diff options
Diffstat (limited to '')
11 files changed, 656 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);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/adjoint.php b/vendor/markbaker/matrix/classes/src/Functions/adjoint.php new file mode 100644 index 0000000..aafbb0f --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/adjoint.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix adjoint() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the adjoint of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\adjoint')) {
+ function adjoint($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::adjoint($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/antidiagonal.php b/vendor/markbaker/matrix/classes/src/Functions/antidiagonal.php new file mode 100644 index 0000000..8904912 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/antidiagonal.php @@ -0,0 +1,31 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix antidiagonal() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+namespace Matrix;
+
+/**
+ * Returns the antidiagonal of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\antidiagonal')) {
+ function antidiagonal($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::antidiagonal($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/cofactors.php b/vendor/markbaker/matrix/classes/src/Functions/cofactors.php new file mode 100644 index 0000000..c071e45 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/cofactors.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix cofactors() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the cofactors of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\cofactors')) {
+ function cofactors($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::cofactors($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/determinant.php b/vendor/markbaker/matrix/classes/src/Functions/determinant.php new file mode 100644 index 0000000..d3573ab --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/determinant.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix determinant() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the determinant of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return float Matrix determinant
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\determinant')) {
+ function determinant($matrix): float
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::determinant($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/diagonal.php b/vendor/markbaker/matrix/classes/src/Functions/diagonal.php new file mode 100644 index 0000000..8993db3 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/diagonal.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix diagonal() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the diagonal of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\diagonal')) {
+ function diagonal($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::diagonal($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/identity.php b/vendor/markbaker/matrix/classes/src/Functions/identity.php new file mode 100644 index 0000000..7f870db --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/identity.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix identity() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the identity of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The identity matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\identity')) {
+ function identity($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::identity($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/inverse.php b/vendor/markbaker/matrix/classes/src/Functions/inverse.php new file mode 100644 index 0000000..4bf08d0 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/inverse.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix inverse() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the inverse of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\inverse')) {
+ function inverse($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::inverse($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/minors.php b/vendor/markbaker/matrix/classes/src/Functions/minors.php new file mode 100644 index 0000000..f34833b --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/minors.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix minors() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the minors of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The new matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\minors')) {
+ function minors($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::minors($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/trace.php b/vendor/markbaker/matrix/classes/src/Functions/trace.php new file mode 100644 index 0000000..0c395f6 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/trace.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix trace() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the trace of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return float The trace of the matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\trace')) {
+ function trace($matrix): float
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::trace($matrix);
+ }
+}
diff --git a/vendor/markbaker/matrix/classes/src/Functions/transpose.php b/vendor/markbaker/matrix/classes/src/Functions/transpose.php new file mode 100644 index 0000000..8413634 --- /dev/null +++ b/vendor/markbaker/matrix/classes/src/Functions/transpose.php @@ -0,0 +1,32 @@ +<?php
+
+/**
+ *
+ * Function code for the matrix transpose() function
+ *
+ * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license https://opensource.org/licenses/MIT MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Returns the transpose of a matrix or an array.
+ *
+ * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+ * @return Matrix The transposed matrix
+ * @throws Exception If argument isn't a valid matrix or array.
+ */
+if (!function_exists(__NAMESPACE__ . '\\transpose')) {
+ function transpose($matrix): Matrix
+ {
+ if (is_array($matrix)) {
+ $matrix = new Matrix($matrix);
+ }
+ if (!$matrix instanceof Matrix) {
+ throw new Exception('Must be Matrix or array');
+ }
+
+ return Functions::transpose($matrix);
+ }
+}
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