Implemented matrix determinant

Author: andrewdalpino

src/Matrix.php

@@ -621,6 +621,30 @@ public function inverse() : self
         return self::quick($c);
     }
 
+    /**
+     * Calculate the determinant of the matrix.
+     * 
+     * @throws \RuntimeException
+     * @return float
+     */
+    public function det() : float
+    {
+        if ($this->m !== $this->n) {
+            throw new RuntimeException('Determinant is not defined for a'
+                . ' non square matrix.');
+        }
+
+        list($b, $swaps) = $this->ref();
+
+        $dHat = 1.;
+
+        for ($i = 0; $i < $this->m; $i++) {
+            $dHat *= $b[$i][$i];
+        }
+
+        return (-1.) ** $swaps * $dHat;
+    }
+
     /**
      * Return the elementwise reciprocal of the matrix.
      *
@@ -725,16 +749,19 @@ public function dot(Vector $b) : self
 
     /**
      * Calculate the row echelon form of the matrix using Gaussian elimination.
+     * Return the matrix in ref and the number of swaps in a tuple.
      * 
      * @throws \RuntimeException
-     * @return self
+     * @return array
      */
-    public function ref() : self
+    public function ref() : array
     {
         $minDim = min($this->shape());
 
         $b = $this->a;
 
+        $swaps = 0;
+
         for ($k = 0; $k < $minDim; $k++) {
             $index = $k;
 
@@ -754,6 +781,8 @@ public function ref() : self
 
                 $b[$k] = $b[$index];
                 $b[$index] = $temp;
+
+                $swaps++;
             }
 
             $diag = $b[$k][$k];
@@ -769,7 +798,7 @@ public function ref() : self
             }
         }
 
-        return self::quick($b);
+        return [self::quick($b), $swaps];
     }
 
     /**
@@ -779,7 +808,9 @@ public function ref() : self
      */
     public function rref() : self
     {
-        $b = $this->ref()->asArray();
+        list($b, $swaps) = $this->ref();
+
+        $b = $b->asArray();
 
         $row = $col = 0;
 

src/Vector.php

@@ -185,7 +185,9 @@ public static function range(float $start, float $end, float $interval = 1.) : s
      */
     public static function linspace(float $start, float $end, int $n) : self
     {
-        $interval = abs($end - $start) / ($n - 1);
+        $range = abs($end - $start);
+
+        $interval = ($range / ($n - 1)) - (self::EPSILON * $range);
 
         return self::range($start, $end, $interval);
     }

tests/MatrixTest.php

@@ -344,6 +344,12 @@ public function test_inverse()
         $this->assertEquals($y, $z->asArray());
     }
 
+    public function test_det()
+    {
+        $this->assertEquals(-5301.999999999999, $this->a->det());
+        $this->assertEquals(-544., $this->c->det());
+    }
+
     public function test_reciprocal()
     {
         $z = $this->a->reciprocal();
@@ -385,7 +391,7 @@ public function test_reduce()
 
     public function test_ref()
     {
-        $z =  $this->a->ref();
+        list($z, $swaps) = $this->a->ref();
 
         $y = [
             [22, -17, 12],

tests/VectorTest.php

@@ -105,7 +105,10 @@ public function test_build_linspace()
     {
         $z = Vector::linspace(-5, 5, 9);
 
-        $y = [-5., -3.75, -2.5, -1.25, 0., 1.25, 2.5, 3.75, 5.];
+        $y = [
+            -5., -3.7500001000000003, -2.5000002, -1.2500003, -4.0000000023354687E-7,
+            1.2499994999999995, 2.4999994, 3.749999299999999, 4.9999991999999995,
+        ];
 
         $this->assertInstanceOf(Vector::class, $z);
         $this->assertCount(9, $z);