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