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<?php
namespace Matrix;
class Functions
{
/**
* Calculate the adjoint of the matrix
*
* @param Matrix $matrix The matrix whose adjoint we wish to calculate
* @return Matrix
*
* @throws Exception
*/
private static function getAdjoint(Matrix $matrix)
{
return self::transpose(
self::getCofactors($matrix)
);
}
/**
* Return the adjoint of this matrix
* The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.
* The adjugate has sometimes been called the "adjoint", but today the "adjoint" of a matrix normally refers
* to its corresponding adjoint operator, which is its conjugate transpose.
*
* @param Matrix $matrix The matrix whose adjoint we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function adjoint(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Adjoint can only be calculated for a square matrix');
}
return self::getAdjoint($matrix);
}
/**
* Calculate the cofactors of the matrix
*
* @param Matrix $matrix The matrix whose cofactors we wish to calculate
* @return Matrix
*
* @throws Exception
*/
private static function getCofactors(Matrix $matrix)
{
$cofactors = self::getMinors($matrix);
$dimensions = $matrix->rows;
$cof = 1;
for ($i = 0; $i < $dimensions; ++$i) {
$cofs = $cof;
for ($j = 0; $j < $dimensions; ++$j) {
$cofactors[$i][$j] *= $cofs;
$cofs = -$cofs;
}
$cof = -$cof;
}
return new Matrix($cofactors);
}
/**
* Return the cofactors of this matrix
*
* @param Matrix $matrix The matrix whose cofactors we wish to calculate
* @return Matrix
*
* @throws Exception
*/
public static function cofactors(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Cofactors can only be calculated for a square matrix');
}
return self::getCofactors($matrix);
}
/**
* @param Matrix $matrix
* @param int $row
* @param int $column
* @return float
* @throws Exception
*/
private static function getDeterminantSegment(Matrix $matrix, $row, $column)
{
$tmpMatrix = $matrix->toArray();
unset($tmpMatrix[$row]);
array_walk(
$tmpMatrix,
function (&$row) use ($column) {
unset($row[$column]);
}
);
return self::getDeterminant(new Matrix($tmpMatrix));
}
/**
* Calculate the determinant of the matrix
*
* @param Matrix $matrix The matrix whose determinant we wish to calculate
* @return float
*
* @throws Exception
*/
private static function getDeterminant(Matrix $matrix)
{
$dimensions = $matrix->rows;
$determinant = 0;
switch ($dimensions) {
case 1:
$determinant = $matrix->getValue(1, 1);
break;
case 2:
$determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) -
$matrix->getValue(1, 2) * $matrix->getValue(2, 1);
break;
default:
for ($i = 1; $i <= $dimensions; ++$i) {
$det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1);
if (($i % 2) == 0) {
$determinant -= $det;
} else {
$determinant += $det;
}
}
break;
}
return $determinant;
}
/**
* Return the determinant of this matrix
*
* @param Matrix $matrix The matrix whose determinant we wish to calculate
* @return float
* @throws Exception
**/
public static function determinant(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Determinant can only be calculated for a square matrix');
}
return self::getDeterminant($matrix);
}
/**
* Return the diagonal of this matrix
*
* @param Matrix $matrix The matrix whose diagonal we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function diagonal(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Diagonal can only be extracted from a square matrix');
}
$dimensions = $matrix->rows;
$grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
->toArray();
for ($i = 0; $i < $dimensions; ++$i) {
$grid[$i][$i] = $matrix->getValue($i + 1, $i + 1);
}
return new Matrix($grid);
}
/**
* Return the antidiagonal of this matrix
*
* @param Matrix $matrix The matrix whose antidiagonal we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function antidiagonal(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Anti-Diagonal can only be extracted from a square matrix');
}
$dimensions = $matrix->rows;
$grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
->toArray();
for ($i = 0; $i < $dimensions; ++$i) {
$grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i);
}
return new Matrix($grid);
}
/**
* Return the identity matrix
* The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix
* with ones on the main diagonal and zeros elsewhere
*
* @param Matrix $matrix The matrix whose identity we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function identity(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Identity can only be created for a square matrix');
}
$dimensions = $matrix->rows;
return Builder::createIdentityMatrix($dimensions);
}
/**
* Return the inverse of this matrix
*
* @param Matrix $matrix The matrix whose inverse we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function inverse(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Inverse can only be calculated for a square matrix');
}
$determinant = self::getDeterminant($matrix);
if ($determinant == 0.0) {
throw new Exception('Inverse can only be calculated for a matrix with a non-zero determinant');
}
if ($matrix->rows == 1) {
return new Matrix([[1 / $matrix->getValue(1, 1)]]);
}
return self::getAdjoint($matrix)
->multiply(1 / $determinant);
}
/**
* Calculate the minors of the matrix
*
* @param Matrix $matrix The matrix whose minors we wish to calculate
* @return array[]
*
* @throws Exception
*/
protected static function getMinors(Matrix $matrix)
{
$minors = $matrix->toArray();
$dimensions = $matrix->rows;
if ($dimensions == 1) {
return $minors;
}
for ($i = 0; $i < $dimensions; ++$i) {
for ($j = 0; $j < $dimensions; ++$j) {
$minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j);
}
}
return $minors;
}
/**
* Return the minors of the matrix
* The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or
* more of its rows or columns.
* Minors obtained by removing just one row and one column from square matrices (first minors) are required for
* calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of
* square matrices.
*
* @param Matrix $matrix The matrix whose minors we wish to calculate
* @return Matrix
* @throws Exception
**/
public static function minors(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Minors can only be calculated for a square matrix');
}
return new Matrix(self::getMinors($matrix));
}
/**
* Return the trace of this matrix
* The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right)
* of the matrix
*
* @param Matrix $matrix The matrix whose trace we wish to calculate
* @return float
* @throws Exception
**/
public static function trace(Matrix $matrix)
{
if (!$matrix->isSquare()) {
throw new Exception('Trace can only be extracted from a square matrix');
}
$dimensions = $matrix->rows;
$result = 0;
for ($i = 1; $i <= $dimensions; ++$i) {
$result += $matrix->getValue($i, $i);
}
return $result;
}
/**
* Return the transpose of this matrix
*
* @param Matrix $matrix The matrix whose transpose we wish to calculate
* @return Matrix
**/
public static function transpose(Matrix $matrix)
{
$array = array_values(array_merge([null], $matrix->toArray()));
$grid = call_user_func_array(
'array_map',
$array
);
return new Matrix($grid);
}
}
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