LUDecomposition::det() - Code Metrics - Inspection of "Cell formats with escaped spaces were causing inco..." - PHPOffice/PhpSpreadsheet - Measure and Improve Code Quality continuously with Scrutinizer

Failed Conditions

Push — develop ( a6bb49...7a4cbd )

by Adrien

created 2018-06-24 10:35 UTC

LUDecomposition::det() A

↳ Parent: LUDecomposition

Complexity

Conditions	3
Paths	3

Size

Total Lines

Duplication

Lines	0
Ratio	0 %

Importance

Changes

Metric	Value
cc	3
nc	3
nop	0
dl	0
loc	12
rs	9.8666
c	0
b	0
f	0

<?php

namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;

use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;

/**
 *    For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
 *    unit lower triangular matrix L, an n-by-n upper triangular matrix U,
 *    and a permutation vector piv of length m so that A(piv,:) = L*U.
 *    If m < n, then L is m-by-m and U is m-by-n.
 *
 *    The LU decompostion with pivoting always exists, even if the matrix is
 *    singular, so the constructor will never fail. The primary use of the
 *    LU decomposition is in the solution of square systems of simultaneous
 *    linear equations. This will fail if isNonsingular() returns false.
 *
 *    @author Paul Meagher
 *    @author Bartosz Matosiuk
 *    @author Michael Bommarito
 *
 *    @version 1.1
 */
class LUDecomposition
{
    const MATRIX_SINGULAR_EXCEPTION = 'Can only perform operation on singular matrix.';
    const MATRIX_SQUARE_EXCEPTION = 'Mismatched Row dimension';

    /**
     * Decomposition storage.
     *
     * @var array
     */
    private $LU = [];

    /**
     * Row dimension.
     *
     * @var int
     */
    private $m;

    /**
     * Column dimension.
     *
     * @var int
     */
    private $n;

    /**
     * Pivot sign.
     *
     * @var int
     */
    private $pivsign;

    /**
     * Internal storage of pivot vector.
     *
     * @var array
     */
    private $piv = [];

    /**
     * LU Decomposition constructor.
     *
     * @param Matrix $A Rectangular matrix
     */
    public function __construct($A)
    {
        if ($A instanceof Matrix) {

            // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
            $this->LU = $A->getArray();
            $this->m = $A->getRowDimension();
            $this->n = $A->getColumnDimension();
            for ($i = 0; $i < $this->m; ++$i) {
                $this->piv[$i] = $i;
            }
            $this->pivsign = 1;
            $LUrowi = $LUcolj = [];


            // Outer loop.
            for ($j = 0; $j < $this->n; ++$j) {
                // Make a copy of the j-th column to localize references.
                for ($i = 0; $i < $this->m; ++$i) {
                    $LUcolj[$i] = &$this->LU[$i][$j];
                }
                // Apply previous transformations.
                for ($i = 0; $i < $this->m; ++$i) {
                    $LUrowi = $this->LU[$i];
                    // Most of the time is spent in the following dot product.
                    $kmax = min($i, $j);
                    $s = 0.0;
                    for ($k = 0; $k < $kmax; ++$k) {
                        $s += $LUrowi[$k] * $LUcolj[$k];
                    }
                    $LUrowi[$j] = $LUcolj[$i] -= $s;
                }
                // Find pivot and exchange if necessary.
                $p = $j;
                for ($i = $j + 1; $i < $this->m; ++$i) {
                    if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
                        $p = $i;
                    }
                }
                if ($p != $j) {
                    for ($k = 0; $k < $this->n; ++$k) {
                        $t = $this->LU[$p][$k];
                        $this->LU[$p][$k] = $this->LU[$j][$k];
                        $this->LU[$j][$k] = $t;
                    }
                    $k = $this->piv[$p];
                    $this->piv[$p] = $this->piv[$j];
                    $this->piv[$j] = $k;
                    $this->pivsign = $this->pivsign * -1;
                }
                // Compute multipliers.
                if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
                    for ($i = $j + 1; $i < $this->m; ++$i) {
                        $this->LU[$i][$j] /= $this->LU[$j][$j];
                    }
                }
            }
        } else {
            throw new CalculationException(Matrix::ARGUMENT_TYPE_EXCEPTION);
        }
    }

    //    function __construct()


    /**
     * Get lower triangular factor.
     *
     * @return Matrix Lower triangular factor
     */
    public function getL()
    {
        for ($i = 0; $i < $this->m; ++$i) {
            for ($j = 0; $j < $this->n; ++$j) {
                if ($i > $j) {
                    $L[$i][$j] = $this->LU[$i][$j];
                } elseif ($i == $j) {
                    $L[$i][$j] = 1.0;
                } else {
                    $L[$i][$j] = 0.0;
                }
            }
        }

        return new Matrix($L);

    }

    //    function getL()


    /**
     * Get upper triangular factor.
     *
     * @return Matrix Upper triangular factor
     */
    public function getU()
    {
        for ($i = 0; $i < $this->n; ++$i) {
            for ($j = 0; $j < $this->n; ++$j) {
                if ($i <= $j) {
                    $U[$i][$j] = $this->LU[$i][$j];
                } else {
                    $U[$i][$j] = 0.0;
                }
            }
        }

        return new Matrix($U);

    }

    //    function getU()


    /**
     * Return pivot permutation vector.
     *
     * @return array Pivot vector
     */
    public function getPivot()
    {
        return $this->piv;
    }

    //    function getPivot()


    /**
     * Alias for getPivot.
     *
     *    @see getPivot
     */
    public function getDoublePivot()
    {
        return $this->getPivot();
    }

    //    function getDoublePivot()


    /**
     *    Is the matrix nonsingular?
     *
     * @return bool true if U, and hence A, is nonsingular
     */
    public function isNonsingular()
    {
        for ($j = 0; $j < $this->n; ++$j) {
            if ($this->LU[$j][$j] == 0) {
                return false;
            }
        }

        return true;
    }

    //    function isNonsingular()


    /**
     * Count determinants.
     *
     * @return array d matrix deterninat
     */
    public function det()
    {
        if ($this->m == $this->n) {
            $d = $this->pivsign;
            for ($j = 0; $j < $this->n; ++$j) {
                $d *= $this->LU[$j][$j];
            }

            return $d;

        }

        throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
    }

    //    function det()


    /**
     * Solve A*X = B.
     *
     * @param mixed $B a Matrix with as many rows as A and any number of columns
     *
     * @throws CalculationException illegalArgumentException Matrix row dimensions must agree
     * @throws CalculationException runtimeException  Matrix is singular
     *
     * @return Matrix X so that L*U*X = B(piv,:)
     */
    public function solve($B)
    {
        if ($B->getRowDimension() == $this->m) {
            if ($this->isNonsingular()) {
                // Copy right hand side with pivoting
                $nx = $B->getColumnDimension();
                $X = $B->getMatrix($this->piv, 0, $nx - 1);
                // Solve L*Y = B(piv,:)
                for ($k = 0; $k < $this->n; ++$k) {
                    for ($i = $k + 1; $i < $this->n; ++$i) {
                        for ($j = 0; $j < $nx; ++$j) {
                            $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
                        }
                    }
                }
                // Solve U*X = Y;
                for ($k = $this->n - 1; $k >= 0; --$k) {
                    for ($j = 0; $j < $nx; ++$j) {
                        $X->A[$k][$j] /= $this->LU[$k][$k];
                    }
                    for ($i = 0; $i < $k; ++$i) {
                        for ($j = 0; $j < $nx; ++$j) {
                            $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
                        }
                    }
                }

                return $X;
            }

            throw new CalculationException(self::MATRIX_SINGULAR_EXCEPTION);
        }

        throw new CalculationException(self::MATRIX_SQUARE_EXCEPTION);
    }
}


1			<?php
2
3			namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
4
5			use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
6
7			/**
8			* For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
9			* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
10			* and a permutation vector piv of length m so that A(piv,:) = L*U.
11			* If m < n, then L is m-by-m and U is m-by-n.
12			*
13			* The LU decompostion with pivoting always exists, even if the matrix is
14			* singular, so the constructor will never fail. The primary use of the
15			* LU decomposition is in the solution of square systems of simultaneous
16			* linear equations. This will fail if isNonsingular() returns false.
17			*
18			* @author Paul Meagher
19			* @author Bartosz Matosiuk
20			* @author Michael Bommarito
21			*
22			* @version 1.1
23			*/
24			class LUDecomposition
25			{
26			const MATRIX_SINGULAR_EXCEPTION = 'Can only perform operation on singular matrix.';
27			const MATRIX_SQUARE_EXCEPTION = 'Mismatched Row dimension';
28
29			/**
30			* Decomposition storage.
31			*
32			* @var array
33			*/
34			private $LU = [];
35
36			/**
37			* Row dimension.
38			*
39			* @var int
40			*/
41			private $m;
42
43			/**
44			* Column dimension.
45			*
46			* @var int
47			*/
48			private $n;
49
50			/**
51			* Pivot sign.
52			*
53			* @var int
54			*/
55			private $pivsign;
56
57			/**
58			* Internal storage of pivot vector.
59			*
60			* @var array
61			*/
62			private $piv = [];
63
64			/**
65			* LU Decomposition constructor.
66			*
67			* @param Matrix $A Rectangular matrix
68			*/
69			public function __construct($A)
70			{
71			if ($A instanceof Matrix) {
			0 ignored issues – show introduced 2018-03-14 12:08 UTC by Report Bug Copy Issue Report `$A` is always a sub-type of `PhpOffice\PhpSpreadsheet\Shared\JAMA\Matrix`. Loading history...
72			// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
73			$this->LU = $A->getArray();
74			$this->m = $A->getRowDimension();
75			$this->n = $A->getColumnDimension();
76			for ($i = 0; $i < $this->m; ++$i) {
77			$this->piv[$i] = $i;
78			}
79			$this->pivsign = 1;
80			$LUrowi = $LUcolj = [];
			0 ignored issues – show Unused Code introduced 2017-12-03 09:09 UTC by Report Bug Copy Issue Report The assignment to `$LUrowi` is dead and can be removed. Loading history...
81
82			// Outer loop.
83			for ($j = 0; $j < $this->n; ++$j) {
84			// Make a copy of the j-th column to localize references.
85			for ($i = 0; $i < $this->m; ++$i) {
86			$LUcolj[$i] = &$this->LU[$i][$j];
87			}
88			// Apply previous transformations.
89			for ($i = 0; $i < $this->m; ++$i) {
90			$LUrowi = $this->LU[$i];
91			// Most of the time is spent in the following dot product.
92			$kmax = min($i, $j);
93			$s = 0.0;
94			for ($k = 0; $k < $kmax; ++$k) {
95			$s += $LUrowi[$k] * $LUcolj[$k];
96			}
97			$LUrowi[$j] = $LUcolj[$i] -= $s;
98			}
99			// Find pivot and exchange if necessary.
100			$p = $j;
101			for ($i = $j + 1; $i < $this->m; ++$i) {
102			if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
103			$p = $i;
104			}
105			}
106			if ($p != $j) {
107			for ($k = 0; $k < $this->n; ++$k) {
108			$t = $this->LU[$p][$k];
109			$this->LU[$p][$k] = $this->LU[$j][$k];
110			$this->LU[$j][$k] = $t;
111			}
112			$k = $this->piv[$p];
113			$this->piv[$p] = $this->piv[$j];
114			$this->piv[$j] = $k;
115			$this->pivsign = $this->pivsign * -1;
116			}
117			// Compute multipliers.
118			if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
119			for ($i = $j + 1; $i < $this->m; ++$i) {
120			$this->LU[$i][$j] /= $this->LU[$j][$j];
121			}
122			}
123			}
124			} else {
125			throw new CalculationException(Matrix::ARGUMENT_TYPE_EXCEPTION);
126			}
127			}
128
129			// function __construct()
			0 ignored issues – show Unused Code Comprehensibility introduced 2017-05-10 12:16 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
130
131			/**
132			* Get lower triangular factor.
133			*
134			* @return Matrix Lower triangular factor
135			*/
136			public function getL()
137			{
138			for ($i = 0; $i < $this->m; ++$i) {
139			for ($j = 0; $j < $this->n; ++$j) {
140			if ($i > $j) {
141			$L[$i][$j] = $this->LU[$i][$j];
142			} elseif ($i == $j) {
143			$L[$i][$j] = 1.0;
144			} else {
145			$L[$i][$j] = 0.0;
146			}
147			}
148			}
149
150			return new Matrix($L);
			0 ignored issues – show Comprehensibility Best Practice introduced 2017-12-03 09:09 UTC by Report Bug Copy Issue Report The variable `$L` does not seem to be defined for all execution paths leading up to this point. Loading history...
151			}
152
153			// function getL()
			0 ignored issues – show Unused Code Comprehensibility introduced 2016-08-14 05:24 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
154
155			/**
156			* Get upper triangular factor.
157			*
158			* @return Matrix Upper triangular factor
159			*/
160			public function getU()
161			{
162			for ($i = 0; $i < $this->n; ++$i) {
163			for ($j = 0; $j < $this->n; ++$j) {
164			if ($i <= $j) {
165			$U[$i][$j] = $this->LU[$i][$j];
166			} else {
167			$U[$i][$j] = 0.0;
168			}
169			}
170			}
171
172			return new Matrix($U);
			0 ignored issues – show Comprehensibility Best Practice introduced 2017-12-03 09:09 UTC by Report Bug Copy Issue Report The variable `$U` does not seem to be defined for all execution paths leading up to this point. Loading history...
173			}
174
175			// function getU()
			0 ignored issues – show Unused Code Comprehensibility introduced 2016-08-14 05:24 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
176
177			/**
178			* Return pivot permutation vector.
179			*
180			* @return array Pivot vector
181			*/
182			public function getPivot()
183			{
184			return $this->piv;
185			}
186
187			// function getPivot()
			0 ignored issues – show Unused Code Comprehensibility introduced 2016-08-14 05:24 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
188
189			/**
190			* Alias for getPivot.
191			*
192			* @see getPivot
193			*/
194			public function getDoublePivot()
195			{
196			return $this->getPivot();
197			}
198
199			// function getDoublePivot()
			0 ignored issues – show Unused Code Comprehensibility introduced 2016-08-14 05:24 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
200
201			/**
202			* Is the matrix nonsingular?
203			*
204			* @return bool true if U, and hence A, is nonsingular
205			*/
206			public function isNonsingular()
207			{
208			for ($j = 0; $j < $this->n; ++$j) {
209			if ($this->LU[$j][$j] == 0) {
210			return false;
211			}
212			}
213
214			return true;
215			}
216
217			// function isNonsingular()
			0 ignored issues – show Unused Code Comprehensibility introduced 2016-08-14 05:24 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
218
219			/**
220			* Count determinants.
221			*
222			* @return array d matrix deterninat
223			*/
224			public function det()
225			{
226			if ($this->m == $this->n) {
227			$d = $this->pivsign;
228			for ($j = 0; $j < $this->n; ++$j) {
229			$d *= $this->LU[$j][$j];
230			}
231
232			return $d;
			0 ignored issues – show Bug Best Practice introduced 2017-12-03 09:09 UTC by Report Bug Copy Issue Report The expression `return $d` returns the type `integer` which is incompatible with the documented return type `array`. Loading history...
233			}
234
235			throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
236			}
237
238			// function det()
			0 ignored issues – show Unused Code Comprehensibility introduced 2017-05-10 12:16 UTC by Report Bug Copy Issue Report `50%` of this comment could be valid code. Did you maybe forget this after debugging? Sometimes obsolete code just ends up commented out instead of removed. In this case it is better to remove the code once you have checked you do not need it. The code might also have been commented out for debugging purposes. In this case it is vital that someone uncomments it again or your project may behave in very unexpected ways in production. This check looks for comments that seem to be mostly valid code and reports them. Loading history...
239
240			/**
241			* Solve A*X = B.
242			*
243			* @param mixed $B a Matrix with as many rows as A and any number of columns
244			*
245			* @throws CalculationException illegalArgumentException Matrix row dimensions must agree
246			* @throws CalculationException runtimeException Matrix is singular
247			*
248			* @return Matrix X so that LUX = B(piv,:)
249			*/
250			public function solve($B)
251			{
252			if ($B->getRowDimension() == $this->m) {
253			if ($this->isNonsingular()) {
254			// Copy right hand side with pivoting
255			$nx = $B->getColumnDimension();
256			$X = $B->getMatrix($this->piv, 0, $nx - 1);
257			// Solve L*Y = B(piv,:)
258			for ($k = 0; $k < $this->n; ++$k) {
259			for ($i = $k + 1; $i < $this->n; ++$i) {
260			for ($j = 0; $j < $nx; ++$j) {
261			$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
262			}
263			}
264			}
265			// Solve U*X = Y;
266			for ($k = $this->n - 1; $k >= 0; --$k) {
267			for ($j = 0; $j < $nx; ++$j) {
268			$X->A[$k][$j] /= $this->LU[$k][$k];
269			}
270			for ($i = 0; $i < $k; ++$i) {
271			for ($j = 0; $j < $nx; ++$j) {
272			$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
273			}
274			}
275			}
276
277			return $X;
278			}
279
280			throw new CalculationException(self::MATRIX_SINGULAR_EXCEPTION);
281			}
282
283			throw new CalculationException(self::MATRIX_SQUARE_EXCEPTION);
284			}
285			}
286

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LUDecomposition::det() A

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