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_inv.js
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_inv.js
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const clone = require('./clone');
const det = require('./det');
const identity = require('./identity');
const mergeR = require('./mergeR');
const LU = require('./LU');
const mul = require('./mul');
const {
isArray,
column, columns,
row, rows,
interchangeRows } = require('./utils');
module.exports = function _inv(m) {
const _rows = rows(m);
const cols = columns(m);
if (_rows !== cols)
throw new Error('for calculating inverse you have to pass a square matrix(n x n)');
let determinant;
if (_rows > 3)
determinant = det(clone(m));
else
determinant = det(m);
if (determinant === 0)
return 0;
const [lt, ut] = LU(m);
const In = identity(_rows);
const ut_In = mergeR(ut, In);
const lt_In = mergeR(lt , In);
const inv_lt_In = inverseLT_In(lt_In, _rows);
const inv_ut_In = inverseUT_In(ut_In, _rows);
const inv_lt = extractInv(inv_lt_In , _rows);
const inv_ut = extractInv(inv_ut_In , _rows);
return mul(inv_ut , inv_lt);
}
function extractInv(In_Inv , rows){
const inv = [];
for(let i = 0;i < rows;i++){
inv[i] = [];
for(let j = rows;j < 2 * rows;j++){
inv[i][j % rows] = In_Inv[i][j];
}
}
return inv;
}
function inverseLT_In(UT_In, rows) {
let j = 0;
for (let i = 0; i < rows; i++) {
let k = i;
let pivot = UT_In[k][j];
while (pivot === 0) {
k++;
if (k > rows - 1) return UT_In;
pivot = UT_In[k][j];
}
if (i !== k) {
interchangeRows(UT_In, i, k);
}
if (k > rows - 1)
UT_In[i] = UT_In[i].map(x => x / pivot);
for (let u = i + 1; u < rows; u++) {
let underPivot = UT_In[u][j];
if (underPivot === 0) continue;
if (k <= rows - 1) {
underPivot /= pivot;
}
UT_In[u] = UT_In[i].map((x, z) => (UT_In[u][z] - (x * underPivot)));
}
j++;
if (j === rows - 1) break;
}
return UT_In;
}
function inverseUT_In(UT_In, rows) {
let j = rows - 1;
for (let i = rows - 1; i >= 0; i--) {
let k = i;
let pivot = UT_In[k][j];
while (pivot === 0) {
k--;
if (k < 0) return UT_In;
pivot = UT_In[k][j];
}
if (i !== k) {
interchangeRows(UT_In, i, k);
}
if (k <= (rows - 1)){
UT_In[i] = UT_In[i].map(x => x / pivot);
pivot = 1;
}
for (let u = i - 1; u >= 0; u--) {
let upperPivot = UT_In[u][j];
if (upperPivot === 0) continue;
if (k <= rows - 1) {
upperPivot /= pivot;
}
UT_In[u] = UT_In[i].map((x, z) => (UT_In[u][z] - (x * upperPivot)));
}
j--;
if (j === 0) break;
}
return UT_In;
}