimensional array we can think of as a matrix, the y in the formula is arr_y, and it is considered a matrix (5, 10, 15), but it should be written vertically.

Then we can find that the matrix is multiplied, transpose, and inverse by the formula, so the following code gives:

Public Function Get_complement ($data, $i, $j)
{
/* x and Y are the number of rows and columns of the matrix data */
$x = count ($data);
$y = count ($data [0]);
/* data2 for the remaining matrix */
$data 2 = [];
for ($k = 0; $k < $x-1; $k + +) {
if ($k < $i) {
for ($kk = 0; $kk < $y-1; $kk + +) {
if ($kk < $j) {
$data 2[$k] [$KK] = $data [$k] [$KK];
} else {
$data 2[$k] [$KK] = $data [$k] [$kk + 1];
}
}
} else {
for ($kk = 0; $kk < $y 1; $kk + +) {
if ($kk < $j) {
$data 2[$k] [$KK] = $data [$k + 1][$kk ];
} else {
$data 2[$k] [$KK] = $data [$k + 1][$kk + 1];
}
}
}
}
return $data 2;
}

/* Calculate Matrix determinant */
Public Function Cal_det ($data)
{
$ans = 0;
if (count ($data [0]) = = = 2) {
$ans = $data [0][0] * $data [1][1]-$data [0][1] * $data [1][0];
} else {
for ($i = 0; $i < count ($data [0]); $i + +) {
$data _temp = $this->get_complement ($data, 0, $i);
if ($i% 2 = = = 0) {
$ans = $ans + $data [0][$i] * ($this->cal_det ($data _temp));
} else {
$ans = $ans-$data [0][$i] * ($this->cal_det ($data _temp));
}
}
}
return $ans;
}

/* The adjoint matrix of the computed matrix */
Public Function Ajoint ($data)
{
$m = count ($data);
$n = count ($data [0]);
$data 2 = [];
for ($i = 0; $i < $m; $i + +) {
for ($j = 0; $j < $n; $j + +) {
if (($i + $j)% 2 = = = 0) {
$data 2[$i] [$j] = $this->cal_det ($this->get_complement ($data, $i, $j));
} else {
$data 2[$i] [$j] =-$this->cal_det ($this->get_complement ($data, $i, $j));
}
}
}
return $this->trans ($data 2);
}

/* Transpose Matrix */
Public function trans ($data)
{
$i = count ($data);
$j = count ($data [0]);
$data 2 = [];
for ($k 2 = 0; $k 2 < $j; $k 2 +) {
for ($k 1 = 0; $k 1 < $i; $k 1 +) {
$data 2[$k 2][$k 1] = $data [$k 1][$k 2];
}
}
/* Transpose The matrix to get the adjoint matrix */
return $data 2;
}

/* Inverse of the matrix, the input parameter is the original matrix */
Public Function Inv ($data)
{
$m = count ($data);
$n = count ($data [0]);
$data 2 = [];
$det _val = $this->cal_det ($data);
$data 2 = $this->ajoint ($data);
for ($i = 0; $i < $m; $i + +) {
for ($j = 0; $j < $n; $j + +) {
$data 2[$i] [$j] = $data 2[$i] [$j]/$det _val;
}
}
return $data 2;
}

/* To find the product of two matrices */
Public Function GetProduct ($data 1, $data 2)
{
/* $data 1 is the left multiplicative matrix */
$m 1 = count ($data 1);
$n 1 = count ($data 1[0]);
$m 2 = count ($data 2);
$n 2 = count ($data 2[0]);
$data _new = [];
if ($n 1!== $m 2) {
return false;
} else {
for ($i = 0; $i <= $m 1-1; $i + +) {
for ($k = 0; $k <= $n 2-1; $k + +) {
$data _new[$i] [$k] = 0;
for ($j = 0; $j <= $n 1-1; $j + +) {
$data _new[$i] [$k] + = $data 1[$i] [$j] * $data 2[$j] [$k];
}
}
}
}
return $data _new;
}

/* Multivariate linear equations */
Public Function Getparams ($arr _x, $arr _y)
{
$final = [];
$arr _x_t = $this->trans ($arr _x);
$result = $this->getproduct ($this->getproduct ($this->inv ($this->getproduct ($arr _x_t, $arr _x)), $arr _x_ T), $arr _y);
foreach ($result as $key = = $val) {
foreach ($val as $_k = $_v) {
$final [] = $_v;
}
}
return $final;
}

The last Getparams () method is the last method of finding a B-parameter array, passing in a two-dimensional array arr_x, and a one-dimensional array arr_y.

This is typically used for big data analysis to simulate and predict the following developments and trends based on big data.

Implementing multivariate linear regression simulation curve with PHP