Chi squared inverse left tailed (#1964)

* Implementation of the CHISQ.INV() method for ChiSquared distribution left-tail

CHANGELOG.md

@@ -9,7 +9,7 @@ and this project adheres to [Semantic Versioning](https://semver.org).
 
 ### Added
 
-- Implemented the CHITEST() and CHISQ.DIST() Statistical function.
+- Implemented the CHITEST(), CHISQ.DIST() and CHISQ.INV() and equivalent Statistical functions, for both left- and right-tailed distributions.
 - Support for ActiveSheet and SelectedCells in the ODS Reader and Writer. [PR #1908](https://github.com/PHPOffice/PhpSpreadsheet/pull/1908)
 
 ### Changed

src/PhpSpreadsheet/Calculation/Calculation.php

@@ -508,7 +508,7 @@ class Calculation
         ],
         'CHISQ.INV' => [
             'category' => Category::CATEGORY_STATISTICAL,
-            'functionCall' => [Functions::class, 'DUMMY'],
+            'functionCall' => [Statistical\Distributions\ChiSquared::class, 'inverseLeftTail'],
             'argumentCount' => '2',
         ],
         'CHISQ.INV.RT' => [

src/PhpSpreadsheet/Calculation/Statistical/Distributions/ChiSquared.php

@@ -11,6 +11,8 @@ class ChiSquared
 
     private const MAX_ITERATIONS = 256;
 
+    private const EPS = 2.22e-16;
+
     /**
      * CHIDIST.
      *
@@ -127,6 +129,35 @@ public static function inverseRightTail($probability, $degrees)
         return $newtonRaphson->execute($probability);
     }
 
+    /**
+     * CHIINV.
+     *
+     * Returns the inverse of the left-tailed probability of the chi-squared distribution.
+     *
+     * @param mixed (float) $probability Probability for the function
+     * @param mixed (int) $degrees degrees of freedom
+     *
+     * @return float|string
+     */
+    public static function inverseLeftTail($probability, $degrees)
+    {
+        $probability = Functions::flattenSingleValue($probability);
+        $degrees = Functions::flattenSingleValue($degrees);
+
+        try {
+            $probability = self::validateFloat($probability);
+            $degrees = self::validateInt($degrees);
+        } catch (Exception $e) {
+            return $e->getMessage();
+        }
+
+        if ($probability < 0.0 || $probability > 1.0 || $degrees < 1) {
+            return Functions::NAN();
+        }
+
+        return self::inverseLeftTailCalculation($probability, $degrees);
+    }
+
     public static function test($actual, $expected)
     {
         $rows = count($actual);
@@ -167,4 +198,104 @@ protected static function degrees(int $rows, int $columns): int
 
         return ($columns - 1) * ($rows - 1);
     }
+
+    private static function inverseLeftTailCalculation($probability, $degrees)
+    {
+        // bracket the root
+        $min = 0;
+        $sd = sqrt(2.0 * $degrees);
+        $max = 2 * $sd;
+        $s = -1;
+
+        while ($s * self::pchisq($max, $degrees) > $probability * $s) {
+            $min = $max;
+            $max += 2 * $sd;
+        }
+
+        // Find root using bisection
+        $chi2 = 0.5 * ($min + $max);
+
+        while (($max - $min) > self::EPS * $chi2) {
+            if ($s * self::pchisq($chi2, $degrees) > $probability * $s) {
+                $min = $chi2;
+            } else {
+                $max = $chi2;
+            }
+            $chi2 = 0.5 * ($min + $max);
+        }
+
+        return $chi2;
+    }
+
+    private static function pchisq($chi2, $degrees)
+    {
+        return self::gammp($degrees, 0.5 * $chi2);
+    }
+
+    private static function gammp($n, $x)
+    {
+        if ($x < 0.5 * $n + 1) {
+            return self::gser($n, $x);
+        }
+
+        return 1 - self::gcf($n, $x);
+    }
+
+    // Return the incomplete gamma function P(n/2,x) evaluated by
+    // series representation. Algorithm from numerical recipe.
+    // Assume that n is a positive integer and x>0, won't check arguments.
+    // Relative error controlled by the eps parameter
+    private static function gser($n, $x)
+    {
+        $gln = Gamma::ln($n / 2);
+        $a = 0.5 * $n;
+        $ap = $a;
+        $sum = 1.0 / $a;
+        $del = $sum;
+        for ($i = 1; $i < 101; ++$i) {
+            ++$ap;
+            $del = $del * $x / $ap;
+            $sum += $del;
+            if ($del < $sum * self::EPS) {
+                break;
+            }
+        }
+
+        return $sum * exp(-$x + $a * log($x) - $gln);
+    }
+
+    // Return the incomplete gamma function Q(n/2,x) evaluated by
+    // its continued fraction representation. Algorithm from numerical recipe.
+    // Assume that n is a postive integer and x>0, won't check arguments.
+    // Relative error controlled by the eps parameter
+    private static function gcf($n, $x)
+    {
+        $gln = Gamma::ln($n / 2);
+        $a = 0.5 * $n;
+        $b = $x + 1 - $a;
+        $fpmin = 1.e-300;
+        $c = 1 / $fpmin;
+        $d = 1 / $b;
+        $h = $d;
+        for ($i = 1; $i < 101; ++$i) {
+            $an = -$i * ($i - $a);
+            $b += 2;
+            $d = $an * $d + $b;
+            if (abs($d) < $fpmin) {
+                $d = $fpmin;
+            }
+            $c = $b + $an / $c;
+            if (abs($c) < $fpmin) {
+                $c = $fpmin;
+            }
+            $d = 1 / $d;
+            $del = $d * $c;
+            $h = $h * $del;
+            if (abs($del - 1) < self::EPS) {
+                break;
+            }
+        }
+
+        return $h * exp(-$x + $a * log($x) - $gln);
+    }
 }

tests/PhpSpreadsheetTests/Calculation/Functions/Statistical/ChiInvLeftTailTest.php

@@ -0,0 +1,37 @@
+<?php
+
+namespace PhpOffice\PhpSpreadsheetTests\Calculation\Functions\Statistical;
+
+use PhpOffice\PhpSpreadsheet\Calculation\Functions;
+use PhpOffice\PhpSpreadsheet\Calculation\Statistical;
+use PHPUnit\Framework\TestCase;
+
+class ChiInvLeftTailTest extends TestCase
+{
+    protected function setUp(): void
+    {
+        Functions::setCompatibilityMode(Functions::COMPATIBILITY_EXCEL);
+    }
+
+    /**
+     * @dataProvider providerCHIINV
+     *
+     * @param mixed $expectedResult
+     * @param mixed $probability
+     * @param mixed $degrees
+     */
+    public function testCHIINV($expectedResult, $probability, $degrees): void
+    {
+        $result = Statistical\Distributions\ChiSquared::inverseLeftTail($probability, $degrees);
+        if (!is_string($expectedResult)) {
+            $reverse = Statistical\Distributions\ChiSquared::distributionLeftTail($result, $degrees, true);
+            self::assertEqualsWithDelta($probability, $reverse, 1E-12);
+        }
+        self::assertEqualsWithDelta($expectedResult, $result, 1E-12);
+    }
+
+    public function providerCHIINV()
+    {
+        return require 'tests/data/Calculation/Statistical/CHIINVLeftTail.php';
+    }
+}

tests/data/Calculation/Statistical/CHIINVLeftTail.php

@@ -0,0 +1,64 @@
+<?php
+
+return [
+    [
+        4.671330448981,
+        0.3, 7,
+    ],
+    [
+        12.548861396889,
+        0.75, 10,
+    ],
+    [
+        3.283020286760,
+        0.93, 1,
+    ],
+    [
+        1.832581463748,
+        0.6, 2,
+    ],
+    [
+        0.454936423120,
+        0.5, 1,
+    ],
+    [
+        4.351460191096,
+        0.5, 5,
+    ],
+    [
+        1.323303696932,
+        0.75, 1,
+    ],
+    [
+        0.210721031316,
+        0.1, 2,
+    ],
+    [
+        3.218875824869,
+        0.8, 2,
+    ],
+    [
+        1.212532903046,
+        0.25, 3,
+    ],
+    [
+        '#VALUE!',
+        'NaN', 3,
+    ],
+    [
+        '#VALUE!',
+        0.25, 'NaN',
+    ],
+    'Probability < 0' => [
+        '#NUM!',
+        -0.1, 3,
+    ],
+    'Probability > 1' => [
+        '#NUM!',
+        1.1, 3,
+    ],
+    'Freedom > 1' => [
+        '#NUM!',
+        0.1, 0.5,
+    ],
+];