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Use polynomial-time algorithm to compute determinant.

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Bryan Cuccioli 2013-05-19 01:26:15 -04:00
parent 65b5d08f51
commit 169c3ea593
1 changed files with 53 additions and 35 deletions
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88
src/function/matrix/det.js
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@ -76,43 +76,61 @@ function _det (matrix, rows, cols) {
);
}
else {
// this is a matrix of 3 x 3 or larger
var d = 0;
for (var c = 0; c < cols; c++) {
var minor = _minor(matrix, rows, cols, 0, c);
//d += Math.pow(-1, 1 + c) * a(1, c) * _det(minor);
d += multiply(
multiply((c + 1) % 2 + (c + 1) % 2 - 1, matrix[0][c]),
_det(minor, rows - 1, cols - 1)
); // faster than with pow()
}
return d;
}
}
/**
* Extract a minor from a matrix
* @param {Array[]} matrix A square, two dimensional matrix
* @param {Number} rows Number of rows of the matrix (zero-based)
* @param {Number} cols Number of columns of the matrix (zero-based)
* @param {Number} row Row number to be removed (zero-based)
* @param {Number} col Column number to be removed (zero-based)
* @private
*/
function _minor(matrix, rows, cols, row, col) {
var minor = [],
minorRow;
for (var r = 0; r < rows; r++) {
if (r != row) {
minorRow = minor[r - (r > row)] = [];
for (var c = 0; c < cols; c++) {
if (c != col) {
minorRow[c - (c > col)] = matrix[r][c];
var det = 1;
var lead = 0;
for (var r = 0; r < rows; r++) {
if (lead >= cols) {
break;
}
var i = r;
// Find the pivot element.
while (matrix[i][lead] == 0) {
i++;
if (i == rows) {
i = r;
lead++;
if (lead == cols) {
// We found the last pivot.
if (util.deepEqual(matrix, math.eye(rows).valueOf())) {
return math.round(det, 6);
} else {
return 0;
}
}
}
}
if (i != r) {
// Swap rows i and r, which negates the determinant.
for (var a = 0; a < cols; a++) {
var temp = matrix[i][a];
matrix[i][a] = matrix[r][a];
matrix[r][a] = temp;
}
det *= -1;
}
// Scale row r and the determinant simultaneously.
var div = matrix[r][lead];
for (var a = 0; a < cols; a++) {
matrix[r][a] = matrix[r][a] / div;
}
det *= div;
// Back-substitute upwards.
for (var j = 0; j < rows; j++) {
if (j != r) {
// Taking linear combinations does not change the det.
var c = matrix[j][lead];
for (var a = 0; a < cols; a++) {
matrix[j][a] = matrix[j][a] - matrix[r][a] * c;
}
}
}
lead++; // Now looking for a pivot further right.
}
// If reduction did not result in the identity, the matrix is singular.
if (util.deepEqual(matrix, math.eye(rows).valueOf())) {
return math.round(det, 6);
} else {
return 0;
}
}
return minor;
}