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Diffstat (limited to '')
| -rw-r--r-- | vendor/markbaker/matrix/classes/src/Functions.php | 337 |
1 files changed, 337 insertions, 0 deletions
diff --git a/vendor/markbaker/matrix/classes/src/Functions.php b/vendor/markbaker/matrix/classes/src/Functions.php new file mode 100644 index 0000000..fe7d11c --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions.php @@ -0,0 +1,337 @@ +<?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, string $type = 'inverse')
+ {
+ if (!$matrix->isSquare()) {
+ throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix');
+ }
+
+ $determinant = self::getDeterminant($matrix);
+ if ($determinant == 0.0) {
+ throw new Div0Exception(ucfirst($type) . ' 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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